The stellar IMF at very low metallicities
  The theory for the formation of the first population of stars (Pop III)
predicts an initial mass function (IMF) dominated by high-mass stars, in
contrast to the present-day IMF, which tends to yield mostly stars with masses
less than 1 M_Sol. The leading theory for the transition in the characteristic
stellar mass predicts that the cause is the extra cooling provided by
increasing metallicity. In particular, dust can overtake H_2 as the leading
coolant at very high densities. The aim of this work is to determine the
influence of dust cooling on the fragmentation of very low metallicity gas. To
investigate this, we make use of high-resolution hydrodynamic simulations with
sink particles to replace contracting protostars, and analyze the collapse and
further fragmentation of star-forming clouds. We follow the thermodynamic
response of the gas by solving the full thermal energy equation, and also track
the behavior of the dust temperature and the chemical evolution of the gas. We
model four clouds with different metallicities (10^{-4}, 10^{-5}, 10^{-6}
Z_Sol, and 0), and determine the properties of each cloud at the point at which
it undergoes gravitational fragmentation. We find evidence for fragmentation in
all four cases, and hence conclude that there is no critical metallicity below
which fragmentation is impossible. Nevertheless, there is a clear change in the
behavior of the clouds at Z = 10^{-5} Z_Sol, caused by the fact that at this
metallicity, fragmentation takes longer to occur than accretion, leading to a
flat mass function at lower metallicities.
