The influence of streaming velocities and Lyman-Werner radiation on the
  formation of the first stars
  The first stars in the Universe, the so-called Population III stars, form in
small dark matter minihaloes with virial temperatures $T_{\rm vir} < 10^{4}$~K.
Cooling in these minihaloes is dominated by molecular hydrogen (H$_{2}$), and
so Population III star formation is only possible in those minihaloes that form
enough H$_{2}$ to cool on a short timescale. As H$_{2}$ cooling is more
effective in more massive minihaloes, there is therefore a critical halo mass
scale $M_{\rm min}$ above which Population III star formation first becomes
possible. Two important processes can alter this minimum mass scale: streaming
of baryons relative to the dark matter and the photodissociation of H$_{2}$ by
a high redshift Lyman-Werner (LW) background. In this paper, we present results
from a set of high resolution cosmological simulations that examine the impact
of these processes on $M_{\rm min}$ and on $M_{\rm ave}$ (the average minihalo
mass for star formation), both individually and in combination. We show that
streaming has a bigger impact on $M_{\rm min}$ than the LW background, but also
that both effects are additive. We also provide fitting functions quantifying
the dependence of $M_{\rm ave}$ and $M_{\rm min}$ on the streaming velocity and
the strength of the LW background.
