SUMMARY

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SUMMARY

1. Statistical equilibrium and radiative transfer in
   molecular (H2) cloud Derivation of physical
   parameters of molecular clouds
2. High-mass star formation theoretical problems
   and observational results

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Statistical equilibriumandradiative transfer

• Statistical equilibrium equations coupling with
  radiation field
• The excitation temperature emission, absorption,
  and masers
• The 2-level system thermalization
• The 3-level system population inversion ? maser

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• Problem
• Calculate molecular line brightness I? as a
  function of cloud physical parameters
• ? calculate populations ni of energy levels of
  given molecule X inside cloud of H2 with kinetic
  temperature TK and density nH2 plus external
  radiation field.
• Note nX ltlt nH2 always e.g. CO most abundant
  species but nCO/ nH2 10-4 !!!

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Radiative transfer equation the line case
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2
A21
B21
B12
C12
C21
1
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3-level system
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A32
B23
C23
B32
C32
A31
B31
B13
C13
C31
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A21
B21
B12
C12
C21
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J2
A21 10 A10 A31 0
A21
J1
A10
J0
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nH2 ncr Tex(1-0) gt TK
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nH2 ncr Tex(1-0) lt 0 i.e. pop.
invers. MASER!!!
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Radio observations

• Useful definition brightness temperature, TB
• In the radio regime Rayleigh-Jeans (h? ltlt kT)
  holds
• In practice one measures mean TB over antenna
  beam pattern, TMB
• Flux measured inside solid angle ?

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• Angular resolution HPBW 1.2 ?/D
• Beam almost gaussian ?B p/(4ln2) HPBW2
• One measures convolution of source with beam
• Example
• gaussian source ? gaussian image with
• TMB TB ?S/(?B ?S)
• S? (2k/?2) TB ?S (2k/?2) TMB (?B ?S)
• TS (TS2 TB2)1/2

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extended source ?Sgtgt ?B ? TMB TB
pointlike source ?Sltlt ?B ? TMB TB ?S/?B
ltlt TB
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Estimate of physical parametersof molecular
clouds

• Observables TMB (or F?), ?, ?S
• Unknowns V, TK, NX, MH2, nH2
• V velocity field
• TK kinetic temperature
• NX column density of molecule X
• MH2 gas mass
• nH2 gas volume density

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Velocity field

• From line profile
• Doppler effect V c(?0- ?)/?0 along line of
  sight
• in most cases line FWHMthermal lt FWHMobserved
• thermal broadening often negligible
• line profile due to turbulence velocity field
• Any molecule can be used!

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Star Forming Region
channel maps
integral under line
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rotating disk
line of sight to the observer
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GG Tau disk
13CO(2-1) channel maps
1.4 mm continuum
Guilloteau et al. (1999)
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GG Tau disk
13CO(2-1) 1.3mm cont.
near IR cont.
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infalling envelope
line of sight to the observer
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VLA channel maps
100-m spectra
red-shifted absorption
bulk emission
blue-shifted emission
Hofner et al. (1999)
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• 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

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Kinetic temperature TKand column density NX

• LTE nH2 gtgt ncr ? TK Tex
• t gtgt 1 TK (?B/?S) TMB but no NX! e.g. 12CO
• t ltlt 1 Nu ? (?B/?S) TMB e.g. 13CO, C18O, C17O
• TK (h?/k)/ln(Nlgu/Nugl)
• NX (Nu/gu) P.F.(TK) exp(Eu/kTK)

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• t 1 t -ln1-TMB(sat)/TMB(main) e.g. NH3
• TK (h?/k)/ln(g2 t1/g1 t2) ? Nu? tTK ?
• NX (Nu/gu) P.F.(TK) exp(Eu/kTK)

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• If Ni is known for gt2 lines ? TK and NX from
  rotation diagrams (Boltzmann plots) e.g. CH3C2H

P.F.S gi exp(-Ei/kTK) partition function
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CH3C2H
Fontani et al. (2002)
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CH3C2H
Fontani et al. (2002)
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• Non-LTE numerical codes (LVG) to model TMB by
  varying TK, NX, nH2 e.g. CH3CN

Olmi et al. (1993)
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• Problems
• calibration error at least 10-20 on TMB
• TMB is mean value over ?B and line of sight
• t gtgt 1 ? only outer regions seen
• different t ? different parts of cloud seen
• chemical inhomogeneities ? different molecules
  from different regions
• for LVG collisional rates with H2 needed

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• Possible solutions
• high angular resolution ? small ?B
• high spectral resolution ? parameters of gas
  moving at different Vs along line profile
• ? line interferometry needed!

