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

compared to the analytic predictions of Tan and McKee (2004). At a density
and temperature of 10 8 cm −3 and 1000 K, respectively, we find a value of K ′
∼ 1.33 from their equation (7), where K ′ is the entropy parameter, defined by
K ′ =
P/ργ 1.88 × 1012cgs =
T
300 K
nH
10 4 cm −3
−0.1
. (2.6)
We estimate that the total star-disk system mass (red line in Fig. 2.7) is
∼ 100 M⊙ at the end of our simulation and set ɛ∗d equal to 1 for the no
feedback case, where ɛ∗d is the fraction of infalling mass that is able to reach
the star-disk system without being diverted by protostellar outflows, again in
the terminology of Tan & McKee. From their equation (8), we then calculate
an expected accretion rate onto the star-disk system of < ∼ 10 −2 M⊙ yr −1 . In
our simulation we find that over the 5000 yr of sink accretion, mass flows onto
the star-disk system very steadily at approximately the same rate of ∼ 10 −2
M⊙ yr −1 , which is also near the value for the average accretion rate onto the
main sink particle (see Chapter 2.4.2.4). Fig. 2.7 further shows that once the
first sink forms, the disk mass stays fairly constant at ∼ 35 M⊙ as mass falling
from the outer regions onto the disk replaces the material accreted onto the
sinks at similar rates.
Tan and McKee (2004) furthermore predict the time needed to build
up a given stellar mass in their equation (9). If we assume a value of 1 for
fd, the ratio of disk to stellar mass, then the time to build up a 43 M⊙ star
(the final mass of the main sink - see Chapter 2.4.2.4) is roughly 9000 yr. The
simulation yields a similar though smaller value of 5000 yr, which reflects the
slightly higher accretion rate of our simulation. Finally, if we estimate a value
of 1 for fKep, the ratio of rotational to Keplerian velocity at the sonic point,
then from equation (15) of Tan and McKee (2004) we find a predicted disk
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