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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!

slide3

Star Forming Region

channel maps

integral

under line

slide4

rotating disk

line of sight to the observer

slide5

GG Tau disk

13CO(2-1) channel maps

1.4 mm continuum

Guilloteau et al. (1999)

slide6

infalling

envelope

line of sight to the observer

slide7

VLA channel maps

100-m spectra

red-shifted

absorption

bulk emission

blue-shifted

emission

Hofner et al. (1999)

slide8
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)

slide11
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)

slide12
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

slide13

CH3C2H

Fontani et al. (2002)

slide14

CH3C2H

Fontani et al. (2002)

slide16
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
slide17
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
slide19
(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
slide20

τ> 1  thermalization

observed TB

observed TB ratio

TK = 20-60 K

nH2≈ 3 106 cm-3

satisfy observed

values

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
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