Line Of Sight Radiative Transfer Analysis Of B68 And Tmc1-c
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Line of Sight Radiative Transfer Analysis of B68 and TMC1-C Christopher H. De Vries California State Univerisity, Stanislaus Five Parameter Infall Model
We present the results of an analysis of CS J = 2 → 1 and N2H+ J = 1 → 0 spectral line observations of B68 and TMC1C using best fit analytic radiative transfer models to simulate the emission along each line of sight. The radiative transfer model is designed to simulate self-absorbed asymmetric line profiles by assuming that there is an excitation temperature gradient along each line of sight and that there is a uniform infall or outflow velocity which results in a blue or red asymmetric line profile. Observation of optically thin isotopologues of CS and N2H+ indicate that the molecular line profiles in B68 and TMC1-C are self-absorbed, making these analytic line of sight models appropriate tools to analyze observations of these regions. Analysis of each line of sight using the analytic radiative transfer model yield maps of the five parameters that make up the model: line of sight velocity, infall speed, optical depth, peak excitation temperature, and line width. By mapping these parameters of the fit to the line profiles, we are able to find regions which have distinct spectral features, which may indicate a kinematically distinct regions of the larger cloud. Analysis of B68 and TMC1-C indicates that these clouds are complex regions which may both contain regions of infall, outflow, high optical depth, low optical depth, high peak excitation, and low peak excitation temperatures within the same core. In both clouds the region with the highest optical depth does not match the region with the highest excitation temperature, indicating that these regions should not be thought of as spherical dense central peaks, but rather complex dynamical structures. We identify spectrally unique signatures in each cloud and attempt to build a coherent picture of the physical state and dynamical processes in these star-forming regions.
3.65
4.5
3.60
4.0
0
3.5
Dec Offset (asec)
3.55
3.0
3.50
-50
2.5
-50
3.45
2.0
3.40
-100
3.35 50
0 RA Offset (asec)
-50
3.30
100
50
0 RA Offset (asec)
Dec Offset (asec)
Dec Offset (asec)
5.5
0.03 -50
5.0
-0.01 -0.05 50
0 RA Offset (asec)
-50
0
-50
-100
50
0 RA Offset (asec)
(75'',-30'')
(45'',-30'')
50
0 RA Offset (asec)
200
0
-200 -400 RA Offset (asec)
-600
5.4
-200
5.3
0
-800
400
200
-50
6.0 600
400
5.5 400
(-15'',-30'')
-600
-800
0.4 0.3 0.2
5.0
200
200
4.5
0
0.0 -0.1
0
4.0
-0.2
-200
-0.3
3.5
-400
-400 400
200
0
-200 -400 RA Offset (asec)
-600
3.0
-800
5.2
0.1
-0.4 400
200
0
-200 -400 RA Offset (asec)
-600
-800
TMC1-C Sigma (km/s)
-0.5
0.25
600
0.21
400 0.17
200
0.13
0
-200 -400
(0'',-30'')
-200 -400 RA Offset (asec)
TMC1-C Vin (km/s)
600
0.05
(15'',-30'')
0
6.5
-200
3.5
-50
5.5
0
-400
4.0 100
5.6
2
0.15 Maps of each parameter of the Hill5 fit to the CS J = 2 → 1 emission of B68 and TMC1-C are shown to the left and right, respectively, of this text. The contours represent the integrated CS J = 2 → 1 intensity, while the color maps represent each parameter of the fit. Below the text individual spectral line fits to CS J = 2 → 1 spectra for B68 0.13 and to an N H+ J = 1 → 0 spectrum which includes 7 hyperfine components all fit with a single Hill5 model for 2 TMC1-C. Note that the B68 line of sight velocity fit shows a gradient consistent with that observed previously by Lada et 0.11 al. (2003) in optically thin tracers, while the infall velocity fit shows the pulsation which they previously characterized in this source. The model also indicates that the integrated intensity peak corresponds to a peak in the excitation temperature, while the majority of the gas, indicated by the optical depth, is located more in the center of the cloud. 0.09 TMC1-C shows very complex structure including a velocity gradient along the ridge in the line of sight velocity map, and oscillation between infall, outflow, and infall once again on the infall velocity map. The peak excitation temperature map as well as the optical depth map are consistent with a ridge of dense gas containing a few dense 0.07 knots.
