A Thesis On Microquasars

Hard X-ray and Gamma Ray Properties of Cosmic Sources A Thesis submitted to the University of Mumbai for the Ph. D. (Science) Degree in Physics

Submitted by Manojendu Choudhury

Under the Guidance of Prof. A. R. Rao

Tata Institute of Fundamental Research Mumbai 400 005 June 2004

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To My Parents

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Acknowledgements

First and foremost, I wholeheartedly acknowledge the institutional structure, geographical location, general ambiance and the colonnade of TIFR for providing the ideal site where, perhaps, the most eventful years of my life, in both professional and personal fronts, were unfolded. The academic environment of TIFR provided me a very thorough introduction to the rigours of the research life, providing a gamut of diverse experiences, transforming me from a “green rookie” to a level from where (hopefully) I can take off to the next step to establish myself. I will always remain in gratitude to my thesis supervisor Prof. A. R. Rao, for picking me up from a situation of dire nothingness, setting me on a path, providing me a goal to strive for, and for letting me believe in myself when most others had given up. I am indebted to Prof. P. C. Agrawal, Prof. R. K. Manchanda, Prof. K. P. Singh, Prof. J. S. Yadav, Prof. T. P. Singh and Prof. M. N. Wahia for providing me various academic opportunities, discussions, and constant support during the various stages of my doctoral tenure. I would like to mention Dr. B. Paul separately for all the above, plus many a friendly chatting sessions. I thank the scientific staff of the department for a very congenial atmosphere in the department, and I should mention Magnes and Shobha for their general cheerful disposition and very helpful nature. The greatest treasures that I will carry with me from my stay here are the friendships that I forged over the years. Santosh, Gulab and Sachi provided a unique environment of camaraderie and togetherness in the department. Discussions and conversations with them consisted of a complete package of friendship, understanding and professional acumen, covering all aspects of science, life and everything else that may follow! I really pride ourselves at creating an atmosphere devoid of petty individualism and jealous competition, so common among contemporaries. I can defnitely not fail to mention our immediate juniors in the office, Vikram and Sarita, who cheerfully sustained the very friendly air in the office rooms and the tea-tables. In the department, I acknowledge the companionship of Poonam, Sambaran, Harsha, Surajit, Uddipan, and last but definitely not the least, Rituparno. In the institute, Pratik-da always provided a sense of togetherness unique to him (even now he is waiting for me to finish my typing, get the i

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Acknowledgements

printout, so that he may guide me to the book-binders). Funda-da (Pranab Sen) left a unique impression in me, Surjeet was always a constant and consistent friend, Yogesh, Yeshpal, Ashok (MP), Arvinder, Amitava, Krishnan, Rahul Jain, Neel made my later years in the institute very enjoyable, while Dr. Paul (Dilip), Shubham, Tirtha, Roop, Rajesh, Anwesh-da, Bhaswati-di, Arun, Rudrajyoti Palit, Bahniman-da, Soumen-da made the early years unforgettable. I hope Shankar, Anand, Dipanker, Holla, Eknath, Suman, Manna, Shamik and others of the footballing fraternity continue with the tradition of kicking the ball regularly. I will always remember Girish Nathan, Kiran and Anjum for their company in our first year (graduate school), and I will never forget Biswajit’s antics, in and out of the cricket field. I may have, inadvertently forgotten, to name many people who made my stay in the hostel a memorable experience. It will be a sacrilege if I fail to mention my ‘Guruji’, Shri Namdeo Panchalji, who introduced Hindustani classical music to me in the last two and a half years, and in the process rendered me a most creative and fulfilling avocation. I sincerely appreciate the friendship of Dr. C. H. Ishwar-Chandra and the continued academic collaboration with him. I am indebted to Dr. Ashok K. Jain for his support, encouragements, academic discussions and research collaborations. I look forward to the continued association along with the current ensuing collaboration with Vivek Agrawal and V. Girish. I cherish the friendship and support of Dr. Sergio Mendoza, and I hope to continue my association with him and his beloved country, Mexico, where I was treated with great warmth and affection. I also acknowledge the hospitality of Dr. Divakara Mayya in Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Puebla, Mexico. I gladly acknowledge the Kanwal Rekhi Scholarship of the TIFR Endowment Fund, which provided partial support to this thesis. I acknowledge the Department of Astronomy and Astrophysics, TIFR, and the NATO Advanced Study Institute for providing me 
 Summer School at financial and other logistical support enabling me to attend the Les Houches, France on, “Accretion discs, jets and high energy phenomena in astrophysics”. I thank the IAU for providing partial support for my participation in the “IAU Colloquium 194: Compact binaries in the Galaxy and beyond”, at La Paz, Mexico, as
 well as providing complete support for the “IAU Asia Pacific Regional Meeting” at Tokyo, Japan. I also acknowledge the Kyoto University (Dept. of Physics Yukawa Institute), ISAS and University of Tokyo (Dept. of Physics) for providing the complete support for my participation in the international conference on “Stellar-mass, Intermediatemass and Supermassive Black Holes” at Kyoto, Japan. I acknowledge Dr. G. C. Dewangan (Gulab) and Prof. R. Griffiths for inviting me at the Carnegie Mellon University, Pittsburgh for a short visit. I should mention that Dr. S. V. Vadawale (Santosh) played

iii host to me in Boston during my participation in the international meeting on “X-ray Timing: RXTE and beyond”, organized by the Harvard University. I also acknowledge the Instituto de Astronomia, Universidad Nacional Autonoma de Mexico (UNAM), as well as INAOE, Puebla, Mexico, for inviting me to short visits at the respective institutes. I also acknowledge the National Centre for Radio Astronomy, for providing support for my participation at the “Summer school on radio interferometry and aperture synthesis”, which introduced the rudiments of radio astronomical data analysis, with emphasis on GMRT, which I hope will be of enormous benefit to me in near future. No words can do justice to the support of my family, especially my wife, Rajul, who has been the bed-rock of my support base through all times, good and bad; without her understanding and endearing inspiration I wouldn’t have reached this day, when I can see the completion of my thesis. Lastly, I would like to express all my love and wishes to the little bundle of joy, our eleven days old son.

Contents Acknowledgements

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Synopsis 1

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Introduction 1.1 High energy physical processes and phenomena . . . . . . . . . 1.1.1 Accretion disc as a source of high energy emission . . . 1.2 Black hole sources: stellar mass and supermassive . . . . . . . . 1.3 Microquasars: general properties and behaviour . . . . . . . . . 1.3.1 Transient X-ray blackhole binaries . . . . . . . . . . . . 1.3.2 Persistent sources: canonical states of X-ray emission . 1.4 Accretion in X-ray binaries . . . . . . . . . . . . . . . . . . . . 1.4.1 Unification of hydrodynamic solutions of accretion flow 1.4.2 Hard X-ray emission models . . . . . . . . . . . . . . . 1.4.3 Geometrical structure of the accretion system . . . . . . 1.5 Outflows from microquasars . . . . . . . . . . . . . . . . . . . 1.6 Aim of this thesis . . . . . . . . . . . . . . . . . . . . . . . . .

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X-ray detectors and techniques of instrumentation; Radio astronomy 2.1 X-ray detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Modern X-ray observatories . . . . . . . . . . . . . . . . . . . . . 2.2.1 The Rossi X-ray Timing Explorer (RXTE) . . . . . . . . . . 2.2.2 Compton Gamma Ray Observatory (CGRO) . . . . . . . . . 2.2.3 Other notable X-ray missions . . . . . . . . . . . . . . . . 2.3 X-ray astronomical data analyses and techniques . . . . . . . . . . 2.3.1 RXTE data analysis . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Timing analysis . . . . . . . . . . . . . . . . . . . . . . . . iv

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Cygnus X-3: spectral studies 3.1 Why Cygnus X-3? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 General properties of Cygnus X-3 . . . . . . . . . . . . . . . . . . . . 3.3 General spectral features of Cygnus X-3 . . . . . . . . . . . . . . . . . 3.3.1 A historical perspective . . . . . . . . . . . . . . . . . . . . . . 3.3.2 X-ray wide band spectra from RXTE . . . . . . . . . . . . . . . 3.4 Correlation of radio & X-ray emission in Cygnus X-3: Spearman’s Partial Rank Correlation test . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Spearman’s Partial Rank Correlation test . . . . . . . . . . . . 3.5 X-ray spectral pivoting in the low (hard) state . . . . . . . . . . . . . . 3.6 X-ray spectral evolution driving the radio flares: high (soft) state . . . . 3.7 Complete X-ray spectral evolution . . . . . . . . . . . . . . . . . . . .

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Cygnus X-3: temporal studies 4.1 Binary modulation and correction with a given ephemeris 4.2 Radio X-ray correlation of Cygnus X-3 . . . . . . . . . 4.3 Power Density Spectrum (PDS) . . . . . . . . . . . . . 4.3.1 Power Density Spectrum (PDS) of Cygnus X-3 . 4.4 Time lag between soft and hard X-rays . . . . . . . . . .

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2.3.3 Spectral analysis . . . . . . . . . . . . . . . Radio astronomy . . . . . . . . . . . . . . . . . . . 2.4.1 Green Bank Interferometer (GBI) observatory 2.4.2 Giant Metrewave Radio Telescope (GMRT) .

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Disc-jet connection in microquasars: low (hard) states 5.1 Radio:X-ray correlation of the persistent sources: hard states . . . . . . 5.1.1 Cygnus X-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 GRS 1915+105 . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Cygnus X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Uniform behaviour of X-ray spectral shape with radio emission . . . . . 5.2.1 The X-ray soft state and suppressed radio emission . . . . . . . 5.3 Universal correlation and its origin . . . . . . . . . . . . . . . . . . . . 5.4 X-ray spectral shape as the “driver” of the radio emission . . . . . . . . 5.5 Summary: the generalized picture of the accretion - ejection mechanism in the ‘low’ - hard state of Galactic microquasars . . . . . . . . . . . .

94 97 98 99 103 106 109 111 114 115

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Two Component Accretion Flow model 6.1 Two Component Accretion Flow (TCAF) . . . . . . . . . . . 6.2 Outflow of mass . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The magnetized TCAF model . . . . . . . . . . . . . . . . . 6.4 Phenomenological picture of accretion and ejection connection 6.4.1 Cygnus X-3 . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Hybrid Comptonization . . . . . . . . . . . . . . . .

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Summary and conclusions 7.1 Summary and conclusions . . 7.1.1 Cygnus X-3 . . . . . . 7.1.2 Generalized picture of quasars . . . . . . . . 7.2 Future directions . . . . . . .

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Synopsis

An X-ray is a quantum of electromagnetic radiation with an energy, to an order of magnitude approximation, some 1000 times greater than that of optical photons. Traditionally, the soft X-ray band is defined as the energy range 0.5 – 12 keV (corresponding to wave length of 25 – 1 ), the hard X-ray extends to 50 keV and the energy range beyond it till a few MeV is regarded as soft gamma rays, although this classification is not very stringent. High energy astronomy pertains to the observation of the sky in this regime of the electromagnetic spectrum. The study of cosmic sources at these high energies of X-rays and gamma-rays began only in the early 1960’s, after the serendipitous discovery of the low mass X-ray binary (LMXRB) Sco X-1, which houses a neutron star (the compact object) and a low mass optical companion in the main sequence. Simple extrapolation from the optical regime suggests that, assuming the physical processes giving rise to these X-ray, gamma ray emissions are thermal, the temperature of the radiating matter should be of the order    K for X-ray photons and greater for gamma ray photons. The fundamental physical mechanisms which give rise to high energy emissions from a thermalised distribution of matter are few, viz. thermal black body radiation, bremsstrahlung, Compton scattering. Soon, however, it was discovered, mainly from the supernova remnants, that non-thermal physical processes also play very important part in these high energy emission. Such physical processes may also involve bremsstrahlung and Compton scattering, in addition to synchrotron emission. This interplay of thermal / non-thermal emission is best observed in accreting black hole (both stellar mass and super massive) and neutron star systems. Various theoretical paradigms exist today which attempt to comprehensively explain the accretion phenomena in these systems. Shakura & Sunyaev laid the foundation of the first standard disc models (now known as SS discs). However these discs were untenable due to instability arising out of temperature crossing the hydrogen ionization point, and this led to the classic disc instability paradigm which sought to explain various transitions and variabilities in the accretion disc systems. Improved wide band X-ray observational capabilities enabled the spectral energy distribution (SED) of these sources to reveal the ubiquitous vii

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Synopsis

presence of power law component extending well into hard X-ray and gamma ray band, along with any soft component (black body, generally multicoloured). Thereafter various paradigms involving hybrid (i.e. both thermal and non-thermal) Comptonization, advection dominated accretion flow (ADAF), Compton reflection, bulk motion Comptonization, two component accretion flows, etc., with or without magnetic field, were developed to explain the hard power law extension, the various states of black hole transitions and their variabilities. Models involving synchrotron emission, Compton selfsynchrotron, etc., are also used to explain the high energy emission in these sources. Long term monitoring of the various high energy SEDs and variabilities of these sources are needed to devise any comprehensive physical and geometrical picture of the processes. Quasars, which fall in the broader classification of radio loud Active Galactic Nuclei (AGN), were discovered in the radio band of electromagnetic radiation during the era of the very early discovery of X-ray sources. These were subsequently identified to be accreting supermassive black holes     of galactic scales with outflows in the form of a jet observable in the radio band by virtue of the physical mechanism of synchrotron emission. Therefore a paradigm of accretion being related to ejection was gradually developed, although it was not observable in the radio quiet AGNs. The discovery of Galactic X-ray binaries exhibiting (superluminal) radio jets, with both physical and temporal (variability) scale roughly at 6 orders of magnitude less than those of quasars, led to the notion of ubiquitous presence of outflow in the form of collimated jets in accreting black hole systems and low magnetic field (    G) neutron stars, lending them the terminology of microquasars. The observation of microquasars over the AGN is advantageous for, chiefly, two reasons. Firstly, these sources are located within the Galaxy, the astronomical equivalence of our own backyard. And, secondly, the characteristic dynamical time scales in the flow of matter are proportional to the black hole mass and any variability time scale of hours to days of microquasars correspond to analogous phenomena with duration of hundreds to thousands of years in AGNs, assuming that the same fundamental physical processes underlie the behaviour of these sources. Therefore monitoring the microquasars for a few days may sample phenomena not possible to observe in quasars. These features led to the current upsurge in the observational study of these sources. The aim of this thesis is to gather together a comprehensive picture of the high energy observational features of Galactic microquasars, with a particular emphasis on the enigmatic source Cygnus X-3, in order to develop a phenomenological understanding of the fundamental processes and geometrical structure of these systems. Since accretion (inflow of matter, generally in the form of discs) and ejection (outflow of matter in collimated jets) are closely related, a correlated study of high energy and radio

ix emission is presented to provide a coherent picture of the systems. Microquasars, generally black hole candidates (BHCs), mimic, at a much smaller scale, the main astrophysical attributes of a quasar: general relativistic accretion identified by the X-rays and gamma rays from the surrounding accretion discs, and the special relativistic outflows in the form of collimated jets with low opening angles (  !#" ) observed by means of their synchrotron emission. Of the 200 Galactic X-ray binaries catalogued so far, about 20 are radio loud, half of which show evidences of radio jets, a few of them superluminal (eg. GRS 1915+105, GRO J1655-40). These X-ray binary sources have some common salient characteristics which may be enumerated as follows:Structural characteristics:$ They consist of one compact object (generally a black hole candidate) and one normal star, generally from the main sequence. $ The compact object accretes matter from the companion, via an accretion disc. The donor may lose mass through Roche lobe overflow or via stellar wind. The extent of the inner disc is a function of time (and probably accretion rate), the explanation of the variability generally depends on the particular model adopted to explain the X-ray characteristics. $ The outflow of matter takes place via a collimated beam, visible in the radio, at times infra-red or, arguably, even X-ray. The conical jet has a small opening angle ( % ! " ) directed perpendicular to the accretion plane. This system may show precessional movement in some cases.

From the observational point of view, the study of the behavioural pattern of these sources, in the various electromagnetic bands, may be classified into three different types of analysis: 1) image analysis, which gives the (extended) spatial information about the source, 2) temporal analysis, which gives the variability of the source with respect to time, and 3) spectral analysis, which gives the pattern of the emission with respect to the energy (or frequency / wavelength), and provides the best analytical tool for identifying the physical processes giving rise to the emission. Some basic generic patterns of the temporal and spectral characteristics (in the X-ray regime) of the microquasars are highlighted below:Temporal characteristics:$ The X-ray light curve may show a variety of diverse variabilities, even for a single source, depending on the particular states or transitions among them during the period of observation.

Synopsis

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$ The power density spectra (PDS) shows, typically, a power law dependence with a positive index in the region of 0.01 – 1 Hz, flat spectra for the next decade of frequency range, followed by a power law decay (i.e. negative index) of power in the 10 –100 Hz. The PDS of the neutron stars is generally shifted towards the higher frequency region by an order of magnitude. $ Various types of quasi periodic oscillations (QPOs) are observed in most of the microquasars, prominently in the low-hard state of X-ray emission.

Spectral characteristics:$ The spectra constitutes of continuum component and line emissions (mostly Fe K & ). The continuum, for a canonical black hole candidate, consists of two components, a soft thermal (originating from a multi-coloured disc) and a hard nonthermal (generally characterized by a power law). The Fe line is now considered an essential feature of black hole X-ray spectroscopy. $ The standard black hole candidates, viz. Cygnus X-1, exhibit two distinctly different kinds of behaviour, i) low-hard, with the soft X-ray flux low and spectral behaviour comparatively harder, and ii) high-soft, with the soft X-ray flux higher and the SED dominated by the softer X-ray. But the individual spectra of the sources may differ dramatically from one another.

While these sources may or may not show radio flaring episodes which entail huge blobs of matter being ejected (superluminally) from the system, recently it was realized that non-thermal radio emission is a ubiquitous feature during the quieter phases. The non-thermal emission forms a substantial fraction (5%–50%) of the energy budget. Historically, the radio and X-ray studies were done in a disjoint manner for these sources, and the development of the models describing the accretion and ejection took place independently. In the last decade first efforts were made to create models to treat accretion and ejection in a unified scenario, underlying the physical connection between the two. Meanwhile, observational strategies were developed independently to monitor some of these sources in the radio and X-ray at a regular basis to study the long-term behavioural patterns in these systems, chiefly to observe the transient features of mostly transient and a few persistent sources. The most methodical and consistently regular of these strategies were the ones carried out in the radio at the Green Bank Interferometer (GBI) operated by NRAO, and concurrently in the soft and hard X-rays by All Sky Monitor aboard the Rossi X-ray Timing Experiment (RXTE - ASM, 2-12 keV) and the Burst and Transient Sources Experiment aboard the Compton Gamma Ray Observatory (CGRO BATSE, 20-100 keV), respectively.

xi Given the various diverse types of temporal variabilities and spectral characteristics of the high energy emissions of the different microquasars, along with their different types of radio emissions (from the outflow), there was no single consistent picture that could provide a general scenario of the disc (accretion) – jet (ejection) connection in these systems. Our investigation commenced with the next logical step of understanding this connection at a broad scale across the diverse type of sources of this class exhibiting their characteristic idiosyncratic behaviour, in order to provide a unified, consistent set of observational features with the aim of developing a phenomenological model to unravel the physical and geometrical structure of these X-ray binary systems. We achieved this by carrying out a systematic correlation analysis among the radio, soft and hard X-rays, for the sources Cygnus X-3, GRS 1915+105 and Cygnus X-1, using the available data from the archives of GBI (2.2 & 8.3 GHz), RXTE-ASM (2-12 keV), CGRO-BATSE (20-100 keV), during the long term steady hard states of these systems. These three persistent X-ray as well as radio sources were the only ones monitored simultaneously by these three observatories. The results of the correlation studies from these sources was complemented by the observations reported for GX 339-4 (and also V404 Cyg), scattered in the literature, to provide a qualitative self-consistent picture of the disc-jet connection, using the Two Component Advection Flow (TCAF) model. In this thesis, our emphasis lies in the detailed multi-band (X-ray and radio) study of the enigmatic binary system Cygnus X-3, where we provide the complete evolution of the radio flaring episodes of Cygnus X-3 driven by the X-ray spectral states in the system. In addition, we report the temporal properties of the X-ray emission in this particular binary system and provide a time scale of anti-correlation between the soft and hard X-rays in the system. Of all the Galactic microquasars, Cygnus X-3 is one of the brightest in both radio and X-ray bands, but one of the least understood of all binary systems. Located at a distance of 9 kpc in one of the Galactic arms, it exhibits a binary period of 4.8 hours in both X-ray as well as infra-red bands, while the radio emission doesn’t show the binary modulation. The emission lines of He I and He II in the infra-red band with the absence of any H lines suggest the presence of dense winds and the companion to be of the WolfRayet type, establishing the system to be a High Mass X-ray binary (HMXRB). The nature of the compact object of the binary system is still not conclusively ascertained, and a prime motive of undertaking the detailed X-ray spectral study was to glean the observational features that may pertain to any particular class of compact objects, black hole or neutron star. To attain this goal we carried out a thorough and comprehensive analysis of the Xray emission of the source from the complete data set of the the RXTE archives available publicly. This satellite observatory combined the dual advantage of the best X-ray tim-

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Synopsis

ing capabilities (PCA) along with a very wide band X-ray spectral coverage (PCA and HEXTE). Furthermore, RXTE has an extensive collection of data sets covering the microquasars at a (semi) regular basis. The analysis consisted of, downloading the raw data of all the observations for this source, reducing and filtering the data in accordance with the housekeeping files, extraction of lightcurve and the spectra keeping the diverse conditions of the source as well as the observatory in consideration, creating the response matrix for the obtained spectra, analyzing the lightcurves and the spectra using the designated software, and finally, interpreting the analyzed result in conjunction with, chiefly, (contemporaneous) radio observations. The background spectra and lightcurves for PCA were reduced from the model background event files provided by the PCA team, while the two HEXTE detectors alternately point on and away from the source, measuring the source and background flux with a duty cycle of 16 seconds. The PCA background has a time resolution of 16 seconds, as a result the timing studies above ' !( keV can not be done at a time scale less than this. All the X-ray spectra are obtained at the time resolution of 16 seconds. The long term X-ray spectral variation of this source shows two distinct states, high and low, and correspondingly soft and hard (although the individual spectral model components are different from a canonical high-soft and low-hard state of stellar mass black hole candidates, characterized chiefly by Cygnus X-1). Correspondingly the radio emission can be broadly classified into two types, persistent and flaring. The persistent emission predominates the X-ray hard (as well as low) state. In the X-ray soft (as well as high) state the persistent radio emission is quenched, interspaced by the flaring events, both minor and major. The major radio flares are among the brightest in the Galaxy, occurring only during the X-ray high (soft) state. The distinct features of the X-ray spectra of this source are: 1) very high absorption in the soft X-ray regime, probably by the dust and/or halo engulfing the binary system, whose most likely origin is in the wind from the Wolf-Rayet companion, which obscures the thermal blackbody spectra, 2) above 5 keV, the continuum is complex and a mixture of model components consisting of thermalised Comptonization and a power law is needed to model the spectra in the low (hard) state, while the high (soft) state, in most cases, shows a very strong multicoloured disc black body emission and a Comptonization component, as a result the unusual hump in the 5-30 keV region present in the low (hard) state is absent in this high (soft) state, 3) the hard X-ray tail, which may be characterized by power law, is present in both the low (hard) and high (soft) states, 4) EXOSAT, ASCA & Chandra observations have revealed three Fe lines (6.4 keV, 6.7 keV & 6.9 keV) along with two absorption edges (7.1 keV & 9.1 keV) present in the source, but the resolution of the RXTE-PCA is not good enough to resolve these to desired accuracy.

xiii Detailed analyses of the X-ray spectra show a definite pivoting at about 12-20 keV in the hard state. In the soft state the picture is different with the thermal emission from the accretion becoming the prominent feature of the SED, in most cases. There is a definite causal relationship between the X-ray spectral evolution and the radio flaring events, which may be explained by classifying this state into three sub-states: 1) the radio quiescent phase, in which the thermal multicoloured disc black body and the Comptonizing component are equally strong, 2) pre-radio flare, during which the Comptonizing component becomes vanishingly small ( )* !,+ ), suggesting the evacuation of the central Compton cloud, resulting in the flare, which may occur at a time scale of less than a day, 3) post-radio flare, in which the succession of radio flares, both minor and major, are brought to an end by a change in the X-ray spectrum, with the spectral shape hardening and the thermal disc black body component vanishing, following which the source makes transition into the low (hard) state. Unless this spectral hardening takes place, the succession of flares, minor ones interspaced by a few major ones, continues with the Comptonizing component remaining significantly less than the thermal component. Thus, a picture of a complete evolution of the occurrence of radio flares in relation to the X-ray spectra is obtained, for the first time for this source. These spectral features tilt the balance of evidence in the favour of the compact object being a black hole, although a definitive statement can only be made after ascertaining the mass function of the system. To obtain the long term behavioural pattern of this source we carried out a systematic correlation analysis among radio (GBI. 2.2 GHz), soft and hard X-ray (RXTE - ASM: 2-12 keV & CGRO - BATSE: 20-100 keV) emissions, during the period for which these three observatories were simultaneously monitoring the source, as mentioned before. We employ the Spearman’s Partial Rank correlation test for the correlation among the three variables. In the high (soft) state, the long-term correlation results are not very significant, due to the complex evolution of the radio as well as X-ray emission, as explained earlier. In the low (hard) state, the soft X-ray is very strongly correlated to the radio emission, while the hard X-ray is anti-correlated to both soft X-ray as well as radio emission. This interesting correlation result is explained by the pivoting in the spectra, at about 12-20 keV, being correlated to the radio emission. The short term temporal properties of the X-ray emission of Cygnus X-3 is perhaps the least studied aspect of this source, also among all other microquasars this source’s X-ray temporal properties are least explored. The principal reason for this is the fact that the binary modulation of 4.8 hours is too strong and smothers any other variability pattern that may emerge out of any analysis in the study of the shorter time scale variability. Hence, our first step was to correct for the binary modulation using the binary template for a quadratic ephemeris which is amazingly stable for more than two decades of obser-

xiv

Synopsis

vation. The long term RXTE-ASM monitoring data, containing all sorts of variabilities including the period of major radio flares, folded by the template shows very meagre residue, proving its applicability to correct for the binary modulation. The latest template was obtained from the ROSAT, ASCA, BeppoSAX, RXTE and IXAE pointing and monitoring, which was used to correct for the binary modulation in the flux variability in the light curves obtained at all the different X-ray energy bands, after making appropriate scaling adjustments, for all RXTE-PCA pointed observations analyzed in this thesis. The binary correction using this template is very good at the rising and falling phase, highlighting the small variations which were otherwise smothered by the binary modulation of the ephemeris, whereas at the peak the smooth nature of the template is not always successful to correct the generally random fluctuations in the emission. The correlation among the radio, soft and hard X-ray emissions remains the same after the correction for the binary modulation, and detailed tests show that the anti-correlation time-scale between the soft and hard X-rays, due to the pivoting of the spectra, is less than a day. The power density spectra of this source has a feature distinct from its counterparts, the shifting of the spectra towards low frequency. In this pattern of temporal variability it resembles less like other Galactic microquasars and bit more like the massive AGNs with a central massive black hole. One may reconcile the absence of power in the high frequency regime to the reprocessing of the X-ray photons in the dust and/or halo engulfing the system, reducing the amplitude of the fast X-ray variability. The most interesting result of the X-ray timing properties reported of the source, by us, is the anti-correlated time lag of 400–900 seconds between the soft and hard X-rays in the low (hard) state of the system. Unless corrected for the binary modulation, this delay is not observable. Also, this delay is observed only in the hard (low) states, the non flaring soft (high) state doesn’t show any such delay. This anti-correlated delay between the soft and hard X-ray flux, with the hard X-ray lagging, provides the dynamical time scale of the pivoting of the spectra, in the hard state. It is noteworthy that from the long term correlation among the monitoring data in the radio, soft and hard X-ray bands we had predicted an anti-correlation time scale shorter than a day. This is the first such observation for this source and will provide stringent constraints on the accretion models for microquasars in general. The generalization of the X-ray:radio correlation, during the low (hard) state, for different types of microquasars, was done by repeating the correlation study of the long term radio(GBI, 2.2 GHz), soft and hard X-ray (RXTE - ASM: 2-12 keV & CGRO BATSE: 20-100 keV) monitoring data of two more sources with apparently diverse behavioural pattern, viz. GRS 1915+105 & Cygnus X-1, and collating the existing results

xv of another black hole candidate GX 339-4. It was successfully demonstrated that all these three sources, plus Cygnus X-3, show a very similar behaviour during the low (hard) state, i.e. pivoting of the X-ray spectra correlated to the radio emission, with the radio emission being higher in the comparative softer state (within the bounds of the hard state). The only difference lies in the pivoting energy of the individual sources. GRS 1915+105 has a pivot point between 20-30 keV, Cygnus X-1 between 50-100 keV and GX 339-4 has it at -/. keV. We also established that the pivot point moved further into the hard X-ray / low gamma ray regime as the intrinsic luminosity of the sources in the soft X-ray band weakened. Furthermore, continuing the X-ray:radio association beyond the X-ray state transition it is revealed that the radio emission is quenched, to varying degrees, for all the sources (during the non-flaring periods). Therefore, for the first time, a uniform behavioural pattern was found of the radio emission and correlated X-ray spectral emission evolution, encompassing various microquasars with apparently different characteristics. Most remarkably, all the sources (along with another black hole candidate, V404 Cygni), were found to show a linear monotonic increase of radio emission with the soft X-ray flux, spanning a 5 orders of magnitude variation in the intrinsic luminosities, with the radio emission suppressed for the intrinsically weaker X-ray emitters (during the non-flaring state). Arguing that radiation in both the bands, radio as well as X-ray, are unlikely to originate from a single mechanism (like synchrotron emission), we invoked the TCAF model to explain the accretion-ejection behaviour in these systems. According to the TCAF model, the Compton scattered X-rays in a black hole source originate from a region close to the compact object, confined within the Centrifugal Boundary Layer (CENBOL). The X-ray spectral shape in various ‘states’ of the source essentially depends on the location of the CENBOL. At low accretion rates, the CENBOL is far away from the compact object and the X-ray spectrum is dominated by a thermal (-non thermal)-Compton spectrum, originating from the high temperature region within the CENBOL. In the transition state, the CENBOL comes closer to the compact object and the CENBOL can sometimes give rise to radial shocks, causing intense quasi-periodic oscillations. In the high state, the increased accretion rate produces copious photons in the accretion disc which cool the Compton region, giving rise to very intense disc blackbody emission along with bulk motion Comptonization (a power-law in hard X-rays with a photon index of 2.5). The outflow rate is found to be a monotonic function of the compression ratio of the gas at the shock region. In this scenario, at low accretion rates, the CENBOL is far away from the compact object, a weak shock can form with low compression ratio, giving low and steady outflow. If this outflow gives rise to radio emission, one can expect a relation between the radio emission and

Synopsis

xvi

the X-ray emission. In this state (off state to low-hard state), an increased accretion rate increases the overall amount of energy available to the Comptonizing region and hence increasing the X-ray emission. The CENBOL location would be pushed inward, increasing the compression ratio (and hence increasing the radio emission) and also can increase the temperature and optical depth of the Comptonizing region, thus giving rise to a pivoting behavior at hard X-rays as seen in Cygnus X-1 and GX 339-4. At increased accretion rate, the CENBOL can come closer to the compact region, giving the spectral and radio properties as seen in GRS 1915+105 and Cygnus X-3. For a given accretion rate the compression ratio, after reaching a critical value (with the shock region coming correspondingly closer to the event horizon), causes the source to transit into the highsoft state state, for which the radio emission is progressively suppressed, clearly seen in Cygnus X-3, GRS 1915+105, Cygnus X-1 and GX 339-4. During the flaring states, the TCAF model predicts ejection of the central Compton cloud resulting in the radio flares, with the size of the ejected blob determining the flux in the radio band. This model further predicts the absence of radio flares during periods dominated by bulk motion Comptonization, when the infalling matter falls directly into the event horizon due to its bulk motion, resulting in quenched radio emission. The observational evolution of the X-ray spectra with the radio flaring of Cygnus X-3 may be explained by transition between these two states, during the high (as well as soft) state. Thus, in this thesis we provide a comprehensive phenomenological modeling of the class of Galactic X-ray binary system exhibiting jets, called microquasars, with very special emphasis on the enigmatic source, Cygnus X-3. The future works should entail a detailed quantitative modeling of the complete behavioural pattern of the source Cygnus X-3. Then one has to reconcile the qualitative as well as quantitative features of the accretion–ejection mechanism in these systems with other cosmic sources showing accretion as well ejection at diverse physical scales, namely the AGNs at one and the YSOs (Young Stellar Objects) on the other. Chapter-wise organization of the thesis:$ Chapter 1 gives introduction to astronomical high energy phenomena, with emphasis on accretion discs as sources of high energy emission. It further discusses the cosmic black hole systems: stellar mass and supermassive, and introduces the concept of microquasars and their importance, laying down the aim of this thesis. $ Chapter 2 deals with X-ray detectors and techniques of instrumentation as well as radio astronomy observatories. The modern X-ray observatory RXTE and its

xvii data analysis techniques is illustrated in detail, this being the principal observatory whose data is analyzed in these thesis. Other high energy observatories, viz. CGRO is also mentioned. A brief introduction to radio astronomical observatories, namely GBI and GMRT are provided. $ Chapter 3 starts with general introduction to Cygnus X-3. Thenceforth it provides the detailed spectral analysis and features of this source, providing an X-ray spectral behavioural evolution during the radio flares. $ Chapter 4 demonstrates the temporal properties of Cygnus X-3. Here the long term radio : X-ray correlation tests and results are presented. Further, a recipe is provided for the correction of X-ray binary modulation with the given ephemeris. Thereafter the power density spectra and time lag between soft and hard X-ray emissions is obtained. $ Chapter 5 provides the generalized accretion - ejection mechanism of microquasars by extending the long term radio : X-ray monitoring to other persistent sources. Uniform behaviour of X-ray spectral shape with radio emission and universal correlation is obtained in both low (hard) as well as -non flaring- high(soft) states. $ Chapter 6 describes the TCAF model, elucidating a qualitative phenomenological explanation of our multi-band data analyses results, providing a uniform picture of the disc - jet connection in the microquasars. $ Chapter 7 summarizes the results and the phenomenological models and outlines future directions for further study of the accretion - ejection mechanism.

Chapter 1 Introduction

An X-ray is a quantum of electromagnetic radiation with an energy, to an order of magnitude approximation, some 1000 times greater than that of optical photons. Traditionally, the soft X-ray band is defined as the energy range 0.5 – 12 keV (corresponding to wave length of 25 – 1 ), the hard X-ray extends to 50 keV and the energy range beyond it till a few MeV is regarded as soft 0 -rays, although this classification is not very stringent. High energy astronomy pertains to the observation of the sky in this regime of the electromagnetic spectrum. The study of cosmic sources at these high energies of X-rays and 0 -rays began only in the early 1960’s, after the serendipitous discovery of the low mass X-ray binary (LMXRB) Sco X-1, which houses a neutron star (the compact object) and a low mass optical companion in the main sequence. These early observations were made by rocket flights, which provided only a few minutes of data. This field of astronomy matured with the advent of use of balloon flights and the first generation Xray astronomy satellites during the 1970’s. Post 1980’s the enormous advancement and progress in the computational and technological capabilities completely revolutionized this branch of astronomy so much so that currently high energy astronomy is, perhaps, the most ‘happening’ branch of astronomy and astrophysics.

