MOLECULE DESTRUCTION AND FORMATION IN MOLECULAR CLOUDS MICHAEL D. SMITH1 , GEORGI PAVLOVSKI1 , MORDECAI-MARK MACLOW2 , ALEXANDER ROSEN1 , TIGRAN KHANZADYAN1 , ROLAND GREDEL3 and THOMAS STANKE4 1 Armagh Observatory, Armagh, U.K. 2 American Museum of Natural History, New York, U.S.A. 3 Max-Planck-Institut für Astronomie, Heidelberg, Germany 4 Max-Planck-Institut für Radioastronomie, Bonn, Germany
Abstract. We show that supersonic turbulence accelerates the transition of an atomic cloud into a molecular cloud, quantified here through a demo model and 3D numerical simulations which explicitly include atomic-molecular chemistry. Specific sites where amplified formation may be detectable are suggested.
1. Introduction The means of production of a molecular interstellar phase is a central issue for both star and galaxy formation theories. Clouds of molecules could form by coagulation (collisional agglomeration) of smaller pre-existing clouds, gravi-thermal instability, condensation out of large atomic clouds and by shock-sweeping. Individual molecules form by association on dust grains or, if dust is absent, via H collisions with available H− . If the molecules in the interstellar medium form at a typical density of 30 cm−3 , then a uniform atomic cloud could form on a timescale (Hollenbach and McKee, 1979): tR ∼ 108 g (n/30 cm−3 )−1 yr,
(1)
with a factor g to account for correction terms, uncertainties (e.g. Biham et al., 2001; Hartmann et al., 2001) and the dust properties relative to standard interstellar values. This, with g close to unity, was considered as roughly consistent with estimates of cloud ages, until recently. There is now ample evidence that clouds of various types are generally young: their lifetimes are comparable to their dynamical time scales (e.g. BallesterosParedes et al., 1999). As a consequence, molecular material is recycled through the ISM quite rapidly with the aid of supersonic turbulence and shock sweeping. Moreover, supersonic turbulence clearly dominates the motions in clouds. Since turbulence is expected to decay on very short time scales (MacLow, 1999), there is no force to balance the clouds against gravitational collapse and star formation occurs globally on a few free-fall times (Elmegreen, 2000). Astrophysics and Space Science 289: 333–336, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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This implies that molecule formation is also somehow accelerated. We explore here the means of achieving this through turbulence. Supersonic turbulence leads to non-uniformity: at any instant, a fraction of the gas is highly compressed and will be forming molecules locally at a high rate. Can this proceed fast enough and be sufficiently global to generate a molecular cloud? To answer this we require a 3D model for supersonic turbulence which follows molecule formation and destruction. Relevant numerical models have so far been limited to simple single-component equations of state. By assuming an atomicmolecular transition to take place at a density of, say, 30 cm−3 , distributions of molecular clouds are then predicted. Here, we summarise the major findings of the first simulations of decaying supersonic turbulence with molecular chemistry and cooling. We begin by demonstrating that supersonic turbulence should accelerate molecule formation. We confirm this through the simulations. Finally, we discuss locations where the signals of cloud and molecule formation may be detectable. 1.1. A DEMONSTRATION MODEL Assume a cloud of atomic gas of uniform density, ρo and volume V. The molecule formation rate is Rρo2 V. Now, mix in the turbulence characterised by a Mach number, M. This ‘Mach turbulence’ provides density contrasts of order M2 and we represent the cloud now by two components. A low density component of density ρ occupies a volume fraction M2 /(M2 +1) and a high density component of density (1+M2 )ρ occupies a volume 1/(M2 +1). Mass conservation yields ρ, and the molecule formation rate then becomes (M 2 + 1)(M 4 + 3M 2 + 1) . (2) R ρ dV = R ρo2 V × (2M 2 + 1)2 Hence, at high M, turbulence accelerates H2 formation by a factor M2 /4. Even for moderate M, the speed up is considerable: for M = 4, the rate is 4.8 Rρo2 V. 1.2. S IMULATIONS OF TURBULENCE : MOLECULE REFORMATION 3D simulations of decaying supersonic turbulence with the ZEUS-3D code have been executed (Pavlovski et al., 2003). The code was modified by physics and chemistry pertaining to H, H2 , C, CO, O, OH and H2 O, appropriate for high density regions, assumed to be shielded from ionising, dissociating or heating radiation. Many of the findings, however, have broader implications. Beginning with a uniform density of 106 cm−3 and a 60 km s−1 root mean square turbulence, collisional dissociation reduced the 1016 cm cloud to an atomic form within 40 years. Then, within 300 years over half the molecules had reformed and at 600 yr, 80% had reformed, as illustrated in Figure 1. In an undisturbed medium, however, the H2 would take 3000 yr to reform according to the above formula. [ 158 ]
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Figure 1. The molecular fraction during decaying turbulence, illustrating the distributed reformation. See Pavlovski et al. (2003) for details.
