Jeff Mangum's Science and Technical References: Molecular Excitation

TIP Last Update: JeffMangum - 03 February 2011


  1. Pety, J., Liszt, H. S., and Lucas, R. 2011, "The CO-H2 conversion factor of diffuse ISM: Bright 12CO emission also traces diffuse gas", To be published in the proceedings of the Zermatt 2010 conference: "Conditions and impact of star formation: New results with Herschel and beyond"
    • A large fraction of the CO emission in our Galaxy comes from warm (50-100 K), low density (100-500 cm^(-3)), weakly UV-shielded, diffuse gas (i.e. carbon atoms are mostly locked-up into C+).
  2. Liszt, H. S., Pety, J., and Lucas, R. 2010, A&A, 518, A45, "The CO luminosity and CO-H2 conversion factor of diffuse ISM: does CO emission trace dense molecular gas?"
    • Commonality of the CO- {H_2} conversion factors in diffuse and dark clouds can be understood from considerations of radiative transfer and CO chemistry. There is unavoidable confusion between CO emission from diffuse and dark gas and misattribution of CO emission from diffuse to dark or giant molecular clouds. The character of the ISM is different from what has been believed if CO and {H_2} that have been attributed to molecular clouds on the verge of star formation are actually in more tenuous, gravitationally-unbound diffuse gas.
    • Conversely, it is also the case that molecular gas is detected in the local ISM even when CO emission is not. Lines of sight with {N_{CO}} > 10^{12} ~{cm}^{-2}, {N_{H_2}} > 10^{19} ~{cm}^{-2} have long been detectable in surveys of uv absorption (Sheffer et al. 2008; Burgh et al. 2007; Sonnentrucker et al. 2007; Sheffer et al. 2007), with expected integrated CO brightnesses as low as {{W}_{{CO}}} = 0.001 {{~K~km~s^{-1}}} (Liszt 2007b). And, as discussed here, mm-wave {{HCO^+}} and CO absorption from clouds with {N_{H_2}} > 10^{20}~~{cm}^{-2} are also more common than CO emission along the same lines of sight (see Liszt & Lucas 2000; Lucas & Liszt 1996, and Appendix A).
    • Find a constancy of the CO-H2 conversion factor due to radiative transfer and chemistry.
    • Note that many lines of sight lacking molecular absorption data show CO emission well beyond the galactic extent of the dense gas layer.
    • The similarity of the CO-H2 conversion factors in diffuse and fully molecular gas must have lead to confusion whereby CO emission arising in diffuse gas has been attributed to "molecular clouds".
    • The CO sky is mostly an image of the CO chemistry.
  3. Kutner, M. L. 1984, Fundamentals of Cosmic Physics, 9, pp. 233-316 "Probing Molecular Clouds"
  4. Goldsmith, P. F. 1996, in "Millimeter-Wave Astronomy: Molecular Chemistry & Physics in Space", Proceedings of the 1996 INAOE Summer School of Millimeter-Wave Astronomy held at INAOE, Tonantzintla, Puebla, Mexico, 15-31 July 1996. Edited by W. F. Wall, A. Carramiñana, and L. Carrasco. Kluwer Academic Publishers, 1999., p.57 "Probing Molecular Clouds - Their Density and Structure"