1.1 High energy physical processes and phenomena Simple extrapolation from the optical regime suggests that, considering a thermal origin of the physical processes giving rise to these high energy X-ray & 0 -ray, the temperature of the radiating matter should be of the order of 1 – , K for X-ray photons and greater for the 0 -ray emission. The fundamental physical mechanisms which give rise to high energy emissions from a thermalised distribution of matter are few, viz. thermal black 1

Chapter 1. Introduction

2

body radiation, bremsstrahlung, Compton scattering. Soon, however, it was discovered, mainly from the supernova remnants, that non-thermal physical processes also play very important part in these high energy emission. Such physical processes may also involve bremsstrahlung and Compton scattering, in addition to synchrotron emission. Black body radiation. The spectrum of thermalised emission of a black body is given by (see, for eg. Rybicki and Lightman 1979) 2 3

: (< : 546798 ; =  3?>@BA 8 C

(1.1)

where 4ED temperature of the body, D frequency of the radiation and < , F , 8 ; D Plank constant, Boltzmann constant and velocity of light, respectively. A temperature of  K will render most of the radiation in the X-ray band. Thermal bremsstrahlung. Free-free emission occurs with the interaction (acceleration) of energetic electron with the near stationary nuclei, with a fractional deposition of the energy into the electromagnetic radiation. For a hot thermal plasma the spectrum is given by XZY :?JKJMLON

LQ    GIH  46 (1.2) R P 8 81[ FS4UTWV J]L where 4\D temperature, D electron density, HED atomic no. of Y the conJ cerned nuclei, D space density of nuclei in laboratory frame and  4^_D 81[ the Gaunt factor which gives the correction due to the collision parameters after integrating over velocity. 2

Synchrotron radiation. The process of radiation due to acceleration of charged particles, normally electrons, in a region containing magnetic field is known as synchrotron radiation process for relativistic velocities of the electrons (in the nonrelativistic limit the process is known as cyclotron emission). 2

   Ga`Rbdc 8

N

X V 8

T

bBe

X V

(1.3)

where `D magnetic field and fgD spectral index when the spectrum is a powerJ law of electron energy distribution, given by ih_jGkhmlon .

1.1. High energy physical processes and phenomena

3

Comptonization. The scattering of an energetic photon with a stationary electron is known as Compton scattering, where fractional energy is transferred to the electron. The inverse of this process involves transfer of energy from energetic electronto a low energy photon (inverse Compton scattering), and it is a very important physical mechanism generating high energy radiation in cosmic sources. The interaction between ensembles of photons and electrons is known as ‘Comptonization’. The evolution of the photon and electron energy distributions subject to Comptonization is governed by the Kompaneets equation (Kompaneets 1957, also see Rybicki and Lightman 1979) prq p prq N FS4 N qzyq : y

r u x p#st 7 p u (1.4) PR; : T u : p uwv T{ st}| q LB~ A ; s   D time measured in units of mean time between scatwhere terrings. Eq. 1.4 may be expressed in terms of the Compton  parameter in an integrated form p#q p prq N qzyq : y

x u : p p u (1.5) 7 u p uv  T{ L L P L ; : ~ A J LB†o‡ q and is the occupation number where u 7€< FS4 , ‚7„ƒ…FS4  8r  which is defined as the number of particles or photons per state. If the energy y † 3 density of isotropic radiation in the frequency interval to is ˆ , then the †3 8 8 8 < and the occupation number is given by number density of photons is ˆ 8r 8 3 Q q ˆ ; (1.6)  7
‰ 8 < Q‹Š 8 The value of the Compton  parameter determines the type of Comptonization i.e. saturated or unsaturated. General solutions of the Kompaneets equation need to be obtained numerically, although it is possible to find analytic solutions, under some approximations. There have been many such attempts in this direction (e.g. see Sunyaev and Titarchuk 1980, 1985, Lightman and Zdziarski 1987, Titarchuk 1994, Poutanen and Svensson 1996, etc.) and accordingly many different Comptonization models, which are valid under various sets of approximations, are available for modeling the X-ray spectra from cosmic sources. X-ray line emission. Excitation of the lowest-shell electrons (K,L, etc.) into the unbound state results in emission of radiation in the X-ray band when the empty levels are filled by transition form outer shells. However, in order to excite these low shell electrons the excitation energy need to be very high as well, which is

Chapter 1. Introduction

4

only possible in environment with extremely high temperature or with extremely high density high energy photon fields. Thus, the X-ray line spectroscopy provides us a powerful method for plasma diagnostics under extreme conditions.

1.1.1 Accretion disc as a source of high energy emission The most common physical phenomenon that gives rise to emission in the X-ray band is accretion of matter onto compact objects. This process involves accumulation of diffuse gas or matter onto the compact object under the influence of gravity, and is expected to be responsible for the observed properties of a wide range of X-ray sources from X-ray binaries to Active Galactic Nuclei (AGNs) (Frank et al. 1992). A mass P being accreted to a body of mass  and radius Œ will lose potential ‘  , which, if converted to electromagnetic radiation, will cause the system to energy Ž_ ’ have a luminosity of :  P

PR; :1•!– (1.7) 7”“ 7 7k— PR; Œ ( Œ ; : D Schwarzschild radius, and —R7™: ˜  •!– Œš gives the efficiency where •– 7€(    “ of the accretion process. Thus the efficiency of energy conversion due to accretion simply depends upon the compactness of the accreting body. For a white dwarf star with  7„ , •!– 7€.m›  x m and Œ”œm›ž  m Ÿ —¡7€.m› 1l x . Correspondingly for 1   neutron star with R = 15 km, —7E Š 1 , and for black holes — ranges from 0.06 (Schwarzschild blackhole) to 0.426 (maximally rotating Kerr blackhole). Thus, black holes, particularly, maximally rotating ones, are the most powerful energy sources in the Universe and accretion is the process by which the energy is released. Despite this high efficiency of emission of electromagnetic energy, the balance between the outwardly directed radiation pressure (obtained from Thomson cross-section) and inwardly directed gravitational pressure limits the luminosity to a limiting value, called Eddington luminosity, which is given by ’j¢ ‰ Q ( •~ – P ; Q N  A n 7 7£ Š .W›¤  ˜ (1.8)   T ¥ It should be noted that this is derived assuming spherically symmetric geometry. It is possible to exceed the Eddington limit by adopting a different geometry, but not by a large factor. Further, the limit applies to steady-state situations and in none steady-state situations like supernova explosions the Eddington limit can be exceeded by a large margin. 1

the efficiency for nuclear burning in neutron stars is only ¦§¡¨© ¨B¨?ª

1.2. Black hole sources: stellar mass and supermassive

5

Thus observation of accretion of matter onto compact objects provides a unique opportunity to investigate the most powerful energy sources in the Universe. Two such classes of objects exist in the universe known to us:1. Active Galactic Nuclei. These are supermassive blackholes, with the mass of compact object «   lr¬ , at the centre of galaxies. The blackhole accretes mass from the interstellar medium around it, disrupting the stellar structures and consuming the matter within the envelope of its horizon. 2. Galactic X-ray binaries. These binary system have stars with a compact object, neutron stars or blackhole candidates, accreting matter from the companion star, which is normally in the main sequence.

1.2 Black hole sources: stellar mass and supermassive Since the efficiency of conversion of gravitational energy into electromagnetic radiation is more for blackholes, as compared to neutron stars, they provide a unique opportunity to understand the behaviour of matter under extreme physical conditions. Also, the phenomena of accretion makes the black hole ‘visible’ to observers from a distance, which otherwise doesn’t allow any particle, including light photons, to escape and thus render the direct observations of these sources impossible. Therefore these sources offer the opportunity to experimentally verify the general theory of relativity directly, and hence put to test the underlying fundamental principles of our understanding of the physical structure of the universe. It is presently established that blackholes exist in two classes, supermassive and stellar mass blackholes.2 As mentioned above, the accretion phenomenon is ubiquitously observed in Active Galactic Nuclei (henceforth referred to as AGNs) as well as the Galactic X-ray blackhole binary systems. The more interesting observational feature seen in these sources is that accreted matter is more often than not ejected out in the form of a jet perpendicular to the accretion disc. In fact, the observations, in the radio band, of outflowing conical jets from the core of the galaxies, often exhibiting superluminal (with apparent velocity greater than that of light) expansion, were reported before the phenomenon of accretion was inferred from the observational studies, for the extra-Galactic sources. Quasars, a sub-class of AGNs, were discovered in the radio band of electromagnetic radiation during the era of the very early discovery of X-ray 2

recently there are growing arguments regarding a third kind, the intermediate mass blackhole, but a discussion on this topic is beyond the purview of this thesis

6

Chapter 1. Introduction

sources. These were subsequently identified to be accreting supermassive black holes   6I    of galactic scales with outflows in the form of a jet observable in the radio band by virtue of the physical mechanism of synchrotron emission. Therefore a paradigm of accretion being related to ejection was gradually developed, although it was not observable in the radio quiet AGNs. The discovery of Galactic X-ray binaries exhibiting (superluminal) radio jets, with both physical and temporal (variability) scale roughly at 6 orders of magnitude less than those of quasars, led to the notion of ubiquitous presence of outflow in the form of collimated jets in accreting blackhole systems and low magnetic field ( E   G) neutron stars, lending them the terminology of microquasars. There are obvious advantages of observing microquasars (over quasars) in order to understand their physical and geometrical structures:1. Microquasars are located within the Galaxy, the astronomical equivalence of our own backyard. Their proximity enables the study of both the lobes of the outflowing jet more feasible and practical. The measurement of both the components as well as evolution of the flux and size ratio of the two components are essential to attempt a detailed modeling of the jets. Further, the improved accuracy of the measurement of the jet properties provide more accurate values of the basic parameters of such astrophysical structures. 2. The characteristic dynamical time scales in the flow of matter are proportional to the black hole mass and any variability time scale of hours to days of microquasars correspond to analogous phenomena with duration of hundreds to thousands of years in AGNs, assuming that the same fundamental physical processes underlie the behaviour of these sources. Therefore monitoring the microquasars for a few days may sample phenomena not possible to observe in quasars. Over the last few years of intense observations one disadvantage has become glaring in the case of the microquasars:1. The dynamical time scales of the fast variability, milli-second variation for microQ quasars and correspondingly  s for AGNs, do not provide enough photon count for any meaningful statistical analysis, because the present day detectors do not possess the capability to capture enough photons necessary during the small time span of the very fast variability. Despite this one deficiency, in the recent past there has been tremendous upsurge in the observational study of the microquasars, and understandably so.

1.2. Black hole sources: stellar mass and supermassive

7

Fig. 1.1: The similarities between quasars and micro-quasars. Both systems contain similar basic ingredients viz. (1) a central black hole, (2) an accretion disk and (3) collimated jets of relativistic particles. The difference between them lies in the mass scale. Microquasars have stellar mass blackhole of the order of a few solar mass and the jets travel to a distance of a few light years whereas in quasars the black hole mass is supermassive of the order of ­¯®±°j²³­¯®´ solar mass and the jet can travel to a distance of a few million light years. This figure is taken from Mirabel and Rodriguez (1998)

Chapter 1. Introduction

8

1.3 Microquasars: general properties and behaviour Microquasars, generally black hole candidates (BHCs), mimic, at a much smaller scale, the main astrophysical attributes of a quasar: general relativistic accretion identified by the X-rays and gamma rays from the surrounding accretion discs, and the special relativistic outflows in the form of collimated jets with low opening angles ( µ 15 ¶ ) observed by means of their synchrotron emission. Of the 200 Galactic X-ray binaries catalogued so far, about 20 are radio loud, half of which show evidences of radio jets, a few of them superluminal (eg. GRS 1915+105, GRO J1655-40). These X-ray binary sources have some common salient characteristics which may be enumerated as follows:Structural characteristics:$ They consist of one compact object (generally a black hole candidate) and one normal star, generally from the main sequence. $ The compact object accretes matter from the companion, via an accretion disc. The donor may lose mass through Roche lobe overflow or via stellar wind. The extent of the inner disc is a function of time (and probably accretion rate), the explanation of the variability generally depends on the particular model adopted to explain the X-ray characteristics. $ The outflow of matter takes place via a collimated beam, visible in the radio, at times in the infra-red or, arguably, even in the X-ray. The conical jet has a small opening angle ( µ 15¶ ) directed perpendicular to the accretion plane. This system may show precessional movement in some cases.

From the observational point of view, the study of the behavioural pattern of these sources, in the various electromagnetic bands, may be classified into three different types of analysis: 1) image analysis, which gives the (extended) spatial information about the source, 2) temporal analysis, which gives the variability of the source with respect to time, and 3) spectral analysis, which gives the pattern of the emission with respect to the energy (or frequency / wavelength), and provides the best analytical tool for identifying the physical processes giving rise to the emission. The spectral analysis identifies the individual physical mechanism which gives rise the electromagnetic emission. A complete understanding requires the combined understanding of the all the three analysis. Some basic generic patterns of the temporal and spectral characteristics (in the X-ray regime) of the microquasars are highlighted below:-

1.3. Microquasars: general properties and behaviour

9

X-ray temporal characteristics:$ The X-ray light curve may show a variety of diverse variabilities, even for a single source, depending on the particular states or transitions among them during the period of observation. $ The power density spectra (PDS) shows, typically, a power law dependence with a positive index in the region of 0.01 – 1 Hz, flat spectra for the next decade of frequency range, followed by a power law decay (i.e. negative index) of power in the 10 –100 Hz range. The PDS of the neutron stars is generally shifted towards the higher frequency region by an order of magnitude. $ Various types of quasi periodic oscillations (QPOs) are observed in most of the microquasars, prominently in the low-hard state of X-ray emission.

X-ray spectral characteristics:$ The spectra constitutes of continuum component and line emissions (mostly Fe K & ). The continuum, for a canonical black hole candidate, consists of two components, a soft thermal (originating from a multi-coloured disc) and a hard nonthermal (generally characterized by a power law). The Fe line is now considered an essential feature of black hole X-ray spectroscopy. $ The standard black hole candidates, viz. Cygnus X-1, exhibit two distinctly different kinds of behaviour, i) low-hard, with the soft X-ray flux low and spectrum comparatively harder, and ii) high-soft, with the soft X-ray flux higher and the spectrum dominated by the softer X-ray. But the individual spectra of the sources may differ dramatically from one another.

1.3.1 Transient X-ray blackhole binaries Most of the Galactic blackhole candidates are transient in nature, which implies that the source is not continuously detectable by the X-ray astronomical detectors given the current sensitivities of these instruments (with improving sensitivity it is increasingly possible to probe into the “off” state of X-ray emission of these sources). The identification of the optical counterparts during the “off” state of the X-ray emission has recognized many new blackhole candidates by virtue of the mass function of the binary system which is given by · QÀ¿ Q Q  »K¼d½¾ : y …£7€¸º‰ ¹ 7 (1.9) ( … »   ˜ “

10

Chapter 1. Introduction

Fig. 1.2: The long term monitoring of transient X-ray binary blackhole candidates by RXTE– ASM. These sources are also the Galactic superluminal sources.

where  &  » D masses of the companion star and the compact object respectively, ˜ ¿ D inclination angle of the orbit of the binary system, D period of the binary system ¸ and D velocity amplitude obtained from the Doppler shifts of the spectral lines of the ¹ companion due to the orbital motion. These sources are normally Galactic sources that brandish superluminal motion, in the form of outflowing jets. Normally these superluminal expansions occur during the X-ray “on” state. The X-ray bright state may persist from less than a day to more than a decade (see Figure 1.2).

1.3.2 Persistent sources: canonical states of X-ray emission These sources, in obvious contrast to the transient ones, never go “off” in the X-ray band. Always ‘visible’ (Figure 1.3), they present the opportunity to study the X-ray emission behaviour in the various states in which they may exist, evolving from one to another in a cyclic process. There are very few persistent established Galactic blackhole candidates, whose mass function is known, viz. Cygnus X-1, GX 339-4. As evident from Figure 1.3, they exhibit prolonged episodes of high and soft states, whose spectral shapes are intrinsically different and hence are classified into different states (Tanaka

1.3. Microquasars: general properties and behaviour

11

Fig. 1.3: The long term monitoring of persistent X-ray binaries by RXTE–ASM. Cygnus X-1 (top panel) is an arche-typical blackhole candidate, and Cygnus X-3 (bottom panel).

and Lewin 1995), the “high-soft” and “low-hard” states. The suffix ‘soft’ and ‘hard’ are added to emphasize the X-ray spectral shape during the concerned states. With detailed studies of different Galactic BHCs the presence of other states like intermediate and very-high states have emerged. In general the spectra is described by two continuum components, 1) soft thermal component believed to originate from a multi-coloured disc, and 2) hard non-thermal component characterized by a power law. Figure 1.4 shows the wide band X-ray/0 -ray spectra of Cygnus X-1 in three different canonical states which clearly demonstrate the differences in the spectral properties of these X-ray states. High-soft state. In this state the soft X-ray flux is higher and the spectral energy distribution (SED) is dominated by the softer X-ray flux below 10 keV, i.e. of the two continuum components describing the spectra the multicoloured disc black body component dominates the SED, which most likely originates in the inner regions of the accretion disc. The powerlaw component is, at times, regarded as the blackhole accretion signature (Tanaka 2000). The temporal characteristic feature of this state is the strong aperiodic variability over a wide range of time scales from milliseconds to minutes reflected in a typical power-law shape of the power density spectrum.

Chapter 1. Introduction

12 Soft

Intermediate

Hard

Fig. 1.4: The various canonical states of Galactic blackhole candidates, characterized by the arche-typical BHC Cygnus X-1. The figure obtained from Gierli´nski et al. (1999)

Low-hard state. In this state the soft X-ray flux is low and spectral behaviour comparatively harder, i.e. the powerlaw component dominates the SED. This powerlaw component is commonly regarded as a signature of Comptonization process in the system. The temporal behaviour is characterized by the presence of quasi-periodic oscillations (QPO). Other states. During the intermediate state the shape of the SED is intermediate between the high-soft and low-hard states described by the two continuum components of the canonical states, while the lightcurve shows the presence of QPOs. The very-high state has the SED with a shape similar to the intermediate state but with total luminosity higher than that of the high-soft state. For completeness sake one may also mention the “off” state, during which the transient sources are not detectable.

1.4 Accretion in X-ray binaries Accretion, by definition, means accumulation of diffuse gas or matter onto some object under the influence of gravity. The importance of this phenomenon as a source of

1.4. Accretion in X-ray binaries

13

Fig. 1.5: The two types of accretion process in X-ray binaries. Left panel: accretion via stellar winds, more common in HMXBs. Right panel: accretion via Roche-lobe overflow, predominant in the LMXBs.

highly energetic emission was realized with the discovery of X-ray binary systems and subsequently applied to interpret the properties of cataclysmic variables and AGNs. The Newtonian dynamics states that a test particle with initial velocity •Á  falling onto a massive object due to gravitational attraction (conserving angular momentum) is described by : : y < : (  •Á : 7*• Á  (1.10) “ • •  Ä : Ä where <Ã7 Á • D specific angular momentum, and • are polar coordinates. Hence [ for a non-zero < the particle can never reach • 7k . Using Einstein’s general relativistic treatment the dynamics of the same particle in the Schwarzschild metric is given by : : : y < : (  ( Å  < ; : •Á :  : “  “  7 i  Æ C  

 (1.11) ; Q • • • where < & Æ are constants of motion, • Á 7/Ç • ÇrÈ where È is proper time, while : t  < X and : :  iÆ   are constants ŸÉ< and • Á  (in Newtonian case). Due to the term l Ê̍Ë Ž X the ; • Î • – particle is allowed to fall to 7Í if <£E( . Hence, relativistically the effect of gravity is ‘increased’ close enough to • 79 overcoming the centrifugal barrier. Also, there is a last stable orbit (Schwarzschild metric) with radius • 7I. •,– beyond which the circular orbits cease to exist and the particle spirals rapidly towards the singularity (see Longair 1994, for a detailed treatment). Accretion flow is essentially of two types, ‡ 1)‡ Bondi type flow, which has (quasi) spherical geometry with angular momentum ) , and 2) disc type flow, where the ŽWÏ

Chapter 1. Introduction

14

‡ ‡ ‡ D the inflow is flattened into a disc with high angular momentum, , where ŽWÏ ŽWÏ  • – angular momentum at minimum stable orbit . . Even for the first case it can be shown that for a spherically symmetric infalling cloud with axisymmetric rotation the infalling gas passes through a shock at the equator dissipating the kinetic energy perpendicular to the equatorial plane, resulting (in most cases) in the formation of a disc (Hartmann 1998). This implies that even if the accreting matter is falling at an arbitrary angle with respect to the general rotation axis, the velocity components parallel to the rotation axis gets canceled and the matter eventually settles down in the plane perpendicular to the rotation axis forming an accretion disk. In X-ray binaries, the accretion of material happens in two modes (Figure 1.5):$ Wind Accretion. More common in the High Mass X-ray Binary systems (HMXB),

the companion loses mass in the form of stellar wind. The material of the wind : t X Ð , where  » D mass of X-ray emitting Ò ŽÑ 7 within the capture radius, Œ compact object, and Ó³D velocity of wind relative to the  » , is trapped by the gravitational potential and accreted in. $ Roche-lobe accretion. Predominant in Low Mass X-ray Binary system (LMXB), the companion expands to fill the Roche-lobe and matter flows through the inner Lagrangian point to enter the gravitational pit of the compact object. The conservation of angular momentum ensures the formation of an accretion disc (Frank et al. 1992). In this case the efficiency of the disc formation is definitely higher.

The necessary conditions for the accretion to occur are two-fold, firstly, energy needs to be dissipated as the matter falls into the gravitational well, and secondly, the angular momentum needs to be transferred outwards. Without fulfilling these two conditions, the matter will remain in a circular ring (keplerian stable orbit) around the compact object. The theoretical difficulty lies in accounting for a physical mechanism of angular momentum transfer as, the only obvious agent available, the ordinary fluid viscosity is far too weak to be a significant factor. Shakura and Sunyaev (1973) took the first step in developing a phenomenological understanding of the process by introducing an anomalous internal stress (vertically averaged along the disc axis), Ô ‘ given by Ô ‘ 7a&

(1.12) ¸ where D vertically averaged pressure, &‚D normalized proportionality constant, such ¸ that U)k&ž) . This idea perpetuated the concept of anomalous viscous stress, defined by the parameter & , as the agent necessary to transfer the momentum and energy. 3 A Sunyaev later commented that he was not absolutely convinced about the introduction of the Õ parameter. Little did they realize the forthcoming impact of this Õ 3

1.4. Accretion in X-ray binaries

15

commonly used modification of the Shakura-Sunyaev (SS) prescription is to assume a : :  ; B × Ø ; ; × × kinematic viscosity of the form , where D the ver& & 8³Ö Ö ÙÛÚ Ö ¸ ±Ü tically averaged sound speed ( is vertically averaged density, Ø 7 Ø iŒššD vertical Ü half-thickness of disc, and D angular velocity of test particle circular orbits (KepÙÝÚ lerian angular velocity). When inserted into the standard viscous form of the stress, this gives Ç Œ Ç (1.13) Ô ‘ 7 Œ Ù 7a& Ù Ü8 Ç#Œ ¸ Ç#Œ Š ÙÑÚ Here 7 if the iŒšD actual angular velocity in the flow, which may differ from Ù Ù Ù Ú flow is not completely geometrically thin. If , then within factors of order of Ù Ù6Ú unity, i.e. the disc is geometrically thin equation 1.13 gives the same stress as equation 1.12, with the only difference that the stress here depends explicitly on the shear of the flow, just like an ordinary viscous flow (for detailed explanation see Longair 1994, Frank et al. 1992, Blaes 2003). The conditions for the validity of the thin disc are that 1) at any radius • , the vertical height Ø\Þ • , 2) rotation velocity Ó1ß_à the sound speed ;!× within the disc (i.e. internal pressure gradients should not inflate the disc). In such cases the : accretion flow is extremely turbulent with the Reynolds number á9 £  ˜ . Carrying on with the recipe of Shakura and Sunyaev (1973) for the thin disc, the luminosity and the emission spectra of the disc are given by (Longair 1994) ’  N † P Á ä ‰ † h 7â Êã  † s ( • • 7 “ • (1.14) ( ä T ÊæåÀçÌè > > > † 2 Q urx Q íì?î1ï u C  l ˜ u ˜ Q u ˜ â  G (1.15) Ê ‹ å ë é ê 8 8 where • äÑD inner most radius of the disc, • and • D the boundaries of the muljðòñ ôódõ u FS4^ . The integral of equation 1.15 is definite, ticoloured disc considered and 7€…< > 2 8r Q hence  ÝG and • radii. At ˜ between the frequencies corresponding to • jðòñ 8 8 • öó÷õ , the specfrequencies less than that corresponding to the temperature of the disk at : ôódõ 2 trum has a shape of the Rayleigh-Jeans spectrum i.e.  öG whereas at frequencies 8 8 greater than that corresponding to the temperature at • , the spectrum has a shape of 3 >@BA 2 öðøñ  = l the high frequency tail of the blackbody spectrum i.e.  jG . 8 The optically thick SS discs (or & discs) became the hallmark of the accretion disc theory because of the rather robust spectral predictions. The predicted emission from these disc should consist of a sum of blackbody spectra, peaking at a maximum temperature of k Šëù keV for near Eddington accretion rates or at a Š . keV for an accretion rate of ú + Eddington, onto a typical blackhole ( ú ,  ). These discs, however, were soon discovered to be unstable, at low mass accretion rate, due to instability induced

Chapter 1. Introduction

16

by the transition of neutral hydrogen to ionized gas (gas pressure dominated regime) causing opacity variation in the solution (see Figure 1.6). At the temperature when the hydrogen ionizes, the (Wien’s) photons are absorbed and the energy is not allowed to escape, heating up the disc which causes a runaway heating until most of the hydrogen is ionized. Thus, introduction of instability due to the temperature crossing hydrogen ionization at any point in the disc causes the whole disc to become unstable. This led to the classic disc instability paradigm, which was successful in explaining the dwarf-novae type of outbursts in white-dwarf binaries. In the case of neutron stars and blackhole binaries, the X-ray irradiation contributes to the hydrogen ionization and hence controls the disc evolution. At higher mass accretion rates (the radiation pressure dominated regime, i.e. total pressure G4 x ) instability is introduced as a small increase in temperature causes large increase in heating rate, and hence to further increase in temperature. This runaway heating stabilizes only when the time scale for the radiation to diffuse out is longer than the accretion time scale, i.e. the photons are advected into the blackhole (slim disc – optically thick accretion: Abramowicz et al. 1988). The spectra of these slim discs differ from the SS discs as the energy generated in the innermost radii of the disc is preferentially advected (Watarai and Mineshige 2001), but the disc structure at such high mass accretion rate is uncertain. Alternative solutions to the SS disc models predict a truncated disc with an optically thin, X-ray hot accretion flow in the inner regions. The first such a solution was given by Shapiro-Lightman-Eardley model (SLE: Shapiro et al. 1976) of accretion flow (see Figure 1.6), where the electrons cool by radiation while the protons cool by Coulomb collisions, and hence the flow is intrinsically a two temperature plasma. 4 In the SLE flow the electrons radiate most of the gravitational energy through Comptonization of photons from the outer disc. The other popular solution of the optically thin accretion flow also assumes that the gravitational energy is given mainly to the protons, while the electrons are heated via Coulomb interaction, forming, again, essentially a two temperature plasma; but in this case the protons carry most of the energy inside the blackhole horizon, resulting in an advection dominated accretion flow (ADAF: Narayan and Yi 1995). The ADAF solution is supposed to be more stable than the SLE solution. A chief drawback in these models is that the proton temperature approaches the virial temperature, hence the pressure support becomes important and the flow no longer remains geometrically thin. Another model with the truncated disc geometry is the two component accretion flow model (TCAF) (Chakrabarti 1996a), which assumes a thermal 4

ûoüþýaû , with maximal temperature possibly as high as û b bÿ




X ¨ V

K

1.4. Accretion in X-ray binaries

17

ck thi ion y all ct tic adve p o

. log m

Radiation pressure instability

AF

SL E

AD

Hydrogen ionization instability log τ (vertical optical depth through the disk)



Fig. 1.6: The multiple solutions to the accretion flow equations, plotted as a function of (mass accretion rate) vs. (optical depth) of the fluid flow in the disc. The right hand solution is the SS disc modified by advective cooling in the highest mass accretion rates and by atomic opacities at lowest mass accretion rates. The left hand solution is the optically thin flows, the ADAF and SLE solutions. (The figure obtained from Done (2002)



multicoloured outer disc and a hot inner sub-Keplerian flow separated by a centrifugally bounded layer (CENBOL), with the presence of bulk-motion Comptonization in the inner Comptonizing cloud (Chakrabarti and Titarchuk 1995, 1996). This TCAF model will be discussed in more detail in chapter 6.

1.4.1 Unification of hydrodynamic solutions of accretion flow Of the four physically distinct sequences of accretion discs thermal equilibria that exist t locally (Figure 1.7), two correspond to &w)& Ê  •  , and other two correspond to &Åt t & Ê  •  , where & Ê D implies critical ‘viscosity’, which depends strongly on the radius and weakly on the mass of the central accreting object. Chen et al. (1996) state a value t t of & Ê  Š while Bjornsson et al. (1996) find & Ê -£ after treating the microphysics and inner boundary conditions more accurately. The two low viscosity flow sequences of models are further differentiated by the optical opacity (Ô ) of the flow, optically thin or thick, while the two high viscosity sequences by whether advection is negligible or Ò , to that of radiated energy dominant (quantified by the ratio of the advected energy, ó Ê ). These four sequences, which are effectively a highlight of the local classification ó









Chapter 1. Introduction

18



Fig. 1.7: The four types of accretion flows labelled with their cooling mechanisms. The solutions are plotted as a function of accretion rate ( ) against the vertically averaged surface mass density ( ). (The figure is taken from Bjornsson et al. (1996))



at a fixed radius of the accretion disc, are as follows:t Ò Ê varies: This “S” shaped sequence has three Type (1): &€) & Ê ÔI-*

ó [ [ ó  branches: 1) lower D gas pressure dominated, radiatively cooled, optically thick classical SS disc with modified (multi-coloured disc) blackbody radiation, where the bend (i.e. instability) is due to strong opacity dependence on temperature (the characteristic of dwarf novae), for higher accretion rate the opacity is determined by electronscattering and the branch is both thermally and viscously stable; 2) middle D optically thick, radiation pressure dominated (and cooled), but thermally and viscously unstable classical SS disc (physically unviable); 3) upper D optically thick, radiation pressure supported, advection cooled, thermally & viscously stable, slim accretion disc branch. t Þ : This “ ” shaped sequence has three Ò Ê Type (2): &Å-„& Ê Ô varies, ó  ó [ branches: 1) right D identical (with higher viscosity) to the lower branch of type Ê 1; 2) upper D thermally and viscously unstable discs with – × Í and ¸ ó  ¸ ó ÔU  , the solution is obtained phenomenologically for the latter parameter value; 3) left D optically thin and very hot SLE solutions with protons having much





















1.4. Accretion in X-ray binaries

19

higher energies than electrons, where radiative processes include bremsstrahlung, synchrotron & Comptonization. t Ò Ê Type (3): & )™& Ê ÔE)

varies: This - shaped sequence has two ó [ [ ó  branches: lower D SLE models; upper D gas pressure dominated, very hot ADAF discs (with very low radiative frequency), where the spectra are dominated by Comptonization of bremsstrahlung and synchrotron soft photons and pairs are suppressed by strong advective cooling. t Ò Ê Type (4): &9- & Ê Ô varies, -Í : This straight line sequence has two ó  ó [ branches: 1) lower D ADAF solution, similar to upper branch of type 3; 2) upper D copious electron– positronpair production in hot, effectively optically thin plasma cloudL where two conditions are met i) temperature of plasma is sufficiently : high, FS4 P ;  Š and ii) optical depth to photon-photon interactions is suffi ciently large. The radiation field may include bremsstrahlung, Comptonization of internally generated bremsstrahlung photons, as well as from a hybrid population of electron– positron pair population (Coppi 1992).



















1.4.2 Hard X-ray emission models Wide-band X-ray spectroscopy reveals the presence of hard X-rays, in all spectral states, as a generic feature of accretion onto a blackhole and this emission cannot be explained by the standard SS disc models. The only physical phenomenon that can account for emission in this energy band is magnetic reconnection, while the physical mechanism most easily and commonly used to explain the wide band spectra is Comptonization (successive Compton scatterings of soft photons). A very brief outline of the attempts to explain the hard X-ray emission models is as follows:$ MHD dynamo – disc viscosity. For an SS disc, to produce the hard X-rays a large amount of gravitational energy has to be dissipated in optically thin medium, and an obvious candidate (perhaps the only one) is the magnetic flares above the disc, generated by the Balbus-Hawley MHD dynamo responsible for the disc viscosity (Balbus and Hawley 1991). Buoyancy causes the magnetic field loops to rise to the surface of the disc and hence they may reconnect in regions of fairly low particle density. $ Comptonization from hybrid thermal/non-thermal pair plasma. This model involves the seed soft (X-ray) photons getting Comptonized by a cloud of hot electron or electron– positron pair plasma (Coppi 1992). The thermal population of

Chapter 1. Introduction

20

L A plasma assumes a given temperature, 4 and a Thomson optical depth, Ô . The deviation of the electronpopulation in the corona from the Maxwellian may be explained by a hybrid thermal /non-thermal population of (pair) plasmas (Poutanen and Coppi 1998). Selected electron from a thermal distribution are accelerated to relativistic energies (Zdziarski 2000), probably in the reconnections (for a review see Poutanen 1998). $ Compton reflection. This implies photo-electric absorption and Compton downscattering of hard radiation from the disc which may be cold (White et al. 1988, Lightman and White 1988, George and Fabian 1991, Magdziarz and Zdziarski 1995) or ionized (Done et al. 1992) or may switch between the two states (Zycki et al. 1998). These reprocessed photons may again act as seed for the Comptonizing corona. The energy balance of the cold and hot phases determine the temperature and the shape of the emerging spectrum (Haardt and Maraschi 1991, 1993, Stern et al. 1995, Poutanen and Svensson 1996). $ Bulk motion Comptonization. Accretion flow (passing through a shock) forms a quasi-spherical inflow, the free-falling electrons near the horizon has large bulk motion Comptonizes the seed photon from the optically thick, cold, geometrically thin, accretion disk, giving rise to the power law spectrum (Chakrabarti and Titarchuk 1995, 1996). This model will be discussed in more detail in conjunction with the TCAF model in chapter 6.

1.4.3 Geometrical structure of the accretion system There are various proposed geometrical structures defining the accretion flow into the compact object (blackhole event horizon) and the Comptonizing corona which is the origin of the high energy tail in the spectra:$ A hot (magnetic) slab-corona sandwiching the cold accretion disc. In extreme cases of complete dissipation of energy the spectra resemble the Seyfert galaxies (Haardt and Maraschi 1991, 1993). The predicted steep spectra is not in accordance with the observations (Poutanen 1998, Done 2001). $ Patchy static magnetic corona above the disc. For the cold disc the predicted spectrum is harder, but the reflection albedo expected is generally too small for neutral disc (Gierlinski et al. 1997). Also, the predicted anisotropic break is not really observed. For the ionized disc, the formalism of accretion disc is complicated with repercussions on the Compton reflected spectra (Ross et al. 1999, Done and Nayakshin 2001b,a).