50
100
-0.09
τr
5.7
Fitting Results
B68 Sigma (km/s)
Dec Offset (asec)
4.5
-100
100
0
TMC1-C Tpeak (K)
6.0
0.07
τ
200
6
400
6.5
0
-100
200
-400
7.0
0.11
Tbg
8
7.5
50 0.15
-50
400
10 400
-200
0.5
-50
B68 Tpeak (K)
0
12 600
1.0
B68 Vin (km/s) 50
600
Dec Offset (asec)
100
vc
4
1.5
-100
vc
TMC1-C VLSR (km/s)
14
Dec Offset (asec)
0
TMC1-C Optical Depth
5.0
50
Tpk
τf
Dec Offset (asec)
3.70
50
Dec Offset (asec)
B68 Optical Depth
Τex
The figure to the right illustrates the excitation temperature variation along the line of sight for the Hill5 model we use to fit the line profiles. Note that the 5 parameters which are fit for each line of sight include the peak excitation temperature (TP ), the total optical depth (τ ), the line of sight velocity (VLSR), the infall velocity (VC ), and the line width (σ).
Dec Offset (asec)
B68 Vlsr (km/s)
The model we use to fit the spectral line along each line of sight is the Hill5 model described in De Vries & Myers (2005). This model assumes that excitation rises from the background temperature (Tbg ) to a peak temperature (TP ) linearly and then falls again linearly back to the background temperature for the observed molecular transition. Each side of the cloud is free to move with a line of sight velocity vC in opposite directions producing either infall or outflow motions. This velocity gradient is added to the average line of sight velocity (vLSR) of the cloud. The total optical depth is split evenly between each side of the cloud and spread in a Gaussian distribution with a velocity width σ over the central velocity of that portion of the cloud. This five parameter model allows us to replicate the asymmetric line shape typically seen in optically thick tracers for infalling molecular cloud cores and extract a parameterization consistent with those motions.
Dec Offset (asec)
Abstract
0.09
400
200
0
-200 -400 RA Offset (asec)
-600
-800
0.05
+
(-45'',-30'')
TMC-1C N2H J=1-0
1.5
1.0
1.0
0.6 0.4
TA (K)
⋆
TA (K)
0.8
0.2 0.0 -0.22.0 2.5 3.0 3.5 4.0 4.5 5.0 Velocity (km/s)
Conclusions The visualization of 3-D molecular line data sets with two spatial dimensions and a third velocity dimension can be difficult. Most methods rely on taking slices in velocity and treating each component as separate, however in the case of infall motions the components along the line of sight are not truly separate, but the result of absorption along the line of sight. Rather than try more complex visualization methods we advocate the use of this simple radiative transfer model to fit, visualize, and interpret the two component spectra that may most likely be the result of self-absorption along the line of sight. Of course the model we propose in De Vries & Myers (2005) is not a perfect or unambiguous representation of the cloud and makes several simplifying assumptions, including that each half of the cloud is moving with a uniform velocity, that the excitation gradients are linear along the line of sight, and that the excitation near the edge of the cloud is that of the microwave background. However, this model presents a few necessary assumptions in order to create an analytic fit to the data with a minimum of adjustable parameters. As such it may prove to be a useful parameterization even beyond regions where strictly applicable.
0.5 0.0 -4
-2
0
2
4 6 Velocity (km/s)
8
10
12
14
Collaborators
I am collaborating on this work with Philip Myers (Harvard-Smithsonian Center for Astrophysics), Tyler Bourke (HarvardSmithsonian Center for Astrophysics), Charles Lada (Harvard-Smithsonian Center for Astrophysics), Edwin Bergin (University of Michigan), and Scott Schnee (California Institute of Technology).
References De Vries, C. H., & Myers, P. C. 2005, ApJ, 620, 800. Lada, C. L., Bergin, E. A., Alves, J. F., & Huard, T. L. 2003, ApJ, 586, 286. I am grateful for support from NSF grant AST-0708158 and the Naraghi family.
