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

to a radial extent of rpres ∼ 5000 AU, matching well the predicted size of
rpres = cs t = 4400 AU.
3.3.4 Protostellar Mass Growth
The sink growth in both cases is very similar for the first ∼ 200 yr,
up to the point the main sinks reach 12 M⊙. This is similar to some of the
simulations presented in Smith et al. (2011) in which feedback did not cause
a significant decline in sink growth until it grew to > 10 M⊙. Afterwards, we
find the deviation in sink accretion history to be significant, leading to a final
mass of 27 M⊙ in the ‘no-feedback’ case and 15 M⊙ in the ‘with-feedback’ case.
In our ‘no-feedback’ case, the average accretion rate is 5.4 × 10 −3
M⊙ yr −1 . For the first 600 yr, M∗ evolves with time as t 0.64
acc . After the ejection
of the secondary sink, the growth rate declines significantly to M∗ ∝ t 0.13
acc (see
Figure 3.9). Even after the growth of the disk and envelope is halted, tidal
torques are able to continuously funnel additional mass onto the sink.
With feedback, the average accretion rate drops to 3×10 −3 M⊙ yr −1 . M∗
evolves more slowly as t 0.56
acc for the first 500 yr, and afterwards the accretion
rate drops to nearly zero. Given this strong protostellar feedback onto the
disk, we can devise a simple analytical estimate for the final mass attainable
by Pop III stars as follows:
M∗ = ˙ M∗tfeed, (3.17)
where, tfeed is the timescale over which Pop III accretion will be essentially
shut off. Given that Pop III stars must accrete through a disk, and assuming
for simplicity the thin-disk approximation,
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