1.5. Outflows from microquasars

21

$ Cloudlets. The cold disc within the hot corona is disrupted to form cold dense optically thick clouds, that can reprocess hard X/0 -ray radiation to produce seed photons (feedback) for Comptonization (Kuncic et al. 1997). $ Truncated disc with inner X-ray hot flow / Sombrero (Poutanen 1998). This is favoured by advective flow model (with the optically thin Bondi like flow replacing the inner part of the accretion disc), as well as the bulk motion Comptonization or the TCAF paradigm, which can explain the state transitions (Figure 1.8).

Fig. 1.8: The geometry for the sombrero shaped truncated disc with inner hot X-ray flow. (The figure is taken from Done 2002)

1.5 Outflows from microquasars Relativistic outflows, or ‘jets’, represent one of the most obvious, important but poorly explained phenomena associated with accreting relativistic sources in general and microquasars in particular. Historically, the key observational aspects were studied in the radio regime of the electromagnetic spectrum. Their earliest associations were observed to be with the quasars, the radio-loud sub class of the AGNs, and it was subsequently recognized that jets are a common consequence of the accretion process. However, the study of the outflow (in conjunction with the inflow – accretion) in the Galactic microy quasars didn’t commence until the discovery of superluminal motion in GRS 1915 105, in the last decade (Mirabel and Rodriguez 1994). Till date a wide variety of radio emission behavioural characteristics, patterns and evolutions have been observed, and only recently any systematic understanding of the accretion – ejection connection has gradually started to develop. In Figure 1.9 the radio outflow in three microquasars systems is depicted. Flare events. Short term injection of energy and matter in the form of an expanding plasma cloud collimated into a jet results in a radio flaring event, which are characterized by an optically thin spectrum and are normally associated with the X-ray transients (in their outburst/bright phase) and persistent sources like Cygnus X-3 and

Chapter 1. Introduction

22

Fig. 1.9: Radio images of relativistic jets from Galactic microquasars, a) Superluminal motion in GRS 1915 105 observed by MERLIN (Fender et al. 1999b), b) arcsec- scale jet from Cygnus X-3 observed by VLA (Mart´ı et al. 2001), c) two VLBI images of XTE J 1550-564 shortly after and four years later following a major flare (Hannikainen et al. 2001). This figure is taken from Fender (2003)

1.5. Outflows from microquasars

23

y GRS 1915 105 which exhibit such flaring episodes in their X-ray high (as well as soft) states. The synchrotron bubble model is characterized by the rise phase corresponding to a decreasing optical depth at frequencies which were initially synchrotron self-absorbed and this is manifested in an inverted radio spectrum during this rise phase, with possible Doppler effects on the profile. A possible alternative scenario is that the rise phase represents a finite period of particle injection/acceleration resulting in an outflow; the characteristics of this phenomena would be an optically thin spectrum and a duration at least coupled to events in the observer’s frame, i.e. emission from the accretion disc. Currently, observations are not in a position to rule out either of these possibilities (see Fender 2003, and references therein). The time delays in the propagation of a shock may (misleadingly) mimic the ’synchrotron bubble’ effect.

Steady jets. In addition to the flaring events, persistent sources show a steady radio emission during the low-hard states, even for sources which do not exhibit the flaring events. Figure 1.10 shows two such observations using VLBI. These steady jets are characterized by ‘flat’ spectrum ( &9  ) which may extend through and beyond the radio band, and may possess polarization at a level of 1-3%. The variability in the radio emission in this state is supposed to be associated with the X-ray emission and this feature will be studied in great detail in this thesis, for Cygnus X-3 in particular (chapter 3) and other microquasars in general (chapter 5) to understand the disc-jet connection. The attempts to form a theoretical understanding of the origin of the collimated outflows in cosmic sources have been aplenty and varied. Earlier, hydrodynamic and magnetohydrodynamic formulations were made considering the jets as a separate entity (Fukue 1982, Chakrabarti 1986). Thereafter efforts were made to correlate the disc structure with the outflow (eg. Konigl 1989, Chakrabarti and Bhaskaran 1992). Chakrabarti (1999) investigates the outflow from shock compressed fluid around compact objects. Numerical simulations, perhaps, provide one of the most realistic approximation to the actual physical situation. The chief thrust in this field has been in understanding matter deflection from the equatorial plane towards the axis (eg. Eggum et al. 1985, Molteni et al. 1994), which currently involves the magnetohydrodynamical formalism (see, for eg. Kato et al. 2004a,b). Blandford and Begelman (1999) proposed a generalized ADAF model in which only a small fraction of the gas supplied actually falls on to the black hole, as the gas is supplied conservatively to a black hole at rates well below the Eddington rate it may not be able to radiate effectively and the net energy flux, including the energy transported by the viscous torque, is likely to be close to zero at all radii, resulting in a gas that accretes with positive energy so that it may escape. This paradigm was known as the advection dominated inflow-outflow solutions (ADIOS).

Chapter 1. Introduction

24

Fig. 1.10: Steady radio jets in the low-hard state of X-ray emission for Cygnus X-1 (left panel: Stirling et al. 2001) and GRS 1915 105 (right panel: Dhawan et al. 2000), as observed by the VLBI.

1.6 Aim of this thesis In the cosmic sources which are intrinsically bright in the high energy band of the electromagnetic spectrum, the primary phenomenon that gives rise to this X/0 -ray emission is accretion. In the previous sections it has been highlighted that diverse types of possible mechanisms exist for the accretion to take place in these class of sources. Given the multitudinous observational features, as well as the various possible theoretical alternatives, a clear picture of the physical and geometrical structure of the accretion process is yet to emerge. Further, in addition to this phenomenon, the process of Comptonization plays an equally important role in generating the emission in this high energy (hard X-ray and soft 0 -ray) regime. According to the CGRO–BATSE catalogue of sources monitored by the occultation method, the Galactic blackhole (X-ray) binary system Cygnus X-1 is the brightest in the sky in this regime of X/0 -ray emission (Harmon et al. 2004). This source, as mentioned before, falls in the class of Galactic microquasars systems, which as a class display this accretion phenomenon most evidently among the Galactic sources. Till recently, in most of the attempts to understand these physical processes and phenomena in this class of

1.6. Aim of this thesis

25

sources, the inflow used to be treated in an isolated manner from the outflow, which is ubiquitously present, normally in the form of collimated jets. Understanding the basic mechanism of the jet formation and particle acceleration requires a detailed study of the energetics (Fender 2001a) and a long term multi-wavelength monitoring of these systems spanning the extremes of the electromagnetic band. Thus far, the observed features of the outflow and its association with the inflow, across different sources, has failed to produce any universally consistent picture of the nature of the disc-jet association in these sources. It has to be realized that accretion and ejection need to be considered in a unified manner to develop the primary paradigm of understanding of the physical processes in this systems, i.e. the high energy (X/0 -ray) emission needs to be studied along with the radio emission from these sources (microquasars). Considering the diverse theoretical and observational features of the accretion-ejection phenomena, the pressing need of the hour, from an observational approach, is to investigate and understand this phenomena across the diverse type of sources, in order to provide a unified, consistent set of observational features with the aim of developing a phenomenological model to unravel the physical and geometrical structure of these Xray binary systems. This approach requires a long term study of the associated radio as well high energy (X/0 -ray) emission of these sources, and this defines the primary goal of this thesis.

Chapter 2 X-ray detectors and techniques of instrumentation; Radio astronomy

Although astronomy is one of the ancient forms of science, the field of high energy astronomy is newly developed, reaching its maturity only in the last decade. The primary, and perhaps the only, reason for it is the interaction of X-rays with the material of the atmosphere, as a result of which the observations need to be conducted above the atmosphere. Figure 2.1 shows the transparency of the Earth’s atmosphere for photons as a function of the energy (frequency) of the electromagnetic waves. As depicted in the figure, electromagnetic waves in the high energy regime, from far ultra-violet to high energy 0 -rays cannot penetrate beyond an altitude of 30 km from the surface of the earth. Balloons, which can attain this height, were extensively used in the early historical phase of this branch of astronomy. These observations are limited, in the low energy, to 20 keV only. Soft X-ray observation (0.5 – 20 keV) was made possible by the advent of the satellite technology. Satellites have also made long duration observations possible, otherwise the total duration of observations done using rocket or balloon flights didn’t normally last for more than a few minutes or hours, respectively. The role of the balloon flights is now limited to the development and/or testing of new instruments. Currently the prominent operational satellites observatories for observing in the X-ray range are CHANDRA, XMM-NEWTON, RXTE, INTEGRAL. The CHANDRA and XMM-NEWTON X-ray observatories employ the method of X-ray focusing using the grazing angle X-ray optics. Using the X-ray focusing method these latest generation observatories have reached comparable sensitivity and data quality in the other established branches of astronomy such as optical astronomy and radio astronomy. In this chapter the basics of X-ray detectors are discussed, with some detailed information regarding two observatories, RXTE and CGRO, whose data have been used in this thesis. For the 26

2.1. X-ray detectors

27

Fig. 2.1: Transmission properties of the Earth’s atmosphere at different wavelengths. The solid line shows the altitude at which half of the radiation from space get attenuated.

sake of completeness we also mention the other notable X-ray observatories of recent past and the present. Thereafter we provide a brief note on the data analysis techniques for these satellite observatories. The last section describes radio astronomy with GBI, whose regular monitoring of the Galactic X-ray binaries has played an extremely important part in the research of the disc-jet connection in the Galactic microquasars, and whose data has been used extensively in this thesis.

2.1 X-ray detectors X-ray detectors are essentially photon counting devices, with the detection of one photon being registered as an event. These events are tagged by the time of event occurring and also the energy channel to which it belongs to, the latter being converted into energy by the response matrix of the concerned detector. The interaction between the high energy photons, that constitute the high energy band of electromagnetic radiation, and matter

Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

28

is capable of depositing large amount of energy in the matter, which may be collected and measured electronically. The matter (of the detector) that interacts with the photons may be in any of possible states, solid, liquid or gas. Basically, there are three physical mechanisms by which the high energy photons interact with the matter in the detector and transfer its energy (Longair 1994):$ Photo-electric effect. The X-ray photon is absorbed by the atom and an elec-

tron is ejected from the inner shell, with an energy equal to the difference of the initial photon energy and the binding energy of the electron. This mechanism dominates for photons with energy µ 100 keV. The cross section of interaction is proportional to H , where H is the atomic number of the material, and hence material with high H are normally chosen for such detectors.



$ Compton scattering. The photon is scattered by an outer shell electron by an Ä Ä angle , depositing some energy on the scattered electron. determines the energy transferred to the electron, and may take any value from zero to a large fraction of the incident photon energy. This mechanism dominates for initial photon energy 400 keV. The cross-section of interaction is given by the relativistic KleinNishima formula, and depends linearly on the atomic number H of the matter, Ä apart from a function of the incident photon energy and scattering angle .



$ Pair production. In an interaction with the coulomb field of a nucleus, the photon gets absorbed and an electron- e pair is generated. The photon need to have energy more then twice the electron rest-mass energy i.e. - 1.02 MeV, and any excess photon energy goes into the kinetic energies of the newly generated electrone pair. The cross-section is very low upto several MeV of incident photon energy.





An X-ray detector converts the energy of the incident X-ray photons into a measurable electrical signal. The resolution and accuracy of the various measurements, viz. the position, energy and arrival time of the incoming photon, depends on the characteristics of the detector. An ideal X-ray detector should combine the precise measurement of position, energy and time of the X-ray interaction along with a large collecting area, good detection efficiency, ability to handle large count rate, low internal background, stable performance over long time etc. Clearly it is impossible to have an ideal X-ray detector and the different types of X-ray detectors available have different strengths and weakness. Depending on the needs of the observations required of a detector, the one with the most desirable characteristics are chosen, with a compromising trade-off with the other features that are non-essential for the particular type of observation. A detailed discussion of various X-ray detectors is given in Knoll (2000). The most common class of detectors are as follows:-

2.1. X-ray detectors

29

Proportional counters. Proportional counters have been the ‘workhorse’ of X-ray astronomy since its early inception and are still in active use. These consist of a windowed gas cell, subdivided into a number of low and high electric field regions by some arrangement of electrodes. Incident X-ray photon interacts with the gas by photo-electric effect ejecting an electron. This energetic electron further ionizes the gas generating more electron-ion pairs until it dissipates all its energy. The number of electron-ion pair thus generated is proportional to the energy of the incident X-ray photon. These electrons are accelerated when they enter the regions of high electric field and generate more electron-ion pairs, which are all attracted towards the electrodes of opposite charges and generate an electric pulse. The electric field is controlled in such a way that the final number of electron-ion pairs is still proportional to the energy of the incident photon. Thus, measuring the height of the electric pulse gives the energy of the X-ray photon. Proportional counters are sensitive at energies less then 50 keV. Scintillation detectors. These work by converting the energy of the incident X-ray photon into visible light. The X-ray photon first interacts by the photo-electric effect generating an energetic electron. The interaction of this electron with the crystalline structure of the detector then generates visible photons as a result of a complex sequence of excitations and de-excitations. The visible photons are then converted into an electric signal by means of a photo-multiplier tube (PMT). The alkali halides NaI and CsI, activated by a small amount of either thallium or sodium impurity, are the scintillators of choice so far in X-ray astronomy. This is because these can be made into large area crystals, have good X-ray stopping power, are efficient light producers and are transparent to their own light. Some other materials such as plastics or the higher-Z bismuth germanate (BGO) are also used as X-ray scintillators. Scintillators can be used for detecting photons with energies up to a few MeV. They also offer very good time resolution. However again their major weaknesses are poor energy resolution and the lack of imaging capabilities. Semi-conductors (solid state detectors). The principle of operation of semi-conductor detectors is analogous to that of the proportional counters. The intrinsic crystalline structure takes the role of the detecting volume (of gas in the proportional counters) where the incident X-ray photons interact by photo-electric effect. However, in the solid state detectors, electron-hole pairs are created, instead of the electron-ion pair in the proportional counters. Average energy to create one electron-hole pair in a semi-conductor is smaller by a factor of 10 compared to the average energy to create one electron-ion pair in the proportional counter gas. Thus for a given energy of incident X-ray photon,

30

Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

the efficiency of creating electron-hole pairs in a semi-conductor detector is about ten times that of the primary electron-ion pairs in proportional counter. Therefore the semiconductor detectors offer better energy resolution. Typical semi-conductors are based on Silicon (Si) or Germanium (Ge). However, on the downside, Si or Ge based detector have to be operated at cryogenic temperatures to overcome the thermal noise, and hence it is not currently feasible to devise large area detectors based on these materials. In the past few years new class of semi-conductors such as Cadmium-Zinc-Telluride (CZT) or Cadmium-Telluride (CdTe) have been discovered which may be operated at near room temperature. At the same time, advances in micro-electronics have presented the opportunity to use large number of such small detectors in an array formation, providing position sensitivity and hence imaging capability. It is believed that such array of small CZT/CdTe detectors will become the most widespread detectors in the field of X-ray astronomy in future.

X-ray CCDs. The charge coupled device (CCD), a special type of semi-conductor detector, is intrinsically pixillated and hence has the inherent advantage of imaging capabilities without the need of creating an array. CCDs are mainly Si based devices which offer very good energy resolution. As with any general semi-conductor, X-ray photon interacts in the active volume of CCD, generating electron-hole pairs. However, unlike the general solid state detectors, the electron are not immediately absorbed by the electrodes. Rather, they are stored in the particular pixel at which the interaction has taken place, and are read out later. This storage capability of CCD has revolutionized the field of optical astronomy where the photons can be accumulated over large time interval yielding very high sensitivity. However, in the X-ray regime, the CCD has to be read out after every X-ray photon interaction. The readout from a CCD is time consuming and hence even though CCDs offer very good imaging and spectral resolution, their temporal resolution is limited. The process of manufacturing CCDs with large area is a difficult engineering feat. Another practical difficulty, from astronomical point of view, of the present day CCDs is that, because of low H of Si, they are only sensitive to X-rays with energy ) 10 keV. Hence, CCDs are almost always used as focal plane detector for an X-ray telescope, which themselves are limited to energies ) 10 keV.

2.2. Modern X-ray observatories

31

Fig. 2.2: Schemtic representation of the The Rossi X-ray Timing Explorer (RXTE)satellite observatory, with its three detector systems (see http://heasarc.gsfc.nasa.gov/docs/xte/xtegof.html). (The figure is obtained from http://heasarc.gsfc.nasa.gov/Images/xte/xte spacecraft.gif)

2.2 Modern X-ray observatories 2.2.1 The Rossi X-ray Timing Explorer (RXTE) The Rossi X-ray Timing Explorer (RXTE) is a satellite X-ray astronomical observatory, launched on December 30, 1995 from NASA’s Kennedy Space Center. The mission is managed and controlled by NASA’s Goddard Space Flight Center (GSFC) in Greenbelt, Maryland. The most attractive feature of RXTE is the unprecedented time resolution in combination with wide-band X-ray spectral capability with moderate spectral resolution, to explore the variability of X-ray sources. Time scales from microseconds (lowest achieved for X-ray astronomy, so far) to months are covered in an instantaneous spectral range from 2 to 250 keV (ideally). Originally designed for a required lifetime of two years with a goal of five, RXTE has passed that goal and is still performing well. The satellite has a low-earth circular orbit at an altitude of 580 km, corresponding to an orbital period of about ù minutes, with an inclination of 23 ¶ . The three instruments on RXTE are the Proportional Counter Array (PCA), co-pointed with detectors on the High Energy X-Ray Timing Experiment (HEXTE), and the All-Sky Monitor (ASM). The first two are for pointed observations (PCA & HEXTE), while the last (ASM) monitors the



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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

X-ray sky, scanning 70% of the sky in each satellite orbit. In this thesis, data from each of these instruments have been used extensively, and hence features of all of these three are presented here. Schematics of the instruments in the orbiting satellite is shown in Figure 2.2, and the salient features of the various design parameters and performance are tabulated in table 2.2.1. Major scientific results from RXTE are: the discovery of kHz QPO and the detection of X-ray afterglow from the gamma-ray bursts. RXTE also carried out extensive observations of black hole candidates and bursting pulsars which provides stringent test of accretion theories. A brief introduction to each of the instruments follows:Proportional Counter Array (PCA). Developed at GSFC, it consists of : a system of five large proportional counter units (PCU), each with an area of 1300 cm yielding a : total collecting area of 6500 cm . The large area along with the active anti-coincidence features provides very high sensitivity, and hence the extraordinarily high time resolution. Each unit is filled with Xenon gas and achieve low background through efficient veto schemes including side and rear chambers and a propane top layer. A mechanical hexagonal collimator is carried on each proportional counter which provides a field of view of 1 ¶ (FWHM). Because of large effective area, a few seconds exposure detects weak sources (flux € mCrab). The PCA is effective over the energy range of 2  60 keV with 18% energy resolution at 6 keV. The detailed description on the PCA design as well as the in orbit performances are given in Jahoda et al. (1996). The High Energy X-ray Timing Experiment (HEXTE). Developed by Center for Astrophysics & Space Sciences (CASS), University of California, San Diego (UCSD), it consists of two independent clusters (called Cluster A and B), containing four NaI/CsI phoswich scintillation detectors (each containing a collimator, phoswich detector, photomultiplier tube, gain control detector and associated electronics), passively collimated to a 1¶ field of view co-aligned with the PCA field of view. Each detector has a net : open area of about 225 cm and covers the energy range of 15  250 keV with an average energy resolution of 15.4% (FWHM) at 60 keV. Each cluster can “rock” (beam switch) along mutually orthogonal directions to provide background measurements 1 ¶ .5 or 3 ¶ away from the source every 16 to 128 s. The field of view of each : detector is limited by a Pb collimator. Automatic gain control is provided by using a x ˜ Am radioactive source mounted in each detector’s field of view. The detailed description on the HEXTE design as well as the orbit performances are given in Rothschild et al. (1998). Events detected by HEXTE will be processed on board by its own data system before insertion into the telemetry stream at an average data rate of 5 kbit/s. Data products include

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Table 2.1: Design parameters and performances of various RXTE instruments (from RXTE web site)

PCA

HEXTE

ASM

Energy range Energy resolution Time resolution Spatial resolution Detectors Collecting area Layers Sensitivity Background Energy range Energy resolution Time sampling Field of view Detectors Collecting area Sensitivity Background Energy Band Energy resolution Scan time Angular resolution Spatial resolution Detectors Collecting area Net area Sensitivity

2  60 keV 18% at 6 keV 1 È collimator with 1 ¶ FOV (FWHM) 5 proportional counters : 6500 cm 1 Propane veto; 3 Xenon, each split into two; 1 Xenon veto layer 0.1 mCrab 2 mCrab 15  250 keV 15% at 60 keV 8 microsecond 1 ¶ FWHM 2 clusters of: 4 NaI/CsI scintillation counters 2 › 800 cm 1 Crab = 360 counts s l ˜ per HEXTE cluster 50 counts s l ˜ per HEXTE cluster 2  10 keV 20% in 2  10 keV (3 energy channels) 90 minutes, 80% of the sky per orbit 0.2 ¶ 3’ › 15’ 3 Scanning Shadow Cameras : 180 cm: (without masks) 90 cm (3 detectors) 20 mCrab in 90 minutes and  10 mCrab a day



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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

event mode, binned spectra and light curves, and a burst-triggered event buffer. The detailed description on the HEXTE design as well as the in orbit performances are given in Rothschild et al. (1998). All Sky Monitor (ASM). Developed by Center for Space Research (CSR) at Massachusetts Institute of Technology (MIT), it is perhaps the most ingenious of all the three instruments aboard RXTE. It consists of three Scanning Shadow Cameras (SSC) on one : : rotating boom with a total effective area of 90 cm (180 cm without masks). Each SSC is a one-dimensional “Dicke camera” consisting of one dimensional mask and a one dimensional position sensitive proportional counter. The field of view of a single SSC is 6¶1› 90¶ FWHM and the angular resolution in the narrow direction is 0. ¶ 2. A motorized drive rotates the SSCs from field to field in 6 ¶ steps. At each resting position, a 100 s exposure of the X-ray sky is made and hence a complete rotation of the SSCs takes place in 90 minutes. During each rotation, about 80% of the sky is surveyed to a depth of 20 mCrab. The limiting sensitivity of the SSCs becomes  10 mCrab in one day. The detailed description on the ASM design as well as the in orbit performances are given in Levine et al. (1996).

2.2.2 Compton Gamma Ray Observatory (CGRO) Historically the second of NASA’s Great Observatories was christened Compton Gamma Ray Observatory (CGRO)(the first one being the Hubble Space Telescope). CGRO, at 17 tons, was the heaviest astrophysical payload ever flown at the time of its launch on April 5, 1991 aboard the space shuttle Atlantis. After successful operation for 9 years it was safely de-orbited and re-entered the Earth’s atmosphere on June 4, 2000. Compton had four instruments that covered an unprecedented six decades of the electromagnetic spectrum, from 30 keV to 30 GeV. Of these, three were instruments for pointed observations, the Oriented Scintillation Spectrometer Experiment (OSSE), the Imaging Compton Telescope (COMPTEL) and the Energetic Gamma Ray Experiment Telescope (EGRET). These three instruments cover an unprecedented broad range of energies in the 0 -rays, from 50 keV to 30 GeV. The fourth instrument was an all sky monitor Burst And Transient Source Experiment (BATSE) which continuously observes the entire sky in the hard X-ray and soft gamma-ray range of 20 keV to 600 keV. Figure 2.3 shows the schematic diagram of the CGRO satellite along with the location of individual instruments. The major scientific results from CGRO are, the discovery of an isotropic distribution of the gamma-ray bursts, discovery of “bursting pulsar” as well as the discovery that the blazar active galactic nuclei as primary source of the highest energy

2.2. Modern X-ray observatories

35

Fig. 2.3: Schemtic representation of the Compton Gamma Ray Observatory (CGRO)satellite observatory, with all of its detector systems. (The figure is obtained from http://cossc.gsfc.nasa.gov/images/epo/gallery/cgro/cgro line labels.jpg)

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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

cosmic gamma-rays. CGRO also obtained first map of the Milky Way at the energy of :

Al 0 -ray line. Of the four instruments on board the CGRO, data from two instruments have been utilized for the work in this thesis, viz. BATSE and OSSE. A brief introduction to these instruments follows:-

Burst And Transient Source Experiment (BATSE). The Burst And Transient Source Experiment (BATSE) serves as the all-sky monitor for the Compton Observatory, detecting and locating strong transient sources called 0 -ray bursts as well as outbursts from other sources over the entire sky. There are eight BATSE detectors, one facing outward from each corner of the satellite, which are sensitive to gamma-ray energies from 20 keV to 600 keV. Each detector module contains two NaI(Tl) scintillation detectors: a Large Area Detector (LAD) optimized for sensitivity and directional response, and a Spectroscopy Detector (SD) optimized for energy coverage and energy resolution. The eight planes of the LADS are parallel to the eight faces of a regular octahedron, with the orthogonal primary axes of the octahedron aligned with the coordinate axes of the CGRO spacecraft. The LAD detector is a disk of NaI scintillation crystal 20 inches in diameter and one-half inch thick, mounted on a three-quarters inch layer of quartz. A light collector housing on each detector brings the scintillation light into three 5-inch diameter photomultiplier tubes. The signals from the three tubes are summed at the detector. A quarter-inch plastic scintillation detector in front of the LAD is used as an anti-coincidence shield to reduce the background due to charged particles. The spectroscopy detector is an uncollimated NaI(Tl) scintillation detector 5 inches in diameter and 3 inches thick. A single 5 inch photomultiplier tube is directly coupled to the scintillation detector window. The crystal housing has a 3-inch diameter 0.05 inch thick beryllium window on its front face in order to provide high efficiency down to 10 keV. Each of the eight BATSE detector modules sends data to the Central Electronics Unit (CEU). The CEU produces data for telemetry at a uniform rate of one packet every 2.048 seconds. BATSE detects 0 -ray bursts on-board by examining the count rates of each of the eight LADs for statistically significant increases above background on each of three time scales: 64 ms, 256 ms, and 1024 ms. The discriminator rates in channels 2 and 3 (approximately 60 to 325 keV) are used. The background rate is determined for each detector over a commandable time interval currently set at 17.4 seconds. The statistical significance required for a burst trigger is set separately for each of the three time scales, with a quantization of 0.0625 sigma. The software and data analysis of BATSE is given by Hakkila (1990), while the experiment is outlined by Fishman et al. (1989).

2.2. Modern X-ray observatories

37

Oriented Scintillation Spectrometer Experiment (OSSE) The Oriented Scintillation Spectrometer Experiment (OSSE) consists of four NaI scintillation detectors, sensitive to energies from 50 keV to 10 MeV. Each of these detectors can be individually pointed. This allows observations of a 0 -ray source to be alternated with observations of nearby background regions, enabling the measurement of background contamination quite accurately. The synchronization of the four detectors is provided by the central electronics, which provides the data acquisition timing and coordination of the pointing directions. The experiment’s data acquisition and control system incorporates varied modes of operation depending on the type of information desired during a particular observation. The primary element of each detector system is the NaI(Tl) portion of a 330 mm diameter NaI(Tl)-CsI(Na) phoswich consisting of a 102 mm thick NaI(Tl) crystal optically coupled to a 76 mm thick CsI(Na) crystal. Each phoswich is viewed from the CsI face by seven 89-mm diameter photomultiplier tubes (PMTs), providing an energy resolution of 8% at 0.661 MeV. Active gain stabilization is used to maintain this energy resolution by individually adjusting the gain of each of the seven PMTs. Using the different scintillation decay time constants of NaI(Tl) and CsI(Na), the detector event processing electronics differentiates the events occurring in the NaI crystal from those occurring in the CsI, allowing the CsI portion of the phoswich to act as anti-coincidence shielding for the NaI portion. The instrumental details and related necessary information are given by Messina et al. (1992), and the in orbit performance details are reported by Johnson et al. (1993). An in-depth account of technical details of the various detectors aboard the CGRO is given in http://cossc.gsfc.nasa.gov/nra/appendix g.html.

2.2.3 Other notable X-ray missions A few other notable X-ray missions of the recent past and the present are ROSAT, ASCA, BeppoSAX, CHANDRA, XMM-NEWTON, INTEGRAL. All these are satellite based observatories dedicated for high energy astronomy. The Roentgen Satellite (ROSAT) was a collaborative mission from Germany, US and UK, sensitive in the energy range of 0.1 keV – 2 keV.was a collaborative mission from Germany, US and UK, sensitive in the energy range of 0.1 keV – 2 keV. Operating between June 1991 – February 1999, it featured an X-ray imaging telescope with the best ( €( arcsec) spatial resolution of its generation. The Advanced Satellite for Cosmology and Astrophysics (ASCA) was a Japanese mission (following GINGAand preceding the ASTRO-E II to be launched within a couple of years) sensitive in 0.1 keV – 10 keV energy range. Operating between February 1993 – March 2001, it consisted a high throughput X-ray optics using CCD detectors for X-ray astronomy for the first time. The CHANDRAand XMM-NEWTONmissions

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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

are an advanced versions of ROSAT and ASCA respectively. CHANDRA, the third of NASA’s Great Observatories (originally known as AXAF, it was re-christened after its launch, after the great Indian astrophysicist, Prof. S. Chandrashekhar), is sensitive in the energy range of 0.1 keV – 10 keV. Launched on 23 July 1999 and still currently active, it features an unprecedented imaging capability with spatial resolution of ) 1 arcsec. XMM-NEWTONis a mission from the European space Agency featuring large collecting area. Launched on 10 December 1999 and is still currently active, it is sensitive in 0.1 keV – 10 keV energy range. BeppoSAXwas an Italian-Dutch mission which was operational between April 1996 – April 2000. It was the first X-ray mission with a scientific payload covering more than three decades of energy - from 0.1 to 300 keV with a relatively large effective area, medium energy resolution and imaging capabilities in the range of 0.1-10 keV (CGRO covered five decades of energy in the 0 -ray band). The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) is the European Space Agency mission launched on 17 October 2002. It is the successor of CGRO. These missions are not described here because data from these have not been used in the present work, but a detailed introduction to this observatories may be found at the web site http://www.heasarc.gsfc.nasa.gov.

2.3 X-ray astronomical data analyses and techniques The analysis of X-ray emission from the satellite observatories essentially involve two basic steps:1. Extraction, from the ’low level’ data, of the (meaningful) standard products, viz. the image (spatial distribution of the electromagnetic flux in a given energy band), lightcurve (time-series of flux variation in a given energy band) and spectrum (distribution of the electromagnetic flux as a function of energy). 2. Analysis of these standard products to understand the physical mechanism and phenomena of the processes giving rise to these electromagnetic emission. The observations are made as per the proposals of the observers, selected on the basis of scientific merits by a review committee. The data is immediately made available to the observer (and his team of collaborators) for scientific analysis, and after a stipulated time (generally a year or so, but may differ for different observatories), the data is archived and made available to the general public, anywhere on earth, available through the internet. The specific software for the extraction of standard products from the different observatories are also made publicly available through the internet.

2.3. X-ray astronomical data analyses and techniques

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The telemetry data received from the satellite is in highly instrument specific format, which is converted into FITS (Flexible Image Transport System) format by the mission operations centre who also performs some preliminary analysis to verify the data integrity and goodness, before making it available to the guest observer. The FITS format, originally developed for the exchange of scientific images, is a standard for any type of data exchange. It is basically a standard format for describing the format of the data. Even if the data is available as a FITS format, the underlying structure of the data is still highly instrument/mission specific. Since X-ray detectors are essentially photon counting devices, the basic X-ray data usually comprise lists of detected photons, known as events, stored along with some other attributes. These attributes normally consist of time-tag of the event (photon arrival), the position (in detector and sky coordinates) and an energy. Thus each event can be thought of as occupying a position in a 4-dimensional space, the four dimensions being the time, the u and  coordinates and the energy. In case the X-ray detector is of non-imaging type then, obviously, the two position attributes are absent. The events may have other instrument specific attributes such as the pattern of pixels for the CCD detector or grating order for the grating instruments. The analyst’s first step, that of data reduction, involves the following couple of substeps: 1) scientific filtering of the events, i.e. selection of data events depending on required scientific criteria, viz. location in the sky, particular time interval, background noise level, etc., 2) extraction of the standard products from the ’raw’ event data provided by the concerned mission operation center, using the mission specific softwares. The analyses of these standard products, in a mission independent way, may be done by the generic softwares viz. FTOOLS and XANADU packages, etc, made available freely (in a combined package called LHEAsoft) by the High Energy Astrophysics Science Archive Research Center (HEASARC) 1 , GSFC, NASA. The HEAsoft package also contains many mission specific data reduction software, many general utilities to manipulate FITS files as well as high level mission independent data analysis software for detailed timing, spectral and imaging analysis. The complete reduction and analysis of the RXTE data, for the work presented in this thesis, has been done using the LHEAsoft package (described in the following sub-section). For the CGRO data, the standard products for the OSSE and BATSE instruments are obtained from the CGRO archives, and hence the detailed data reduction are not explained here. The analysis of the standard products has been done using the FTOOLS and the XANADU packages.

1

http://heasarc.gsfc.nasa.gov

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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

2.3.1 RXTE data analysis The ASM monitoring data is reduced by the instrument team at the MIT, and the standard products (lightcurves in three energy bands plus the combined total energy range) made available via the web site “http://xte.mit.edu”. The RXTE data, supplied to the observer, of PCA & HEXTE, is already low-level filtered and converted to FITS by the RXTE GOF (Guest Observer Facility) at GSFC, NASA. For the PCA and ASM, this is achieved by the Experiment Data System (EDS). The EDS consists of eight Event Analyzers (EA), of which six are dedicated to the PCA and two to the ASM. Each EA contains an Intel 80286 processor and associated memory. The EAs can be programmed independently to process incoming events from the instruments in any of the following modes: 1) transparent mode, using 1, 2, or 3 EAs, 2) event mode, using 1 or 2 EAs, 3) binned mode (time and/or energy), 4) burst catcher mode, 5) Fourier transform mode, 6) pulsar fold mode, 7) autocorrelation mode, 8) arrival time differences histogram mode. Each RXTE pointed observation has a unique observation ID (also known as ObsId) of the format “NNNNN-TT-VV-SSX” where: $ NNNNN is the five proposal number assigned by the GOF $ TT is the two-digit target number assigned by the GOF. In the case of only one target in the proposal, the target number may be zero. $ VV is the two-digit viewing number, assigned by GOF, which tracks the number of scheduled looks at the target. $ SS is the two-digit sequence number used for identifying different pointings that make up the same viewing. $ X is a special character, which if present, indicates different types of observation e.g. slew, scan, grid observations or observations with data gaps or segments of a long observation etc.

