Post on 14-Mar-2021
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.