Copyright by Athena Ranice Stacy 2011 - The University of Texas at ...

disk accretion onto a primordial protostar may be terminated. We now wish
to assess how important this neglected feedback would be up to the stage
simulated here.
In Fig. 2.12, we compare the accretion luminosity, Lacc, with the Ed-
dington luminosity due to electron scattering and due to H − opacity. Deter-
mining Lacc requires an estimate of the protostellar radius R∗. In the initial adi-
abatic accretion phase, before Kelvin-Helmholtz contraction has commenced,
the photospheric opacity of the protostar is dominated by H − bound-free ab-
sorption (i.e., ‘Phase I’ of Omukai and Palla 2003). The extremely strong
sensitivity of the H − bound-free opacity to temperature (κH − ∝ T 14.5 ) locks
the photospheric temperature to ∼ 6000 K. We estimate that the protostar
emits as a blackbody at this temperature and furthermore assume that the
protostellar luminosity during this phase is dominated by Lacc. This is justi-
fied as long as tacc < ∼ tKH, where tacc is the accretion timescale and tKH the
Kelvin-Helmholtz time. We then have
L∗I Lacc = GM∗ ˙ M
R∗
= 4πR 2 ∗ σSBT 4 , (2.11)
where L∗I is the protostellar luminosity during the adiabatic accretion phase,
σSB is the Stefan-Boltzmann constant, and T = 6000 K. This results in
R∗I 50R⊙
M∗
M⊙
1/3 ˙M
˙Mfid
1/3
, (2.12)
where R∗I is the protostellar radius during the adiabatic accretion phase, and
˙
Mfid 4.4 × 10 −3 M⊙ yr −1 , the fiducial accretion rate used by Stahler et al.
(1986) and Omukai and Palla (2003). Our simple estimate of how R∗I varies
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