Molecular Cloud Modelling

  1. Brinch, C. and Hogerheijde, M. 2010, A&A, 523, A25, "LIME - A Flexible, non-LTE Line Excitation and Radiation Transfer Method for Millimeter and Far-Infrared Wavelengths"
    • Update to RATRAN
    • NOTE: Cannot explicitly model masing lines, but can handle maser emission (pretty much the same limitation as with LVG). Problem is when tau becomes very negative and the intensity runs-off to infinity.
  2. Keto, E. and Rybicki, G. 2010, ApJ, 716, 1315, "Modeling Molecular Hyperfine Line Emission"
    • Excellent comparison of two viable HF modelling procedures
    • Contains appendix of N2H+ statistical weights, A-values, frequencies, and collisional rates.
    • Compare simulations of N2H+ hyperfine lines made with approximate and more exact rates and find that satisfactory results are obtained.
    • Collisional rates between the individual hyperfine levels themselves have been calculated for only three molecules: HCN (Monteiro & Stutzki 1986), NH3 (Chen et al. 1998), and N2H+ (Daniel et al. 2005) and even then for only a limited number of hyperfine levels.
    • The hyperfine levels of molecules that emit in the millimeter radio spectrum are typically separated by energies in the milli-Kelvin range whereas the separations between rotational levels are several tens to hundreds of Kelvin. Therefore, the hyperfine levels may sometimes be populated approximately in statistical equilibrium even if the rotational levels are not.
    • We do not need to actually compute or store the populations of the hyperfine levels. The assumption of HSE is equivalent to the assumption that the spectral line profile function of the rotational transition including the hyperfine structure is the sum of the spectra of the individual hyperfine lines with the same relative intensities as in optically thin emission. Because these relative intensities depend only on the dipole matrix elements of the hyperfine radiative transitions, we compute the composite profile function once and then replace the simple line profile function of the rotational transition with the composite profile function everywhere in the calculation.
    • The proportional approximation represents a better match to the data, yet for some purposes the HSE approximation may be good enough.
    • Based on this example, the proportional approximation is adequate for N2H+ and could be useful for other molecules with unknown hyperfine collision rates.
  3. Ossenkopf, V., Krips, M., and Stutzki, J. 2008, A&A, 485, 917 "Structure Analysis of Interstellar Clouds: I. Improving the lambda-Variance Method"
    • Used to characterize the power spectrum of interstellar turbulence.
  4. Daniel, F. and Cernicharo, J. 2008, A&A, 488, 1237 "Solving Radiative Transfer with Line Overlaps Using Gauss-Seidel Algorithms"
    • A slightly faster (factor of 2-4) way to solve line overlap problem.
  5. Choi, M. 2002, ApJ, 575, 900-910 "Modeling Line Profiles of Protostellar Collapse Observed with High Angular Resolution"
  6. Yates, J. A., Doty, S. D., Ossenkopf, V., Hogerheijde, M. R., Juvela, M., Wiesemeyer, H., & Schöier, F. L. 2002, A&A, 395, 373-384 "Numerical Methods for Non-LTE Line Radiative Transfer: Performance and Convergence Characteristics"
  7. Ward-Thompson, D. & Buckley, H. D. 2001, MNRAS, 327, 955-983 "Modelling Submillimetre Spectra of the Protostellar Infall Candidates NGC 1333-IRAS 2 and Serpens SMM4"
    • NOTE: Stenholm model
  8. Jessop, N. E. & Ward-Thompson, D. 2001, MNRAS, 323, 1025-1034 "The Initial Conditions of Isolated Star Formation - IV. C18O Observations and Modelling of the Pre-Stellar Core L1689B".
    • NOTE: Lambda iteration / CO depletion
  9. Evans, N. J., II, Rawlings, J. M. C., Shirley, Y. L., & Mundy, L. G. 2001, ApJ, 557, 193-208 "Tracing the Mass during Low-Mass Star Formation. II. Modeling the Submillimeter Emission from Preprotostellar Cores"
  10. van der Tak, F. F. S., van Dishoeck, E. F., & Caselli, P. 2000, A&A, 361, 327-339 "Abundance Profiles of CH3OH and H2CO Toward Massive Young Stars as Tests of Gas-Grain Chemical Models"
