The Inhomogeneous Ionizing Background Following Reionization
  We study the spatial fluctuations in the hydrogen ionizing background in the
epoch following reionization (z ~ 5--6). The rapid decrease with redshift in
the photon mean free path (m.f.p.), combined with the clustering of
increasingly rare ionizing sources, can result in a very inhomogenous ionizing
background during this epoch. We systematically investigate the probability
density functions (PDFs) and power spectra of ionizing flux, by varying several
parameters such as the m.f.p., minimum halo mass capable of hosting stars, and
halo duty cycle. In order to be versatile, we make use of analytic,
semi-numeric and numeric approaches. Our models show that the ionizing
background indeed has sizable fluctuations during this epoch sourced by the
clustering of sources, with the PDFs being a factor of few wide at half of the
maximum likelihood. The distributions also show marked asymmetries, with a
high-value tail set by clustering on small scales, and a shorter low-value tail
which is set by the mean free path. The power spectrum of the ionizing
background is much more sensitive to source properties than the PDF and can be
well-understood analytically with a framework similar to the halo model
(usually used to describe dark matter clustering). Nevertheless, we find that
Lya forest spectra are extremely insensitive to the details of the UVB, despite
marked differences in the PDFs and power spectra of our various ionizing
backgrounds. Assuming a uniform ionizing background only underestimates the
value of the mean ionization rate inferred from the Lya forest by a few
percent. Instead, analysis of the Lya forest is dominated by the uncertainties
in the density field. Thus, our results justify the common assumption of a
uniform ionizing background in Lya forest analysis even during this epoch.
