  We use cosmological simulations of high-redshift minihalos to investigate the
effect of dark matter annihilation (DMA) on the collapse of primordial gas. We
numerically investigate the evolution of the gas as it assembles in a
Population III stellar disk. We find that when DMA effects are neglected, the
disk undergoes multiple fragmentation events beginning at ~ 500 yr after the
appearance of the first protostar. On the other hand, DMA heating and
ionization of the gas speeds the initial collapse of gas to protostellar
densities and also affects the stability of the developing disk against
fragmentation, depending on the DM distribution. We compare the evolution when
we model the DM density with an analytical DM profile which remains centrally
peaked, and when we simulate the DM profile using N-body particles (the 'live'
DM halo). When utilizing the analytical DM profile, DMA suppresses disk
fragmentation for ~ 3500 yr after the first protostar forms, in agreement with
earlier work. However, when using a 'live' DM halo, the central DM density peak
is gradually flattened due to the mutual interaction between the DM and the
rotating gaseous disk, reducing the effects of DMA on the gas, and enabling
secondary protostars of mass ~ 1 M_sol to be formed within ~ 900 yr. These
simulations demonstrate that DMA is ineffective in suppressing gas collapse and
subsequent fragmentation, rendering the formation of long-lived dark stars
unlikely. However, DMA effects may still be significant in the early collapse
and disk formation phase of primordial gas evolution.