The two main instruments PCA and HEXTE are non-imaging instruments. Hence data from these instruments consist of time-tagged events along with energy. However, due to very large effective area, particularly for the PCA, it is not possible to transmit each event separately. Therefore the detected events are analyzed and binned on-board by the EDS. The PCA can provide the same data in five different modes, two of which are standard, known as “standard-1” and “standard-2” modes. The former mode data contains the light curve of the source with 125 ms time resolution but without any spectral information, whereas the latter data contains the 129 channel spectra accumulated

2.3. X-ray astronomical data analyses and techniques

41

every 16 seconds. Other three modes are proposal specific. These modes basically obtain data with the different levels of trade-off between the timing and spectral resolutions i.e. modes with very high time resolution (micro-seconds) have low or no spectral resolution whereas the modes with moderate time resolution (milli-seconds) have higher spectral resolution (16 to 128 channels). Similarly HEXTE also provides multiple modes of the same data. It has one standard mode called the “archive” mode accumulating 64 channel spectra every 16 seconds and one user specified mode. The detailed descriptions of the RXTE data as well as all available data modes is given in the RXTE handbook “The ABC of XTE”2 . The user level software for the reduction of the PCA and HEXTE, as well as for background estimation, response matrix generation etc. is developed and maintained by the RXTE-GOF. This software is available as a part the LHEAsoft software from the HEASARC. For spectral analysis, typically the “standard-2” mode data from PCA and “archive” mode data from HEXTE may be used. A standard tool saextrct is available to extract the spectra from the PCA or HEXTE data. Similarly standard tools are available for generating the observation specific response matrix as well as background data e.g. pcarsp and pcabackest for PCA and hxtrsp and hxtback for HEXTE respectively. Normally only PCA data is used for timing analysis, as the large area provides sufficient photon count, even at high time resolution ( sub-millisecond), to provide meaningful statistics. In the present work, a “Single-Bit” mode data is used for timing analysis which provides the highest time resolution, typically 16 – 125 s but no spectral information. Such data are normally available in two different energy ranges, 2 – 6 keV and 6 – 15 keV. Again the same tool saextrct is used to extract high time resolution light curve from the “Single-Bit” mode data. The detailed description of RXTE data reduction pro: cess is given in the “RXTE Cook Book” maintained by the RXTE-GOF at HEARSRC, NASA.



2.3.2 Timing analysis The purpose of this analysis is to study the variability of the intensity of emission in the concerned energy band, with the aim of ascertaining the physical processes giving rise to the emission. A light curve with appropriate time resolution is the starting point of the timing analysis. The most common types of variability observed and analyzed is periodicity and/or stochastic variability. The Fourier analysis is perhaps the most sturdy and common mode of statistical analysis of the variability (see chapter 4 for a discussion). The XRONOS package (available with LHEAsoft) is used as the standard 2

Available on-line at http://heasarc.gsfc.nasa.gov/docs/xte/abc/contents.html

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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

timing analysis in this thesis.

2.3.3 Spectral analysis A spectrum is the distribution of flux as a function of energy. The understanding of this distribution provides the knowledge of the underlying physical processes giving rise to the emission. The various emission mechanisms (described in chapter 1) have their characteristic shape of distribution, and hence any complex spectrum may be explained by a combination of the concerned processes. The spectral analysis of an X-ray spectra as observed by the detectors is a complex and involved process, as the interaction of the X-ray photon with the detector matter by which the X-ray photons are detected causes distortion in the spectral distribution of the original emission. Hence the knowledge of the detector response is essential to deconvolve the finally obtained spectra. Detector response matrix and spectral fitting. The final spectral distribution obtained by the X-ray detector is a convolution of the incident X-ray spectrum with the response matrix of the spectrometer. In any X-ray detector there is a finite probability that an incident photon with certain energy will be detected as having some other energy (due to the statistical nature of the interaction), which is determined by the type of detector and physics of X-ray interaction. Also, interactions like photoelectric absorption cause additional features like escape peak which distort the spectrum. Further, certain physical processes involved in the detection process (viz. Comptonization) will cause a deviation in the statistical distribution of the photons, as a function of energy as only a fraction of the photon energy is deposited, thereby making the original spectrum an inherently unknown quantity which is irretrievable. For each energy of an incident photon, the detected spectrum has a spread across almost all channels. This final spectrum, may be obtained by using the response matrix of the detector, which is a two dimensional matrix which gives the probability that a photon of given energy will be detected in a given energy channel. Evidently, the proper understanding of the response matrix of the detector is essential for inferring the incident X-ray spectrum. The X-ray spectrum is represented by a distribution of photon counts over the pulse height channels, where the total counts in any given channel is the sum of contribution to that particular channel from the original photon distribution over all energies (in practice all energies over · which the detector is sensitive). By general convention the spectral analysis is carried 2 out in units of count-rate rather than total counts. Thus, the observed count rate   in 2 a given channel from the incident spectrum ih] (photon flux density at energy h , in



2.3. X-ray astronomical data analyses and techniques

43

: photons cm l s l ˜ keV l ˜ )3 is given by ·  † 2 2 (2.1) U 7I⠌  ] h  ih_ Æ]ih_ h [ 2 where Œ  h_ is the response matrix of the detector which gives the probability of 2 [ · detecting a photon with energy h in the channel and Æ_ih] is the effective area of the detector at energy h . In principle, the incident source spectrum ih_ can be obtained· from the observed 2 spectrum   by inverting the above equation 2.1, but in practice the response matrix 2 · Œ  h_ is generally non-invertible. Therefore the source spectrum ih_ is, in general, 2 [ · obtainable directly from the observed spectrum U  . The general practice not possibly is to choose a model spectrum ih] such that it can be described in terms of a few parameters, ih f f : Š Š Š  , convolve the model spectrum with the detector response matrix 2 [ ˜ [ to get the predicted count spectrum   and then compare it with the observed count n 2 spectrum U  . A “fit statistic” is computed from the comparison, which enables one to judge whether the model spectrum describes the observed spectrum properly or not. The model spectrum which agrees best with the observed spectrum is then assumed to be the true incident spectrum. This process is known as fitting a model spectrum to the observed spectrum. The most common fit statistic in use for determining the “best-fit” : fit which is defined as model is the















2 : ~ 2 :  Ì   Ì (2.2) n  ~ 2 ~ 2 2 where   is the error for channel I. If C(I) are counts in channel then   is 2 usually estimated by U  . The best-fit model spectrum is generally obtained by determining the “goodness-of: fit” of the model using the -statistic which provides a well established goodness-of-fit criterion for a given number of degrees of freedom or dof, : (which is the number of 8 · exceeds a critical value, channels minus the When : : number of model parameters). · “reduced ” ( ) \ (Bevington 1969), the concerned model is to be rejected on 8 statistical basis. Even if the best-fit model, ih f‹ does pass the goodness-of-fit test, the [ possibility of any other model ih f  fitting the data equally well or better cannot be [ ruled out. The choice of correct model is a matter of scientific judgment. Thereafter, a ”confidence interval” for the best fit model parameters (Lampton et al. 1976) is computed to define the acceptable range (error) of the best fit parameter values. In this thesis, the confidence interval, or the errors for a single parameter is calculated at 90% confidence (Arnaud and Dorman 2002). X X X 3 The X-ray spectra can also be shown in units of keV cm e s e keV e or keV cm e s e keV e V V V V

 : 7  U 2    

 











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Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

The XSPEC package. The most commonly used software package for the general X: ray spectral fitting using the “best fit” statistic (normally the fit) is the XSPEC (Arnaud 1996), which is a sub-package of the XANADU available as a part of the LHEAsoft package. XSPEC is a command driven, interactive, completely detector-independent, X-ray spectral fitting program. To work with data from any detector, all that the XSPEC needs is the observed spectrum data file (generally identified by a “.pha” extension), the detector response matrix (generally identified by a “.rsp” extension; in some cases two separate files, the ancillary response file “.arf” and the redistribution matrix file “.rmf” are required to specify complete response matrix) and the spectral background noise data file, all in the standard FITS format. This package contains many built in components for the source model spectrum such as blackbody spectrum, power-law spectrum, Gaussian or Lorentzian line, etc, a combination of which may describe the source spectrum. But, it is also possible to add a custom defined model component into the XSPEC package. Apart from fitting the model spectrum to the observed spectrum, XSPEC also features different methods to find out the confidence intervals for the parameters of the best-fit model.



Calibration issues. The response matrix of a given instrument, in principle, depends on the physics of the detector and hence can be estimated by purely theoretical considerations. However it is not always feasible to consider each and every detail of the detector in practice, and an experimental method for determining the correct detector response matrix is needed. This process of experimentally determining the detector response, i.e. establishing a relation between the incident and observed X-ray spectrum is known as calibration. Generally the calibration process involves shining the detector with available monochromatic X-ray source and subsequent recording of the corresponding output spectrum. The final response matrix has to be determined by reasonable interpolation. A point to be noted is that even though the individual detectors are very well calibrated, their absolute calibration may differ slightly. Hence, combining data from different detectors is a very contentious issue, as the observation of the same source, such as Crab, may give slightly different parameter values for different observatories/instruments (Vadawale et al. 2001b). This issue needs very careful consideration when attempt is made to fit the X-ray spectral data simultaneously from different detectors. Source model component spectrum The X-ray spectral analysis software package, XSPEC, contains a wide range of model components. Many different combinations of these model components are possible to define the assumed source X-ray spectrum. It is

2.3. X-ray astronomical data analyses and techniques

45

also possible to add new model components to XSPEC. Some of the model components which are used in this thesis are described below:powerlaw. A commonly used spectral component, it is defined as J (2.3) ih]j7 ih ì ] l  J D its normalization are the two paramewhere D the power-law index and ters of the model. Power-law X-ray spectrum can be generated by many different physical processes such as synchrotron radiation, shock acceleration etc. But, importantly, if the signal-to-noise ratio of the data is not very good then the shape of the X-ray spectrum due to most of the other mechanisms can be approximated by a power-law, and hence it is one of the most commonly used spectral component in X-ray astronomy.



 "! $#

%

diskbb. This represents a multi-coloured disc black body spectra from a basic accretion disc emission (equation 1.15). It has two parameters, the temperature at inner disk J in keV and normalization which is given by radius 4 ðòñ : J N Œ Ä …F P  ¼ ðòñ (2.4) 7   ï T

& ' )( ( *

&

D the radius of the where D the distance of the source (units of 10 kpc), Œ Ä ðøñ inner edge of the disk (units of km) and D the inclination angle of the system. The multicolor disc-blackbody is mostly used to model the X-ray spectrum from GBHCs, particularly during their high / soft states.

CompST. This is the simplest Comptonization model based on the work of Sunyaev and Titarchuk (1980). This model has three parameters, a temperature FS4 in keV · and optical depth Ô of the Comptonizing plasma and a normalization which is analytically described as J 7 ,‰ † : (2.5) ¹ · † J D total no. of photons from the source, D distance to the source, where Q , here Y is the spectral index,  is the injected photon energy D factor – ód (units of temperature) and P is the incomplete function.

+

, -.,  0-./2, 1 / 3

64 5

%

CompTT. An improved version of Comptonization (after Titarchuk 1994) taking the relativistic effects into consideration. This is a tabular model which takes the seed

46

Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy photon energy as an explicit parameter 4 . Also, there are two different Compðòñ tonization geometries possible which are specified by an additional ‘geometry’ parameter. This process is typically used to model the X-ray spectrum of low / hard states of GBHCs.

gaussian. A simple gaussian line profile given by Æ_ih]j7

7 (

¹‰ ~ : = l

98  e < / X -;: :

(2.6)

V

~ : D ~ line energy (keV), D line width and D total photons/cm /s in where h ˜ ¹ the line. If  0 then it is treated as a delta function ih_ .

=

edge. An absorption edge given by ih]

where h  D

7£

7 = l

threshold energy and ÔUD

$> - :': ?A@ / e Ë

for h)h  for h-h 

(2.7)

absorption depth at the threshold.

In the work leading to this thesis, the RXTE–ASM monitoring data, CGRO–BATSE monitoring data and GBI monitoring data were obtained as the standard products from the archives of these observatories available publicly over the world wide web. The standard timing analysis of these data have been made using the XRONOS software available as a part of the LHEAsoft package, while any non-standard analysis and file-manipulation has been done by programs developed by us. For the RXTE–PCA & HEXTE data analysis, the ‘low-level’ data have been downloaded from the RXTE archives, the lightcurves and spectra were reduced using the FTOOLS package (whichever current version that was available during the time), and the standard timing as well as spectral analysis were done using the XRONOS and XANADU package, available with LHEAsoft. In this case too, any non-standard analysis and file-manipulation (viz. correcting the X-ray emission from Cygnus X-3 for binary modulation) has been done using programs developed by us.

2.4 Radio astronomy 2.4.1 Green Bank Interferometer (GBI) observatory The present work has used radio observations from the radio telescope Green Bank Interferometer. The observation and data reduction was carried out by the GBI team, and

2.4. Radio astronomy

47

Fig. 2.4: The three telescopes of the Green Bank Interferometer.

we only used publicly available radio monitoring data (lightcurves) of the Galactic microquasars and hence the details of the radio data reduction are not described. The Green Bank Interferometer (GBI) is located in Green Bank, West Virginia, US and is operated by the National Radio Astronomy Observatory (NRAO), US. It consists of three radio telescopes of 26m diameter with a baseline of 2400 m. It operates simultaneously at two frequencies 2.25 GHz and 8.3 GHz with 35 MHz bandwidth. The sensitivity of the observatory is 6 mJy (S band, 2.2 GHz) and 10 mJy (X band, 8.3 GHz) rms noise measured in 5 minutes scan. GBI used to monitor almost all interesting radio sources in the sky few times a day, however, from October 2000 on-wards the monitoring program has been stopped due to lack of funding. Earlier monitoring data is archived and is freely available and extensively used in this thesis.

B

2.4.2 Giant Metrewave Radio Telescope (GMRT) Although data from this observatory has not been used in this thesis, some preliminary observations have established the prospect of future study of microquasar systems (viz. Cygnus X-3) from this observatory, and hence a very brief mention of it is made here.

48

Chapter 2. X-ray detectors and techniques of instrumentation; Radio astronomy

Located in Khodad, about 80 km from Pune, India, Giant Metrewave Radio Telescope (GMRT) is the world’s most powerful radio telescope operating in the frequency range of about 50 to 1500 MHz. Operated by The National Centre for Radio Astronomy, T I F R, it consists of 30 fully steerable gigantic parabolic dishes of 45 m diameter each spread over distances of upto 25 km. The number and configuration of the dishes was optimized to meet the principal astrophysical objectives which require sensitivity at high angular resolution as well as ability to image radio emission from diffuse extended regions. Fourteen of the thirty dishes are : located more or less randomly in a compact central array in a region of about 1 km , and the remaining sixteen dishes are spread out along the 3 arms of an approximately ‘Y’-shaped configuration over a much larger region, with the longest interferometric baseline of about 25 km. The array operates in six frequency bands centred around 50, 153, 233, 325, 610 and 1420 MHz. All these feeds provide dual polarization outputs. In some configurations (eg. 1420 MHz), dualfrequency observations are also possible.

Chapter 3 Cygnus X-3: spectral studies

3.1 Why Cygnus X-3? In chapter 1 it was explained and emphasized that a long term multi-wavelength monitoring was mandatory to provide a comprehensive picture of the observational features of the various microquasars, which may provide a handle to probe the accretion-ejection connection mechanism of these systems. Ideally, the source should be persistent in the multi wave bands, covering both quiescent (non-flaring) and flaring states, displaying both transient ejection events and the steady jets in the low-hard states. As mentioned in chapter 2, RXTE–ASM, CGRO–BATSE and GBI provide the only continuous monitoring data in the X-ray and radio bands, publicly available, for the period when these three observatories were simultaneously operational. Fender and Kuulkers (2001) provide a list of Galactic X-ray binaries which are observable in the X-ray and radio bands, of which most are the transient type. Collating these sources with those monitored by the three observatories, we found three X-ray binaries (black hole candidates) viz. Cygnus X-1, GRS 1915+105 and Cygnus X-3, which are persistent in radio, soft and hard X-ray bands and for which (quasi) simultaneous data from the three observatories are available. Of these three sources, Cygnus X-1 doesn’t show the huge transient outflow (burst) episodes. Whereas GRS1915+105, since its discovery in the last decade, is perhaps the most studied and reported source. Cygnus X-3, on the other hand, despite being one of the commonly observed source, is neglected in the literature in the recent times, especially so in the high energy band in the post RXTE era. The likely reason for this is, perhaps, the difficulty in explaining the X-ray observational features (viz. spectral, temporal). But given the diverse behavioural pattern in the X-ray as well other wavelengths displayed by this source, it was imperative that a detailed multi-wavelength study, with emphasis on the X-ray spectral and temporal evolution, be carried out. The diversity of 49

50

Chapter 3. Cygnus X-3: spectral studies

Fig. 3.1: Chandra image of Cygnus X-3 highlighting the halo (and/or dust) engulfing the system, which may originate from the wind of the companion.

the X-ray behavioural patterns in this source is surpassed only by GRS 1915+105, which is extensively reported in the literature.

3.2 General properties of Cygnus X-3 Cygnus X-3 is one of the earliest Galactic X-ray sources to be detected (Giacconi et al. 1967), and therefore obviously is one of the brightest X-ray objects in the sky. Thereafter, in a programme to detect radio counterparts of the early X-ray sources, a comparatively weak radio counterpart for this source was discovered by Westerbork synthesis telescope (Braes and Miley 1972) and NRAO Green Bank Interferometer (Hjellming et al. 1972), during what we understand now as the low state with core jet outflow. Soon, however, huge radio outbursts were observed by Algonquin Radio Observatory, Ontario, Canda (Gregory et al. 1972) followed by GBI (Hjellming and Ballick 1972) and other various radio observatories (Anderson et al. 1972, D’Addario and Stull 1972, Aller and Dent 1972, Dent et al. 1972, Gary et al. 1972, Branson et al. 1972). During the same time infra-red (Becklin et al. 1972) and mm wavelength (Pomphrey and Epstein 1972) emissions were also discovered from the source. Using hydrogen–line absorption in front of

3.2. General properties of Cygnus X-3

51

Fig. 3.2: Chandra image of Cygnus X-3 highlighting the elongated X-ray excess, which may be due to dust from the companion, or material from a previous jet emitted from the compact object.

the source in the line of sight, Lauque et al. (1972) derived the location of the source in one of the Galactic arms at a distance of 8 – 11 kpc from earth (see Bonnet-Bidaud and Chardin 1988, for a review), which was later corroborated by the method of determining the geometric distance by measuring the apparent delay of the intensity variation of the radiation of the halo scattered by interstellar dust, due to smearing out in the halo itself (Predehl et al. 2000, see Figure 3.1). All attempts to detect the optical counterpart were unsuccessful (see Bonnet-Bidaud and Chardin 1988, for a review), therefore we can safely conclude that any possible counterpart in the optical has magnitude more than 26. The X-ray emission displayed a modulation of 4.8 hours (Parsignault et al. 1972, Sandford and Hawkins 1972), which was also observed in the infra-red band (Becklin et al. 1973), and this was attributed to the binary orbital motion. At the same time the source was plagued with a variety of aperiodic variabilities, including outbursts, in all the bands(Becklin et al. 1974). Since the early days of its observations, the system was recognized to be of the accreting binary type, with one of the components of the binary being a compact star, accreting matter from the companion, which loses material

52

Chapter 3. Cygnus X-3: spectral studies

via strong winds (Davidsen and Ostriker 1974, Pringle 1974), with the whole system engulfed in a spherical shell of gas (Milgrom 1976). This idea was further developed by Fender et al. (1999a), who suggested that the stellar wind is compressed into a flattened disc with dimensions much larger than the binary system. Given the compactness of the system as suggested by the binary period, initially it was assumed to be a low mass X-ray binary system (LMXB), but the infra-red observations of broad emission lines of He I and He II, along with the absence of hydrogen, suggest presence of dense wind and indicate the companion to be a Wolf-Rayet star (van Kerkwijk et al. 1992), the helium core of a massive star embedded in dense wind (van Kerkwijk et al. 1996). The measurement of the radial velocity in the infra-red band and its interpretation as due to binary Doppler shift has led to the derivation of a large mass function for the source (Schmutz et al. 1996). But this simplistic explanation of the He II line shift is strongly disputed by the relative phasing of the infra-red and the X-ray binary modulation, as pointed out by van Kerkwijk (1993) who indeed suggests that the He line emissions originate in the two temperature wind from the Wolf-Rayet companion, and the line-shift occurs as the wind recedes and approaches the observer, as a function of the binary motion. Since the velocity measured is that of the wind, the motion of the Wolf-Rayet companion remains undetermined and hence the mass function of the system is unknown. Interestingly, quite recently Stark and Saia (2003) have suggested an upper limit to the mass of the compact object of 3.6 M  . They measured the Doppler shift of the He-like K & like line of iron XXV (Paerels et al. 2000, Kitamoto et al. 1994) and ascribing it to originate from very near the surface of the compact object they provide a conservative estimate of the stellar masses and the separation of the binary system. Till date, all the models of the infra-red emission from the source consider the (wind from the) Wolf-Rayet companion to be the only source of radiation in this band. Recently Heindl et al. (2003) have reported an extended emission in the
X-ray band (using the CHANDRA observatory), which has a dimension of  Š pc at a distance of ( Š pc from the source (assuming Cygnus X-3 to be at a distance of 10 kpc). Shown in Figure 3.2, the the lines numbered 1, 2, etc. correspond to different roll angles, all of which give the same extended structure in space, negating the possibility of any artefactual manifestation of the point spread function. Persistent in all the bands in which detected so far, Cyg X-3 does provide a stable system to study the accretion and ejection phenomena, across various possible states. The evolution the X-ray spectral features, correlated to the radio emission, provides a challenge for the current generation of astrophysicists to understand and explain the disc jet connection in this (class of) object(s).

3.3. General spectral features of Cygnus X-3

53

3.3 General spectral features of Cygnus X-3 3.3.1 A historical perspective Complex features like absorption edges (Bleach et al. 1972) and broad iron line (from Ariel-5 satellite – Sandford et al. 1975, which was later resolved to consist of three separate iron lines by ASCA– Kitamoto et al. 1994) were observed quite early in this source. UHURUdetected that the source existed in two different states with different levels of X-ray emission flux (Leach et al. 1975), which were found to possess different spectral shapes from the rocket flight observations (Serlemitsos et al. 1975). Efforts were made to study the binary phase resolved X-ray spectra of the source in both its high (Blissett et al. 1981) and low state (Becker et al. 1978), with conflicting results. The latter reported an excess of soft X-ray flux at the phase 0 (minimum) of the binary modulation, which was not seen in the high state. The issue is not settled till date because of the high absorption of the soft X-ray flux in the line of sight to the source, caused probably due to the circumstellar matter that may have been caused by the strong wind ejection from the Wolf-Rayet companion. Accretion disc corona has also been considered a medium of X-ray reprocessing (White and Holt 1982) along with the X-ray scattering halo (Molnar and Mauche 1986). The first attempts of detailed X-ray spectroscopy was attempted by the EXOSAT (Rajeev et al. 1994) and GINGA (Nakamura et al. 1993) observatories, while observations from ASCAfurther improved the resolution of the spectra in the soft X-ray regime, facilitating the identification of the three iron line features (Kitamoto et al. 1994). Rajeev et al. (1994) explained the X-ray spectral energy distribution (SED), in both (low) hard and (high) soft state with a composite model consisting of a disc black body component and a non-relativistic thermal Comptonization component-CompST (Sunyaev and Titarchuk 1980) along with the line and edge features, from the EXOSAT pointed observations, covering the 1-100 keV band. They also found a low energy thermal bremsstrahlung component, more significantly in the (high) soft state. These observations also unambiguously resolved two absorption edge components, at 7.1 keV (neutral Fe) and 9.2 keV (iron XXV - XXVI). From the GINGAobservations, Nakamura et al. (1993) explained the X-ray continuum SED, in both the states, by a composite model consisting chiefly of a disc black body component and a powerlaw component with an exponential cut-off. They pay stress on the emission from an X-ray halo, the scattering of the low energy X-ray emission in the circumstellar medium (Molnar and Mauche 1986), otherwise, they claim, the absorption due to effective hydrogen column density N will be severely underestimated. Nevertheless, they report very high absorption in the low energy regime, giving unreasonably high values of the effective hydrogen density column

C

Chapter 3. Cygnus X-3: spectral studies

54

C

N . While Rajeev et al. (1994) speculated the presence of a Comptonizing cloud along with a thermal accretion disc, Nakamura et al. (1993) postulated the presence of three kind of hot gases with differing ionization levels. From the ASCAobservations the broad iron K & line emission feature was resolved to be consisting of three separate compo Š  keV, a H-like line at ùŠ ù  Š ,( keV and a neutral nents, a He-like line at ùŠëù line at ùŠ .  Š ,. keV (Kitamoto et al. 1994). Also, various other emission lines viz., K & line of He-like and H-like ions of S, Ar, Ca, along with Fe, were observed in the data from this observatory, confirming the presence of a photo-ionized plasma in the system, which might extend asymmetrically (Kawashima and Kitamoto 1996). The presence of these line emissions was later confirmed by the CHANDRA observatory (Paerels et al. 2000).

FD

ED

 D

3.3.2 X-ray wide band spectra from RXTE The X-ray SED typically shows two different states, low (and correspondingly hard) and high (and correspondingly soft), distinguished by the shape of the X-ray spectra characterized (Choudhury and Rao 2002), chiefly but not totally, by the presence (or absence) of multicoloured disk blackbody component and the power-law index (albeit with the individual model components more complicated than the canonical X-ray states of classical black hole candidates characterized, chiefly, by Cygnus X-1, see, for eg. Tanaka and Lewin 1995). To get a broad-band (5–150 keV) spectral picture we used 72 sets of the pointed observations of both the narrow field of view instruments aboard the RXTE: viz. PCA and the HEXTE. A systematic error of 2% was added to the PCA Standard 2 data (all PCUs added), which included all the 129 channel PHA data, and it was simultaneously fit with 64 channel data from only the cluster 0 of the HEXTE, to get a proper fit (Vadawale et al. 2001b). Of these 72 sets of observations, there are only in effect 48 independent observations on different days (others are extended observations on the same day), of which 11 are in the low (hard) state and the rest are in the high (soft) state. To get a proper idea of the spectral state during the pointed observations, in table 3.1 we give the flux as observed by three monitoring instruments: viz.1) ASM aboard the RXTE, in the soft X-ray energy region (2-10 keV), 2) BATSE aboard the CGRO, in the hard X-ray energy region (20-100 keV), and 3) GBI in the radio band, of the electromagnetic spectrum. The background noise was removed from the source PHA file during the fit, and the background PHA file was generated from the model of background noise for the corresponding epoch of RXTE observation, as provided. The resolution of the three iron lines (Kitamoto et al. 1994) and the two absorption edges (Rajeev et al. 1994) are beyond the capability of the PCA, hence we fix the relative separation of line and edge energies as reported by Rajeev et al. (1994), Nakamura

s

JH

photons cm

;

BATSE

50321 50324 50500 50604 50612 50618 50652 50717 50951 50953 51404 51586 51588 51590 51593 51595 51638 51641 51643 51646 51648 51656 51663 51576

8.160 10.291 21.141 28.722 17.675 20.635 7.636 10.778 6.715 5.551 19.67 28.59 23.70 31.12 19.33 19.92 23.13 20.76 24.74 16.02 13.33 16.54 19.75 18.59

0.028 0.035 0.018 0.042 0.034 0.055 0.038 0.052 0.051

GBI (2.2GHZ) 0.101 0.130 3.511 0.737 0.071 0.118 0.071 0.065 0.087 0.140 0.039 0.137

GBI (8.3GHZ) 0.098 0.197 2.478 0.966 0.081 0.205 0.082 0.067 0.087 0.236 0.073 0.320

0.643 0.498

0.644 0.413

0.278 0.229

0.124 0.208

4.536

2.299

I

0.153 1.759 3.521

ASM

I

0.233 0.331 6.345

MJD

H

0.702 0.242

spectral state low low low high high high high high low low low high high high high high high high high high high high high high

G

1.211 0.417

I

GBI (8.3GHz) 0.090 0.316 0.964 0.550 0.083 0.083 0.098 0.080 0.223 0.049 0.171

I

0.039 0.009 0.034 0.041 0.001 0.005 0.056 0.051 0.043 0.046 0.058

GBI (2.2GHz) 0.095 0.111 0.729 0.115 0.071 0.061 0.087 0.049 0.069 0.044 0.072 0.020

spectral state low low high high high high high low low low high high high high high high high high high high high high high high

mJy

JG I

50319 7.495 50322 10.298 50325 15.279 50501 21.29 50609 22.137 50616 26.746 50624 32.351 50661 8.150 50950 5.573 50952 5.453 50954 5.384 51585 14.76 51587 26.53 51589 25.98 51592 20.80 51594 19.53 51637 31.49 51639 28.41 51642 28.41 51644 18.91 51647 14.11 51650 20.70 51661 23.48 51575 24.81 units: counts s ;

JG H

ASM

H

G

BATSE

G

MJD

3.3. General spectral features of Cygnus X-3

Table 3.1: The MJD of the pointed observations of RXTE along with the average flux obtained by ASM (2–10 keV), BATSE (20–600 keV) and GBI (radio–2.2 & 8.3 GHz).

55

Chapter 3. Cygnus X-3: spectral studies

56

et al. (1993), Kitamoto et al. (1994), and treat the edge energy at 7.1 keV and the normalization of all the lines and edges as the variable parameters in the fit. Throughout we fix the line width at 80 eV (reasonably accepted value as obtained by Kitamoto et al. 1994, from ASCAobservations). This mode of tying the line energies with one edge : energy doesn’t affect the continuum fitting, but brings the value corrsponding to the best fit parameteres within the acceptable limit. The spectra is fit separately for the high/soft and low/hard states. The unfolded spectra of an observation in high/soft state (MJD 50616) is shown in left panel of Figure 3.3, and that of one of the low/hard states (MJD 50954) is shown in right panel of Figure 3.3. The criteria of choosing these two as the representative of their respective states are: 1) exposure time, 2) quality of data, i.e. better background subtraction. Since the resolution of the PCA is poor in the lower energies and the absorption due to effective hydrogen column is a very sensitive parameter in this region, we neglect :Ì: : data below 5 keV and fix the:Ì: height: of hydrogen column l (low/hard state) and 5 ›Û  l (high/soft state), as to N value of 1.6 ›Û  reported by Rajeev et al. (1994). Also, the regime below 5 keV is dominated by the photo-ionization lines (Kawashima and Kitamoto 1996, Paerels et al. 2000), suggesting reprocessing of the X-ray emission in the hot gas constituting the circumstellar matter, most probable origin of it is the dense stellar wind of the Wolf-Rayet companion. The resolution of these low energy features being beyond the capability of RXTE–PCA was also a reason for neglecting the flux µ 5 keV. A distinct feature of the X-ray spectrum in the low (hard) state is the shape of the spectrum in the region 10-25 keV, which looks like a hump like feature. Normally such feautres in X-ray binary blackhole candidates are taken as signatures of Compton reflection component, but attempts to fit such a reflection model provided very high values of the albido. The details of the results of the X-ray spectral parameter values of the continuum components are given in table 3.2 for all the low (hard) state observations (11) and some representative high (soft) state observations (Choudhury and Rao 2002). Subsequently, the background modelling as well the response matrix of PCA has improved and the picture has changed slightly in the high/soft state ( 3.6).



C

("K

("K

L

The high (soft) state continuum emission spectra is best fit by a combination of multicoloured disc blackbody and CompST (Sunyaev and Titarchuk 1980) components. (Powerlaw is needed to fit hard X-ray continuum in certain states instead of the multicoloured disc blackbody, see section 3.6.) Incorporation of any extra component viz. powerlaw, in addition to the disc blackbody and CompST, doesn’t improve the quality of the fit. The low hard state continuum emission spectra is best fit by a combination of CompST and a powerlaw, with the conspicuous absence of the multicoloured (disc) blackbody component. The X-ray spectra of black hole sources contain a thermal and

3.3. General spectral features of Cygnus X-3

57

Fig. 3.3: A: The spectra of observation on MJD 50616 showing all the components, viz. three Fe lines, two absorption edges, multicoloured disk blackbody and the powerlaw continuum. B: The spectra of observation on MJD 50954 showing all the components, viz. three Fe lines, two absorption edges, compST (Sunyaev and Titarchuk 1980) and the powerlaw continuum.

a non-thermal part, which are conventionally modeled as a disc black body spectrum and a power-law (or cut-off power-law) or more realistic models incorporating Compton scattering from thermal as well as non-thermal electrons (Zdziarski et al. 2001). Since our aim is to make a wide band description of the spectra to understand the broad features, we have adopted an analytically simpler model consisting of a disk black-body and Comptonization from thermal electrons (Sunyaev and Titarchuk 1980 - the CompST model), plus an additional power law, in the low (as well as hard) state. Iron line features, although significant in both states, are more prominent in the low (hard) state. Absorption edges also form very important spectral features in both the states. Since the hot circumstellar gas obscures the low energy X-ray emission, the continuum disc (multicoloured) blackbody emission, contributing in the energy range µ 5 keV needs more rigorous analysis and better resolved spectra, which is beyond the scope of the current analytical procedures and the observatory in consideration. Although CompST is a non-relativistic model, Vadawale et al. (2002) have shown that CompST model gives

Chapter 3. Cygnus X-3: spectral studies

58

Table 3.2: X-ray spectral parameters of Cygnus X-3 . The results in this table were reported in Choudhury and Rao (2002), where the then current version of FTOOLS were used (v5.0). Subsequently better background emission and response matrix have changed the picture little bit for the high (soft) state ( 3.6).

M

Low/hard state. Best fit parameters for CompST+power law L L :3 » MJD kT (keV) (d.o.f.) MJD kT (keV) 50319 4.45 2.47 1.26(86) 50321 4.39 ä 50321 4.47 2.61 1.18(108) 50322 4.91 ä 50322 4.36 2.70 0.92(108) 50324 4.17 50325 5.58 2.45 0.60 (108) 50717 5.09 50950 4.97 2.10 1.26(88) 50951 4.74 50952 5.02 2.03 1.43(86) 50953 5.06 50954 4.87 2.01 1.42(108) High/soft state. Best fit parameters :3 for diskbb+power law » MJD kT (keV) (d.o.f.) MJD kT (keV) 50604 1.49 2.55 0.53(109) 50609 1.59 50612 1.62 2.25 1.22(109) 50616 1.55 50618 1.53 2.34 0.83(109) 50624 1.52 50500 1.74 2.98 0.55(109) 50501 2.91 ä 50501 2.56 2.98 0.59(109)

N

%



%



N

:3

2.51 2.51 2.67 2.55 2.08 2.02



(d.o.f.) 0.90(108) 1.08(108) 0.77(108) 0.74(86) 1.34(89) 1.45(91)

%



:3

%

»

»

2.21 2.53 2.63 3.06

(d.o.f.) 1.19(109) 0.65(109) 0.60(109) 0.54(109)

* extended observation

a functionally correct description of the more elaborate numerical codes, although with slightly different parameters. Moreover, such composite models have been used earlier for Cygnus X-3 (Rajeev et al. 1994). The most striking feature of the X-ray wide-band spectra obtained from RXTE observations is the unambiguous presence of the non-thermal tail extending beyond 150 keV (Choudhury and Rao 2002), in both the states of X-ray emission. Such features are commonly observed in the Galactic black hole binary candidates, viz. GRS 1915+105 (Zdziarski et al. 2001), Cygnus X-1 (Zdziarski et al. 2002), GX 339-4 (Wardzi´nski et al. 2002), and also some neutron star binary systems. For the black hole systems this power law tail can be interpreted as due to two component (thermal and non-thermal) Comptonization (Zdziarski 2000), or due to the existance of the bulk motion Comptonization (Chakrabarti and Titarchuk 1995), espcially in the high/soft state. Detailed X-ray spectral analysis, correlated with the radio emission, will be dealt with in the following sections, and their theoretical interpretations will be presented in chapter 6.

