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

the power-law fits discussed in Chapter 4.3.1, and we set M∗ Msink in the
following analysis. In doing this we have made the simplifying assumption
that nearly all of the gas accreted onto the sink quickly flows through the
relatively low-mass disk onto the dominating massive star. We also extend the
fits to 10 5 years, roughly the point when KH contraction will cease and the
star settles onto the MS, with a final radius of 5 R⊙. Although the Pop III
radial evolution and MS size is based on work that does not account for varying
accretion rates and stellar rotation, which may inflate the radius, this should
still give a general picture of how the Pop III rotational velocity will evolve.
The resulting evolution of v∗ = J∗/R∗ for each sink is shown in Fig. 4.6.
Note that during the stars’ initial slow expansion, the velocity is not quite at
break-up because the stars are gathering mass from gradually increasing radii.
Once the stars begin KH contraction, however, the total angular momentum of
the stars in fact exceeds break-up, but in this case we assume that the angular
momentum will slow the KH contraction accordingly, and we adjust the stellar
radius such that the star will again rotate at break-up speed. By setting the
right-hand side of Equ. (4.7) equal to JKep, we find that the radius during this
third slowed contraction phase will evolve according to
d
dt ln R∗III = − d
ln M (4.10)
dt
Once this phase begins, the star will rotate at break-up speed, v∗ = vmax
GMsink/R∗.
Given this model, at 10 5 years the star within sink A has mass of 125
M⊙, a radius of 7 R⊙, and a rotational velocity of 1800 km s −1 . The star
within sink B has mass of 15 M⊙, a radius of 12 R⊙, and a rotational velocity
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