Moreover, the distribution of molecules closely follows the distribution of total density. Hence, molecules are present throughout the cloud, not confined to the high density regions where molecule formation is presently taking place. We thus conclude that the generated shocks sweep through the entire cloud, leaving almost no region unturned. In decaying turbulence, the speed up in reformation mainly takes place during the short time that the turbulence is strong, immediately following the decay (if necessary) of shocks to non-dissociative speeds. Pavlovski et al. (2003) found that the energy in molecular turbulence decays steeper than isothermal turbulence. Hence the brief time in which high Mach number turbulence is present is responsible for the majority of reformed molecules. 1.3. O BSERVING MOLECULE FORMATION To form clouds and molecules in 1 Myr, a density of 3000 cm−3 is required in a uniform medium. This is reduced to an average density of just ∼ 500 (M/5)2 cm−3 in a turbulent medium with an effective RMS Mach number of 5. Compressed layers possess a density ρ=
(M 2 + 1)2 ρo , 2M 2 + 1
(3)
i.e. a number density of 6600 cm−3 for our example. Such a clump could just be observed, as now demonstrated. The question remains: at what density will the formation of molecules become detectable in the infrared? If we assume that each H2 formation generates a fraction of ξ photons in transitions from the first to the ground vibrational level, 11% per cent of these are in the 2.12µm S(1) line and this line represents 19% of the K-band emission (the percentages being taken from the cascade calculation following UV fluorescence), then the total K-band surface brightness is 3.4 × 10−7 ξ fH T 0.5 Lpc n24 W m−2 s−1 sr−1 where fH is the atomic hydrogen fraction, n4 = n/(104 cm−3 ) and Lpc = L/(1 pc). In observer’s mumbo-jumbo, this [ 159 ]
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converts to a K-band flux of 2.0 × 10−18 W m−2 arcsec−2 and a S(1) flux of 3.8 × 10−19 W m−2 arcsec−2 taking ξ = 0.5, fH = 0.5 and the other fiducial values. These values are indeed just on the verge of detectability with modern instruments. The flux derived here is over 1,000 times that predicted by Le Bourlot et al. (1995) for a dense cloud under equilibrium conditions. We believe that certain Bok globules may provide the isolated dense conditions corresponding to the above estimates of physical parameters. Large Bok globules such as CB 34 (Khanzadyan et al., 2002) and B 335 (Hodapp, 1998) may be in the process of condensing out of atomic halos within an interstellar medium recently shaken by strong turbulence. A search for atomic hydrogen halos, other indicators for atomic gas or direct narrow-band spectroscopy may help determine if the broadband emission is being produced by H2 ro-vibrational transitions or scattering from internal or external radiation sources. MML is partially supported by NSF grant AST99-85392, simulations on FORGE & UKAFF (PPARC), and support for AR from PPARC.
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