The Persistence of Population III Star Formation
  We present a semi-analytic model of star formation in the early universe,
beginning with the first metal-free stars. By employing a completely
feedback-limited star formation prescription, stars form at maximum efficiency
until the self-consistently calculated feedback processes halt formation. We
account for a number of feedback processes including a meta-galactic
Lyman-Werner background, supernovae, photoionization, and chemical feedback.
Halos are evolved combining mass accretion rates found through abundance
matching with our feedback-limited star formation prescription, allowing for a
variety of Population III (Pop III) initial mass functions (IMFs). We find
that, for a number of models, massive Pop III star formation can continue on
until at least $z \sim 20$ and potentially past $z \sim 6$ at rates of around
$10^{-4}$ to $10^{-5}$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$, assuming these stars
form in isolation. At this point Lyman-Werner feedback pushes the minimum halo
mass for star formation above the atomic cooling threshold, cutting off the
formation of massive Pop III stars. We find that, in most models, Pop II and
Pop III star formation co-exist over cosmological time-scales, with the total
star formation rate density and resulting radiation background strongly
dominated by the former before Pop III star formation finally ends. These halos
form at most $\sim 10^3$ M$_\odot$ of massive Pop III stars during this phase
and typically have absolute magnitudes in the range of $M_\text{AB} = -5 $ to $
-10$. We also briefly discuss how future observations from telescopes such as
JWST or WFIRST and 21-cm experiments may be able to constrain unknown
parameters in our model such as the IMF, star formation prescription, or the
physics of massive Pop III stars.