    • NOTE: CH3OH Trot a tracer of evolution.
    • NOTE: H2CO abundance constant -> no grain contribution
  11. Park, Y.-S. & Hong, S. S. 1998, ApJ, 494, 605 "Three-Dimensional Non-LTE Radiative Transfer of CS in Clumpy Dense Cores"
    • NOTE: Nice discussion of Monte Carlo model.
  12. Myers, P. C., Mardones, D., Tafalla, M., Williams, J. P., & Wilner, D. J. 1996, ApJ, 465, L133 "A Simple Model of Spectral-Line Profiles from Contracting Clouds"
  13. Boss, A. P. 1993, ApJ, 410, 157-167 "Collapse and Fragmentation of Molecular Cloud Cores. I - Moderately Centrally Condensed Cores"
  14. Wolfire, M. G., Hollenbach, D., Tielens, A. G. G. M. 1993, ApJ, 402, 195-215 "CO(J = 1-0) Line Emission from Giant Molecular Clouds"
    • NOTE: Good appendix on microturbulent and macroturbulent models.
  15. Richer, J. S. & Padman, R. 1991, MNRAS, 251, 707 "The Position-Velocity Diagrams of Protostellar Discs"
  16. Kwan, J. 1978, ApJ, 223, 147-160 "Radiation Transport and the Kinematics of Molecular Clouds"
  17. de Jong, T., Chu, S.-I., & Dalgarno, A. 1975, ApJ, 199, 69-78 "Carbon Monoxide in Collapsing Interstellar Clouds"
  18. White, R. E. 1977, ApJ, 211, 744-754 "Microturbulence, Systematic Motions, and Line Formation in Molecular Clouds"
  19. Leung, C. M. 1978, ApJ, 225, 427-441 "Radiative-Transfer Effects and the Interpretation of Interstellar Molecular Cloud Observations. I - Basic Physics of Line Formation"
  20. Goldreich, Peter; Kwan, John, 1974, ApJ, 189, 441-454 "Molecular Clouds"
  21. Bernes, C. 1979, A&A, 73, 67-73 "A Monte Carlo Approach to Non-LTE Radiative Transfer Problems"
  22. Choi, M., Evans, N. J., II, Gregersen, E. M., & Wang, Y. 1995, ApJ, 448, 742 "Modeling Line Profiles of Protostellar Collapse in B335 with the Monte Carlo Method"
  23. Goldsmith, P. 2001, ApJ, 557, 736-746 "Molecular Depletion and Thermal Balance in Dark Cloud Cores"
  24. Langer, W. D. & Penzias, A. A. 1990, ApJ, 357, 477 "C-12/C-13 Isotope Ratio Across the Galaxy from Observations of C-13/O-18 in Molecular Clouds"
  25. Ossenkopf, V. 1997, New Astronomy, 2, No. 4, 365-385 "The Sobolev Approximation in Molecular Clouds"
  26. Wilking, B. A. 1989, PASP, 101, 637 "The Formation of Low-Mass Stars"
  27. Jorgensen, J. K., Schoier, F. L., and van Dishoeck, E. F. 2005, A&A, 435, 177 "Molecular Freeze-Out as a Tracer of the Thermal and Dynamical Evolution of Pre- and Protostellar Cores"
    • Excellent discussion of molecular freeze-out.
    • Characterized as a function of protostellar evolution.
    • Shows model pictures of different stages of freeze-out.
  28. Jorgensen, J. K., Schoier, F. L., and van Dishoeck, E. F. 2005, A&A, 437, 501 "H2CO and CH3OH Abundances in the Envelopes Around Low-Mass Protostars"
    • Further analysis and characterization of molecular freeze-out.
    • Formaldehyde abundance in most sources well-fit by constant abundance as function of radius.
    • O/P ratio = 1.6+-0.3, implying thermalization of H2CO at low temperatures on icy grain mantles.
    • NGC1333-IRAS4A is best fit by a "drop abundance" profile where the drop is about a factor of 10.
  29. van der Tak, F. F. S., Caselli, P., and Ceccarelli, C. 2005, A&A, 439, 195 Line Profiles of Molecular Ions Toward the Pre-Stellar Core LDN 1544
  30. Pavlyuchenkov, Ya. etal. 2007, ApJ, 669, 1262 Molecular Line Radiative Transfer in Protoplanetary Disks: Monte Carlo Simulations Versus Approximate Methods
    • Nice analysis of various radiative transfer modeling methods as applied to protoplanetary disk sources.
  31. Maret, S., etal. 2004, A&A, 416, 577, "The H2CO Abundance in the Inner Warm Regions of Low Mass Protostellar Envelopes"
    • Models H2CO emission with abundance jumps of approximately a factor of 100 at point where Tk = 100 K (ice evaporation point).
    • Studies various ways to reproduce the abundance jump with other physical effects (velocity profile, density profile, ortho-para ratio, evaporation temperature, etc.) and finds no variations in these parameters that can better fit models with abundance jumps.