3.4. Correlation of radio & X-ray emission in Cygnus X-3: Spearman’s Partial Rank Correlation test59

Fig. 3.4: The combined simultaneous lightcurve of Cygnus X-3 in the soft X-ray (2 -12 keV,RXTE–ASM, top panel), hard X-ray (20 - 100 keV, CGRO–BATSE, middle panel) and the radio (2.2 GHz, GBI, bottom panel). The various ‘states’ of the source are separated by vertical dashed lines and identified with numbers. The arrows on the top panel give the start time of RXTE pointed observations and the three inverted arrows give the days for which wideband X-ray spectral studies are carried out.

3.4 Correlation of radio & X-ray emission in Cygnus X-3: Spearman’s Partial Rank Correlation test Cygnus X-3 is one of the brightest radio source ever associated with an X-ray binary (Waltman et al. 1995). Since its discovery in the radio band (Braes and Miley 1972, Hjellming et al. 1972), it has been found to be a persisting source in this band, exhibiting regular radio outbursts (Gregory et al. 1972, Hjellming and Ballick 1972). These large outbursts, which may get brighter than 10 Jy, were found to occur only during the high (soft) state of X-ray emission (Watanabe et al. 1994). Normally, there is a period of quenched radio emission, with flux µ 30 mJy, preceding the loud outburst episode (Waltman et al. 1996, Fender et al. 1997b). Watanabe et al. (1994) also hint at a correlation between the soft X-ray (as observed by ASM aboard the Ginga observatory) and the



60

Chapter 3. Cygnus X-3: spectral studies

quiescent radio emission (as seen by the GBI), during the low-hard state, but a detailed correlation analysis is not presented, possibly due to the sparse sampling of the source by the GINGAsatellite during its course of regular monitoring. McCollough et al. (1999) report a correlation test between the hard X-ray (as observed by the BATSE aboard the CGRO) and the radio (GBI), in the various states of radio and X-ray emission. They report 1) anti-correlation between the radio and hard X-ray emission during the quiescent period, 2) correlation between the radio and hard X-ray emission during the major flaring period, and 3) no correlation between the radio and hard X-ray emission during the minor flaring period. Continuing our mission of the study of long term multiwavelength (radio & X-ray) monitoring of this source, we perform a Spearman’s Partial Rank Correlation test, to analyse the association between the radio (2.2 GHz, GBI), soft Xray (2 - 12 keV, RXTE–ASM) and hard X-ray (20 - 100 keV, CGRO–BATSE), covering the period when these three observatories were simultaneously monitoring the source. The Spearman’s test provides the most comprehensive correlation among three variables (Macklin 1982), investigating the possible role of the third variable in the correlation that (may) arise between the other two variables.

3.4.1 Spearman’s Partial Rank Correlation test The Spearman partial rank correlation test is used to determine the correlation between two or more variables. The partial rank coefficient is computed from the sampling distribution which may be derived by analogy with a parametric statistic (Macklin 1982). For correlation among three variables, say A, B & C, the null-hypothesis is that the correlation between A and B arises entirely from those of C with A and B separately. The value of the correlation coefficient lies between -1 and 1. The negative value signifies anti-correlation. The significance level associated with the correlation between A and B, independent of C, is given by the D-parameter, which is normally distributed about zero with unit variance if the null-hypothesis, that the A-B relation arises entirely from those of C with A and B separately, is true (Macklin 1982). Three variables can be mutually correlated, but independent, in the following way: Let X, Y, Z be three variables which are completely independent of each other. Define A, B, C as follows: A=X+Y B=Y+Z C=Z+Y We can see that A, B, C are mutually correlated, but each correlation is independent of the third parameter. We have explicitly verified this by taking 200 sets of X, Y, and Z (each of them a random number) and calculating the correlation coefficient and D

3.4. Correlation of radio & X-ray emission in Cygnus X-3: Spearman’s Partial Rank Correlation test61

+

parameter for A, B, and C defined above. We find significant correlation among all three ( 0.5) while the D parameter for all the three cases indicate that each correlation is independent of the third parameter. On the other hand, defining the 3 parameters as: A=X B=X+Y C=X+Z shows a D parameter of 0.3 for B:C correlation showing that this correlation is entirely dependent on the common parameter A. The Spearman’s Rank Correlation (SRC) coefficient and the realted parameters (D parameter & null hypothesis coefficient) were computed for the monitoring data obtained from RXTE–ASM, CGRO–BATSE and GBI, as explained in the previous section. The lightcurve of the period covered in this correlation test is shown in Figure 3.4, where the daily averaged flux level is depicted. Historically, the behaviour of radio emission in Cygnus X-3 is classified into: 1) quiescent period ( 50–100 mJy), 2) major flaring ( 1Jy) with a preceding quenched state ( 10–20 mJy), and 3) minor flaring ( 100–150mJy) with partial quenching state (see Waltman et al. 1995, McCollough et al. 1999). Accordingly we have demarcated four regions in Figure 3.4, region 1 and 4 corresponding to the quiescent state (although region 4 contains two minor flares along with the long quiescent period), region 2 corresponding to the major flaring state and region 3 corresponding to the minor flaring state. The number of data points in region 1 (of Figure 3.4) is meagre and hence is not included in the correlation tests. Table 3.3 shows the SRC coefficient, null hypothesis probability and the D-parameter, using 10 day averages of the data for the different periods (and their combination) as demarcated in Figure 3.4. Reducing the number of days for averaging does not significantly change the results. The most interesting result is that the soft X-ray and radio are very strongly correlated, with a very high significance level, in region 4 and regions 3 & 4 combined. ~ It can also be ruled out (at - 5 level) that this correlation is influenced by the third parameter, the hard X-ray emission. Though these two parameters are correlated even in the flaring state (region 2) at a much reduced significance level, the correlation tests in this region could be influenced by the high variability at time scales shorter than the period chosen for taking the averages (10 days). Hence we concentrate on the results obtained for region 4 and region 3 & 4 combined. It is also found that the soft X-ray is anti-correlated with the hard X-ray emission. The anti-correlation between the radio and hard X-ray emission, though strong, could be influenced by the other two correlations, particularly when we examine the data for the region 3 & 4 combined. The similarity of





Chapter 3. Cygnus X-3: spectral studies

62

Table 3.3: The Spearman Rank Correlation (SRC) coefficient, null-hypothesis probability and D-parameter between the radio, soft X-ray and hard X-ray for different periods demarcated in Figure 3.4.

Region 4 ASM:GBI GBI:BATSE ASM:BATSE Region 3 ASM:GBI GBI:BATSE ASM:BATSE Region 2 ASM:GBI GBI:BATSE ASM:BATSE Region 3 & 4 ASM:GBI GBI:BATSE ASM:BATSE

SRC coeff.

Null Prob.

D-Parameter

0.84  0.75  0.74

6.3 ›Û  l ̘ ˜ 9.2 ›Ñ 1l ̘ ˜ 3.1 ›Ñ  l ̘ ˜

5.2  2.7  2.2

0.66  0.43  0.71

8.3 ›Û  l x: 4.7 ›Û  l 1.9 ›Û  l x

2.7 0.4  3.2

0.56 0.10  0.50

Q 3.5 ›Û  l 6.3 ›Û  l : ˜ 1.1 ›Û  l

4.1 2.7  3.8

0.83  0.72  0.79

: 2.1 ›Û  l Q 4.7 ›Ñ 1l ˜ 4.1 ›Ñ  l ˜

6.2  1.5  3.8

O QP

the behaviour of region 4 and regions 3 & 4 combined suggest that the emission mechanism during the minor flaring and the quiescent period are the same, and hence these two can be clubbed together as one class (see Choudhury et al. 2002). This suggests that the X-ray spectral behaviour controls the radio emission during this state of low flux core-jet outflow. Figure 3.5 shows the variation of flux in radio (correlated) and hard X-ray (anti-correlated) with soft X-ray flux during the low-hard state (region 4 of Figure 3.4), which clearly demonstrates the simple monotonic dependence of the both with the soft X-ray (ASM) during the few hundred days when the source was in this state. This result vindicates the study of McCollough et al. (1999) and (Watanabe et al. 1994). The positive correlation between the soft X-ray and the radio flux, during the (low) hard state is the strongest seen in such systems. The strong and significant anti-correlation between the hard X-ray and both soft X-ray as well as radio is also a unique feature not reported before for any other binary microquasar system. A detailed spectral analysis to investigate the apparently contradictory results of the radio – X-ray correlation (soft and hard) was the next necessary step needed to probe the disc - jet connection in the system.

3.5. X-ray spectral pivoting in the low (hard) state

63

Fig. 3.5: The variation of flux in radio (GBI, 2.2 GHz, shown as stars) and hard X-ray (BATSE, 20-100 keV, shown as circles) with soft X-ray (ASM, 2-10 keV), during the low-hard state of Cygnus X-3 (region 4 of Figure 3.4). Each data point is an average value for 10 days.

3.5 X-ray spectral pivoting in the low (hard) state Most observations of Cygnus X-3 by RXTE are done in the high (soft) state, with the aim of studying the X-ray spectra during the radio flaring episodes. In the low (hard) state, there are about ten indpendent observations, during this period of simultaneous monitoring (shown in the top panel of Figure 3.4), or otherwise, comprising three major group of separated observations. We present the X-ray spectra of three such observations that span the range of observed X-ray and radio fluxes within the precincts of the low (as well as hard) state. In Figure 3.6 the three unfolded spectra are overlaid on the top panel with the PHA ratios for the two extreme spectra shown in the bottom panel. Some salient features of these spectra are given in table 3.4. As explained in the previous section, during the low-hard state, encompassing the regions 3 & 4 of Figure 3.4, the continuum spectra (5 – 150 keV) is best described by the Comptonization of seed photons from a thermal multi-coloured accretion disk by a thermal Comptonizing plasma cloud (CompST - Sunyaev and Titarchuk 1980, Nakamura et al. 1993, Rajeev et al. 1994) along with a non-thermal powerlaw emission (Choudhury and Rao 2002, Choudhury et al. 2002). The iron lines and absorption edges are fit by following the recipe expounded in the pre-

Chapter 3. Cygnus X-3: spectral studies

64

Fig. 3.6: Top panel: The unfolded X-ray spectra of Cygnus X-3 during the radio quiescent period on three different occasions (1: MJD 50954; 2: MJD 50661; 3: MJD 50717). Bottom panel: PHA ratio of spectra from the extreme observations.

L vious section. The best fit values of the electron temperature (kT ) of the Compton cloud and the powerlaw photon index ( » ) for the three spectra are given in Table 3.4. Other simple models like cutoff powerlaw (along with a powerlaw), broken power-law, etc. do not consistently fit all the observed spectra with physically feasible parameter values and give much inferior fits. It can be seen from the figure that there is a systematic change in the shape of the spectrum with increasing soft X-ray flux (and radio flux, see Table 3.4). The X-ray spectrum, when the radio flux is low, is quite flat in the 20 – 40 keV region and the spectral curvature increases with the soft X-ray flux. The spectral evolution, during the (low) hard state can be clearly intrepreted as a pivotal behaviour correlated to the radio emission, with the pivot point lying in the energy range 10 – 20 keV. The total flux in the wide energy band (5-60 keV) in X-ray remains constant, the increase in soft X-ray (5-12.5 keV) is at the expense of corresponding decrease in the hard X-ray (12.5-60 keV) flux (Table 2). Thus, in the low-hard state, the following picture emerges: 1) the physical process causing the soft X-ray emission, generally attributed to the accretion phenomenon (inflow of matter), is the causal factor determining the resultant flux of radio emission (outflow of matter), 2) the radio emission is coming from a rather weak jet (outflow), embedded inside the thermal plasma cloud

%

3.6. X-ray spectral evolution driving the radio flares: high (soft) state

65

Table 3.4: The observed flux and X-ray spectral parameters of Cygnus X-3 during the three pointed RXTE observations.

50717

MJD 50661

50954

A.Flux ASM (cts s l ˜ ) : 11.11 8.18 BATSE (ph cm l È l ˜ ) 0.038 0.051 GBI-2.2GHz (mJy) 115 64 GBI-8.3GHz (mJy) 165 73 B. LBest fit parameters for CompST+power law
kT (keV) 5.09  Š . 4.37  Š  » 2.55 2.19  Š ,  Š (( :3 (d.o.f.) 0.74(86) 1.80(59)



%

D

D

D

D

+

5.37 0.058 43 53

D


4.87  Š  2.01  Š  1.42(108)

D

+

whose opacity determines the amount of radio flux coming out, 3) the physical processes giving rise to soft and hard X-ray emissions are competing with each other, resulting in the anti-correlation. The decreasing opacity of the thermal Comptonizing plasma cloud plays a major role in the X-ray state transition from low-hard to the high-soft state (Rajeev et al. 1994), with a corresponding change in the radio emission. Here we show that it plays a similar role in a very small scale of change within the precincts of the low-hard state. Such a pivoting behaviour, with the soft X-ray flux correlated to the radio emission and the corresponding hard X-ray flux anti-correlated to the soft X-ray flux as well as radio emission, had not been reported for any microquasar system. This unique observational feature provides a unique insight into disc - jet connection in such binary systems. This establishes, with an aura of definiteness, the close connection between the physical mechanisms that give rise to the accretion and ejection phenomena. This result will be generalised for other prominent Galactic microquasar systems in chaper 5 and a phenemenological interpretation will be attempted in chapter 6. In the following section, we continue the study of the long term X-ray spectral evolution, correlated to the radio emission, in the (high) soft state.

Chapter 3. Cygnus X-3: spectral studies

66

Fig. 3.7: The soft X-ray (RXTE–ASM, 2-12 kev) and radio (GBI, 2.2GHz) monitoring of the source during the X-ray high state. The days for which the X-ray spectra obtained from the pointed observations using RXTE–PCA are reported here are indicated by arrows. The insets in the two right hand panels highlight the minor flares. The colour of the pointed arrow denotes the particular phase of the X-ray spectra, as observed by the RXTE–PCA. The colour scheme is as follows: purple radio quiescent phase, pink pre-radio flare & orange post-radio flare.

R

R

R

3.6. X-ray spectral evolution driving the radio flares: high (soft) state

67

3.6 X-ray spectral evolution driving the radio flares: high (soft) state The Spearman’s Partial Rank Correlation test doesn’t reveal any appreciable correlation between the radio and the high energy emissions in the (high) soft state, compared to the very strong and significant results in the (low) hard states. The chief reason for this is perhaps two-fold, 1) the dynamical time scale of the variability in this state is faster than a few days, 2) and more importantly this state incorporates more complex evolution, which includes the major radio flares preceded by quenched radio emission, with the X-ray spectral evolution deviating from the linear monotonic pivotal behaviour. Hence the only procedure available to monitor the radio – X-ray association is to study the spectral evolution from the pointed observations from RXTE–PCA along with the daily monitoring in the radio band by GBI. Scouting through the complete date set of observations made by RXTE–PCA of Cygnus X-3, during the period when RXTE and GBI were serendipitously monitoring the source, we found four episodes of radio flaring, minor as well as major, well covered in the X-ray regime. These episodes are depicted in Figure 3.7, with the arrows depicting the days of RXTE–PCA observation analysed and reported here. The X-ray spectra in this state is generally dominated by the thermal multicoloured disc black body component, along with a hard component best described by a thermal COmptonizing model, viz. CompST model Sunyaev and Titarchuk (1980), except for the post flare phase, when the spectral shape hardens in the soft X-ray region, and the spectral components that fit the spectra best in this phase is the combination of CompST and power law, identical to the (low) hard state, although the spectral state remains in the high state. The X-ray spectra may be classified into three phases:The radio quiescent phase. The X-ray spectra has a strong disk black body and an equally strong Comptonising component. Pre-radio flare. The Comptonising component becomes very small (near vanishing), resulting in a flare. The flare may result in a time scale of a day or less (minor ones). Post-radio flare. The succession of radio flares, both minor as well as major, is stopped by the change in the X-ray spectrum, with the spectral shape hardening in the soft X-ray region. During this phase the disk black body component becomes insignificant, the spectral shape is explained by the similar combination of nonthermal components, viz. CompST and power law.

Chapter 3. Cygnus X-3: spectral studies

68

The above classification is done by comparing the relative flux of the individual model components viz., disc black body and CompST, the identification of the post-radio flare phase is easily achieved by the disappearance of the disck black body component and its replacement by the powerlaw component (table 3.5). In Figure 3.7 the colour of the pointed arrow denotes the particular phase of the X-ray spectra, as observed by the RXTE–PCA. The colour scheme is as follows: purple D radio quiescent phase, pink D pre-radio flare & orange D post-radio flare. In Figure 3.8, the same colour represents the total spectrum in the corresponding phase, with the individual components of the spectra fowllows the following convention: green D disc blackbody, blue D CompST and red D powerlaw. The evolution of the X-ray spectra during the each individual flaring episodes, as covered by the RXTE pointed observations are as follows:$ MJD 50490 – 50510. There are essentially two independent X-ray pointing during this flare; on MJD 50495, the spectra is in the post-radio flare phase, with the CompST and the powerlaw component. On MJD 50500 the X-ray spectra is in the phase of the quiescent phase, with the disc black body reappearing (although it contributes only 25% of the toal flux, see table 3.5) in place od the powerlaw. There aren’t any X-ray observation during this episode, although the source exhibits minor radio flares after a few days. $ MJD 50600 – 50650. There are ten X-ray pointings during this episode, and we present the spectra of three such occasions, which are adequate to elucidate the spectral evolution. On MJD 50604 the spectra, described by disc black body & CompST, has only 10% of Comptonizing component and susequently there is a minor radio flare ( µ  mJy) the following day, followed by loud radio flares
( . Š Jy) after about six days. This state of depleted Comptonizing component persists with the reoccurance of the minor and major flares, for eg. on MJD 50624 the Comptonizing component has only 15% contribution, and the next day there is a minor flare ( µ  mJy). This succession of the flaring episodes come to a rest after the disc black body component vanishes (MJD 50632) and replaced by a powerlaw. The spectral components are identicial to those of the (low) hard state, albeit with high soft X-ray flux, and the source subsequently comes down to the (low) hard state, with the corresponding pattern of radio emission.

+

+

$ MJD 51580 – 51590. During this episode of mnor flaring, four X-ray spectra are enough to bring forth the pattern vanishing Comptonizing flux preceding a flare. On MJD 51586 the CompST component contributes  + to the total flux, and
within the span of a day there is a minor radio flare ( /  mJy), which subsides

3.6. X-ray spectral evolution driving the radio flares: high (soft) state

69

Fig. 3.8: The X-ray spectral energy distribution (SED) and the individual continuum components, during the radio quiescent, pre-radio flare & post-radio flare phases. The quiescent phase has disk black body and Comptonising component at near equal ratio, the pre-radio flare has vanishingly small Comptonising component, and the post-radio flare has the disk black body component replaced by a simple power law. The colour coding of the total spectra and their components are as follows: Total spectra purple radio quiescent phase, pink pre-radio flare & orange post-radio flare; individgreen disc blackbody, blue CompST and red ual continuum components powerlaw.

R

S

R

R

R

R

S

R

Chapter 3. Cygnus X-3: spectral studies

70

Table 3.5: Model parameters of the continuum components and their flux contributions of the X-ray SED Quiescent Radio Emission Disk Black Body % of Total Flux 24.05 51.51 72.55

û éëê (keV) Total Flux 6.6 1.53 V 6.9 1.55 5.3 1.56 4.5 1.53 3.6 1.63 5.8 1.70 Post-Radio Flare

Flux 6.0 5.9 4.4 3.8 3.3 5.0

Disk Black Body % of Total Flux 90.91 85.51 83.02 84.44 91.67 86.21

Total Flux 8.5 V 9.9 7.9

Flux 4.2 4.0 2.7

Power law % of Total Flux 49.41 40.40 34.18

Total Flux 7.9 V 6.6 5.1

MJD 50604 50624 51586 51589 51646 51650

MJD 50495 50632 51676

(keV) 1.8 1.44 1.42 Pre-Radio Flare

T

X

V

'W0X0Y0Z\[]_^še [¯e

units: ¨ e

V

T û éëê

Flux 1.9 3.4 3.7

MJD 50500 51587 51588

2.43 2.62 2.62

T ûSü (keV) 23.93 13.39 21.69

U

2.22 1.59 1.39

T û ü (keV) 18.27 18.34 42.31 53.53 54.33 80.79

T û ü (keV) 4.03 5.12 6.18

U

4.07 3.31 3.41 2.40 2.53 9.91

U

8.12 7.05 6.36

Flux 6.0 3.2 1.4

CompST % of Total Flux 75.95 48.49 27.45

Flux 0.6 1.0 0.9 0.7 0.3 0.8

CompST % of Total Flux 9.09 14.49 16.98 15.56 8.33 13.79

Flux 4.3 5.9 5.2

CompST % of Total Flux 50.59 59.60 65.82

V quickly and on MJD 51587 the disc black body and the Comptonizing components are equally strong, with the disc blackbody component gaining strength on the next day (MJD 51588) with 75% of the flux. Continuing the trend of the disappearing of the Comptonizing cloud, on MJD 51589 the Comptonizing flux is only £ !,+ ,
and on MJD 51590 there is a minor flare (  mJy). This episode shows that a minor flare is brought about after the CompST flux gets to £ !,+ or lower. $ MJD 51630 – 51680. During this episode of minor flares ( I mJy) intermixed with huge radio flares ( !. Jy), we show that on MJD 51646 and 51650 the
Comptonising components are + and „ + , with the minor flares occuring nearly throughout this whole episodes, followed by the huge radio flare on MJD 51652. The sampling of the radio monitoring is sparse here, but trend of the data shows convincingly that the radio flares subside after the disc black body component vanishes in the X-ray spectra, replaced by the powerlaw.

+

The general picture of the X-ray spectral characteristics in the radio flaring states can

3.7. Complete X-ray spectral evolution

71

be summed up as follows:1. The radio quiescent emission is marked by the radio emission (2.2 GHz) bordering around 110 mJy and below. The X-ray spectra has strong CompST component with the contributing flux of this component amounting (,+€ ,+ of the total flux. 2. The vanishing of the CompST component (flux going below 15%) always pre
cedes a minor flare, with the radio flux around œ !W  mJy, suggesting the ejection of the central Compton cloud resulting in the flare. The stronger the ejection, the louder the flare. 3. The minor flare may be followed by the filling of the central Compton cloud, i.e. increase in CompST flux, causing the radio emission to become quiescent. Otherwise, if the continuous accretion persists with the central cloud unfilled, i.e. the CompST flux remains low, a major radio flare (2.2 GHz, flux -I  ) follows.

a`

4. The continuing series of minor and major flares come to an end only with the change in the X-ray spectra, i.e. hardening of the soft X-ray band, with the flux level remaining high. This is the most interesting state of the X-ray spectra with the shape being best fit by the model of the low (correspondingly hard) state, i.e. power law and CompST, although the soft X-ray flux remains high. This change in the X-ray spectra puts a brake in the episodes of radio flaring.

3.7 Complete X-ray spectral evolution We report here the complete X-ray spectral evolution of the microquasar Cygnus X3, associated to the radio emission, for the first time for this source. The (low) hard state is best characterised by a non-relativistic thermal Comptonizing component, along with an additional (non thermal) powerlaw component. The radio emission increases monotonically with the increasing soft X-ray flux, anti-correlated to the hard X-ray flux, which is beautifully elucidated by the pivoting in the spectra. The absence of a clear black body component in this state may be attributed to the obsecuring of the source by the circumstellar material. After the state transition into the (high) soft state, the disc black body component becomes prominent, and the spectra in this state is normally characterized by a multicoloured disc black body and CompST (Sunyaev and Titarchuk 1980). The Comptonizing component, characterised by the CompST model, becomes negligibly small preceding a minor radio flare, and on persistance of this state a major radio flare follows. The succession of the flares are put to stop by the vanishing of

72

Chapter 3. Cygnus X-3: spectral studies

the disc black body component, which is replaced by the powerlaw component. The system, at this phase may continue to remain in the ‘high’ state with the disc black body reappearing, or it may susequently transit to the ‘low’ hard state.

Chapter 4 Cygnus X-3: temporal studies

The study of the temporal behavioural pattern of X-ray sources consists of mainly two broad classes, the long term variability which are normally studied by monitoring devices viz. ASM aboard the RXTE, and the short term variability studied by the pointed observations. The long term behavioural pattern of the X-ray variability has been explained to the complete detail (given the observational capabilities of the current generation X-ray detecting instruments) in the last chapter. In this chapter we will first review the long term properties of Cygnus X-3 after performing the correction due to binary orbital modulation of the X-ray emission, thereafter we will discuss the short term variability properties of the X-ray emission from this source.

4.1 Binary modulation and correction with a given ephemeris The X-ray source Cygnus X-3 was detected to be a binary system within a few years of its discovery. The binary modulation is seen in the X-ray (Parsignault et al. 1972, Sandford and Hawkins 1972) and the infra-red bands (Becklin et al. 1973). The evolution of the 4.8 hour binary period of Cygnus X-3 has been studied extensively with the time derivative ( Á ) measured to be 10 lr (van der Klis and Bonnet-Bidaud 1981, 1982, ¸ 1989, Molnar 1988, Kitamoto et al. 1987). Recently, Singh et al. (2002) have extended the data base of the binary period measurements using the The Indian X-ray Astronomy Experiment (IXAE)and archival data from ROSAT, ASCA, BeppoSAX and RXTE. They found that the binary template obtained from the EXOSATdata adequately explains the recent observations and have derived a value of the period derivative of 5.76 0.24 10 l ˜ . Inclusion of second derivative marginally improved the fit, essentially giving

D



73

Chapter 4. Cygnus X-3: temporal studies

74

D

b

an upper limit to the second derivative ( = -1.3 1.6 10 l ˜Ì˜ yr l ˜ ). In order to note ¸ the applicability of the binary correction with the given ephemeris, we have folded the RXTE–ASM data using the quadratic ephemeris of Singh et al. (2002) from MJD 50410 to MJD 51400 (P = 0.19968443 d; Á = 5.76 10 l ˜ ; time of zero phase T = 2440949.892 ¸ JD). The time span chosen for the folding corresponds to the data used by Choudhury et al. (2002) for the detailed X-ray, radio and hard X-ray correlation analysis. The folded light curve is shown in Figure 4.1 (the errors in the data points are smaller than the symbol size). The template data from the EXOSATobservations (van der Klis and BonnetBidaud 1989) is also shown in Figure 4.1, after appropriate scaling. The relative phase of the data and template are not arbitrarily shifted for a proper match: the folded light curve (with the above ephemeris) is overlaid with the vertically shifted and scaled template data. The folded count rate correlates with the template value with a correlation coefficient of 0.95 (for 64 data points). It can be seen from the figure that there are nonstatistical variations due to the source over and above the binary variation. The ASM count rate, C, can be expressed as



7£  Š  D  Š c

y

. Š1 .



D

ed

 Š .

(4.1)

where V is the template value for a given ~ phase as given in van der Klis and BonnetBidaud (1989). The errors are nominal 1 errors obtained by assuming that the fluctuations in each phase bin is random in nature. During this period, Cygnus X-3 shows several X-ray flares and also transition between low-hard to high-soft states (see Figures 3.3 and 3.8). Considering the large variation of the X-ray flux during the period covered, the folded light curve agrees with the template quite well. We have examined the fluctuations in the source counts over and above the binary variations with respect to binary phase as well as the observation duration. Though there is some evidence for large flare like variations during the phase 0.2 to 0.5, the rest of the fluctuations occur throughout without any association with binary phase or time of observations. Note also that we have not done any phase fitting for this analysis. Hence we conclude that the error in the phase of light curve minimum is negligible compared to the overall source fluctuations. Using this information, we can correct each observation for the binary modulation, qs as follows. The quadratic ephemeris to get the zero phase for the < cycle of the period is given as (Singh et al. 2002):

where c = : ˜ ¸

 ¸

4 ñ

7

4

 y

¸

 qzy

; q :

(4.2)

Á . This equation can be inverted to give the binary phase at any time T

4.1. Binary modulation and correction with a given ephemeris

75

Fig. 4.1: The X-ray light curve of Cygnus X-3 obtained from RXTE–ASM for the period of MJD 50410 to 51400 folded at the quadratic ephemeris given by Singh et al. (2002). The template data obtained from EXOSAT(van der Klis and Bonnet-Bidaud 1989) is also shown, with appropriate scaling for the count rates.

as, q 7

54

³4



 

54

‚4

Q

:;

(4.3)

¸ ¸ For the RXTE–ASM data, we have calculated the phase using equation 4.3 and from the corresponding template value, corrected for the linear term in equation 4.1. The binary corrected ASM data is again folded and the folded light curve is shown in Figure 4.2. It can be seen from the figure that for the long term monitoring data a quadratic ephemeris can explain the modulation quite well and this ephemeris may be used to correct the data for the binary variation. However, we caution, that despite the stable profile with a monotonic change in its period for several years, Cygnus X-3 may show jitters in the individual binary phase measurements (see Singh et al. 2002). This implies that either (a) there is an inherent jitter in the minimum of the binary phase or b) it has a stable profile and short term variability is superimposed on it. We have made the binary correction for the subsequent analysis assuming that Cygnus X-3 has a stable profile. The implication of the possible random phase jitter is examined at appropriate places, if required. We have applied the binary correction to the individual RXTE–PCA observations and in Figure 4.3 we show both the uncorrected (top panel) and corrected (bottom panel)

Chapter 4. Cygnus X-3: temporal studies

76

Fig. 4.2: The X-ray light curve of Cygnus X-3 obtained from RXTE–ASM for the period of MJD 50410 to 51400 folded at a binary period of 4.8 hours after the correction for the quadratic ephemeris given by Singh et al. (2002).

lightcurve of the single longest observation (Obs. Id. 10126-01-01-020 & 10126-0101-02) of the source by RXTE. The observation covers about two and a half binary cycles, punctuated by the necessary breaks due to Earth occultation and various other data dropouts. The lightcurve is obtained from single bit data (2–6.5 keV) with all the five PCUs on. The binary template (Figure 4.1) is asymmetric with an unusually broad peak lasting in the € Š Ã Š phase of the binary period with a gradual rise before and a steep fall after the peak. It is evident that the correction for binary modulation is very good for the rising and falling phase of the binary ephemeris, highlighting the small variations which were otherwise smothered by the binary modulation. Again we emphasize here that we have not done any fitting for deriving the zero phase, but have used the quadratic ephemeris to derive it. During the peak the lightcurve shows fluctuations not correctable by the smooth peak of the template. This, generally random, fluctuation is an inherent feature of the source present in all the observations, past and present (see van der Klis & Bonnet-Bidaud van der Klis and Bonnet-Bidaud (1982, 1989). Perhaps, one of the most noteworthy features of Cygnus X-3 is that the binary period has remained consistent for more than 25 years with a linear decay with no second derivative of the period (Singh et al. 2002). The relative phasing of the X-ray and infra-

+

4.1. Binary modulation and correction with a given ephemeris

77

Fig. 4.3: The X-ray light curve of Cygnus X-3 obtained from RXTE–PCA pointed observations (top panel), shown along with light curve (bottom panel) corrected for the binary variation using the quadratic ephemeris given Singh et al. (2002).

red emissions from this source, coupled by the orbital evolution of the line shift of the He I emission lines, gives the picture that the binary modulation is due to the orbital motion of the ionized two temperature wind originating in the companion Wolf-Rayet star irradiated by the X-rays from the compact object (van Kerkwijk 1993). The minimum occurs when the cooler part of the wind in the shadow of the Wolf-Rayet companion is in the line of sight of the observer with the compact object at the superior conjunction. The asymmetry in the binary modulation profile may be due to 1) eccentricity in the binary orbit, and/or 2) asymmetric distribution of matter within the system (Elsner et al. 1980). Given the fact that both the binary period and the template have remained consistent for a period of 25 years, the presence of any reasonable apsidal motion (Ghosh et al. 1981) may be ruled out (van der Klis and Bonnet-Bidaud 1989). Hence, eccentricity, if present in the binary orbit, is negligible to effect any asymmetry in the lightcurve. Therefore it is more likely that an asymmetric distribution of matter, causing an asymmetric distribution of optical depth, introduces the asymmetry in the binary template. In this scenario the orbital period decay is explained by the loss of angular momentum via the wind from the Wolf-Rayet companion. Since the early days of its observation, it is believed that in this source the X-ray

78

Chapter 4. Cygnus X-3: temporal studies

emission is extensively reprocessed, either in the stellar wind (Davidsen and Ostriker 1974, Hertz et al. 1978, Becker et al. 1978) or in a cocoon (X-ray halo) surrounding and extending beyond the binary system (Milgrom 1976, Predehl et al. 2000). There also exist models of X-ray reprocessing in the accretion disk corona (White and Holt 1982, Molnar and Mauche 1986) where the low energy photons are upscattered by Comptonization also producing fluorescence of ionized iron (Rajeev et al. 1994). Nakamura et al. (1993) explain the X-ray spectra as obtained by the GINGA observatory by proposing the presence of three species of ionized gas, fully ionized, almost fully ionized and nearly ionized, engulfing the binary system. Fender et al. (1999a) suggest a WR type wind with the geometry of a disc in the binary plane with a size much bigger than the binary system to be the origin of the binary modulated He emission lines (obtained from infra-red spectra). This wind originates from the companion which is a WN type WolfRayet star. Polarimetric study of the K-band lightcurve also suggests a preferential plane of scattering. In this model the X-ray emission undergoes scattering in this disc-like two temperature wind (van Kerkwijk 1993), resulting in the asymmetry in the binary template. The residue of the (binary) folded lightcurve Figure 4.2 may be attributed to the long term variation of the X-ray emission by virtue of the change in wind and/or cocoon mass distribution, including various state changes from soft (and high) to low (and hard) and vice-versa, accompanied by the correlated radio flares. One small aspect not considered so far is the generally random fluctuation in the X-ray lightcurve at the peak of the binary ephemeris. A very detailed analysis of the nature of this fluctuation may help in determining the geometrical and physical structure of the accreting system involving the wind from the companion and the X-ray halo (Predehl et al. 2000) engulfing the system. Recently, Stark and Saia (2003) have attempted to constrain the binary orbital parameters by measuring the line shift of Helium & line of Fe XXV and Lyman & lines of Si XIV and S XVI as a function of the orbital phase. By ascribing the Fe line to originate very close to the compact object surface and the Si and S line to originate from the wind from the companion, they constrain the masses of the companion and the compact object to be µ 7.3  and µ 3.6  , respectively, provided the orbital inclination is small (i=24 ¶ - this agrees with the limit 0-40 ¶ of Fender et al. 1999a). The phase resolved spectra of the various iron emission lines (6.4 keV, 6.7 keV & 6.9 keV) and the absorption edges (7.1 kev & 9.1 keV) during the both (low) hard and (high) soft states may provide better constraints on the origin of the iron emission lines. The binary modulation of the emission lines reported by Stark and Saia (2003) need to be fit properly with the binary template (Singh et al. 2002) to obtain a more definitive mass function of the system. A long continuous X-ray observation of the source spanning a few orbital periods with very

4.2. Radio X-ray correlation of Cygnus X-3

79

high resolution X-ray spectra will provide a better binary profile which is essential for constraining the binary parameters and obtaining the geometrical and physical structure of the system. Given the consistency of the binary orbital modulation template of the X-ray emission as obtained from the EXOSATobservations (van der Klis and Bonnet-Bidaud 1989) for over a( years, we employ this template for the correction of the modulation of Xray emission using the ephemeris of Singh et al. (2002) for the timing studies presented in the following sections.

