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20 November 2008AST 514
Protostars and Star Formation
Protostars and Star Formation�
AST 51420 November 2008
20 November 2008AST 514
Protostars and Star Formation
Protostar = Pre-main-sequence star
• Gravitationally bound mass destined to become anindividual main-sequence star– perhaps still⇧ accreting mass– but not destined to fragment into multiple stars
• In hydrostatic equilibrium– supported by mainly by pressure– perhaps secondarily by rotation, magnetic field, ...
• Not yet burning hydrogen– luminosity balanced mainly by gravitational contraction
L ≈
ddt
GM 2
R⎛
⎝⎜⎞
⎠⎟
20 November 2008AST 514
Protostars and Star Formation
PMS contraction at constant mass
– Hayashi track• Teff set by ionization of alkali
metals
Iben 1965, ApJ 141, 993…beware invisible decimal points!
M M
: Teff ≈ 4000K
L ∝ R2
tKH ≡GM 2 / R
L∝ M 2 R3
M M
: L ≈ LEdd ( M ,κ )
20 November 2008AST 514
Protostars and Star Formation
T Tauri Stars
• ≡ Low-mass (≤ 3 Μ) protostars• Originally defined by spectroscopic characteristics
– Late-type spectrum except for strong emission lines, esp. Hα• EW(Hα) ≥ 10 Å : Classical T Tauri Stars• EW(Hα )≤ 10 Å : Weak-lined TTS
• 4000±500 K photosphere plus IR & near-UV excesses– IR excess due to a dusty circumstellar disk
– UV excess due to accretion onto stellar surface
Laccretion ≈ GM*M R*
20 November 2008AST 514
Protostars and Star Formation
Disks & Accretion in TT Stars
boundary layer
photosphere
disk
Hartigan et al. 1991, ApJ 382, 617“veiled” optical absorption linesdue to continuum excess fromboundary-layer
Spectral energy distributions
Optical spectra
Hartmann et al. 1998, ApJ 495, 385
200 AU106-7 yr10-8 M yr-110-2 M
RmaxlifetimeMdisk
�
˙ M
Typical inferred disk properties
20 November 2008AST 514
Protostars and Star Formation
Young Stellar Object Sequence• Class 0: Fully embedded in
collapsing core seen only at LWIRor sub-mm λ– Stellar photosphere not seen– Most of mass still infalling, but
evidence for protostar:outflows/jets
– Age ~ 104 yr• Class I: Embedded
– dlog(λFλ)IR/dlogλ>0– Age ~ 105 yr
• Class II: Classical T Tauri– Photosphere+disk seen– Age ~ 106
• Class III: Weak-lined TT– Disk hardly seen in IR SED– Still contracting toward ZAMS
Wilking (1989), after Adams, Lada, & Shu (1987)
20 November 2008AST 514
Protostars and Star Formation
(Giant) Molecular Clouds• Main star-forming environment
– in present-day galaxies, at least• Molecular hydrogen (H2) is almost
invisible; instead– Dust: extinction, IR emission– CO lines, e.g. J=1→0 @ 115 GHz
• Typical Giant MC properties:
M ~ 3×105 M
R ~ 20pc
nH ~ 300cm−3 T ~ 10K
vturb ~ GM 2R ~5kms−110kTmH
B ~ 4πρvturb2 ~ 30µG
⇒Gravitationally bound, with supersonic, magnetized turbulence
Upper: Barnard 68 (visual)Lower: DR21 (Spitzer 3.6-8 µm)
20 November 2008AST 514
Protostars and Star Formation
Initial Mass Function
ξ ≡dN*
d ln M*
∝M*−x , x ≈ 1.35 for M* ≥ M
(Salpeter 1955)
ξ ∝exp −(ln M* − ln Mc )2 / 2σ 2⎡⎣ ⎤⎦ , Mc ≈ 0.1M
, σ ≈ ln(5.) (Miller & Scalo 1979)
M ≤ M (Chabrier 2003)Black points: Orion; blue: M35;green: Pleides. (Kroupa 2002)
log10 M* / M
20 November 2008AST 514
Protostars and Star Formation
What is the origin of the IMF ?
• Nature: Simple physical arguments predict characteristicmain-sequence mass scales:
• Nurture: The mass function of dense clumps (=“coldcores”) in GMCs is similar to the IMF:– Typical properties:
• Rcore~0.1 pc, Tcore≈10 K, nH ≥ 104 cm-3
MHB = 0.08M
≈ 0.3α 3/ 2me−3/ 4mp
−5/ 4 cG
⎛⎝⎜
⎞⎠⎟
3/ 2⎡
⎣⎢⎢
⎤
⎦⎥⎥
Mβ=0.5 ≈133 M
≈ 70mp−2 c
G⎛⎝⎜
⎞⎠⎟
3/ 2⎡
⎣⎢⎢
⎤
⎦⎥⎥
Alves, Lombardi & Lada (2007)
20 November 2008AST 514
Protostars and Star Formation
Characteristic core masses
M (R) =4π3
ρR3 ⇒ R( M ) =3M4πρ
⎛⎝⎜
⎞⎠⎟
1/3
E = Egrav + Etherm = −3GM 2
5R+
MkT(γ −1)µmH
E ≤ 0 if M ≥ M J =5
3(γ −1)µmH
⎡
⎣⎢
⎤
⎦⎥
3/ 23
4π⎛⎝⎜
⎞⎠⎟
1/ 2(kT )3/ 2
G3/ 2ρ1/ 2
≈ 12T
10K⎛⎝⎜
⎞⎠⎟
3/2 nH
103cm−3
⎛
⎝⎜⎞
⎠⎟
−1/2
M
• The Jeans mass ≈ minimum mass of a self-gravitatingsphere with a specified temperature and density.
• Low & Lynden-Bell (1976): minimum T & MJ via radiativecooling & fragmentation:
M J ,min ≈ 0.005
κ e.s.
κ Planck
⎛
⎝⎜
⎞
⎠⎟
1/7
M
20 November 2008AST 514
Protostars and Star Formation
Disks are expected from angular-momentum conservation
• Core sizes ~ 0.1 pc, rotation ~ 0.1 km s-1, masses ~ M
⇒typical angular momentum L ~ 6 x 1054 g cm2 s-1
• ⇒ Collapse at constant L would lead to a centrifugalradius
• However, the cores are probably partially supported bymagnetic field– Slow contraction as the field slips out of the gas via ambipolar
diffusion could shed much of this angular momentum.
RL ≡
J 2
GM 3 ~ 4000 AU ≈ 0.02 pc
20 November 2008AST 514
Protostars and Star Formation
Further Reading
• Protostars and Planets V. Reipurth et al., eds. (Univ.Arizona Press, 2007).
• McKee, C.F. & Ostriker, E.C. 2007, ARAA 45, 565.“Theory of Star Formation”