Collisional Excitation

  1. Troscompt, N., Faure, A., Wiesenfeld, L., Ceccarelli, C., and Valiron, P. 2009, A&A, 493, 687, "Rotational Excitation of Formaldehyde by Hydrogen Molecules: ortho-H2CO at Low Temperature"
    • Rate calculation coefficients are posted to CDS at VizieR.
    • Update to rates calculated by Green (1991).
    • Assume throughout a scaling factor between He and H2 collisions of 1.37, while Green suggests a factor of 2.2 (which they note).
    • Find that scaling factor of 1.37 for He rates (as used by RADEX) is not sufficient to qualitatively account for the substitution of H2 by He.
    • Differences between He and H2 rates largest at low temperature.
    • Cooling of K-doublets strongly dependent on the collider (oH2 or pH2).
    • Note that critical densities for H2 collisions are decreased relative to the 1.37-factor scaled He rates by a factor of 2-3. But, if you use a scaling factor of 2.2, the agreement is pretty good.
    • Rates calculated are only good for Tk <~ 30 K.
    • Accuracy of rates about 10% (very good!).
  2. Troscompt, N., Faure, A. Maret, S., Ceccarelli, C., Hily-Blant, P., and Wiesenfeld, L. 2009, A&A, 506, 1243, "Constraining the Ortho-to-Para Ratio of H2 With Anomalous H2CO Absorption"
    • Find that the ortho-to-para ratio of H2 is close to 0, or that H2 is mostly para in form in cold gas.
    • Derive Tex from Ta*, which is kind of flimsy.
    • Green (1991) rates scaled by 2.2 reproduce p-H2 form of J=1 emission shown in Figure 2, but does not go as deeply into absorption.
    • Assume an extremely high X(H2CO) ~ 6e(-8).
    • Somewhat suspect analysis, overall.
  3. Dubernet, M.-L., Daniel, F., Grosjean, A., and Lin, C. Y. 2009, "Rotational Excitation of ortho-H2O by para-H2 (j2 = 0, 2, 4, 6, 8) at High Temperature", A&A, 497, 911-925
    • Rotational (de)-excitation state-to-state and effective rate coefficients for temperatures up to 1500 K.
    • Includes:
      • The 45 lowest energy levels of o-H2O with:
        • H2 (j2 = 0) and delta(j2) = 0, +2
        • H2 (j2 = 2) and delta(j2) = 0, -2
      • The 10 lowest energy levels of o-H2O with:
        • H2 (j2 = 4) and delta(j2) = 0, -2
        • H2 (j2 = 2) and delta(j2) = +2
      • Estimates for effective rate coefficients for j2 = 6 and 8
    • For the given model the accuracy of the quantum rate coefficients, explicitly given for different temperatures and transitions, is rather homogeneous and lies between 5% and 40% for the first 40 levels of o-H2O.
    • Strongly recommend using these new rates over previous (Green 1993 or Faure 2007) calculated rates.
    • Note that the coupled state (CS) approximation does extremely badly even at high energy for j2 not equal to 0. This is an issue for some previously calculated rates.
    • See The BASECOL Ro-Vibrational Collisional Excitation Database and Utilities for online listings of these excitation rates and others.
  4. Faure, A. and Josselin, E. 2008, A&A, 492, 257 "Collisional Excitation of Water in Warm Astrophysical Media I. Rate Coefficients for Rovibrationally Excited States"
    • More accurate water excitation rates.
  5. Varshalovich, D. A. and Khersonskii, V. K. 1977, ApL, 18, 167-172 "Collisional Excitation of Interstellar Molecules"
  6. Cummins, S. E., Green, S., Thaddeus, P., and Linke, R. A. 1983, ApJ, 266, 331-338 "The Kinetic Temperature and Density of the Sagittarius B2 Molecular Cloud from Observations of Methyl Cyanide"
  7. Flower, D. R. and Launay, J. M. 1985, MNRAS, 214, 271-277 "Rate Coefficients for the Rotational Excitation of CO by Ortho- and Para-H2"
  8. Bieniek, R. J. and Green, S. 1983, ApJ, 265, L29-L33 "Collisional Rates for Vibrational-Rotational Transitions in Circumstellar SiO Masers"
  9. Green, S. 1986, ApJ, 309, 331-333 "Collisional Excitation of Interstellar Methyl Cyanide"
  10. Green, S., Garrison, B. J., Lester, W. A., Jr., Miller, W. H. 1978, ApJS 37, 321-341 "Collisional Excitation of Interstellar Formaldehyde"
  11. Offer, Alison R. and van Dishoeck, Ewine F. 1992, MNRAS, 257, 377 "Rotational Excitation of Interstellar OH by Para- and Ortho-H2"
  12. Flower, D. R.; Offer, A.; Schilke, P., 1990, MNRAS, 244, 4p-8p "The (J, K) = (3, 3) Inversion Line of NH3 - A Possible Interstellar Chronometer"

-- JeffMangum - 2009-04-20
Topic revision: r7 - 2011-10-11, JeffMangum
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