4.2 Radio X-ray correlation of Cygnus X-3 Cygnus X-3 possesses a binary orbital period of 4.8 hours, therefore statistical inference gleaned from daily averaged monitoring data, which covers five orbital periods, should sufficiently be independent of any effects of binary modulation. Nevertheless, in order to establish the correlation result presented in chapter 3 (where the SRC coefficient reported was obtained from ten days averaged flux, covering fifty binary orbits), we repeated the SRC test for the binary corrected X-ray emission (Choudhury et al. 2004). The correlation coefficient and other parameters (Choudhury et al. 2002, 2003) are given in table 4.1 for integration time of data points ranging from 1 to 15 days. The nullhypothesis probability, as a function of bin size, is plotted in Figure 4.4 where it appears that the correlation becomes stronger for smaller bin sizes due to increase in the number of degrees of freedom. Hence, evidently, both from table 2 and Figure 4.4, the correlation time scale is shorter than one day, which is not surprising because for a binary period of 4.8 hours the possible time scales which can come into play, viz. the viscous time scale of the accretion disc, the variability time scale of the accretion disc corona, and the time scale for variation of the jet emission must be smaller than a day. Correlation between soft X-ray and radio emission has been noted in many black hole binary sources (Gallo et al. 2002) and finding similar correlation in Cygnus X-3 (Choudhury et al. 2002) firmly puts Cygnus X-3 as a good candidate for harboring a black hole. Choudhury et al. (2003) point out that correlation between the X-ray and radio emission and the anti-correlation between the soft and hard X-rays are directly related to a causal connection between the spectral shape in the X-rays and the radio emission. By correcting the X-ray light curve for the binary variations, we have shown that the correlation time scale is shorter than a day (Table 4.1 & Figure 4.4). Therefore it is necessary to analyze the pointed continuous observation in the X-ray wide-band in order to determine the dynamic time scale of soft and hard X-ray emission. This will enable us to understand the detailed structure of the accretion disk, and is the focus of

GBI(2.2GHz):BATSE

h

80

D Parameter A:G A:B G:B 17.94 -7.31 -4.37 13.83 -6.38 -3.22 11.15 -6.11 -3.08 9.62 -6.26 -2.17 8.73 -4.64 -3.11 8.54 -4.75 -2.32 7.18 -5.32 -2.06 6.80 -4.60 -2.25 5.27 -6.05 -1.74 6.17 -5.12 -1.19 4.33 -6.26 -1.46 5.09 -4.25 -2.26 5.54 -4.26 -1.13 4.90 -4.33 -1.61

g

h

ASM:BATSE;

Null-hypothesis Probability A:B G:B .28 .68 .15 .49 .13 .12 .12 .27 .23 .79 .41 .20 .19 .25 .62 .17 .16 .15 .56 .99 .19 .76 .33 .19 .74 .31 .70 .19

f

g

f

ASM:GBI(2.2GHz);

A:G .10 .10 .10 .36 .28 .49 .50 .63 .95 .26 .20 .88 .24 .63

r o n p s t q r n m h k l m g k l m l m f k l m f k l m f k l m f k l m f k l m f k l m fh k l m fh k l m f k l m f k l m fh k l k g h j j j j j j j j j j j j j s p o p n t no o p r emkl emhkl 'mgkl cmgkl emgfkl emgfkl cmgfkl mcf kl emgfkl mcf kl cmgkl cmfkl cmfkl cmfkl g j j j j j j j j j j j j j j no no no emkl emkl 'mkl cmq l eml eml cmq l mcn l emo l mco l cmq l cmo l cmq l cmp l h k gh k fh k g k g k g k g k f k g k f k f k f ji ji ji j j j j j j j j j j j

Spearman Rank Corr. Coeff. A:G A:B G:B 0.70 -0.50 -0.45 0.73 -0.57 -0.51 0.76 -0.64 -0.58 0.77 -0.68 -0.60 0.79 -0.69 -0.66 0.82 -0.73 -0.68 0.82 -0.77 -0.70 0.83 -0.77 -0.72 0.81 -0.83 -0.74 0.84 -0.82 -0.73 0.81 -0.86 -0.75 0.87 -0.86 -0.82 0.85 -0.81 -0.74 0.89 -0.87 -0.82

h

No. of points 638 356 246 186 149 125 108 94 84 75 69 63 58 54

g

Bin Size (days) 1 2 3 4 5 6 7 8 9 10 11 12 13 14

f

Chapter 4. Cygnus X-3: temporal studies

Table 4.1: The Spearman Rank Correlation coefficient, the null-hypothesis probability for no correlation and the D-parameter for the effect of the third parameter, among the radio (GBI), soft X-ray (ASM) and hard X-ray (BAT) emission of Cygnus X-3, in the low-hard state with the observed flux averaged for various bin sizes.

4.3. Power Density Spectrum (PDS)

81

Fig. 4.4: The null-hypothesis probability for not having a correlation between the soft X-ray (ASM), radio (GBI) and hard X-ray (BATSE) emissions in Cygnus X-3 for various bin sizes of integration. The first three points in the top panel denote the upper limits.

our future work. A simultaneous radio observation will be imperative in understanding the detailed mechanism of the disk jet connection in the system, which will provide a quantitative estimate of the extent of jet power being emitted in the X-ray band.

4.3 Power Density Spectrum (PDS) X-ray binaries are the cosmic sources which display the smallest scale of temporal variability in the high energy regime. The fastest variability scale is of the order of milliseconds (for a review see van der Klis 2000). These objects emit X-ray photons at a Q very large rate (say,  x photons/sec), of which only a small fraction (say, Ý € rl x ) is detectable by our instruments. Hence, event hough the photon production rate at the 2 s series of source site may be considered a continuous function of time   , the time J s ¿ !  photon arrival times may be expressed in a discrete form 7

Š Š Š [ n  ¶  (with J ð !  the total number of detected photons), which should be [ ideally [available for analn ¶ ysis. However, the maximum telemetry rate of the instruments limit the registration and transmission of all these arrival times. Therefore, the data are binned into equidistant time bins, onboard the satellite observatories. The finally telemetered information con-

u

Chapter 4. Cygnus X-3: temporal studies

82

J J P 7k    , where   is the total number sists of a sequence of numbers u Š Š Š ¶ ¶  [ [ [ of time bins, u represents the number of photons detected during the time bin P . Usu ally the time bins are equidistant and contiguous. The aim is to reconstruct as much as 2 s possible about   from the measured u .  For standard analysis, the rate of background photons is considered negligible, as it is not supposed to vary strongly on the rapid time scales considered of interest, and these variations are uncorrelated to the fluctuations of the source object. If the source doesn’t s vary intrinsically, the will be to a high degree of precision randomly distributed. , ð @ so that the~ u : follow Poisson statistics appropriate to a rate ¬7 u , with a standard  deviation å 7 . õ The standard approach (seeJ van der Klis 1997) is to divide the time series into  J @ u  each, (so that, ideally equal-length J J time segments of time bins [ Fm7I [ Š Š Š [   7I ), in order to calculate the Fourier transform of each segment: ¶

 wv x

y

5'z |{ l ˜ u @ = ;: } z @ > ð { @" | 

~

7k

J

[ Š Š Š [



(

(4.4) [

in order to convert this into a power spectrum for each segment

z

¸

|

5 ( € 5 z: 

~

7k

[ Š Š Š [ |

J 

(

(4.5)

[

5  ‚ "| { 

J @ l u @  , the number ˜ 7 and then to average these power spectra. Here n of photons detected in the segment. With this power spectral normalization (Leahy et al. @ follow 1983),: if the u are distributed according to the Poisson distribution, then the ¸ the distribution ~with 2 degrees of freedom (constituting of ‘noise’ and ‘signal’), so that 79( and 79( . This white noise component with mean level 2 and stan¸ dard deviation 2, induced in the power spectrum, due to Poisson fluctuations in the time series, is called ‘Poisson level’, which can be considered as “background” in the power spectrum, against which other power spectral features caused by the intrinsic variability in the source are observed. In XRONOS (XANADU - LHEASOFT) terminology this particular normalization of the power spectra is known as d/f normalization. The physical dimension of the thus defined powers is the same as that of the time @ series: 7 7 u . The physical interpretation of the in terms of properties of ¸ ¸ the source are inconvenient. Therefore, in recent times, a more evolved power spectral | normalization has become popular , where J where the powers are reported as ¸   D the “count rate”, i.e. 7 4 , where 4 is the duration of the segment. The n  are dimensionless and can be interpreted as estimates of the power density   near 8

 z v x

Š

‡

z

„ƒ†…

z†ˆ

5'z ˆ ˆ ‰‡ ‚‡

z

Š

 z

z

cŠ z  z 

4.3. Power Density Spectrum (PDS)

z

83



~

| 4 , where   is a function of frequency whose integral gives the the frequency 8  8 fractional root-mean-square amplitude • of the variability. This • is defined as

•

Œ‹ { ˜  @"{ | l  ˜  u u |

@

 u 

Ž "ì dì

u |

J

{ l ˜ u @ |  @

(4.6) [

following directly from Parseval’s theorem. The fractional rms amplitude • : due to ˜ :  is given by fluctuations in the given frequency range  8 ˜ [÷8 3 X † • : 7Iâ 3   Š (4.7) ˜ 8 8





  can be interpreted as the functionV whose integral gives the square of the frac8 tional rms amplitude of the: variability in the original time series. The physical unit used for   is (rms/mean) /Hz, where ‘rms’ and ‘mean’ both refere to the time series; 8 “rms/mean” is just the dimensionless quantity • . The averaging of the power spectrum is usually performed both by averaging the individual power spectra (from different segments) together (averaging the ’s with the ¸ same from the  different segments), and by averaging powers at adjacent frequencies ¼  . The goal is to decrease the standard deviation of the power  ˜ [ ¸ ¸ · The calculation of the power spectra from segments provide the study of the estimates. evolution of the power spectrum with time. Thence, one may fit the various functional : shapes   to the power spectra using the minimization. To decipher any critical 8 component in the low frequency end, where large number of individual powers may not be available for the averaging, other fitting procedures may be applied (Papadakis and Lawrence 1993), although such methods are not generally applied. A number of nonFourier methods are also available for the temporal analysis (Deeter 1984, Deeter and Boynton 1982). The power spectral components seen in the X-ray binaries are usually broad (except for the sharp peak component for the pulsars). The very wide power distribution over typically several decades in frequency are called ‘noise’, while the localized broad peaks are called ‘quasi-periodic oscillations’ (see, for eg. van der Klis 1989). Further, the noise which has a high frequency cut-off or steepening towards high frequency are known as band limited noise, and may be classified into various classes depending on their cut-off frequency (van der Klis 1994). These power spectral components are assumed to be underlined variations which are stochastic in nature. Currently very fervent research is being carried all over to create a physical model to explain these PDS features.



z

z ~ z  ’‘ * )“ 0”†•



84

Chapter 4. Cygnus X-3: temporal studies

Fig. 4.5: Left panel: The power density spectrum of observation on MJD 50949–50950 (low and hard state) showing the monotonic power law behaviour of the red noise, with the spectrum merging with the back ground white noise at 0.1 Hz. Right panel: The power density spectrum of observation on MJD 50500–50501 showing the monotonic power law behaviour of the red noise, with the spectrum merging with the back ground white noise at 0.1 Hz.

4.3.1 Power Density Spectrum (PDS) of Cygnus X-3 From a historical perspective, the most commonplace study of the temporal properties of the source has concentrated on the binary modulation and its evolution. A detailed study of its variability characteristics as a function of frequency and comparison with other black hole candidate sources has not been attempted so far. van der Klis and Jansen (1985) report the detection of very low frequency regular oscillations during the rising phase of the binary and Rao et al. (1991) report regular oscillations in hard Xrays. Here we present the PDS for both (low)-hard and (high)-soft states of Cygnus X-3, after correcting for the binary variability (although the binary correction doesn’t have any significant consequence of the power density spectrum, except maybe in the low frequency regime). For the (low)-hard state we consider the set of six pointed observations (RXTE–PCA) between MJD 50949–50954, one pointing per day (Choudhury and Rao 2002), with the spectral pivoting correlated to the radio emission (Choudhury et al. 2002). Each individual pointing lasts for only about half a binary orbit ( *  x s) including a break of about 2000 s due to passage through SAA (see Figure 4.3), and hence there is not

4.3. Power Density Spectrum (PDS)

85

Fig. 4.6: Power Density Spectrum (PDS) of Cygnus X-3 for the RXTE–PCA pointed observations shown in Figure 4.3, after correcting for the binary variations. The PDS is generated separately for three regions of the binary phase namely the fall (phase 0.75 - 1.0 top panel), rise (phase 0 - 0.4 - middle panel) and the peak (phase 0.4 - 0.75 - bottom panel).

86

Chapter 4. Cygnus X-3: temporal studies

adequate coverage for generating a PDS. Therefore we provide the PDS of the combined lightcurve of the six days pointing (Obs. Ids.: 30082-04-01 – 30082-04-06) in Figure Q 4.5, left panel. The PDS has a flat spectra in the low frequency region, ) 3 Àl Ø , followed by a power law dependence till w Š Hz, but then the power merges with the white noise without any exponential cutoff. This feature of lack of significant power above 0.1–1 Hz is the most interesting aspect of the PDS of Cygnus X-3, and this feature is consistent with all the obtained PDS of the source from RXTE observations. As a contrast, in Figure 4.5, right panel, we present the PDS of four observations (Obs. Ids.: 20099-01-01-010,20099-01-01-01,20099-01-01-020,20099-01-01-02), spanning a total period little more than one day, combined together, with the source in the high, and correspondingly soft, state. The observation was carried out on MJD 50500–50501. The low frequency region shows more power as the amplitude of the binary modulation during this state is more pronounced in this state, and despite our correction for this, the modulation manifests itself in the PDS. The higher frequency region shows behaviour similar to that of the low state with the power hitting the deck of background white noise level at 0.1 Hz. To highlight the effect of binary correction on the PDS of this source, we again consider the longest continuous stretch of pointed observation of this source shown in Figure 4.3 (Observ. Id. 10126-01-01-020 & 10126-01-01-02, MJD 50322). Figure 4.6 shows the PDS after the binary correction. To explicitly demonstrate that the shape of residual variability is independent of binary phase, we show in Figure 4.6 the PDS’s separately for the falling part of the light curve (phase 0.75–1.0 - top panel), rising part of the light curve (phase 0–0.4 - middle panel), and the peak of the light curve (phase 0.4 –0.75 - bottom panel). Apart from the larger variability due to flares in the rising part Q (manifest as increased power below 10 l Hz), the shape of the PDS are similar for all the Q three cases. The power-law index in the frequency range 10 l Hz – 0.1 Hz is consistent with -1.5 and the total rms power is a few per cent. One of the remarkable feature of the light curve is the negligible power above 0.1 Hz, and this feature is observable in the PDS obtained from all the lightcurves, spanning both hard and soft states (Figure 4.7). In fact, as shown in Figure 4.7, the PDS show the same characteristic featureless powerlaw behaviour in all the states. : In all the PDS considered above, the spectra is represented in the units of (rms/mean) /Hz (eqs. 4.6,4.7). This is achieved by running the powspec program of the XRONOS package (LHEASOFT v5.2) with the normalization parameter = 2 (or -2).

4

PDS at low frequencies. Reig et al. (2002) have examined the aperiodic variability of two micro-quasars Cyg X-1 and GRS 1915+105 at very low frequencies using the

4.3. Power Density Spectrum (PDS)

87

Fig. 4.7: The PDS of Cygnus X-3 over a wide frequency range obtained using RXTE–ASM and RXTE–PCA at three observation periods.



RXTE–ASM dwell data. At frequencies below 10 l Hz it was found that the PDS is consistent with an index of -1 and the rms power below 10 l Hz is 21 – 27 %, for these two sources (Figure 4.10). Since we have argued that Cygnus X-3 is an archetypical black hole binary (see chapter 3) it is instructive to compare the PDS of Cygnus X-3 at very low frequencies. We have derived the PDS of Cyg X-3 at very low frequencies using RXTE–ASM data using a method similar to that followed by Reig et al. (2002). The results are given in Figure 4.7, along with the PDS obtained using the pointed observations of RXTE–PCA. It is found that below 5 › 10 l Hz, the power-law index is flatter (-0.97 0.17), consistent with that obtained for Cygnus X-1 and GRS 1915+105. The remarkable feature

P



D

88

Chapter 4. Cygnus X-3: temporal studies

Fig. 4.8: The three Power Density Spectra of Cygnus X-3 (reported in the previous section) with the normalization defined by eqs. 4.4 & 4.5, the d/f normalization of XRONOS package, such that the power of the background white noise level corresponds to the value of 2, provided the distribution obeys Poisson statistics.

of Cygnus X-3, however, is the low power - about 3.5% - in this frequency range. The flatter power law at low frequencies ( ) 10 l Hz) and the steeper power-law at higher Q frequencies ( - 10 l Hz) intercept at 10 l x Hz signifying a break in the power spectrum. Though there is a hump like feature at this frequency, we cannot rule out the influence of the binary period ( 10 l x Hz) on the shape of this hump. A long uninterrupted observation would be required to address this issue. The distinct feature of the power density spectra of the source is the shifting of the spectra towards low frequency regime (vis-a-vis the ‘normal’ frequency regime of other Galactic X-ray binaries), corresponding to very massive black hole systems (Hayashida et al. 1998, Czerny et al. 2001). To ascertain this fact we obtain the PDS using the nor-

4.3. Power Density Spectrum (PDS)

89

malization described by eqs. 4.4 and 4.5. This is achieved by running the powspec program of the XRONOS package (FTOOLS v5.2) with normalization parameter = 1 (or -1), the d/f normalization, such that the numerical value of the white noise is 2, provided the distribution obeys Poisson statistics. In Figure 4.8 we plot the three concerned PDS in the frequency range 1 – 50 Hz. It is visually evident that power is not discernible from the background white noise. Fitting a constant (dotted lines in Figure 4.8) for the three PDS we obtain the value of the mean power in this frequency range to be 1.99, 2.06 & 1.99 for MJD 50322, MJD 50949-50954 & MJD 50500-50501, respectively. These PDS are obtained without any correction for the dead time error. The PDS for frequency 9 l x Hz, i.e. the features preceding the power law decay, are not obtainable due to observational constraints of the RXTE–PCA, with the satellite having an orbital period of 96 minutes and it passes through the South Atlantic Anomaly in every orbit. Berger and van der Klis (1994) provide the PDS of this source from the EXOSATobservations, where the frequency dependence of the power in the region 0.05 – 1000 Hz is given. The overlap region of their PDS with the PDS obtained by us (from RXTE–PCA observations) are in agreement, and hence we reiterate that this behaviour is an inherent property of the source and not due to any instrumental or analysis procedural artifact. Sunyaev and Revnivtsev (2000) have compiled the power density spectra (multiplied by frequency) of the most common Galactic X-ray binaries, both neutron stars and black hole candidates (in their low/hard states) (Figure 4.9). The black hole binaries show, typically, a power law dependence with a positive index in the region of 0.01 – 1 Hz, flat spectra for the next decade of frequency range, followed by a power law decay (i.e. negative index) of power in the 10 –100 Hz. The PDS of the neutron stars is generally shifted towards the higher frequency region by an order of magnitude. From the PDS of Cygnus X-3 (Figure 4.6) it is quite apparent that, from the RXTE–PCA pointing observations, we are catching the power law decay portion of the PDS, shifted by a few decades in the lower frequency regime, with the power getting merged with the background white noise at 0.1 Hz. Due to improved continuous observational capabilities of RXTE it is possible to extend the PDS to the lower frequency regime ( Í l x Hz) and hence ascertain from the wide frequency band PDS that, in general, the power above 0.1 Hz is not discernible from the white noise. One may reconcile the absence of power in the high frequency regime to the scattering of the X-ray photons in the wind from the companion Wolf-Rayet star, reducing the amplitude of the fast X-ray variability (Berger and van der Klis 1994). If we reconcile the absence of power above 0.1 Hz to the reprocessing of the X-ray emission in the circumstellar environment, then this feature does provide an interesting sidelight to the paradigm which states that the variability time-scale scales linearly with the mass of the compact object (Hayashida et

90

Chapter 4. Cygnus X-3: temporal studies

Fig. 4.9: Broad band power spectra of X-ray binaries in the low spectral state. This figure is obtained from Sunyaev and Revnivtsev (2000).

4.4. Time lag between soft and hard X-rays

91

Fig. 4.10: Comparison of the ASM PDS of Cygnus X-1 & GRS 1915+105 with that observed at higher frequencies. The dashed lines represent the best fit model to the PDS of Cygnus X-1 at higher frequencies when the source is in the high-soft luminosity state. The dotted line represents the averaged PDS of Cygnus X-1 in the low-hard state. The figure is obtained from Reig et al. (2002).

al. 1998, Czerny et al. 2001), and introduce an additional factor, viz. reprocessing in the dense circumstellar material, where it exists, into the picture. It is also interesting that the PDS at very low frequencies have about an order of magnitude lower power compared to other black hole candidate sources Cygnus X-1 and GRS 1915+105 (Figure 4.10).

4.4 Time lag between soft and hard X-rays In section 4.2 it has been established that the time scale of (anti-)correlation between the soft and hard X-rays, during the ‘low’ as well as ‘hard’ state, is less than a day. Given the sparse sampling of the RXTE–ASM as well as the CGRO- BATSE during the day, it is not feasible to ascertain this time scale more accurately than a day (or more). Therefore a long pointed observation by the pointing instruments viz. RXTE–PCA and HEXTE is needed for the observation of such a delay. Most of the observations of Cygnus X-3 by RXTE are TOO observations during the high, state, triggered by the radio behaviour. Furthermore, the observations during the recent times are of very short durations, at times as low as 1000 seconds.

92

Chapter 4. Cygnus X-3: temporal studies

Fig. 4.11: Cross correlation between soft and hard X-rays (2 - 7 keV & 20 - 50 keV, respectively). Top panel: Observation carried out on MJD 50321. The hard X-ray flux is obtained from RXTE–HEXTE. Middle panel: Observation carried out on MJD 50322. The hard X-ray flux is obtained from RXTE–HEXTE. Bottom panel: Observation carried out on MJD 50949 - 50954. The hard X-ray flux is obtained from RXTE–PCA.

4.4. Time lag between soft and hard X-rays

93

Here we report the results of the search for the (anti-)correlated delay between the soft and hard X-rays, for three observations, carried out on the MJD 50321 (obs. id. 10126-01-01-010 & 10126-01-01-01), MJD 50322 (obs. id. 10126-01-01-020 & 1012601-01-02) and MJD 50949 – 50954 (obs. is. 30082-04-01-00 to 30082-04-06-00). The duration of the observations on the six days MJD 50949 – 50954 consist of about a satellite orbit each, hence the analysis of the combined lightcurve is presented here. The cross-correlation between the fluxes in the 2 - 7 keV and 20 - 60 keV are shown in Figure 4.11. These cross-correlations are obtained after correcting the lightcurves for the binary modulation (section 4.1). The soft X-ray lightcurves are obtained from the RXTE–PCA (pointed) observations while the hard X-ray lightcurves are obtained from RXTE–HEXTE for MJD 50321 & 50322, and from RXTE– PCA for the days MJD 50949 – 50954. On MJD 50322 an anti-correlated delay of  s is observed, whereas from the observations on the other two days a delay of * s are seen, vindicating the results of the SRC test (chapter 3 and section 4.2). Attempts to locate such a direct measurement of (anti-)correlated delay in the ‘high’ as well as ‘soft’ state has not yet yielded any positive detection. Observation of such a direct delay, (anti-)correlated, between the soft and hard Xray is measured for the first time for this source in particular, and Galactic microquasars in general. A physical interpretation of this extremely important observational result is currently beyond the scope of this research, but this feature can be the cornerstone of the building block of a complete theory providing the explanation of the physical mechanism and the geometrical structure of this source, which will further provide the necessary direction to build a general understanding of these Galactic microquasars in general. Current trends indicate that this delay may be the manifestation of the dynamical viscous time scale in the accreting flow of the disc.

Chapter 5 Disc-jet connection in microquasars: low (hard) states

The characterizing feature of the Galactic microquasars is the radio emission, along with the presence of the accretion of mass onto a compact object analogous to the Active Galactic Nuclei (AGNs). In the introductory section of this thesis (chapter 1), the various theoretical paradigms which attempt to explain the accretion phenomenon were stressed upon. Further, the (quasi) simultaneous observations of X-ray binaries in the radio and X-ray bands has led to the notion that the presence of radio jets is ubiquitous in sources with black holes or low magnetic field ( µ   G) neutron stars as compact objects (see Fender 2001b, Fender and Kuulkers 2001). Though superluminally moving radio jets are detected in several microquasars (Mirabel and Rodriguez 1994, Tingay et al. 1995, Hjellming and Rupen 1995, Hjellming and Johnston 1988), which are invariably associated with huge radio flares, only recently it has been realized that non-thermal radio emission is a common feature during relatively quiet phases. Fender (2001b,a) made a detailed calculation of the energetics during such quiet phases and argues that the non-thermal emission forms a substantial part (5%—50%) of the energy budget. Compact radio jets are indeed observed in the low-hard state of several microquasars viz. Cygnus X-1 (Stirling et al. 2001), GRS 1915+105 (Dhawan et al. 2000), 1E 1740.7-2942 (Mirabel et al. 1992), and GRS 1758-258 (Rodriguez et al. 1992). Further, the spectral analysis of the radio emission from X-ray transient blackhole candidates, GS 2023+38, GRO J0422+32 and GS 1354-64 (Fender 2001b) and two persistent X-ray blackhole candidates GX 339-4 (Corbel et al. 2000) and XTE J1550-564 (Corbel et al. 2001) are interpreted to originate from synchrotron emitting, compact conical jets. With a plethora of uncoordinated high energy and radio observations giving rise to a very confused and foggy picture of the disc - jet connection across the various microquasar (X-ray binary) 94

95 systems, a concise systematic study of the long term radio:X-ray correlation, in the lines of the analysis carried out for Cygnus X-3 in chapter 3 was the essential need of the hour. Our effort was to find a possible generalization of the pivoting behaviour the Xray emission, analogous to that of Cygnus X-3, correlated to the radio emission, during the (low) hard state (see chapter 3 for the detailed analysis). While the generalization of the X-ray spectral evolution during the radio flaring states is intended to be the guiding direction of future research work in this field. Fender and Kuulkers (2001) have compiled an extensive list of X-ray binaries, both neutron stars and black hole candidates, for which simultaneous X-ray and radio observations have been made. The Green Bank Interferometer, West Virginia, operated by NRAO, provides data for a number of X-ray sources that were monitored during its several years of operation. Collating these sources with those monitored by RXTE– ASM and CGRO–BATSE we found two X-ray binaries (black hole candidates) viz. Cygnus X-1 and GRS 1915+105, along with Cygnus X-3, which are persistent in radio, soft and hard X-ray bands and for which (quasi) simultaneous data from the three observatories are available. In this chapter, we report the results of our analysis for the two persistent X-ray binaries, microquasars and black hole candidates, Cygnus X-1 and GRS 1915+105 for which quasi-simultaneous radio and X-ray data are available from GBI (2.2 GHz), RXTE–ASM (2 – 12 keV), and CGRO–BATSE (20 – 100 keV). We select data during periods when there are no radio flares and the source is bright both in radio and hard X-rays. We examine radio X-ray correlations in such hard states and show that these correlations are similar to those found in the low-hard states of well studied sources like GX 339-4. We complement our analysis of this state by giving a qualitative self consistent picture of the steady X-ray non-flaring (radio) states of these sources, along with Cygnus X-3 and GX 339-4. In the next chapter (chapter 6) we will attempt to provide a phenomenological picture of the accretion - ejection connection in these Galactic microquasars, using the Two Component Advective Flow (TCAF) model of Chakrabarti (1996a) transition among the X-ray as well radio emission. A brief introduction to the these sources are as follows (for Cygnus X-3 refer to chapter 3):$ GRS 1915+105. The X-ray binary GRS 1915+105 was first detected in 1992 (Castro-Tirado et al. 1992), and since then has been observed in the X-ray, radio and infra-red bands (see Belloni 2002, for a review). From the K-band monitoring of the source (Greiner et al. 2001a) it has been classified as a low mass X-ray binary system with an orbital period of 33 days with a 10  black hole as the compact object (Greiner et al. 2001b). Muno et al. (2001) classify the radio emission into three classes, radio faint, radio steep and radio plateau. This source is

96

Chapter 5. Disc-jet connection in microquasars: low (hard) states extremely variable in nature and has been classified into several variability classes (Belloni et al. 2000), of which the class is the closest analogue to the canonical low-hard states of Galactic black hole sources (Rao et al. 2000).



$ Cygnus X-1. This source, the first to be X-ray detected in the Cygnus region (Bowyer et al. 1965), is the archetypical black hole candidate (Herrero et al. 1995), whose optical counterpart, O9.7Iab super giant HDE 226868, was among the earliest to be identified for an X-ray binary (Bolton 1972, Webster and Murdin 1972). A persistent source in X-ray, radio (Braes and Miley 1971) and optical, it shows a binary modulation with a period of 5.6 d in all the bands (Pooley et al. 1999, Brocksopp et al. 1999). The radio emission is weak, generally around 15 mJy, varying between 10 to 25 mJy in the low-hard X-ray state getting considerably weaker in the high-soft state of X-ray emission (Brocksopp et al. 1999). $ GX 339-4. This X-ray binary system was discovered in 1971 (Markert et al. 1973b,a) whose radio counterpart was first reported by Sood and Campbell-Wilson (1994). It is considered to be a blackhole candidate (Samimi et al. 1979) because of the similarity of the X-ray spectral characteristics and short term variabilities with those of Cygnus X-1 (Tanaka and Lewin 1995), especially in the low-hard state (Corongiu et al. 2003). $ V404 Cygni. This is an X-ray transient whose luminosity can increase by a factor of  during outburst. Simultaneous observations, during the decay phase following an outburst, in the radio (Han and Hjellming 1992) and X-ray (Kitamoto et al. 1990) revealed that the source never entered the soft state during this phase (Zycki et al. 1999). In the quiescent phase the ROSAT–PSPC measured the flux qs from this source to be k Š ,(  Š  ; ˆ È l ˜ (Wagner et al. 1994, for recent observations see Kong et al. 2002).

+D

–

The sources above (plus Cygnus X-3) dealt with in this chapter, with apparently diverging behavioural patterns, span the whole gamut of multifarious characteristic features of the Galactic microquasar systems. Hence, any generalized distinguishing attribute of the disc-jet connection in these systems may be taken as a normal trait for this class of cosmic sources. In the following sections we provide the existing radio - X-ray association in these objects, prior to our study, followed by our statistical analysis of the monitoring data and the X-ray spectral evolution, all in the low-hard states of these systems. For the sake of completeness of the analysis and the inference, we present the main results of Cygnus X-3 in a precis form (for details refer to chapter 3). The existing features of the radio:X-ray correlation of the prominent persisting sources in the (low) hard states, prior to our work are as follows:-

5.1. Radio:X-ray correlation of the persistent sources: hard states

97

$ Cygnus X-3. Radio (GBI, 2.2GHz, monitoring data) and hard X-ray (CGRO– BATSE, 20 – 100 keV, monitoring data) show anti-correlation during the hard state, no correlation during the minor flaring state and correlation during the flaring state (McCollough et al. 1999). Normally the radio flares occur during the high state (Watanabe et al. 1994). $ GRS 1915+105. This source exhibits quite complicated behaviour. It is highly variable in nature, with the radio emission always present in the hard steady Xray state (Muno et al. 2001). Very generic picture gives no correlation between the radio emission and both soft X-ray emission and wide-band (1 - 200 keV) flux, but anti-correlation between hard X-ray (20 - 200 keV) flux and the radio emission, in the hard state (Rau and Greiner 2003). During high radio emission the X-ray spectrum is softer. $ Cygnus X-1. There exists mild correlation between radio (GBI, 2.2 GHz) and soft X-ray (RXTE–ASM, 2-12 keV) and very poor correlation between radio and hard X-ray (CGRO–BATSE, 40 – 140 keV) (Brocksopp et al. 1999) in this object. The radio emission is suppressed during the high-soft state. $ GX 339-4. In this Galactic black hole binary system the radio, soft X-ray as well as hard X-ray are very strongly correlated in the low -hard state (Corbel et al. 2003). Whereas, the radio emission is suppressed (quenched) during the high soft state (Corbel et al. 2000). $ V404 Cygni. In this source, strong correlation between radio and soft X-ray emission (RXTE–ASM, 2 – 12 keV) is seen during the low-hard states, from various quasi-simultaneous observations.It shows similar radio:X-ray emission characteristics as GX 339-4 (Gallo et al. 2003).

5.1 Radio:X-ray correlation of the persistent sources: hard states We repeat the statistical procedures employed to perform the Spearman Partial Rank Correlation test for Cygnus X-3, in order to obtain the Spearman Rank Correlation (SRC) coefficient (Macklin 1982) of the radio (GBI), soft and hard X-rays (RXTE–ASM & CGRO–BATSE) emissions in GRS 1915+105 and Cygnus X-1, during the period when these three observatories were simultaneously operational in regularly monitoring these sources. Here we report the results of the correlation analysis for data averaged

98

Chapter 5. Disc-jet connection in microquasars: low (hard) states

over different time intervals viz., 1, 5 and 10 days as well as correlation between X-ray hardness ratio (ratio of observed BATSE count rate to that of ASM count rate) and radio (ASM count rate is taken as the third parameter) for the duration in which the respective sources were in a relatively long term steady quiescent hard state. Table 5.1 gives the complete result of the Spearman Rank Correlation (SRC) test for the correlation among 1) the radio, soft X-ray and hard X-ray, and 2) the hardness ratio in X-ray and radio (GBI) for GRS 1915+105 and Cygnus X-1 along with Cygnus X-3, during the steady quiescent hard state of X-ray emission, for fluxes in different bands averaged over 1, 5 and 10 days.

5.1.1 Cygnus X-3 A detailed description of the SRC test and the results are given in chapter 3 along with the X-ray spectral fitting correlated to the source, where a pivoting behaviour of the Xray spectra is inferred. Here, in table 5.1 the result of the Spearman Rank Correlation test for fluxes averaged over 1, 5 and 10 days, during the radio quiescent state (Figure1 Choudhury et al. 2002, see Figure 3.4 chapter 3, this thesis), also corresponding to Xray quiescent and hard state.Though the value of the SRC coefficient increases with increasing bin time, it should be noted that the number of degrees of freedom decreases and hence the best correlation result is obtained for one day averaging (as seen by the value of the null hypothesis probability). Hence the correlation time scale is shorter than a day. The X-ray hardness ratio shows a very strong and significant anti-correlation with the radio emission. Interestingly this anti-correlation is stronger and more significant than the anti-correlation of the hard X-ray flux with radio (or soft X-ray). This suggests spectral bending being correlated with the radio emission, amply demonstrated in the top panel of Figure 5.2 (adapted from Figure 3 Choudhury et al. 2002, Figure 3.6, chapter 3 this thesis). The pivoting of the spectrum around 12 keV, as obtained from pointed RXTE observations, explains the anti-correlation between the soft (2 – 10 keV, RXTE– ASM) and hard X-ray (20 – 100 keV CGRO–BATSE) emission. Table 5.2 gives the results of the spectral fitting, along with the soft X-ray (ASM), hard X-ray (BATSE) and radio (2.2 & 8.3 GHz, GBI) flux, of two observations corresponding to the extreme behavior of the source within the precincts of the hard state. In chapter 3, more spectral data were presented which showed a systematic change in the wide band spectrum correlated with the radio flux. The available spectra showed a pivoting behavior around 12 – 15 keV. This fact, coupled with the strong correlation between the soft X-ray and radio as well as that anti-correlation of the hard X-ray flux with radio (and soft X-ray flux) strongly suggest that the spectral shape governed by a pivoting behavior at around 12 keV is responsible for the observed correlations.