We present the results of an analysis of CS J = 2 → 1 and N2H+ J = 1 → 0 spectral line observations of B68 and TMC1C using best fit analytic radiative transfer models to simulate the emission along each line of sight. The radiative transfer model is designed to simulate self-absorbed asymmetric line profiles by assuming that there is an excitation temperature gradient along each line of sight and that there is a uniform infall or outflow velocity which results in a blue or red asymmetric line profile. Observation of optically thin isotopologues of CS and N2H+ indicate that the molecular line profiles in B68 and TMC1-C are self-absorbed, making these analytic line of sight models appropriate tools to analyze observations of these regions. Analysis of each line of sight using the analytic radiative transfer model yield maps of the five parameters that make up the model: line of sight velocity, infall speed, optical depth, peak excitation temperature, and line width. By mapping these parameters of the fit to the line profiles, we are able to find regions which have distinct spectral features, which may indicate a kinematically distinct regions of the larger cloud. Analysis of B68 and TMC1-C indicates that these clouds are complex regions which may both contain regions of infall, outflow, high optical depth, low optical depth, high peak excitation, and low peak excitation temperatures within the same core. In both clouds the region with the highest optical depth does not match the region with the highest excitation temperature, indicating that these regions should not be thought of as spherical dense central peaks, but rather complex dynamical structures. We identify spectrally unique signatures in each cloud and attempt to build a coherent picture of the physical state and dynamical processes in these star-forming regions.
3.65
4.5
3.60
4.0
0
3.5
Dec Offset (asec)
3.55
3.0
3.50
-50
2.5
-50
3.45
2.0
3.40
-100
3.35 50
0 RA Offset (asec)
-50
3.30
100
50
0 RA Offset (asec)
Dec Offset (asec)
Dec Offset (asec)
5.5
0.03 -50
5.0
-0.01 -0.05 50
0 RA Offset (asec)
-50
0
-50
-100
50
0 RA Offset (asec)
(75'',-30'')
(45'',-30'')
50
0 RA Offset (asec)
200
0
-200 -400 RA Offset (asec)
-600
5.4
-200
5.3
0
-800
400
200
-50
6.0 600
400
5.5 400
(-15'',-30'')
-600
-800
0.4 0.3 0.2
5.0
200
200
4.5
0
0.0 -0.1
0
4.0
-0.2
-200
-0.3
3.5
-400
-400 400
200
0
-200 -400 RA Offset (asec)
-600
3.0
-800
5.2
0.1
-0.4 400
200
0
-200 -400 RA Offset (asec)
-600
-800
TMC1-C Sigma (km/s)
-0.5
0.25
600
0.21
400 0.17
200
0.13
0
-200 -400
(0'',-30'')
-200 -400 RA Offset (asec)
TMC1-C Vin (km/s)
600
0.05
(15'',-30'')
0
6.5
-200
3.5
-50
5.5
0
-400
4.0 100
5.6
2
0.15 Maps of each parameter of the Hill5 fit to the CS J = 2 → 1 emission of B68 and TMC1-C are shown to the left and right, respectively, of this text. The contours represent the integrated CS J = 2 → 1 intensity, while the color maps represent each parameter of the fit. Below the text individual spectral line fits to CS J = 2 → 1 spectra for B68 0.13 and to an N H+ J = 1 → 0 spectrum which includes 7 hyperfine components all fit with a single Hill5 model for 2 TMC1-C. Note that the B68 line of sight velocity fit shows a gradient consistent with that observed previously by Lada et 0.11 al. (2003) in optically thin tracers, while the infall velocity fit shows the pulsation which they previously characterized in this source. The model also indicates that the integrated intensity peak corresponds to a peak in the excitation temperature, while the majority of the gas, indicated by the optical depth, is located more in the center of the cloud. 0.09 TMC1-C shows very complex structure including a velocity gradient along the ridge in the line of sight velocity map, and oscillation between infall, outflow, and infall once again on the infall velocity map. The peak excitation temperature map as well as the optical depth map are consistent with a ridge of dense gas containing a few dense 0.07 knots.
