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

the presumed coalescence of two stars. We may also consider the possibility
that the mass of the sink will fragment and a sub-sink stellar multiple will
form in this way. As described by Jappsen and Klessen (2004), this is more
likely for higher values of β, the ratio of rotational to gravitational energy.
As in Goodman et al. (1993) and Jappsen and Klessen (2004), we can arrive
at a simple estimate by assuming that the sinks are undergoing solid-body
rotation, have constant angular velocity Ω, and have uniform density. In this
case, sink A has Ω = 1.5 × 10 −9 s −1 and sink B has Ω = 6 × 10 −10 s −1 . We
also have
β =
(1/2) IΩ2
qGM 2 , (4.11)
/R
where I = pMR 2 is the moment of inertia, p = 2/5, and q = 3/5. In this case
sink A has β = 0.070 and sink B has β = 0.044, very similar to the values
derived for the sinks in Jappsen and Klessen (2004). The requirement for
fragmentation ranges from β > 0.01 to β > 0.1, depending on the true density
structure and thermal properties of gas on sub-sink scales, as well as the effects
of magnetic fields (e.g. Boss and Myhill 1995; Boss 1999). For the above values
of β, it is thus not entirely certain whether subfragmentation would occur, and
this will need to be determined with higher resolution studies.
As discussed earlier, however, disk structure is expected even on sub-
sink scales, so it would also be appropriate to examine the Toomre criterion
for disk fragmentation:
Q = csκ
πGΣ
124
< 1 . (4.12)