  The first Pop III stars formed out of primordial, metal free gas, in
minihalos at z>20, and kickstarted the cosmic processes of reionizaton and
enrichment. While these stars are likely more massive than their enriched
counterparts, the current unknowns of their astrophysics include; when the
first Pop III stars ignited, how massive they were, and when and how the era of
the first stars ended. Investigating these questions requires an exploration of
a multi-dimensional parameter space, including the slope of the Pop III stellar
initial mass function (IMF) and the strength of the non-ionizing UV background.
In this work, we present a novel model which treats both the slope and maximum
mass of Pop III stars as truly free parameters while including the physics of
the fragmentation of primordial gas. Our results also hint at a non-universal
Pop III IMF which is dependent on the efficiency of primordial gas
fragmentation. Our relatively simple model reproduces the results from
hydrodynamic simulations, but with a computational efficiency which allows us
to investigate the observable differences between a wide range of potential Pop
III IMFs. In addition, the evolution of the number density of Pop III stars may
provide insight into the evolution of the H2 dissociating background. While the
slope of the Pop III IMF does not significantly affect the predicted number
density of the first stars, more top heavy IMFs produce Pop III star clusters
which are 2-3 magnitudes brighter than their more bottom heavy counterparts.
While the Pop III star clusters are too dim for direct detection by JWST, we
find they are within the reach of gravitational lensing.
