Mopra Induction Weekend May 2005

1. Determination of physical properties from molecular linesKate BrooksAustralia Telescope National Facility Mopra Induction Weekend May 2005

2. Interstellar Molecules Ehrenfreund & Charnley 2000, ARA&A, 38, 427 137 molecules have been detected in space (205 including isotopomers, 50 in comets)

3. Talk Outline Radiative Transfer 12CO(1-0): Workhorse of mm-line studies Optically thin density tracers (LTE Mass) Temperature tracers Non-LTE models Signatures for infalling gas Bipolar outflows

4. Radiative Transfer Fundamental equation of radiative transfer Absorption emission coefficients Optical depth Kirchhoff’s law valid in TE and LTE Planck law

5. Rayleigh-Jeans approximation to Planck law Brightness Temperature Temperature that would result in brightness if source were a black-body in the Rayleigh-Jeans limit For isothermal medium

6. Optically thin Optically thick

7. Column Density  is related to the level population Integration along the line of sight: Absorption coefficient -> Optical depth  Level population -> Level column density N Total column density : Sum over all levels

8. Excitation Temperature Tex In LTE there is one excitation temperature Tex that describes the level population according to the Boltzmann distribution When collisions dominate: Level population can be described as Boltzmann distribution at kinetic gas temperature Tkin One observed transition and adopting a value for Tkin gives all level populations -> Total column density N

9. Measuring Kinetic Temperature Tkin Optically thick transitions: 2. Line ratios e.g. 13CO(2-1) / 13CO(1-0) 3. Rotation Diagrams e.g. NH3, CH3CCH, CH3CN

10. Critical Density Any spectral-line transition is only excited above a certain critical density Critical density is the density at which: Collisional deexcitation ~ spontaneous radiative decay 12CO(1-0) 115.27 GHZ 4 x 102 cm-3Lowest critical density CS(2-1) 97.98 GHz 1 x 105 cm-3 HCN(1-0 88.63 GHz 1 x 105 cm-3 NH3(1,1) 23.694 GHZ 1 x 103 cm-3

11. 12CO(1-0): Workhorse of mm-line studies Ubiquitous gas tracer - High abundance - Lowest critical density Excellent for global cloud parameters - Temperature - Mass - Structure Limitations - Optically thick - Complex velocity profiles - Confused towards Galactic plane - Depletion at high densities and low temperature

12. Example: The Carina Nebula “ It would be manifestly impossible by verbal description to give any just idea of the capricious forms and irregular gradations of light affected by the different branches and appendages of this nebula. In this respect the figures must speak for themselves.” Sir J. F. W. Herschel 1847

13. Mopra observations of the Carina nebula 12CO(1-0) 115 GHz 1996 2500 pointings 0.1 K rms per channel Brooks et al. 1998, PASA, 15, 202 Example Grid

14. Excitation Temperature 12CO1-0 is optically thick TB = Tex = Tkin Use ‘xpeak’ in miriad to find P(12CO)

15. Excitation Temperature Map “Treasure Cluster”

16. Mass estimates from CO observations Virial Mass Relies on the assumption that the cloud’s kinetic energy stabilizes it against gravitational collapse (Virialised) The overall velocity width of the CO emission line reflects the motion of the gas and ultimately the underlying mass (Virial mass) But … Are molecular clouds virialised? What about external pressure?

17. Mass estimates from CO observations X - Factor CO-to-H2 Conversion factor Galactic Value: XCO ≈ 2.8 x 1020 cm-2 K (km s-1)-1

18. H2 Column Density to Mass Mass = column density x spatial extent Average H2 density Spherical with effective radius R 2R = min + maj Mass determined this way is often called the ‘CO mass’

19. But … To determine Xco we need an independent measure of the mass of the cloud and the distance D in order to work out N(H2)

20. Independent Mass estimate for Xco Virial Mass Not all clouds are virialised Radiative Transfer method Very difficult to do in for other galaxies (minimum 3 lines) Extinction Assumes standard reddening law and dust-to-gas ratio Dust Emission Assumes dust absorption coefficient and dust-to-gas ratio

21. Use Xco with caution Problem for all determinations of the conversion factor. All of them have factors between 2-5 in uncertainty. Galactic: Constant for specific regions only Extra Galactic: Very difficult to measure Xco Localised values that depend on metallicity and galaxy type Sometimes you have little choice e.g. z  6

22. Chemical Characteristics of star-forming regions Pre-stellar core Ions, Long Chains HC5N, DCO+ Cold envelope Simple species, Heavy depletions CS, N2H+ Warm inner envelope Evaporated species CH3OH, HCN Hot core Complex organics CH3OCH3, CH3CN Outflow: direct impact Si- and S-species SiO, SO2 Outflow: walls, entrainment Evaporated ices CH3OH PDR, compact HII regions Ions, Radicals CN/HCN, CO+ Massive Disk Ions, D-rich species, photoproductions HCO+, DCN, CN Debris Disk Dust, CO (E. F. van Dishoeck)

