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

from following the entire accretion history over the stellar lifetime of ∼ 3 Myr.
However, extrapolating from the first 5000 years (see Fig. 4.1) implies that
both stars we have discussed are likely to grow significantly more massive.
They should certainly be massive enough to avoid a white dwarf fate and
make a neutron star or black hole, assuming they do not die as PISNe and
leave behind no remnant at all. If they in fact die as core-collapse SNe, we can
estimate the effect of rotation on the later SN explosion. Though a black hole
remnant is more likely, particularly for the more massive star of sink A, we can
derive a more conservative estimate by considering a neutron star remnant.
As described in Woosley and Heger (2006), the total rotational energy of a
resulting neutron star of radius 12 km and gravitational mass of 1.4 M⊙ will
be Erot 1.1 × 10 51 (5 ms/P ) 2 erg, where P is the rotation period of the
neutron star. They find that for Erot to be comparable to the energy of a
hypernova, ∼ 10 52 erg, P would need to be ≤ 2 ms. In their low-metallicity
models that begin with stars rotating with similar ɛ values to what we found
for sink A (ɛ ∼ 0.45), they infer resulting neutron star rotation rates that
do meet this criterion. They find the same results even for lower ɛ like for
those of sink B, though this is only if magnetic torques are not included in the
model. Thus, even using the more conservative estimate it is conceivable that
the rotational energy reservoir found in sink A and B of our work could be
enough to power a hypernova. If the stars rotate more rapidly, at nearly their
break-up velocity as we predict, then hypernovae would be even more likely.
Will there still be enough angular momentum for the collapsar engine
to work on these stellar scales? If we use the low estimate of J(r) = ɛ JKep(r) =
ɛ √ GMsink r, then on these scales the angular momentum for both sinks still
easily meets the required J > JISCO, especially if their high ɛ values continue as
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