  We introduce a prescription for the luminosity from accreting protostars into
smoothed particle hydrodynamics simulation, and apply the method to simulations
of five primordial minihalos generated from cosmological initial conditions. We
find that accretion luminosity delays fragmentation within the halos, but does
not prevent it. In halos that slowly form a low number of protostars, the
accretion luminosity can reduce the number of fragments that are formed before
the protostars start ionising their surroundings. However, halos that rapidly
form many protostars become dominated by dynamical processes, and the effect of
accretion luminosity becomes negligible. Generally the fragmentation found in
the halos is highly dependent on the initial conditions. Accretion luminosity
does not substantially affect the accretion rates experienced by the
protostars, and is far less important than dynamical interactions, which can
lead to ejections that effectively terminate the accretion. We find that the
accretion rates onto the inner regions of the disks (20 AU) around the
protostars are highly variable, in contrast to the constant or smoothly
decreasing accretion rates currently used in models of the pre-main sequence
evolution of Population III stars.
