Estimate of physical parameters of molecular clouds
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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
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


Velocity field
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!


Estimate of physical parameters of molecular clouds

Star Forming Region

channel maps

integral

under line


Estimate of physical parameters of molecular clouds

rotating disk

line of sight to the observer


Estimate of physical parameters of molecular clouds

GG Tau disk

13CO(2-1) channel maps

1.4 mm continuum

Guilloteau et al. (1999)


Estimate of physical parameters of molecular clouds

infalling

envelope

line of sight to the observer


Estimate of physical parameters of molecular clouds

VLA channel maps

100-m spectra

red-shifted

absorption

bulk emission

blue-shifted

emission

Hofner et al. (1999)


Estimate of physical parameters of molecular clouds

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


Kinetic temperature t k and column density n x
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)


Estimate of physical parameters of molecular clouds

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)


Estimate of physical parameters of molecular clouds

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


Estimate of physical parameters of molecular clouds

CH3C2H

Fontani et al. (2002)


Estimate of physical parameters of molecular clouds

CH3C2H

Fontani et al. (2002)


Estimate of physical parameters of molecular clouds

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

Olmi et al. (1993)


Estimate of physical parameters of molecular clouds

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


Estimate of physical parameters of molecular clouds

Possible solutions:

  • high angular resolution  small ΩB

  • high spectral resolution  parameters of gas moving at different V’salong line profile

     line interferometry needed!


Mass m h 2 and density n h 2
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


Estimate of physical parameters of molecular clouds

  • (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


Estimate of physical parameters of molecular clouds

τ> 1  thermalization

observed TB

observed TB ratio

TK = 20-60 K

nH2≈ 3 106 cm-3

satisfy observed

values


Estimate of physical parameters of molecular clouds

best fits to TB of four C34S lines

(Olmi & Cesaroni 1999)


Estimate of physical parameters of molecular clouds

H2 densities from best fits


Bibliography
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