5.1. Radio:X-ray correlation of the persistent sources: hard states

99

Fig. 5.1: The combined simultaneous light curve of GRS 1915+105 in the soft X-ray (2 – 12 keV, ASM, top panel), hard X-ray (20 – 100 keV, BATSE, middle panel) and the radio (2.2 GHz, GBI, bottom panel). The low-hard states, selected for the present analysis (see text), are separated by vertical dashed lines and identified with numbers.

5.1.2 GRS 1915+105 Figure 5.1 gives the daily averaged light curves of GRS 1915+105 in the soft X-ray (ASM, top panel), hard X-ray (BATSE, middle panel) and the radio (2.2 GHz, GBI, bottom panel) during the period when all the three instruments were simultaneously monitoring the sources. As per the classification of Belloni et al. (2000), the class is the closest analogue to the canonical low-hard states of Galactic black hole sources (Rao et al. 2000). Belloni et al. (2000) identify three stretches of long duration classes and two of them have simultaneous BATSE and GBI observations. These two periods are demarcated by numbers in the top panel of Figure 5.1, and are used for the correlation analysis. The results of the SRC test, given in Table 5.1 are similar to that of Cygnus X-3. The radio and soft X-ray fluxes are well correlated. The anti-correlation of the hard X-ray flux with both radio and soft X-ray flux is not as strong as in the case of Cygnus X-3. The correlation time scale, as can be concluded from the strength of the correlation, is one day or less. The correlation between the X-ray hardness ratio and radio flux again gives results similar to those of Cygnus X-3, suggesting a spectral pivoting correlated to the radio emission. Hence, it is evident that the radio X-ray correlation behavior in the steady long term hard state of this source is similar to that of Cygnus X-3.





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Chapter 5. Disc-jet connection in microquasars: low (hard) states

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Cygnus X-1 SRC Null Prob. D-Par. no. of data points: 268 0.29 1.4 0.33 0.16 1.4 0.70 13.1 0.01 0.93 2.5 no. of data points: 65 0.53 2.0 0.53 2.0 0.72 5.6 0.03 0.84 1.6 no. of data points: 33 0.58 1.4 0.61 2.0 0.72 3.4 0.11 0.55 1.4

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GRS1915+105 SRC Null Prob. D-Par. no. of data points: 108 0.61 6.8 -0.27 0.004 -1.8 -0.23 0.018 -0.8 -4.1 -0.62 no. of data points: 32 0.71 4.4 -0.33 0.067 -1.3 -0.23 0.22 -0.1 -0.65 -1.5 no. of data points: 19 0.67 0.002 3.1 -0.23 0.32 -0.8 -0.13 0.60 0.2 -0.58 0.009 -0.5

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1 day avg. flux ASM:GBI GBI:BATSE ASM:BATSE RATIO:GBI 5 day avg. flux ASM:GBI GBI:BATSE ASM:BATSE RATIO:GBI 10 days avg. flux ASM:GBI GBI:BATSE ASM:BATSE RATIO:GBI

Cygnus X-3 SRC Null Prob. D-Par. no. of data points: 532 0.68 0 15.9 -3.7 -0.43 -6.7 -0.48 -0.65 0 -3.9 no. of data points: 149 0.76 8.1 -2.5 -0.61 -5.3 -0.68 -2.0 -0.71 no. of data points: 75 0.83 6.2 -1.5 -0.72 -3.8 -0.79 -2.1 -0.85

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100

Table 5.1: The Spearman Rank Correlation (SRC) coefficient, null-hypothesis probability and D-parameter among 1) the radio, soft X-ray and hard X-ray fluxes and 2) the hardness ratio of X-ray (ratio of BATSE to ASM flux), the radio and the soft X-ray fluxes, for Cygnus X-3, GRS 1915+105 and Cygnus X-1 in the low-hard state with the observed fluxes averaged for 1, 5 and 10 days.

5.1. Radio:X-ray correlation of the persistent sources: hard states

101

Fig. 5.2: Top Panel: The unfolded spectra of Cygnus X-3 in the low-hard state (radio quiescent period) on two occasions (1: MJD 50954; 2: MJD 50717). Bottom Panel: The spectra of GRS 1915+105 in low-hard state on two occasions (1: MJD 50421; 2: MJD 50737).

Two unfolded spectra for GRS 1915+105 corresponding to GBI 8.3 GHz fluxes of 17 and 77 mJy respectively are overlaid in the bottom panel of Figure 5.2. Table 5.2 gives the details of the soft X-ray (ASM), hard X-ray (BATSE) and radio (2.2 & 8.3 GHz, GBI) flux along with the best fit parameters of the spectral fitting (Vadawale et al. 2001b). It is interesting to note that the wide-band spectra at extreme radio emissions shows a cross-over at higher energies (20 keV) compared to Cygnus X-3 and, by association, we suggest that a spectral pivoting occurring at higher energies is responsible for the observed correlations. A possible reason for a weaker anti-correlation between hard Xray (20 – 100 keV) flux and soft X-ray (2 – 12 keV) flux (and radio) compared to that in Cygnus X-3 is that in the case of Cygnus X-3 the soft X-ray (ASM) and hard X-ray (BATSE) energy ranges are, correspondingly, below and and above the pivot energy of around 12 keV, whereas for GRS 1915+105, the pivot energy is at higher energies of around 20 keV, and the spectrum is relatively harder. Rau and Greiner (2003) have made a detailed study of all the state observations of GRS 1915+105 based on the analysis of four years of pointed RXTE–PCA and HEXTE observations. They find no correlation between radio and soft X-ray flux (1 – 20 keV), however, they find an anti-correlation between radio and hard X-ray (20-100 keV) flux,



Chapter 5. Disc-jet connection in microquasars: low (hard) states

102

Table 5.2: The observed fluxes and X-ray spectral parameters of Cygnus X-3 and GRS 1915+105 during two pointed RXTE observations, corresponding to the extreme behaviour of the sources within the precincts of the respective low-hard states. MJD Flux ASM (cts s e ) X BATSE (ph cm e ¯e ) GBI-2.2 GHzV (mJy) GBI-8.3GHz (mJy) V Best fit parameters kT ü (keV)

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50717 11.11 0.038 115 165

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5.1. Radio:X-ray correlation of the persistent sources: hard states

103

and also find that the slope of hard power law spectrum correlates positively with the radio flux in the low hard state of the source with observations during high radio emission showing a softer spectrum. The latter results agree with our findings presented here. Rau and Greiner (2003) also report spectral pivoting occurring between 20 – 30 keV in Xray spectra in hard state of GRS 1915+105. The results of Rau and Greiner (2003) are consistent with our findings, except that the radio and soft X-ray fluxes are not correlated in their data, whereas we find a good correlation between radio and soft X-ray flux. Our results are based on the ASM data which is not very sensitive to X-rays above 10 keV, whereas Rau and Greiner (2003) use the flux up to 20 keV using a model fit to the joint PCA and HEXTE observations. The lack of correlation between radio:soft X-ray could be due to the spectral pivoting around 20 keV, because of which the soft X-ray flux from RXTE PCA data will comprise of both correlated and anti-correlated fluxes thus weakening or averaging out the correlation.

5.1.3 Cygnus X-1 Figure 5.3 gives the daily averaged light curves of Cygnus X-1 in the soft X-ray (ASM, top panel), hard X-ray (BATSE, middle panel) and the radio (2.2 GHz, GBI, bottom panel) during the period when all the three instruments were simultaneously monitoring the sources. The radio emission is weak, generally around 15 mJy, varying between 10 to 25 mJy in the low-hard X-ray state getting considerably weaker in the high-soft state of X-ray emission (Brocksopp et al. 1999). In Figure 5.3, the region 1 as demarcated in the top panel of the figure denotes the period of the long term low-hard state of the Xray emission. Since our emphasis is on the study of the long-term correlated radio:X-ray behavior of this source in low-hard state, we consider only this period for the SRC test. The results of the SRC test for Cygnus X-1 are given in Table 5.1. The table shows that pattern of the correlation between X-ray and radio emission for Cygnus X-1 seems to be different than for Cygnus X-3 and GRS 1915+105. The soft X-ray and radio fluxes are not as well correlated as for the other two sources, specially for 1 day averages, being only 0.29 compared to 0.68 and 0.56 for Cygnus X-3 and GRS 1915+105 respectively. Nevertheless, the correlation is significant at the level of about one part in 10 . The anti-correlation of hard X-ray (40 – 140 keV, BATSE) flux with the soft X-ray (2 – 10 keV) as well as radio (2.2 GHz, GBI) fluxes found for Cygnus X-3 and GRS 1915+105 is not present in Cygnus X-1. Instead, the SRC test shows that the hard X-ray positively correlates with the both soft X-ray and radio emission. Also the X-ray hardness ratio does not show any correlation with radio flux in the case of Cygnus X-1, unlike for Cygnus X-3 and GRS 1915+105.

104

Chapter 5. Disc-jet connection in microquasars: low (hard) states

Fig. 5.3: The combined simultaneous light curve of Cygnus X-1 in the soft X-ray (2 – 12 keV, ASM, top panel), hard X-ray (40 – 140 keV, BATSE, middle panel) and the radio (2.2 GHz, GBI, bottom panel). The low-hard states, selected for the present analysis (see text), are separated by vertical dashed lines and identified with numbers.

Brocksopp et al. (1999) report a value of the SRC coefficient for soft X-ray:radio flux correlation in low-hard state of 0.3 for 1 day average, after removing the mean orbital light curve, which is close to 0.29 found by us for the same correlation, without removal of the orbital modulation effects. Brocksopp et al. (1999) point out that loose correlation of radio and soft X-ray fluxes (for their 1 day averages) may be partly due to the possible offset between the radio and X-ray long period ( 142 days) light curves. They also give the scatter plot of ASM, BATSE and radio fluxes. The strength of the SRC between the radio and the both soft and hard X-ray are similar (Table 5.1), showing moderately strong correlation, whereas the soft and hard X-ray flux show a very strong positive correlation, the SRC coefficient being 0.70 for 1 day averages. Further, ASM and BATSE observations are at different times during the day implying that intra-day variability is relatively weak compared to variability on longer time scales as both fluxes are strongly correlated over longer time scales. Clearly, the similarity between hard X-ray:radio and soft X-ray: radio flux correlation is because

5.1. Radio:X-ray correlation of the persistent sources: hard states

105

of strong correlation between hard and soft X-ray fluxes. As mentioned earlier, the radio emission in Cygnus X-1 is quite weak (around 15 mJy) varying between 10 and 25 mJy in the low-hard state. As the GBI observations have an error of nearly 4 mJy, a detailed wide-band spectral analysis for two extreme values of radio flux, for finding the relation between the shape of the X-ray spectra and the radio emission and the pivoting behavior and the pivot energy, as done for Cygnus X-3 and GRS 1915+105, is difficult to be carried out for Cygnus X-1. Zdziarski et al. (2002) have shown that the long term variability of the X-ray emission from this source in hard state comprises of two types of spectral variability, one corresponds to the change in the shape of the spectra (with spectral shape pivoting around 80 keV) with change in soft X-ray flux and the other corresponds to the change in total flux, with the spectra simply moving up and down parallel to each other with a constant shape, in the whole X-ray broad band. This may explain the lack of correlation between the X-ray hardness ratio and the radio flux as well as the comparative weakness of the strength of the SRC correlation between ASM and radio flux. Zdziarski et al. (2002) have analyzed the various correlations among the fluxes of the three energy channels of ASM (1.5 – 3, 3 – 5 and 5 – 12 keV) along with the 20 – 100 keV and 100 – 300 keV flux of BATSE and the corresponding specific spectral index of these bands. They conclusively show that in the low-hard state of the X-ray emission, over long periods, the change in the spectral shape occurs with a pivoting around 50 – 90 keV. This explains that the BATSE flux, being dominated by the lower energy photons is very strongly correlated to the ASM flux. The lack of anti-correlation between the X-ray flux hardness ratio and the radio emission may also be explained by this fact, as the lower energy of the BATSE flux, below the pivot point, is correlated to the radio emission along with the ASM flux. Fig. 5.4: The X-ray pivoting behaviour during the low-hard state in Cygnus X-1. The pink and orange points correspond to the high-soft state. Figure obtained from Zdziarski et al. (2002)

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Chapter 5. Disc-jet connection in microquasars: low (hard) states

5.2 Uniform behaviour of X-ray spectral shape with radio emission The results presented in the last section will be discussed along with similar results for GX 339-4 reported by Corbel et al. (2000, 2003). The compact object in GX 339-4 is also believed to be a black hole (Hynes et al. 2003). Corbel et al. (2000) find that for GX 339-4, the radio flux is strongly correlated with both soft (see Figure 5.5) and hard X-ray, covering the range 3-200 keV, in low-hard state, similar to the results obtained by us for Cygnus X-1. If we consider the results of the radio, soft X-ray and hard X-ray correlation analysis for these four sources, at first glance no consistent picture of the correlated variability pattern emerges. However, it is immediately noticeable that Cygnus X-3 and GRS 1915+105 have similar overall correlation pattern. For both, the soft X-ray flux is correlated with the radio flux, and the hard X-ray flux is anti-correlated with the both radio and soft X-ray flux. Additionally, the hardness ratio is also strongly anti-correlated with the radio flux. Wide band X-ray spectral analysis in the hard state for both the sources at different radio flux levels suggests pivoting of the spectrum around 10 – 25 keV correlated with the radio emission. It can also be noticed that correlation among the radio, soft and hard X-ray fluxes for Cygnus X-1 and GX 339-4 is similar. Both show a positive correlation among the radio, soft X-ray and hard X-ray fluxes. For Cygnus X-1 the hardness ratio is not correlated with radio flux. Further, Zdziarski et al. (2002) find a pivoting of the X-ray spectrum of Cygnus X-1 at higher energy of around 50-90 keV. Similarly, the wide band X-ray to 0 -ray spectral analysis of GX 339-4 (Wardzi´nski et al. 2002) has shown that there is a pivoting in the spectrum at energies 300 keV in the low-hard state of the source (Figure 5.6). At this stage it will be worthwhile to note other similarities in the X-ray and radio emission characteristics of Cygnus X-3 and GRS 1915+105 vis a vis Cygnus X-1 and GX 339-4. Most notable are that the first two sources are the strongest and most variable radio sources amongst the Galactic X-ray binaries whereas both Cygnus X-1 and GX 339-4 are amongst the comparatively weak and steady radio sources. On the other hand, both Cygnus X-1 and GX 339-4 have a very hard X-ray spectrum compared to Cygnus X-3 and GRS 1915+105. Thus both X-ray sources with softer X-ray spectrum have a lower pivot energy and Cygnus X-1 with a much harder X-ray spectrum has a much higher pivot energy, indicating that the pivot energy is directly related to spectral shape. The correlation between hard X-ray flux and radio and soft X-ray fluxes observed in Cygnus X-1 and GX 339-4

5.2. Uniform behaviour of X-ray spectral shape with radio emission

107

Fig. 5.5: The X-ray - radio scatter diagram of GX 339-4. The X-ray data obtained from RXTE– ASM monitoring and the radio observations obtained from various observatories. The distinctive feature is the correlation between radio and the soft X-ray flux in the lowhard state, and the suppression of the radio emission in the high-soft state. The figure is obtained from Corbel et al. (2000)

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Chapter 5. Disc-jet connection in microquasars: low (hard) states

Fig. 5.6: The wide-band X-ray spectra of GX 339-4. top panel:The pivoting of the X-ray spectra above 300 keV. Bottom panel: The individual spectral components of the X-ray SED. The figure is obtained from Wardzi´nski et al. (2002)

5.2. Uniform behaviour of X-ray spectral shape with radio emission

109

can then be explained because hard X-ray flux (20 – 100 keV for Cygnus X-1, 20-200 keV for GX 339-4) is around or below the pivot energy in these two sources and will, therefore, be correlated with the soft X-ray and thereby the radio fluxes. Thus, it is quite evident that X-ray fluxes below and above the pivot energy are anti-correlated for these X-ray sources and the reported differences between radio, soft X-ray and hard X-ray correlation amongst these X-ray sources is an instrumental artifact where the ASM and BASTE energy ranges are fixed and the pivot energy varies from source to source. This is supported by finding of Zdziarski et al. (2002) who report an anti-correlation between 1.5 – 3.0 keV and 100 – 300 keV flux and find a very weak correlation between 1.5 – 3.0 keV and 20 – 100 keV flux for Cygnus X-1 in the low-hard state. Thus the X-ray – radio behavior of these X-ray sources are consistent in terms of correlation between soft X-ray, hard X-ray and radio emissions reported here.

5.2.1 The X-ray soft state and suppressed radio emission In the previous section we have shown that the X-ray radio emission characteristics in the hard states of the highly variable sources Cygnus X-3 and GRS 1915+105 are similar to those seen in the low-hard states of the well studied black hole sources Cygnus X-1 and GX 339-4, once we assume different pivot energy correlated to the radio emission. Here we explore whether the suppressed radio emission seen in the high-soft states of Cygnus X-1 (Brocksopp et al. 1999) and GX 339-4 (Corbel et al. 2000) are seen in these two sources. We must caution that the identification of various spectral states using monitoring data is fraught with difficulties of flaring emissions which could be quite delayed in the various emission bands. Corbel et al. (2000) show that with the X-ray state transition from low-hard to highsoft the radio emission evolves from a jet like synchrotron emission to quenched emission in GX 339-4. This state is generally preceded by a low-hard X-ray (with correlated radio emission) and followed by an X-ray off state (with radio off). For a comparative analysis we plot the radio (GBI, 2.2GHz) and soft X-ray (ASM–RXTE, 2-12 keV) scatter diagram in Figure 5.7 for Cygnus X-3 (top panel), GRS 1915+105 (middle panel) & Cygnus X-1 (bottom panel), for the non flaring states which includes hard as well as soft states. We have attempted to distinguish the high and low states by the soft X-ray flux and denoted them by open and filled symbols, respectively. For Cygnus X-3 the major flares are excluded, and in the process we have excluded the (very low) quenched radio emission immediately preceding the major flares. For GRS 1915+105, too, the data for the radio flares are excluded. It is evident that even for these two sources the radio emission is suppressed in the high state, analogous to the canonical high-soft state.

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Chapter 5. Disc-jet connection in microquasars: low (hard) states

Fig. 5.7: The radio (GBI, 2.2GHz) and soft X-ray (ASM–RXTE, 2-12 keV) emission scatter diagram of Cygnus X-3 (top panel), GRS 1915+105 (middle panel) and Cygnus X-1 (bottom panel) for the long-term, steady, hard (filled squares) as well as soft (open circles) states, after removing the data for the flaring states.

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Cygnus X-3 shows a very systematic behaviour, with the radio positively correlated to the soft X-ray in the hard state, until it transits to the soft state, where the radio emission is negatively correlated to the soft X-ray emission. For GRS 1915+105 the transition into the soft state with suppressed radio emission is not that drastic but definitely pronounced. Cygnus X-1 shows a more scattered association between the radio and X-ray emission, but the suppression of the radio emission with higher ASM flux is evident. Hence, it can be comfortably claimed that the suppression of the radio emission with the X-ray state transition is a generally consistent feature of the X-ray binary systems (BHCs), irrespective of their individual spectral characteristics. Therefore a consistent picture of the accretion-ejection picture is emerging from the observational analysis of sources with apparently very diverse behavioural patterns.

5.3 Universal correlation and its origin Thus far we have shown that the four sources, viz. Cygnus X-3, GRS 1915+105, Cygnus X-1 and GX 339-4, all show a consistent picture of accretion-ejection mechanism, with the radio emission correlated to the X-ray spectral pivoting in the low state and suppression of the radio emission in the high state following the X-ray state transition. The most notable feature, however, is the strong positive correlation between the radio and soft Xray flux in the hard state of all the sources. This is similar to the correlation reported for GX 339-4 (Hannikainen et al. 1998, Corbel et al. 2000, Gallo et al. 2002) and V404 Cyg (Gallo et al. 2002). We explore below whether the observed correlation is an universal phenomena among the Galactic black hole candidate sources (Choudhury et al. 2003). In Figure 5.8, we show a scatter plot of the radio flux against the soft X-ray flux for Cyg X-1 (plus sign), Cyg X-3 (filled circles) and GRS 1915+105 (open circles), all in their corresponding low-hard and their analogous states. The data are normalized to a distance of 1 kpc, with the assumed distances of 2 kpc, 8.5 kpc & 12.5 kpc, respectively for the above three sources. For the soft X-ray flux (based on RXTE-ASM data) 75 ASM counts s l ˜ is taken as the observed Crab flux. Individual data points are the average value for a bin size of 5 days. Recently, Gallo et al. (2002) have detected a correlation between the radio flux (S Ê ) and X-ray flux (S » ) of the form S Ê = k S» for GX 339-4 ó Ìð ¶ ó Ìð ¶ and V404 Cyg, all the way from the quiescent level to close to high-soft state transition. This relationship is also shown in Figure 5.8 as a dotted line (for GX 339-4) and dashed line (for V404 Cyg). The extents of the lines correspond to the data used for the fit in Gallo et al. (2002). The remarkable feature of Figure 5.8 is that a simple relation seems to hold for all the black hole sources over close to 5 orders of magnitude variation in the luminosity,





 9 8 P

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Chapter 5. Disc-jet connection in microquasars: low (hard) states

Fig. 5.8: A plot of radio flux at 2.2 GHz (based on GBI data) normalized to a distance of 1 kpc against the soft X-ray flux in 2 – 12 keV (based on RXTE–ASM data) normalized to Crab at 1 kpc for Cygnus X-1, Cygnus X-3 and GRS 1915+105, all in their corresponding low-hard states. The data are averaged for 5 days. The power-law fit (with an index of 0.7) reported for GX 339-4 and V404 Cyg by Gallo et al. (2002) are shown as dotted and dashed lines, respectively. The continuous line is a linear fit to the combined data of Cygnus X-1 and GRS 1915+105.

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in the low-hard state. The data points for Cyg X-1 fall just below the correlation found for GX 339-4, whereas, the data points for GRS 1915+105 lie on the line extrapolated from the correlation derived for V404 Cyg. The data points for Cyg X-3 are parallel to those of GRS 1915+105. It should be noted here that Cyg X-3 shows a very strong orbital modulation which is most probably due to the obscuration of the accretion disk by a cocoon of matter surrounding the accretion disk. Hence the ‘true’ X-ray emission from the accretion disk should be larger than the observed one and the data points should move closer to the extrapolated line from GX 339-4 and V404 Cyg. Since Cyg X-3 is suspected to be a micro-blazar (Fender and Kuulkers 2001), it is also quite possible that the radio emission is over-estimated due to strong beaming and Doppler boosting. It is also noteworthy that GRS 1915+105, the most massive stellar mass black hole known, has the highest intrinsic X-ray emission. =k Fitting individual data points of the sources with a function of the form S Ê ó Ìð ¶ S» gives the value of the constant term as 54 mJy, 235 mJy and 1376 mJy, respectively for Cyg X-1, GRS 1915+105 and Cyg X-3. These values should be compared to those obtained for GX 339-4 and V404 Cyg, 124 mJy and 254 mJy, respectively. The individual data points, however, are also consistent with a linear relation and the continuous line in the Figure 5.8 is a linear fit to the combined data of Cyg X-1 and GRS 1915+105.

 9 8 P



Although we cannot completely rule out the possibility that the individual correlations of these sources may exist due to processes unrelated to one another, the fact that the data points for sources close to their ‘off’ states (GX 339-4 and V404 Cyg) occupy one extreme of observations while sources with repeated radio flares (Cyg X-3 and GRS 1915+105) occupy the other extreme strongly suggests of a common physical mechanism in operation in all the sources. One natural consequence to be explored is whether the radio and the X-ray emissions are emitted directly from the same source region. Since there are very strong observational evidences for the radio emission to be of synchrotron origin, it is tempting to assume that the X-ray emission too is emitted by the same process, but at the base of the jet. There are evidences for X-ray synchrotron emission being responsible for the X-ray spectrum of some black hole sources like XTE J1118+480 (Markoff et al. 2001) and part of the spectrum in sources like GRS 1915+105 (Vadawale et al. 2001b). However, for several black hole sources wide-band X-ray spectrum has been extensively studied and the spectral shape is inconsistent with a simple synchrotron emission. Further, the X-ray:radio correlation appears to be valid from ‘off’ state to low-hard and the associated analogous states, and all the way up to the intermediate state, and it is extremely unlikely that the bulk of the X-ray emission is due to synchrotron emission in all these states. Recently Markoff et al. (2003) have suggested jet synchrotron emission as a possi-

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Chapter 5. Disc-jet connection in microquasars: low (hard) states

ble way to explain the broadband (including X-ray) features of GX 339-4. To explain the observed correlation, their model predicts that the X-ray emission is mostly due to synchrotron emission (with a power-law spectral shape). Since the wide band hard X-ray/ low energy 0 -ray spectra of black hole sources in their hard states like GX 3394 (Wardzi´nski et al. 2002), GRS 1915+105 (Zdziarski et al. 2001), and Cygnus X-1 (Zdziarski 2000) require thermal-Compton emission to explain the spectral shape, we explore below alternate models where the X-ray emission is primarily due to accretion disk emission.

5.4 X-ray spectral shape as the “driver” of the radio emission The wide band X-ray spectral shapes of Galactic X-ray binaries with black holes as compact objects show a systematic and predictable behavior, particularly in well studied sources like Cygnus X-1 (Zdziarski 2000) and GX 339-4 (Wardzi´nski et al. 2002), where, in the low-hard state, the spectral energy distribution peaks at 100–300 keV, with the emission being dominated by thermal-Compton emission from a population of hot electrons. For sources which go to the ‘off’ state the X-ray spectrum is quite similar to the low-hard state, but at a very low intensity. In the intermediate state the soft X-ray flux increases and in the high-soft state the spectrum is dominated by thermal emission from the accretion disk. Although it is quite convenient to assume that the mass accretion rate is responsible for such systematic changes, though there is no strong evidence for this (see Homan et al. 2001, for a different behaviour of XTE J1550-654). Nevertheless, one can safely conclude that some unspecified ‘accretion parameters’ causally affect the wide band X-ray spectral shape of black hole X-ray binaries. The evidences presented in this thesis strongly suggests that the very same ‘accretion parameters’ must be causally responsible for the radio emission, rather than the amount of soft X-ray emission, provided they account for the suppressed radio emission in the soft state. Such a hypothesis neatly explains the behavior of Cygnus X-3, which is quite bright in all the three energy ranges and hence the observational uncertainty is quite low. It can also be noticed from table 5.1 that the most significant correlation for Cyg X-3 is between the radio emission and the ratio of hard X-ray flux to soft X-rays. Though such an explanation is not very clear in other sources, all the available observations are consistent with this. Since the radio emission too shows increasing emission from ‘off’ state to low-hard state (in GX 339-4 and V404 Cyg), correlated behavior in low-hard state (the above two sources and Cygnus X-1), and high radio emission in an intermediate state very close to the high state (in GRS 1915+105 and Cygnus X-3) and suppressed radio emission in the high state (Cygnus X-3, GRS 1915+105, Cygnus X-1 & GX 339-4), we

5.5. Summary: the generalized picture of the accretion - ejection mechanism in the ‘low’ - hard state of Galactic m speculate that the soft X-ray intensity determines the spectral shape and the accretion disc condition in these sources, which in turn determines the amount of radio emission (in the X-ray quiescent hard state of these sources). The transition of the Cygnus X-3 system into flaring state and their corresponding behavior has been discussed in detail in chapter 3, while that of GRS 1915+105 is left as a field of future study, given the varied amount variability exhibited by the source, and the vast amount of archived data available, which will require a very extensive program of analysis and study.

5.5 Summary: the generalized picture of the accretion ejection mechanism in the ‘low’ - hard state of Galactic microquasars In this chapter we have analyzed the (quasi) simultaneous observations on GRS 1915+105 and Cygnus X-1 using the RXTE-ASM, BATSE-CGRO and GBI data and made a detailed study of correlation between radio and X-ray fluxes. Based on this analysis along with discussion of earlier published results on Galactic microquasars we find that:$ A correlation exists between the soft X-ray and radio emission of GRS 1915+105 based on the data during the long state (associated to the low-hard state). The hard X-ray emission is anti-correlated with both radio and soft X-rays. There is a spectral pivoting at around 20 keV, correlated with the radio flux.



$ Comparing these results with those of Rau and Greiner (2003) who found a strong correlation between radio emission and the X-ray spectral index in the states, we conclude that the X-ray and radio emission characteristics of GRS 1915+105 are similar to those of Cyg X-3 (Choudhury et al. 2002). The only difference lies in the values of the pivot energy of the X-ray spectra, which is around 12 keV in Cyg X-3 and around 20 keV in GRS 1915+105.



$ A three way correlation among soft X-ray, hard X-ray and radio emission has been found in the low-hard state of Cyg X-1, confirming the results of Brocksopp et al. (1999). Comparing this result with those of Zdziarski et al. (2002) who have found that soft X-ray and hard X-ray above 100 keV are anti-correlated and also that there is a spectral pivoting at around 50 – 90 keV, we conclude that the Xray:radio behavior of Cyg X-1 is similar to that of Cyg X-3 and GRS 1915+105, but for the fact that the pivoting energy is at a higher value.

116

Chapter 5. Disc-jet connection in microquasars: low (hard) states $ The X-ray:radio properties of Cyg X-1 are quite similar to that of GX 339-4, where a 3-way correlation between soft X-ray, hard X-ray and radio emission has been reported (Corbel et al. 2000, 2003). Though an anti-correlation between soft Xray/radio with hard X-rays has not been reported in this source, we note that the X-ray spectrum during the low-hard states also show a pivoting behaviour at high energies 300 keV (Wardzi´nski et al. 2002). $ The radio emission is suppressed for Cygnus X-1 & GX 339-4 in their high-soft state and similarly for Cygnus X-1 and GRS 1915+105 in their high states (with associated softer spectra). Therefore, all these four sources with apparent diverse X-ray and radio properties show very similar behavioural pattern encompassing the long term steady non-flaring state. $ Compiling the soft X-ray and radio observations of the above sources (GRS 1915+105, Cyg X-3, and Cyg X-1) with the published correlation in GX 339-4 and V404 Cyg (Gallo et al. 2002), we find that all the sources show a monotonic increase of radio emission with the soft X-ray emission, spanning a 5 orders of magnitude variation in their intrinsic luminosities. Cyg X-3 deviates from a single relation by about an order of magnitude which can be reconciled if 1) the observed X-ray intensity is an under-estimate because of obscuration and/or 2) the observed radio intensity is an over-estimate because of beaming and Doppler boosting. $ If a common physical phenomena is responsible for such an uniform relation spanning across ‘off’ state to intermediate state, we argue that both radiations (X-ray and radio) are unlikely to be originating from a single mechanism like synchrotron emission.

Thus we succeed in forming a generalized picture of the disc - jet connection in the Galactic microquasars systems, spanning across (apparently) very diverse types of variability as well as intrinsic high energy and radio emission features. The next logical step would be to construct a concise phenomenological model explaining these observational features and, at the least, putting some constraints on the various physical and geometrical paradigms that exist in the literature today.

Chapter 6 Two Component Accretion Flow model

In the introduction to this thesis (chapter 1) the various existing theoretical paradigms for the accretion phenomena were introduced, with a brief mentioning of the Two Component Accretion Flow (TCAF) model (Chakrabarti 1996a) involving the concept of bulk motion Comptonization. In the subsequent chapters it has been established, with particular emphasis on the X-ray binary system Cygnus X-3, that the accretion and ejection need to be considered in an associated manner to form a unified picture of the physical and geometrical structure of the systems. In this chapter an attempt is made understand and explain the observational features detailed out in the chapters 3 & 5 in the light of the TCAF paradigm in order to provide a unified phenomenological picture, as ordained by the aim of this thesis ( 1.6).

L

Bulk Motion Comptonization. Comptonization, in its most elementary treatment as the cause of the high energy emission (powerlaw tail), is considered as upscattering of the soft photons from the disc by inverse Comptonization by a corona of hot electrons with a Maxwellian (thermal) distribution, with a temperature of 50-100 keV, but this formulation is found to be inadequate. In the bulk-flow Comptonization scenario seed photons gain energy from collisions with radially infalling electron’s in a geometrically thick accretion disc in the inner orbits around the compact object (for a short review, see Chakrabarti and Chattopadhyay 2002). Chakrabarti and Titarchuk (1995) showed that this infalling matter, which needs to enter the event horizon at the velocity of light (Chakrabarti 1996a), is capable of upscattering of the photon even if it is ‘cool’, for the relativistic velocity of the bulk motion (instead of the thermal motion) can Comptonize the seed photons to the said high energy bands. The accretion flow is advective and only 117

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Chapter 6. Two Component Accretion Flow model

Fig. 6.1: Schematic (cartoon) diagram of the TCAF paradigm, highlighting the Keplerian accretion disc and the sub Keplerian accretion flow around the compact object, along with the CENBOL (see text for details).

a few photons scattered from this cold but relativistic electrons escape and produce a powerlaw spectrum.

6.1 Two Component Accretion Flow (TCAF) The TCAF model (Chakrabarti and Titarchuk 1995), which is based on the most general advective flow solutions (see, for eg. Chakrabarti 1990, 1996b,c,d), predicts that the accretion flow onto the compact object (blackhole) consists of two components, namely, a Keplerian and a sub-Keplerian component. The Keplerian component consists of a geometrically thin and optically thick Keplerian accretion disk, where the accreting matter has high viscosity as well as angular momentum, analogous to the SS disc solution of Figure 1.7. The sub-Keplerian flow, which is necessary for the matter to fall into the blackhole horizon, consists of matter with lower viscosity and angular momentum, surrounding the thin accretion disk as well as occupying the space of the inner orbits of the truncated disc. The geometry of the truncated disc is dictated by the fact that the matter entering the horizon has the velocity of the light, and hence the flow cannot be Keplerian anywhere near the last stable orbit. Instead, the disc is truncated a a transition radius,

6.1. Two Component Accretion Flow (TCAF)

119

´

•  Ê £   •!– , beyond which the flow becomes nearly free fall, with possible manifestation of bulk motion Comptonization. Due to the lack of an agent to transfer the angular momentum outwards, the freely falling sub-Keplerian flow has (nearly) constant angular momentum resulting in a strong centrifugal force, which becomes comparable to the gravitational force after some distance. Thus the centrifugal force balances the gravitational attraction and causes a barrier in the sub-Keplerian flow, the Centrifugal pressure supported Boundary Layer (CENBOL). Nevertheless, further close to the black hole the gravity overcomes the CENBOL and the matter enters the event horizon supersonically. The CENBOL may form a standing or a scintillating shock (Molteni et al. 1996, Ryu et al. 1997, for a detailed quantitative treatment see Chakrabarti 1996a). The shock, if present, heats up the post shock region which forms a puffed up hot cloud (Figure 6.1). The soft photons from the disc are energized to hard X-rays by inverse Compton scattering. Therefore the total high energy spectrum is explained by the disc blackbody from the Keplerian component plus the Comptonized component, which may include the non-thermal population with bulk motion. The canonical states of X-ray emission may be explained by the TCAF model as states defined by the accretion rate, both in the t Keplerian disc P Á as well as in the sub-Keplerian cloud P Á . The observational feature of this model is the wide-band X-ray spectra with multi-coloured disc blackbody plus a strong hard (powerlaw) component. The angular momentum of the inflowing matter slows down the radial velocity, increasing the optical depth, which causes the slope of the high energy tail spectra to increase (Chakrabarti et al. 1996, Ebisawa et al. 1996).



