Protostars and Pre-Main Sequence Evolution

Jose Garmilla

Princeton University

October 16, 2012

Outline

Protostars

Gravitational CollapseAccretion PhaseComparissons to Observations

Pre-Main Sequence Evolution

Convective and Radiative ContractionDeuterium Burning and the Stellar Birth LineLithium Burning and Substellar ObjectsDegeneracyT Tauri Stars

Conclusions

ProtostarsGravitational Collapse

Bonnor-Ebbert Mass

Mcrit = 1.18c4s

P1/2surf G

3/2= 1.82

( n

104cm−3

)−1/2(

T

10 K

)3/2

M�

The process starts with cores of M ∼ M�, and R ∼ 0.1 pc.Three phases of collapse

Isothermal Collapse

Adiabatic Collapse

Envelope Accretion

ProtostarsIsothermal and Adiabatic Collapse

Gm

4πr4+

dP

dm= − 1

4πr2

d2r

dt2,

dr

dm=

1

4πr2ρ,

Lr = −64π2acr4

3κR

T 3 dT

dm

dLrdm

= −dE

dt− P

dv

dt

with bc: r = Lr = 0 at m = 0, P = Po LR = 4πR2σT 4eff at m = M

τ ≈ κRρR, tdiff ≈ 3κRρ(∆r)2/c , tff ≈ (Gρ)−1/2

Isothermal Phase: τ � 1, ρ = 10−19–10−13gcm−3, efficientcooling, can assume constant temperature (T ≈ 10 K).

Adiabatic Phase: τ & 1, tdiff � tff, infrared radiation gets trapped,can ignore heat term in energy equation.

ProtostarsIsothermal and Adiabatic Collapse

Larson, 1969

Bodenheimer, 2011

ProtostarsAccretion Phase

Stahler et al., 1980

The central part of the corereaches quasi-hydrostaticequilibrium while the outerregions are still in isothermalcollapse.

tKH ≈ GM2/RL ∼ Myrtacc ≈ M/M ∼ 105 yrtdiff � tacc � tKH , thereforeL ≈ Lacc.

Dust sublimates at T ≈ 1500 K.

ProtostarsComparissons to Observations

Bodenheimer, 2011

Luminosity Problem, for M = 0.5M�Lacc ∼ 10L�.

Kenyon et al., 1993Bodenheimer, 2011

Non-thermal spectrum due wavelengthdependent opacity.

Pre-Main Sequence EvolutionConvective and Radiative Contraction

Palla & Staller, 1999

In the interior,3

16πGac

κRLrP

mT 4>

(∂ lnT

∂ lnP

)S

κK ∝ ρT−3.5

Thin Outer Radiative Zonewith H−,κH− ∝ Zρ0.5T 9

κpPp =2

3g

Pre-Main Sequence EvolutionConvective and Radiative Contraction

Bodenheimer, 2011

Stars above 6M� are already in the main sequence when theaccretion phase is over.

Pre-Main Sequence EvolutionDeuterium Burning and the Stellar Birthline

Stahler, 1988

Deuterium Burns at 106 K

1H + 2D → 3He + γ

ε ∝ f [D/H] ρT 11.8

[D/H] = 2× 10−5, f = 1 Stahler, 1988

Pre-Main Sequence EvolutionDeuterium Burning and the Stellar Birthline

Burrows et al., 2003

Pre-Main Sequence EvolutionLithium Burning and Substellar Objects

Burrows et al., 2003

Cores with M < 0.08M�, can’t burnHydrogen

Lithium Burns at 2.5× 106 K1H + 7Li → 4He + 4He

Burrows et al., 2003

Pre-Main Sequence EvolutionDegeneracy

Bodenheimer, 2011

Burrows et al., 2003

Pe = 1.004 × 1013 (ρ/µe)5/3 dyne cm−2

ρ = 2.4 × 10−8µeT 3/2g cm−3

Pre-Main Sequence EvolutionT Tauri Stars

Lada et al., 1999

Hα, high Li abundance (∼ 10−9H), nearbydark clouds, X-rays emission, strongmagnetic fields (Zeemansplitting∼kilogauss).

Lada et al., 1999

Infrared excess in CTTS, due to dusty disk.

Pre-Main Sequence EvolutionT Tauri Stars

Lamm et al., 2005

Contraction, magnetic star disk interaction, stellar winds.

Conclusions

We have made a lot of progress in understanding the protostar andpre-main sequence phase of star foramtion.

Many challenges remain: The luminosity problem, the role ofmagnetic fields, star disk interaction, stellar winds.

References

Stahler, S. W., ApJ 332, pp. 804, 1988.Palla, F., Stahler, S., ApJ 525, pp. 772, 1999.Burrows, A., Hubbard, W., Lunine, J., Liebert, J., Rev. of ModernPhysics 73, pp. 719, 2001.Bodenheimer, Pirnciples of Star Formation, Springer, 2011.