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Mass MH2 and density nH2

• Column density MH2? (d2/X) ? NX d?
• uncertainty on X by factor 10-100
• error scales like distance2
• Virial theorem MH2? d TS (?V)2
• cloud equilibrium doubtful
• cloud geometry unknown
• error scales like distance

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• (Sub)mm continuum MH2? d2 F? /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 gt 10-20 on TMB
• works only for nH2 ncr

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t gt 1 ? thermalization
observed TB
observed TB ratio
TK 20-60 K nH2 3 106 cm-3 satisfy
observed values
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best fits to TB of four C34S lines
(Olmi Cesaroni 1999)
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H2 densities from best fits
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Bibliography

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

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The formation of high-mass stars observations
and problems (high-mass star ? Mgt8M? ? Lgt103L?
? B3-O)

1. Importance of high-mass stars their impact
2. High- and low-mass stars differences
3. High-mass stars observational problems
4. The formation of high-mass stars where
5. The formation of high-mass stars how

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Importance of high-mass stars

• Bipolar outflows, stellar winds, HII regions ?
  destroy molecular clouds but may also trigger
  star formation
• Supernovae ? enrich ISM with metals ? affect star
  formation
• Sources of energy, momentum, ionization, cosmic
  rays, neutron stars, black holes, GRBs
• OB stars luminous and short lived ? excellent
  tracers of spiral arms

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• Stellar initial mass function (Salpeter IMF)
  dN/dM ? M-2.35 ? N(10MO) 10-2
  N(1MO)
• Stellar lifetime
  t ?
  Mc2/L ? M-3 ? t(10MO) 10-3 t(1MO)
• 105 1 MO stars per 10 MO star!
• ? Total mass dominated by low-mass stars.
  However
• Stellar luminosity
  L ? M4 ?
  L(10MO) 104 L(1MO)
  Luminosity of stars with mass between M1 and M2
• L(10-100MO) 0.3 L(1-10MO)
• ? Luminosity of OB stars is comparable to
  luminosity of solar-type stars!

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The formation of high-mass and low-mass stars
differences and theoretical problems
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stars lt 8MO isothermal unstable clump
accretion onto protostar disk outflow
formation disk without accretion protoplanetary
disk
sub-mm far-IR near-IR visibleNIR visible
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stars gt 8MO isothermal unstable clump
accretion onto protostar disk outflow
formation disk without accretion protoplanetary
disk
sub-mm far-IR near-IR visibleNIR visible
?
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Low-mass VS High-mass

• Two mechanisms at work
• Accretion onto protostar
• Static envelope n?R-2
• Free-falling core n?R-3/2
• tacc M/(dMacc/dt)
• Contraction of protostar
• tKHGM2/RL
• Stars lt 8 Msun tKH gt tacc
• Stars gt 8 Msun tKH lt tacc
• ? High-mass stars form still in accretion phase

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Low-mass VS High-mass

• Two mechanisms at work
• Accretion onto protostar
• Static envelope n?R-2
• Free-falling core n?R-3/2
• tacc M/(dMacc/dt)
• Contraction of protostar
• tKHGM2/RL
• Stars lt 8 Msun tKH gt tacc
• Stars gt 8 Msun tKH lt tacc
• ? High-mass stars form still in accretion phase

n?R-2
n?R-3/2
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Palla Stahler (1990)
tKHtacc
dM/dt10-5 MO/yr
Main Sequence
Sun
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Problem Stellar radiation pressure ( wind
ionizing flux) halt accretion above M8 Msun ?
how to form Mgt8 M? ?
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• Solutions
• Competitive accretion boosts dM/dt by deepening
  potential well through cluster
  dM/dt(Mgt8M?) gtgt dM/dt(M lt8M?)
• Monolithic collapse accretion through diskjet
  focuses dM/dt enhancing ram pressure (disk) and
  allows photons to escape lowering radiation
  pressure (jet)
• Merging of many stars with Mlt 8 M?
  insensitive to radiation pressure but needs
  gt106 stars/pc3 gtgt observed 104 stars/pc3 !!!

