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Estimate of physical parameters of molecular clouds

Estimate of physical parameters of molecular clouds. Observables: T MB (or F ν ), ν , Ω S Unknowns: V , T K , N X , M H 2 , n H 2 V velocity field T K kinetic temperature N X column density of molecule X M H 2 gas mass n H 2 gas volume density. Velocity field.

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Estimate of physical parameters of molecular clouds

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  1. Estimate of physical parametersof molecular clouds • Observables: TMB(orFν), ν,ΩS • Unknowns:V, TK, NX, MH2, nH2 • V velocity field • TK kinetic temperature • NX column density of molecule X • MH2 gas mass • nH2gas volume density

  2. Velocity field From line profile: • Doppler effect: V = c(ν0- ν)/ν0 along line of sight • in most cases line FWHMthermal< FWHMobserved • thermal broadening often negligible • line profile due to turbulence & velocity field Any molecule can be used!

  3. Star Forming Region channel maps integral under line

  4. rotating disk line of sight to the observer

  5. GG Tau disk 13CO(2-1) channel maps 1.4 mm continuum Guilloteau et al. (1999)

  6. infalling envelope line of sight to the observer

  7. VLA channel maps 100-m spectra red-shifted absorption bulk emission blue-shifted emission Hofner et al. (1999)

  8. Problems: • only V along line of sight • position of molecule with V is unknown along line of sight • line broadening also due to micro-turbulence • numerical modelling needed for interpretation

  9. Kinetic temperature TKand column density NX LTEnH2>> ncr TK = Tex τ>> 1: TK≈ (ΩB/ΩS) TMB but no NX! e.g. 12CO τ<< 1: Nu (ΩB/ΩS) TMB e.g. 13CO, C18O, C17O TK= (hν/k)/ln(Nlgu/Nugl) NX = (Nu/gu) P.F.(TK) exp(Eu/kTK)

  10. τ ≈ 1:τ = -ln[1-TMB(sat)/TMB(main)] e.g. NH3 TK= (hν/k)/ln(g2τ1/g1τ2)  Nu τTK  NX = (Nu/gu) P.F.(TK) exp(Eu/kTK)

  11. If Ni is known for >2 lines TK and NX from rotation diagrams (Boltzmann plots): e.g. CH3C2H P.F.=Σ giexp(-Ei/kTK) partition function

  12. CH3C2H Fontani et al. (2002)

  13. CH3C2H Fontani et al. (2002)

  14. Non-LTE numerical codes (LVG) to model TMB by varying TK, NX, nH2e.g. CH3CN Olmi et al. (1993)

  15. Problems: • calibration error at least 10-20% on TMB • TMB is mean value over ΩB and line of sight • τ>> 1  only outer regions seen • different τ  different parts of cloud seen • chemical inhomogeneities  different molecules from different regions • for LVG collisional rates with H2 needed

  16. Possible solutions: • high angular resolution  small ΩB • high spectral resolution  parameters of gas moving at different V’salong line profile  line interferometry needed!

  17. Mass MH2and density nH2 • Column density: MH2 (d2/X)∫ NX dΩ • uncertainty on X by factor 10-100 • error scales like distance2 • Virial theorem: MH2 d ΘS(ΔV)2 • cloud equilibrium doubtful • cloud geometry unknown • error scales like distance

  18. (Sub)mm continuum: MH2 d2 Fν/TK • TK changes across cloud • error scales like distance2 • dust emissivity uncertain depending on environment • Non-LTE: nH2 from numerical (LVG) fit to TMB of lines of molecule far from LTE, e.g. C34S • results model dependent • dependent on other parameters (TK, X, IR field, etc.) • calibration uncertainty > 10-20% on TMB • works only for nH2≈ ncr

  19. τ> 1  thermalization observed TB observed TB ratio TK = 20-60 K nH2≈ 3 106 cm-3 satisfy observed values

  20. best fits to TB of four C34S lines (Olmi & Cesaroni 1999)

  21. H2 densities from best fits

  22. Bibliography • Walmsley 1988, in Galactic and Extragalactic Star Formation, proc. of NATO Advanced Study Institute, Vol. 232, p.181 • Wilson & Walmsley 1989, A&AR 1, 141 • Genzel 1991, in The Physics of Star Formation and Early Stellar Evolution, p. 155 • Churchwell et al. 1992, A&A 253, 541 • Stahler & Palla 2004, The Formation of Stars

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