¢ ¢ P P P Low-hard state. When Á „ Š  ºž Š .”Á (where Á D mass accretion at Eddington limit) Ÿ •  Ê / š  • – , beyond which the flow is Bondi-type, sub-keplerian and hot. This hot, Comptonizing cloud produces hard X-ray by Comptonizing the soft thermal disc (seed) photons. As •  Ê is quite large in this state and the inner disk tem> Q x perature varies as • l (see Longair 1994), the inner disk temperature is quite low in this sate. Also, certain features like presence of quasi-periodic oscillations seen in some systems may be explained by the oscillation of the shock front of the CENBOL (Figure 6.2). The low energy and low angular momentum flow behaves like a spherical Bondi inflow and Parker winds (Parker 1960). Or else, the steady inflow and outflow may not possess shock but the inflow is hot due to slowing down at the centrifugal barrier. In addition, transonic viscous flows are also possible. At low viscosity the shock is obviously weak and the optically thin (sub-Keplerian) flow joins the Keplerian disc far out. The extent of the sub-Keplerian flow may decide the hardness of the X-ray wide-band spectra, with the slope of the omnipresent powerlaw component depending on various physical factors.

µ 

Chapter 6. Two Component Accretion Flow model

120

Fig. 6.2: The accretion flow as per the TCAF paradigm in the low-hard state, with and without the shock barrier. Panel a: Shock is formed, QPOs may or may not be present. Panel b: Shock is not formed, QPOs are not expected. In both cases wind may be formed at low rate. (The figure is obtained from Chakrabarti 2000)

 +P 

¢

¢

P High-soft state. When P Á D mass accretion at Eddington Š Á (where Á limit) Ÿ temperature of the inner accretion disk is high resulting in a strong multicoloured disk blackbody type emission. The cooling of the Compton cloud is very efficient due to the enhanced flux of thermal seed photons, and the disc may extend close to the last stable orbit. The presence of the hard X-ray tail in the spectra may be explained by the bulk motion Comptonization of the seed photons by the energetic matter in the Compton cloud possessing a bulk velocity as the cloud pushes into the blackhole horizon at relativistic speeds. The building blocks of the accretion-ejection flow structure contains, in addition to the ones in the low-hard state, solutions with the inflow passing through the inner sonic point, as well as all the possible combinations of inflow and outflow possessing or not possessing shocks (Chakrabarti 2000).



6.2 Outflow of mass Outflows exist in all sorts of astronomical objects, stellar or otherwise. The primary difference between the outflow from accreting X-ray binaries and the ordinary stellar sources lies in the fact that for the former the mass outflow consists completely of the

6.2. Outflow of mass

121

Fig. 6.3: The accretion flow as per the TCAF paradigm in the high-soft state, with and without the bulk motion Comptonization. Panel c: Bulk motion Comptonization is present, with shocks (if formed) cooled down in accretion, without any QPO or significant wind outflow. Panel d: Flaring outflow state where shocks of intermediate strength may form but since the outflow rate is high it may be periodically cooled to produce strange behaviours. (The figure is obtained from Chakrabarti 2000)

Chapter 6. Two Component Accretion Flow model

122

mass from the inflow. The approach to find the hydrodynamical or magnetohydrodynamical pressure effects leading to the formation of the jets by treating the outflow separating from the inflow has been found to be inadequate. In the TCAF paradigm it is possible to study, self consistently, both the mass inflow and outflow, as the same set of equations govern the mass flow, with the wind type solution guiding the outflow and the accretion type solution deciding the inflow, provided the existence of the CENBOL is accepted. One may strongly assert that whether or not the shock actually forms, the inner dense hot region with (quasi) spherical Bondi-like flow does exist (Abramowicz 1998), even for different physical effects considered (for eg., Chang and Ostriker 1985 showed that preheating of the gas could produce standing shocks at large distances, and Kazanas and Ellison 1986 mentioned that pressure due to pair plasma could produce standing shocks at smaller distances around black hole as well). Therefore it is imperative to investigate the possible role of this region in the formation of¢ outflows. Since the gas will be hot in this P Á ) the cooling of this region by the Compregion, for larger accretion rates (P Á  Š  ¢ tonization from the seed (disc) photons is capable of producing outflows in the low-hard states, although it doesn’t require the very high accretion rate (P Á ”  P Á ) of the ðøñ so called ‘twin-exhaust’ model (Begelman et al. 1984) which requires a similar physical and geometrical structure. Chakrabarti (1999) details the model which assumes a CENBOL of size  • – with the matter passing through a sonic point using the pre-determined funnel where rotating pre-jet matter is accelerated (Chakrabarti 1984), and the outflow rate is analytically completely from the inflow rate alone. Analogous to the solar case where photons from stellar surface deposit momentum to the solar winds (at least upto the sonic point), the hard photons deposit the momentum to the outflowing wind close to the blackhole and keeps the flow roughly isothermal (at least upto the sonic point). With a near Eddington luminosity the outflow could be  lr ¬ year l ˜ (i.e. roughly half the Eddington rate for a stellar mass star). Thus, if the flow is compressed and heated at the centrifugal barrier it would also radiate enough to keep the flow isothermal (at least upto q L the sonic are identical. The electrondensity > point) provided the efficiencies > : falls off : q q L q Q : G • ˜ increases while the photon density falls off as • l , hence the as • l  with the size of the region, resulting in a less number of electron’s per photon, making the process of momentum transfer more efficient, near a blackhole. Assuming the free-falling conical polytropic inflow and the isothermal outflows, Das and Chakrabarti (1999) estimate the ratio of outflowing and · the inflowing rate to be >  Œ = Ë Q :  Á  ¶ l l X (6.1) 7aŒ 7   Á ðòñ ðòñ  and where are the solid angles of the outflow and inflow respectively, Œ is the ¶ ðòñ compression ratio of the in-flowing matter which is a function of the flow parameters



·¶

¹¸

º _»

º

¶

º _» + º

-½¼ ¬ / 

6.2. Outflow of mass

123

¾À Á ¿

Fig. 6.4: Left Panel: Ratio rate and the inflow rate as a function of the compression ratio of the gas at the dense region boundary. Right panel: The variation of the ratio of the polytropic constant in the strong shock limit is shown. (The figure is obtained from Chakrabarti 1999)

Â



such as specific energy and angular momentum (Chakrabarti 1990) and f is given by · : qmy Œ …(

 Œ q 7 7 (6.2) Œa

(



+

º _»

 , n is the polytropic constant = 50öW  l ˜ 0 being the adiabatic index. When ¶ ðòñ [ Œ 0.052 and 0.266 for 0 7 . and . respectively. Assuming a thin inflow    becomes 0.0045 and 0.023 respectively, and outflow 10 " conical angle, the ratio Œ  provided that the outflows are normally concentrated near the axis, i.e. are collimated, ‰ whereas the inflow is near the equatorial plane, which gives éëê 7 . . Thus, the  ù outflow rate is found to depend only on the compression ratio Œ and the collimating property of the outflow é ê and not on the sonic point location, the size of the shock, or the outward radiation force (also the centrifugal force has been ignored) (see Figure 6.4). All these will come into play in the case for a complete general relativistic theory. Note that (in the Figure 6.4) if the denser region does not from ( Œ £ ) then the outflow does not form. Therefore, the outflow is originating in the hot, compressed region. In situations where the assumption that the flow is isothermal (at least) upto the first sonic point is dropped, the outflow becomes a function of many parameters depending on the equation of state, but still qualitatively the solution for the outflow is still similar to the one shown (Figure 6.4)(numerical results are given in Das and Chakrabarti 1999). The left panel of Figure 6.4 shows the behaviour of the outflow for any generic

¹¸

ÃÅÃ ÄÇÆ ?

¸

ÃÅÃ ÄÇÆ ?

º

Chapter 6. Two Component Accretion Flow model

124

¶¶

compression ratio while the right panel shows the same outflow for the polytropic index q qzy ˜ 7( · strong shock case only (Chakrabarti 1999). The most for Œw7

, i.e. the l ˜ obvious feature of the solutions is that the outflow rate is peaked when the shock is of average strength at Œú '( Š   , with the rate falling off very rapidly on either side. If the shock strength is on the higher side ( Œ”-( Š ) the object is in the low-hard state and in the high-soft state on the other side (Œ'D zŸ pure soft state, Œ'D 4–7 Ÿ pure hard state). Usually the outflowing jets are observed to be hollow, hence they must be externally supported (by ambient medium pressure or magnetic hoop stress) as the collimation of these is not explicitly considered in the treatment given above.





+

6.3 The magnetized TCAF model Although magnetic fields are considered to be omnipresent in most of the cosmic sources, in blackhole systems the origin of these is trifle difficult to explain in contrast to the neutron star and white dwarf systems, where they are generated within the compact object itself. The standard approach is to amplify any stochastic magnetic field present to the value required by equipartition. This may employ the use of azimuthal shear in the accretion disc. The value of the magnetic field may vary from  –   G very close to %  G at about 1 AU distance from the blackhole to of mG at 500–1000 AU distance (in the radio lobes) (Fender et al. 1997a, Rodr´ıguez and Mirabel 1999). These values when interpolated close to the black hole assuming a simple • dependence,  give the same order of magnitude value for the magnetic field. The equipartition value of magnetic field in the inner accretion disk is expected to be about  –  G. Thus it is essential to incorporate the magnetic field in any model for an accurate description of the blackhole environment (Vadawale 2003). The introduction of magnetic field in the TCAF paradigm (Nandi et al. 2001) based on the earlier works on magnetic activity in thick accretion disks (Chakrabarti and D’Silva 1994, D’Silva and Chakrabarti 1994) shows that it is possible for the entire Compton cloud to be ejected (by the so called magnetic rubber-band effect by Nandi et al. 2001, see Figure 6.5). The stochastic magnetic (seed) field is supposed to originate in the accreting matter and toroidal magnetic fields are formed due to the shearing of the stochastic field by strong azimuthal velocities in the accretion flow. These flux tubes may rise to the surface of the accreting flow due to buoyancy. After crossing the shock front (CENBOL) the tubes experience drastic increase in the temperature resulting in the enhancement of the buoyant force (in comparison to the radial magnetic tension and drag) which ejects the flux tubes perpendicular to the accretion flow. Such ejection of the magnetic flux tube takes place at the Alfven velocity which can be very large for

P

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Fig. 6.5: A schematic diagram of the accretion disk near a black hole in the presence of magnetic field. It includes a shock ( ) and a sub-Keplerian and a Keplerian disk with boundary at . Stochastic magnetic fields are sheared and amplified as they leave a Keplerian disk. In a hot sub-Keplerian flow these toroidal flux tubes are catastrophically ejected evacuating the post shock region . (The figure is obtained from Nandi et al. 2001).

ÈÊ2Ë

ÈÉ

the post-shock region. Depending on the combination of the various parameters of the accretion flow, if the number of such ejected magnetic flux tube crosses some critical value, it might lead to the complete evacuation of the central Compton cloud.

6.4 Phenomenological picture of accretion and ejection connection Presently we will discuss the applicability of the TCAF framework, developed in the preceding sections, to provide a phenomenological picture of the physical and geometrical structure of Cygnus X-3 (chapter 3) and other microquasars (chapter 5).

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6.4.1 Cygnus X-3 Cygnus X-3 is an X-ray binary with a compact object whose nature has been not yet been identified. Although being one of the brightest radio sources in the sky, there has been only one isolated report of an apparent superluminal motion in the radio band (Newell et al. 1998). One of the primary aim of this thesis was to glean some simple X/0 -ray properties to ascertain the nature of the compact object. During the early days of wideband X/0 -ray spectroscopy the hard powerlaw tail seen in the blackhole systems were believed to be signatures of absence of a hard surface, and hence the presence of an event horizon (Tanaka 2000). In Cygnus X-3 a similar hard tail is seen (Figure 6.6) till 1 MeV (and perhaps beyond). But, subsequent observations of similar spectral characteristics in neutron star X-ray binary systems (see, for eg. Barret et al. 2000, 2003) by RXTE and BeppoSAX negated the possibility of identifying the nature of the compact object by such a simple observational feature (see Barret 2001, 2004, for reviews). Despite of the presence of the powerlaw tail in the neutron star systems, the overall spectral shape, evolution and correlation with radio emission do suggest the compact object to be a likely blackhole candidate.

Fig. 6.6: The hard powerlaw tail in the wide-band X/ -ray spectrum of Cygnus X-3 as observed by CGRO– OSSE.

Ì

Low (hard) state of X-ray emission: Pivoting in X-ray spectra. In chapter 3 a detailed account of the statistical test of the correlation among the radio, soft and hard X-rays were given. Cygnus X-3 is the only source that shows such a strong correlation between soft X-ray and radio, and it is also the only source to distinctly show the anti-correlation between the soft and hard X-rays, during the low-hard state. The quiescent state of Cygnus X-3 has persistent (flat spectrum) radio emission (60 – 100 mJy). This state in Cygnus X-3 is likely to be similar to the “plateau”radio state seen in the most active micro-quasar GRS 1915+105 which shows flat spectrum radio emission for extended durations and the radio emission is identified with a compact jet of size 10 AU (Dhawan et al. 2000). The spectral changes in association with the radio emission is also quite similar to GRS 1915+105 (Choudhury et al. 2003, Vadawale et al.

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2001a). Recently it has been suggested that X-ray emission from BHCs GRS1915+105 (particularly during the “plateau” state) and RXTE J1118+480 could be arising from synchrotron emission from the base of the jet (Vadawale et al. 2001a, Markoff et al. 2003, 2001). Therefore it leads to a speculation that some of the X-ray flux in Cygnus X-3 also could be arising from synchrotron emission from the base of the jet. This can explain the correlation between soft X-ray and radio fluxes but fails to explain the anti-correlation between soft and hard X-ray fluxes. It is quite likely that the soft X-ray emission is due to the accretion disc (directly or indirectly) and the observed correlation is due to a connection between the accretion disk and the jet emission. The X-ray emission from Cygnus X-3 is highly obscured and the bulk of the X-ray emission below 5 keV is due to the emission-line dominated photo-ionized plasma surrounding the compact object (Paerels et al. 2000, Kawashima and Kitamoto 1996). Hence there is no clear evidence for the disc blackbody emission, commonly seen as an X-ray spectral component in the soft X-ray region in other BHCs. Our spectral analysis above 5 keV has identified two spectral components and these, by analogy with other BHCs, can be identified with thermal/non-thermal Comptonization (Zdziarski et al. 2001, Gierli´nski et al. 1999) occurring in the source (or due to X-ray synchrotron emission - see above). If we assume that the region of the Comptonization is confined to a small region near the compact object, we can qualitatively explain the observed correlations under the TCAF described above, in which the Compton spectrum originates from a region close to the compact object, confined within the CENBOL. At low accretion rate, the CENBOL is far away from the compact object, the spectrum is harder with lower outflow (Das and Chakrabarti 1999). On increasing the accretion rate the CENBOL comes closer to the compact object with greater outflow, giving rise to increased radio emission. Though this model qualitatively explains the observed correlations, we must add here that the thermal Compton model is only an approximation and a correct Comptonization model requires an accurate description of the geometry of the emission region. High (soft) state of X-ray emission: Disappearing of Compton cloud. The spectral evolution detailed out in chapter 3 gives a complete picture of the observational features spanning all the possible states of X-ray as well as radio emission. The disappearance of the CompST component in the observations preceding the radio flares suggest the evacuation of the central region around the compact object, where the accretion flow is hot and quasi-spherical. This observational feature provides a direct evidence of the geometrical structure favouring the truncated disc scenario, with the inner orbits having been replaced by Bondi type flow (albeit with comparatively higher angular momentum, assuming the presence of CENBOL). Disappearance of the Compton cloud has been seen

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in GRS 1915+105, during the outflows in the low state (Vadawale et al. 2003, 2001a). It is argued a series of such dips, i.e. evacuation of Compton cloud, give rise to superluminal flares (Naik et al. 2001). Therefore, one may claim that the general evolving picture of the geometrical structure is zeroing onto the truncated disc (sombrero) paradigm. The most intriguing feature of the X-ray spectra of Cygnus X-3 is, perhaps, the post-radio flare state, where the spectral shape is best fit by model components identical to those of the low (hard) state, but the soft X-ray flux is higher, comparable to the high (soft) state. The low temperature of the CompST parameter fit value may suggest the presence of bulk motion Comptonization, which hinders the formation of jet, as matter is accelerated (advectively) into the horizon. Thus, at a qualitative level, the TCAF paradigm may be used to explain the observational features of the microquasar X-ray binary system, Cygnus X-3. Pivoting in the X/0 -ray spectra of other microquasars. Analogous to the explanation for Cygnus X-3, a similar phenomenological picture may be drawn to explain the X-ray radio correlation tests and the X-ray spectral pivoting (at the various energies) of the different types of microquasars, viz. Cygnus X-1, GRS 1915+105, GX339-4, in addition to Cygnus X-3. Though there are models describing the accretion disk emission (Zdziarski 2000) or jet emission (Markoff et al. 2003), there are very few models which self-consistently solve the accretion and ejection phenomena seen in black hole sources. Since our findings suggest a close connection between these two phenomena, we attempt below to qualitatively explain the X-ray radio association using the TCAF paradigm. The X-ray spectral shape in various ‘states’ of the various sources essentially depends on the location of the CENBOL. Analogous to the special case of Cygnus X-3, at low accretion rates the CENBOL is far away from the compact object and the X-ray spectrum is dominated by a thermal-Compton spectrum (if bulk motion Comptonization is absent). In the transition state, the CENBOL comes closer to the compact object and can sometimes give rise to radial shocks, causing intense quasi-periodic oscillations, as seen in GRS 1915+105. In the high state, the increased accretion rate produces copious photons in the accretion disc which cool the Compton region, giving rise to very intense disk blackbody emission along with bulk motion Comptonization (a power-law in hard X-rays with a photon index of 2.5). At some critical accretion rates, the state transitions could be oscillatory as seen in GRS 1915+105 (Chakrabarti and Manickam 2000). The behavior of TCAF disks and the outflow has been stated in detail above (Das and Chakrabarti 1999, Chakrabarti 1999), where the outflow rate is found to be a monotonic function of the compression ratio, Œ , of the gas at the shock region. In this scenario, at

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low accretion rates, the CENBOL is far away from the compact object, a weak shock can form with low compression ratio, giving low and steady outflow. If this outflow gives rise to radio emission, one can expect a relation between the radio emission and the X-ray emission. In this state (off state to low-hard state), an increased accretion rate increases the overall amount of energy available to the Comptonizing region and hence increasing the X-ray emission. The CENBOL location would be pushed inward, increasing the compression ratio (and hence increasing the radio emission) and also can increase the temperature and optical depth of the Comptonizing region, thus giving rise to a pivoting behavior at hard X-rays as seen in Cygnus X-1 and GX 339-4 (50 – 90 and - 300 keV, respectively). At increased accretion rate, the CENBOL can come closer to the compact region, giving the spectral and radio properties as seen in GRS 1915+105 and Cygnus X-3. For a given accretion rate the compression ratio, after reaching a critical value (with the shock region coming correspondingly closer to the event horizon), causes the source to transit into the high-soft state state, for which the radio emission is progressively suppressed (Chakrabarti 1999). This model qualitatively explains all the observed X-ray spectral and radio properties of Galactic black hole sources presented in chapter 5.

6.4.2 Hybrid Comptonization Although the observational features of the X/0 -ray spectra, their evolution with the radio emission, can be qualitatively explained by the TCAF paradigm, in the current state of affairs it is imperative to discuss other possible alternatives for the accretion as well ejection mechanisms. The hybrid Comptonization model of Zdziarski (2000) provides a viable alternative, with a truncated disc (sombrero) geometry, which may explain the X-ray spectral behaviour of the microquasars, Cygnus X-1 in particular (Zdziarski et al. 2002). The hot Comptonizing component consist of thermal as well non-thermal population of matter. Selected electron’s from the thermal distribution may be upscattered to relativistic energies, possibly in the reconnection events. These non-thermal relativistic electron’s Compton upscatter the disc (seed) photons, forming the high energy tail. The relativistic electron’s also transfer some of their energy via Coulomb scattering to the thermal electron’s, heating them to a temperature much above the Compton temperature. The radiation of the corona is also partly Compton-reflected in the disc. In the soft state, the geometry of the system is different, with a patchy-corona above a standard optically thick disc. The soft (seed) photons from the disc are (again) Compton upscattered in the flares, and the emission from the flares is partly Compton-reflected from the disc. This framework may also qualitatively explain the pivoting of the high energy spectra, but it doesn’t concern the radio outflow as an inherent feature of the accretion system. Nevertheless, features of this paradigm may provide a consistent building block in the

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Fig. 6.7: The geometry of the hybrid Comptonization model. Top panel: the accretion in the high state, with the disc extending nearly upto the last stable orbit giving the strong disc blackbody component. The Comptonizing region consist of small active clouds scattered over the disc. Lower Panel: the accretion in the low state, with the truncated disc having the inner orbits replaced by the Comptonizing cloud. (The figure is obtained from Zdziarski et al. 2002)

mechanism of the accretion physics in this class of objects.

Chapter 7 Summary and conclusions

This thesis was aimed at providing a unified, consistent set of observational features of Galactic microquasars, leading to the development of a phenomenological model taking the diverse observational characteristics into account, and thus provide a first step to form a detailed physical theory of the accretion-ejection mechanism in these systems. In the following section we provide a brief summary of our analysis and the conclusions derived from them, with a view for the future direction of work.

7.1 Summary and conclusions 7.1.1 Cygnus X-3 The salient features of the general X-ray spectral studies of Cygnus X-3 are given as follows:$ The X-ray spectra exhibits two distinct states, low (as well as hard) and high (as well as soft), with a high energy tail (extending upto 10 MeV and perhaps beyond) in both these states. $ There is very high inherent absorption in the source which obliterates any signature of the disc blackbody (thermal) emission in the low state. The complicated and peculiar continuum spectral shape is best fit by a combination of Comptonizing component (CompST) and a powerlaw, in this state. $ The continuum spectra of the high (as well as soft) state is best fit by a combination of disc blackbody component plus Comptonizing component (CompST) in most situations.

131

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Chapter 7. Summary and conclusions $ The three iron lines are not resolvable by RXTE– PCA, and hence no attempt is made to derive any physical conjectures from the iron line emissions, in this thesis.

The salient features of the long term multi-wavelength monitoring of Cygnus X-3 are given as follows:$ The soft X-ray (2-12 keV, RXTE– ASM) and radio (2.2 GHz, GBI) are very strongly correlated in the low (as well as hard) state. In the high (as well as soft) state the long term association is not that prominent from the daily monitoring data. $ The soft (2-12 keV, RXTE– ASM) and hard X-rays (20-100 keV, CGRO– BATSE) are anti-correlated in the low (as well as hard) state, the long term association is not so prominent in the daily monitoring data in the high (as well as soft) state. $ Correspondingly, the radio and hard X-ray emissions are anti-correlated in the low (as well as hard) state. $ The hardness ratio of the soft and hard X-rays is also anti-correlated to the radio emission, more strongly so than the hard X-ray emission. $ The time scale of all these correlations is less than a day, revealing that the dynamical time scale need to observed by the pointing instruments for long durations. $ The anti-correlation of the soft and hard X-rays is explained by the pivoting of the wide-band X/0 -ray spectra correlated to the radio emission, in the low (hard) state.

The TCAF paradigm, which deals with the inflow and the outflow in a unified framework, provides a qualitative understanding of the low (hard) state properties of the X-ray as well as the radio emission and their association in the source. In the high (soft) state a more detailed study was required to understand the radio:Xray correlated emission and a complete X-ray spectral evolution was analyses for this state. This state can be further subdivided into three phases, quiescent, pre-radio flare and post-radio flare periods. The salient features of the X-ray:radio association in this state is given below:$ The radio quiescent emission is marked by the radio emission (2.2 GHz) bordering around 110 mJy and below. The X-ray spectra has strong CompST component, the emission due to this component is comparable to that of the multicoloured disc black body component. The fraction of CompST flux amounts to £(,+ ,+ of the total X-ray flux (5-60 keV).

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$ A minor flare is always preceded by the vanishing of the CompST component (flux going below 15% of the total X-ray flux, 5-60 keV). The minor radio flares
have flux around œ£ !   mJy. This phenomenon suggests the ejection of the central Compton cloud resulting in the flare. Also, the extent of reduction of the CompST component is loosely correlated to the maximum flux of the flare, i.e. the stronger the ejection of the cloud the louder the flare. $ The dynamical time scale of the decrease of CompST flux and the observation of the minor flare in the radio may be less than a day. Interestingly, less extent of the decrease of CompST component causes quicker, but milder, flares. $ The minor flare may be followed by the filling of the central Compton cloud, i.e. increase in CompST flux, causing the radio emission to become quiescent. Otherwise, if the continuous accretion persists with the central cloud unfilled, i.e. the CompST flux remains low, a major radio flare (2.2 GHz, flux -I  ) follows.

a`

$ The continuing series of minor and major flares come to an end only with the change in the X-ray spectra, i.e. hardening of the soft X-ray band, with the flux level remaining high. This is the most interesting state of the X-ray spectra with the shape being best fit by the model of the low (correspondingly hard) state, i.e. power law and CompST, although the soft X-ray flux remains high. This change in the X-ray spectra puts a brake in the episodes of radio flaring.

The above sequence strongly suggest the evacuation of a central hot Compton cloud resulting in the massive outflows visible in the radio bands, in this system. Thus, from an observational perspective, a complete X-ray spectral evolution associated with the radio emission, covering all the possible states of X-ray and radio emissions, was obtained for the first time for this source. The TCAF model may be employed with a qualitative basis to explain the physical mechanism and the geometrical structure of the system. A brief outline of the phenomenologically obtained picture is given below:$ In the low (hard) state, the geometrically thin and optically thick Keplerian accretion disc is truncated far off from the last stable orbit, the inner region is filled by the Bondi-type quasi spherical sub-Keplerian inwards flow. The two regions are divided by the CENBOL. $ The soft thermal disc black body photons are Comptonized by the hot plasma in the central Compton cloud, which may or may not possess a bulk motion. These reprocessed photons may get scattered (reflected) from the optically thick disc which may be Comptonized, in a feedback mechanism.

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Chapter 7. Summary and conclusions $ Perturbations in the accretion disc may cause the CENBOL to move in or out, i.e. changing the (radial) dimension of the accretion disc with a correspondingly opposite change in the dimension of the Comptonizing cloud. This feature is manifested in the anti-correlation between the 2-12 keV and the 20-100 keV photons, best visualized by the pivoting of the X-ray wide band spectra. $ Although the exact physical mechanism of the jet (outflow) formation still eludes the current theoretical concepts, in the TCAF paradigm the mass of outflow is found to be depended upon the compression ratio of the gas of the two components (Keplerian and sub-Keplerian) in the accretion flow. The outflow, in the low (hard) state is a direct monotonic function of the ratio, which increases as the accretion rate increases, till the state transition, where the outflow peaks and subsequently falls (monotonically) in the high (soft) state. $ In addition to the steady core jet, visible in the low (hard) state and quenched or quiescent in the high (soft) state, the ejection of the central Compton cloud in the during the high (soft) state causes flaring events (in the radio band). With the accretion disc extending comparatively near the last stable orbit (due to high accretion rate), the Compton cloud finds it difficult to exist in a steady state and hence are ejected out, in bursts of minor and major flares. $ The sequence of ejection of the central Compton clouds is brought to a stop by a change in the X-ray spectra. In this phase, the spectral shape is that of the low (hard) state, but the soft X-ray flux is the same as that of high (soft) state (as per the prevelant classification schemes in the contemporary literature this may be classified as the ‘very high state’). The exact physical features of this state is not known, but tentatively one may speculate the onset of bulk motion Comptonization in this phase, which prevents the formation of outflow (burst, flare etc.) with the inflowing matter advected at great velocities into the event horizon. $ Following this phase, the system most likely transits into the low (hard) state in a span of few days (week or so), and the whole cycle starts again. But it has also been seen to start the minor flaring episodes without going into the intervening episodes without transiting into the low (hard) state.

The temporal analysis of the source, done for the first time in the post RXTE era, yielded the following results:$ The binary modulation period as well as the template was found to be consistent over period of 25 years. This rules out the possibility of any asymmetry in

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the orbital trajectory (resulting in apsidal motion) in the system. Therefore, one may consider some asymmetry in the X-ray cocoon (or X-ray halo) engulfing the system, which is a site of reprocessing the X-ray emissions. $ The residue of the (binary) folded lightcurve (Figure 4.2) may be attributed to the long term variation of the X-ray emission by virtue of the change in wind and/or cocoon mass distribution, including various state changes from soft (and high) to low (and hard) and vice-versa, accompanied by the correlated radio flares. $ At the peak of the binary ephemeris the X-ray emission is seen to fluctuate randomly, this feature is unexplained and need a long term observation and analysis. Given the smoothness of the template in the rising as well as the falling phase, and the random fluctuation in the peak, consistent over decades, does suggest that the randomness is inherent feature of the X-ray emission near the compact object, and otherwise that region is eclipsed by the companion massive Wolf-Rayet star and its wind. $ The power density spectrum (PDS) shows a uniform smooth powerlaw behaviour, irrespective of the state of X-ray emission, quite in contrast to the general patterns in other sources of the same category. Although some periodic fluctuations have been seen in the source in past, the Fourier spectrum of the lightcurves obtained by RXTE–PCA does not reveal any (quasi) periodic structures. $ The PDS merges with the white noise at a very low frequency of 0.1 Hz, in contrast to the general behaviour of the Galactic X-ray binary systems. This may (or may not) be due to the reprocessing of the emission from the inner disc by the cocoon (or halo) engulfing the system. $ The most interesting result of the timing analysis is the anti-correlated delay between the soft and hard X-rays in the low (hard) state. This feature needs to be studied in detail and depth and may provide the foundation for a quantitative modeling of the physical structure in the source.

7.1.2 Generalized picture of disc-jet connection in Galactic microquasars The long term multi-wavelength study of Cygnus X-3 was extended to the other Galactic microquasars, and the following unified results were obtained:$ A correlation exists between the soft X-ray and radio emission of GRS 1915+105 based on the data during the long state (associated to the low-hard state). The



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hard X-ray emission is anti-correlated with both radio and soft X-rays. There is a spectral pivoting at around 20 keV, correlated with the radio flux. $ Comparing these results with those of Rau and Greiner (2003) who found a strong correlation between radio emission and the X-ray spectral index in the states, we conclude that the X-ray and radio emission characteristics of GRS 1915+105 are similar to those of Cygnus X-3. The only difference lies in the values of the pivot energy of the X-ray spectra, which is around 12 keV in Cygnus X-3 and around 20 keV in GRS 1915+105.



$ A three way correlation among soft X-ray, hard X-ray and radio emission has been found in the low-hard state of Cyg X-1, confirming the results of Brocksopp et al. (1999). Comparing this result with those of Zdziarski et al. (2002) who have found that soft X-ray and hard X-ray above 100 keV are anti-correlated and also that there is a spectral pivoting at around 50 – 90 keV, we conclude that the Xray:radio behavior of Cyg X-1 is similar to that of Cyg X-3 and GRS 1915+105, but for the fact that the pivoting energy is at a higher value. $ The X-ray:radio properties of Cyg X-1 are quite similar to that of GX 339-4, where a 3-way correlation between soft X-ray, hard X-ray and radio emission has been reported (Corbel et al. 2000, 2003). Though an anti-correlation between soft X-ray/radio with hard X-rays has not been reported in this source, we note that the X-ray spectrum during the low-hard state in this source too shows a pivoting behavior at high energies 300 keV (Wardzi´nski et al. 2002).



$ The radio emission is suppressed for Cygnus X-1 and GX 339-4 in their high-soft state and similarly for Cygnus X-1 and GRS 1915+105 in their high states (with associated softer spectra). Therefore, all these four sources with apparent diverse X-ray and radio properties show very similar behavioural pattern encompassing the long term steady non-flaring state. $ Compiling the soft X-ray and radio observations of the above sources (GRS 1915+105, Cyg X-3, and Cyg X-1) with the published correlation in GX 339-4 and V404 Cyg (Gallo et al. 2002), we find that all the sources show a monotonic increase of radio emission with the soft X-ray emission, spanning a 5 orders of magnitude variation in their intrinsic luminosities. Cyg X-3 deviates from a single relation by about an order of magnitude which can be reconciled if 1) the observed X-ray intensity is an under-estimate because of obscuration and/or 2) the observed radio intensity is an over-estimate because of beaming and Doppler boosting.

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Fig. 7.1: ASM monitoring Cygnus X-3 during the period of GMRT observations.

$ If a common physical phenomena is responsible for such an uniform relation spanning across ‘off’ state to intermediate state, we argue that both radiations (X-ray and radio) are unlikely to be originating from a single mechanism like synchrotron emission. $ Finally, we invoke a Two Component Advective Flow (TCAF) model (Chakrabarti 1996a) to explain the accretion-ejection behaviour in these systems in the steady hard as well as soft states.

Thus, in this thesis we were able to provide a unified picture of the observational properties and features and provide a phenomenological understanding of the accretion - ejection mechanism of the Galactic microquasar systems, and also provide constraints on the geometrical structure of the accretion process along the way, in accordance to the ‘aim’ specified in 1.6.

L

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7.2 Future directions To further the research and analysis process started in this thesis, the following steps may be considered in continuing the mission of studying and understanding the Galactic microquasar systems:$ Cygnus X-3. Simultaneous observation of the source in the radio, infra-red and X-ray band, to unambiguously determine the jet energetics & the extent of jet component in the X-ray emission, during the low-hard states. $ Cygnus X-3. Simultaneous observation in radio and X-ray bands covering the radio flaring events. Determine the complete physical structure. $ Cygnus X-3. Detailed study of the soft X-ray emission to determine the reprocessing of the X-ray emission in the circum-stellar material. $ Cygnus X-3. Quantitative application of accretion theories (TCAF or any other) to explain the anti-correlated delay of hard X-rays w.r.t. soft X-rays, hence develop a quantitative model for the accretion-ejection connection of the source. $ Microquasars. A long term program of simultaneous observation in radio and X-ray bands. Generalize the features of Cygnus X-3 to the other sources. $ Microquasars & AGNs. Develop a unified picture of the accretion and ejection across the scale of 6 orders of magnitude.

Some preliminary observations of Cygnus X-3 provided a lightcurve with the flux varying in the range 55-70 mJy at 1.4 GHz. These observations were made during the low state of the source. Therefore a groundwork has been made for the multi-wavelength observations of the source using the observatory, and future detailed studies will unravel the mystery of the accretion-ejection mechanism, and possibly the nature of the compact object in the system.

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