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• Discriminate between different models requires
  detailed observational study of environment
  structure (size, mass of cores) and kinematics
  (rotating disks, infall) on scales lt 0.1 pc
• Monolithic collapse
• disks (jets) necessary for accretion onto OB
  star
• cluster natural outcome of s.f. process
• Competitive accretion (merging)
• disks natural outcome of infallang.mom.cons.
• cluster necessary to focus accretion onto OB star

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High-mass star forming regions Observational
problems

• Deeply embedded in dusty clumps ? high extinction
• IMF ? high-mass stars are rare N(1 MO) 100
  N(10 MO)
• large distance gt400 pc, typically a few kpc
• formation in clusters ? confusion
• rapid evolution tacc 20 MO/10-3 MOyr-1 2 104
  yr
• parental environment profoundly altered
• Advantage
• very luminous (cont. line) and rich (molecules)!

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The formation of high-mass stars where they form
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Visible extinction AVgt100!
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NIR-MIR mostly stars
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NIR-MIR and hot dust
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MIR-FIR poor resolution
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FIR but more sensitive to embedded stars! ?
luminosity estimate
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Radio (sub)mm dusty clumps
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Radio (sub)mm molecular lines
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Radio lt 2cm thin free-free ? ? young HII regions
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Radio gt 6cm free-free ? old HII regions
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Typical star forming region

• (IR-dark) Clouds 10-100 pc 10 K 102-103 cm-3
  Av1-10 CO, 13CO nCO/nH210-4
• Clumps 1 pc 50 K 105 cm-3 AV100 CS,
  C34S nCS/nH210-8
• Cores 0.1 pc 100 K 107 cm-3 AV1000
  CH3CN, exotic molecules nCH3CN/nH210-10
• Outflows gt1pc ? Disks???
• (proto)stars IR sources, maser lines, compact
  HII regions

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The formation of high-mass stars how they form
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Possible evolutionary sequence for high-mass stars

• IR-dark (cold) cloud
• fragmentation
• (hot) molecular core
• infallrotation
• (proto)stardiskoutflow
• accretion
• hypercompact HII region
• expansion
• extended HII region

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IR-dark clouds (gt1pc) pre-stellar phase
MSX 8 ?m
MSX 8 ?m
SCUBA 850 ?m
MSX 8 ?m
SCUBA 850 ?m
SCUBA 850 ?m
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Clump
UC HII
HMC
Core
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Hot molecular core site of high-mass star
formation
rotation!
HC HII or wind
HMC
embedded massive stars
CH3CN(12-11)
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Formation of inverse P-Cyg profile
Observed inverse P Cyg profiles (Girart et al.
2009) ? infall!
H2CO(312-211)
CN(2-1)
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Expanding hypercompact HII region Moscadelli et
al. (2007) Beltran et al. (2007)
7mm free-free H2O masers
500 AU
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Expanding hypercompact HII region Moscadelli et
al. (2007) Beltran et al. (2007)
7mm free-free H2O masers
30 km/s
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IRAS 201264104 Cesaroni et al. Hofner et
al. Moscadelli et al.
Keplerian rotation M7 MO
Moscadelli et al. (2005)
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Conclusions

• More or less accepted
• IR-dark clouds precursors of high-mass stars
• Hot molecular cores cradle of OB (proto)stars
• Disk (jet) natural outcome of OB S.F. process
• Still controversus
• Monolithic collapse (like solar-type stars) or
  competitive accretion (in cluster)?
• Role of magnetic field and turbulence

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Bibliography

• Beuther et al. 2007 in Protostars and Planets V,
  p. 165
• Bonnell et al. 2007 in Protostars and Planets V,
  p. 149
• Cesaroni et al. 2007 in Protostars and Planets V,
  p. 197
• Stahler Palla 2004, The Formation of Stars

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