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”