50
100
-0.09
τr
5.7
Fitting Results
B68 Sigma (km/s)
Dec Offset (asec)
4.5
-100
100
0
TMC1-C Tpeak (K)
6.0
0.07
τ
200
6
400
6.5
0
-100
200
-400
7.0
0.11
Tbg
8
7.5
50 0.15
-50
400
10 400
-200
0.5
-50
B68 Tpeak (K)
0
12 600
1.0
B68 Vin (km/s) 50
600
Dec Offset (asec)
100
vc
4
1.5
-100
vc
TMC1-C VLSR (km/s)
14
Dec Offset (asec)
0
TMC1-C Optical Depth
5.0
50
Tpk
τf
Dec Offset (asec)
3.70
50
Dec Offset (asec)
B68 Optical Depth
Τex
The figure to the right illustrates the excitation temperature variation along the line of sight for the Hill5 model we use to fit the line profiles. Note that the 5 parameters which are fit for each line of sight include the peak excitation temperature (TP ), the total optical depth (τ ), the line of sight velocity (VLSR), the infall velocity (VC ), and the line width (σ).
Dec Offset (asec)
B68 Vlsr (km/s)
The model we use to fit the spectral line along each line of sight is the Hill5 model described in De Vries & Myers (2005). This model assumes that excitation rises from the background temperature (Tbg ) to a peak temperature (TP ) linearly and then falls again linearly back to the background temperature for the observed molecular transition. Each side of the cloud is free to move with a line of sight velocity vC in opposite directions producing either infall or outflow motions. This velocity gradient is added to the average line of sight velocity (vLSR) of the cloud. The total optical depth is split evenly between each side of the cloud and spread in a Gaussian distribution with a velocity width σ over the central velocity of that portion of the cloud. This five parameter model allows us to replicate the asymmetric line shape typically seen in optically thick tracers for infalling molecular cloud cores and extract a parameterization consistent with those motions.
Dec Offset (asec)
Abstract
0.09
400
200
0
-200 -400 RA Offset (asec)
-600
-800
0.05
+
(-45'',-30'')
TMC-1C N2H J=1-0
1.5
1.0
1.0
0.6 0.4
TA (K)
⋆
TA (K)
0.8
0.2 0.0 -0.22.0 2.5 3.0 3.5 4.0 4.5 5.0 Velocity (km/s)
Conclusions The visualization of 3-D molecular line data sets with two spatial dimensions and a third velocity dimension can be difficult. Most methods rely on taking slices in velocity and treating each component as separate, however in the case of infall motions the components along the line of sight are not truly separate, but the result of absorption along the line of sight. Rather than try more complex visualization methods we advocate the use of this simple radiative transfer model to fit, visualize, and interpret the two component spectra that may most likely be the result of self-absorption along the line of sight. Of course the model we propose in De Vries & Myers (2005) is not a perfect or unambiguous representation of the cloud and makes several simplifying assumptions, including that each half of the cloud is moving with a uniform velocity, that the excitation gradients are linear along the line of sight, and that the excitation near the edge of the cloud is that of the microwave background. However, this model presents a few necessary assumptions in order to create an analytic fit to the data with a minimum of adjustable parameters. As such it may prove to be a useful parameterization even beyond regions where strictly applicable.
0.5 0.0 -4
-2
0
2
4 6 Velocity (km/s)
8
10
12
14
Collaborators
I am collaborating on this work with Philip Myers (Harvard-Smithsonian Center for Astrophysics), Tyler Bourke (HarvardSmithsonian Center for Astrophysics), Charles Lada (Harvard-Smithsonian Center for Astrophysics), Edwin Bergin (University of Michigan), and Scott Schnee (California Institute of Technology).
References De Vries, C. H., & Myers, P. C. 2005, ApJ, 620, 800. Lada, C. L., Bergin, E. A., Alves, J. F., & Huard, T. L. 2003, ApJ, 586, 286. I am grateful for support from NSF grant AST-0708158 and the Naraghi family.
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