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

years, up to several dynamical times after the sink initially forms. Though
the sink accretion criteria have some small differences in each of these three
studies, this similarity in initial sink growth points especially to the robustness
of the density threshold criterion for initial sink formation. After 5000 years
of accretion, sink A grows to a mass of 34 M⊙, similar to that found in Bromm
and Loeb (2004). However, this is largely due to a significant merger event at
around 3800 years, and before this the mass of sink A is around 1/3 below that
found in Bromm and Loeb (2004). Furthermore, the final sink mass is slightly
less (∼ 20%) than the final mass found in Stacy et al. (2010). The reduced
accretion rate found in this current calculation likely arises because a sink
is not allowed to accrete a particle if that particle is rotationally supported
against infall onto the sink, which is an additional condition that was not
included by Stacy et al. (2010). This condition seems to slightly decrease the
number of sink merger events, though the growth rate between merger events
is also somewhat reduced.
Around 300 years after the formation of sink A, a second sink forms.
Meanwhile, as sink A grows, a disk with radius of about 1000 AU develops
around the sink, and disk fragmentation allows further sinks to form. By the
end of the simulation, 5000 years after sink A first forms, there is a total of
four sinks. The sink that is second-most massive, which we will label sink B,
has grown almost to 9 M⊙ (Fig. 4.1), while the remaining two sinks are ∼
1 and 7 M⊙. The overall accretion rate of sink B, 2 × 10 −3 M⊙ yr −1 , is
around 30% that of sink A, 7 × 10 −3 M⊙ yr −1 . The accretion rate for both
sinks does not stay at a steady value, however, and actually declines as the
sinks grow. To show this we also provide power-law fits to the sink growth
(red lines in Fig. 4.1). For sink A, Msink ∝ t 0.48 , and ˙
M ∝ t −0.52 . For sink B,
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