  The cosmic dark ages ended a few hundred million years after the Big Bang,
when the first stars began to fill the universe with new light. It has
generally been argued that these stars formed in isolation and were extremely
massive - perhaps 100 times as massive as the Sun. In a recent study, Clark and
collaborators showed that this picture requires revision. They demonstrated
that the accretion disks that build up around Population III stars are strongly
susceptible to fragmentation and that the first stars should therefore form in
clusters rather than in isolation. We here use a series of high-resolution
hydrodynamical simulations performed with the moving mesh code AREPO to follow
up on this proposal and to study the influence of environmental parameters on
the level of fragmentation. We model the collapse of five independent minihalos
from cosmological initial conditions, through the runaway condensation of their
central gas clouds, to the formation of the first protostar, and beyond for a
further 1000 years. During this latter accretion phase, we represent the
optically thick regions of protostars by sink particles. Gas accumulates
rapidly in the circumstellar disk around the first protostar, fragmenting
vigorously to produce a small group of protostars. After an initial burst,
gravitational instability recurs periodically, forming additional protostars
with masses ranging from ~ 0.1 to 10 M_sun. Although the shape, multiplicity,
and normalization of the protostellar mass function depend on the details of
the sink-particle algorithm, fragmentation into protostars with diverse masses
occurs in all cases, confirming earlier reports of Population III stars forming
in clusters. Depending on the efficiency of later accretion and merging,
Population III stars may enter the main sequence in clusters and with much more
diverse masses than are commonly assumed.
