High-Redshift Star Formation in a Time-Dependent Lyman-Werner Background
  The first generation of stars produces a background of Lyman-Werner (LW)
radiation which can photo-dissociate molecular hydrogen, increasing the mass of
dark matter halos required to host star formation. Previous studies have
determined the critical mass required for efficient molecular cooling with a
constant LW background. However, the true background is expected to increase
rapidly at early times. Neglecting this evolution could underestimate star
formation in small halos that may have started to cool in the past when the LW
intensity was much lower. Background evolution is a large source of uncertainty
in pre-reionization predictions of the cosmological 21cm signal, which can be
observed with future radio telescopes. To address this, we perform
zero-dimentional one-zone calculations that follow the density, chemical
abundances, and temperature of gas in the central regions of dark matter halos,
including hierarchical growth and an evolving LW background. We begin by
studying the physics of halos subjected to a background that increases
exponentially with redshift. We find that when the intensity increases more
slowly than $J_{\rm LW}(z) \propto 10^{-z/5}$, cooling in the past is a
relatively small effect. We then self-consistently compute the cosmological LW
background over $z=15-50$ and find that cooling in the past due to an evolving
background has a modest impact. Finally, we compare these results to
three-dimensional hydrodynamical cosmological simulations with varying LW
histories. While only a small number of halos were simulated, the results are
consistent with our one-zone calculations.