23. Example: 12CO, 13CO and CS intensities in the Carina nebula

24. Utilising other molecular-line transitions More than 40 emission lines in the Mopra 3-mm band Optically thin density tracers (LTE Mass) Temperature tracers Non-LTE models Signatures for infalling gas Bipolar outflows

25. Optically thin density tracers: Testing 13CO, C18O and CS e.g. Alves et al., 1998 Lada et al., 1994

26. In the study by Lada et al. 1994 “Dust extinction and molecular gas in the dark cloud IC 5146” Direct comparison of 13CO, C18O and CS integrated intensities and column densities with Av to a range in Av between 0-32 mag of extinction. Integrated intensities I(13C0) = 1.88 + 0.72Av K km s-1 (Av ≤ 5 mag) I(C180) = 0.07 + 0.10Av K km s-1 (Av ≤ 15 mag) I(CS) = 0.10 + 0.06Av K km s-1 (Av ≤ 15 mag) Between 8 and 10 mag the 13CO emission appears saturated Uncomfortable prediction of molecular emission and 0 mag

27. Integrated Intensity to Column Density Only one transition is measured and an extrapolation to total column density is done by assuming a LTE population Case Study 13CO(2-1) Integrated intensity W13CO

28. We need a value for Tex • use value determined from 12CO • assume a value (e.g. 35 K) f(35 K) = 0.64 The value of Tex has a large impact on optical depth but not on column density

29. Back to the study by Lada et al. 1994 Assuming LTE For 13CO and C18O: Based on 12CO data: Tex = 10 K For CS: Subthermal excitation: Tex = 5 K Column Densities N(13C0)LTE/Av = 2.18 x 1015 cm-2 mag-1 (Av ≤ 5 mag) N(C180) LTE/Av = 2.29 x 1014 cm-2 mag-1 (Av ≤ 15 mag) N(CS)LTE/Av = 4.5 x 1011 cm-2 mag-1 (Av ≤ 15 mag)

30. Not there yet! Column density to H2 density Gas-to-dust ratio of Savage & Drake (1978) N(H2) = 0.94 x 1021 Av cm-2 Which leads to: N(13C0)/N(H2) = 4 x 105 (Av 5 mag) Mass determined this way is often called the ‘LTE mass’

31. Dust Extinction C18O Dust Emission 0.1 pc Bianchi et al. Depletion T < 15 K and n > 105 cm-3 CO and CS freeze out onto the dust grains Species linked to molecular nitrogen are less affected E.g. NH3, N2H+, N2D+ Alves et al.

32. Simple Line Ratio Analysis Beam filling factor: Ratio of lines with similar frequency (and hence similar ) ->  cancels out Ratio of different species -> Optical Depth (if Tex and the isotopic abundance ratio is known) e.g. 12CO(1-0) / 13CO(1-0) [12CO/13CO] ≈ 89 Ratio of different transitions ( << 1) -> Excitation temperature e.g. C18O(2-1) / C18O(1-0)

33. Note: Different species and different transitions of one species arising in different parts of a region with different beam filling factors Good Thermometers: Molecules with many transitions with a large range of energy levels in a small frequency interval Symmetric top molecules: e.g. Ammonia NH3 Methyl Acetylene CH2C2H Methyl Cyanide CH3CN NH3(1,1): 18 hyperfine components mixed into 5 lines Fitting all 18 components -> optical depth

34. Rotation Diagrams Integrated line intensity versus energy above ground If LTE plot is a straight line with slope ~ (-1/T) Trot = Tkin Garay, Brooks et al., 2002

35. Non-LTE Modelling Additional Considerations - Stimulated emission - Radiative (photon) trapping Large Velocity Gradient (LVG) approximation - assume large-scale velocity gradient exists in cloud - photons are absorbed locally, then immediately escape Maximum Escape Probability models

37. Infall asymmetry Optically thick line Tex (R2) > Tex (R1) Tex (B2) > Tex (B1) Optically thin line B1 B2 R2 R1 Infall region Constant line-of-sight velocity Static envelope

38. Infall Protostar SMM4 in Serpens Narayanan et al., 2002, ApJ, 565, 319

39. 16272-4837 • evidence for infall • infall velocities of 0.5 km s-1 • are obtained using model of Myers et al. (1996) • - Minfall 10-3 Msun yr-1 • evidence for outflow • - voutflow = 15 km s-1 . Garay, Brooks, et al. 2003

40. Outflows Bourke et al. 1997

41. Outflows

42. Protostar IRAM 04191 in Taurus Belloche et al., 2002, A&A, 393, 972

44. Integrated Intensity to Column Density Case Study 13CO(2-1) Integrated intensity W13CO