Fragmentation in Population III Galaxies formed through Ionizing
  Radiation
  Population III stars forming in minihalos tend to be relatively inefficient,
with each minihalo hosting one or a small number of stars which are more
massive than local stars but still challenging to observe directly at high
redshift. Here we explore a possible mechanisms for the generation of larger
clusters of such stars: a nearby ionizing source which ionizes a late forming
halo, delaying its collapse until the halo is sufficiently large that the core
can self-shield and suffer runaway collapse. We use simulations with a simple
but accurate model for the radiative ionizing flux and confirm the basic
predictions of previous work: higher ionizing fluxes can delay the collapse to
lower redshifts and higher masses, up to an order of magnitude above the atomic
cooling limit. In a limited number of runs we also examine the fragmentation of
the cores at even higher resolution, using both simple estimates and sink
particles to show that the number of fragments is generally small, at most a
handful, and that the mass accretion rate on the fragments is of order
$10^{-3}$ M$_\odot$ yr$^{-1}$. This rate is sufficiently high that the descent
on the main sequence (and hence the suppression of accretion) is delayed until
the stellar masses are of order $100-1000$ M$_\odot$, but not high enough to
produce direct collapse black holes of mass $\sim 10^5$ M$_{\odot}$. The
resulting clusters are larger than those produced in minihalos, but are still
likely to fall short of being easily detectable in JWST blind fields.
