Cosmic reionization of hydrogen and helium: contribution from both
  mini-quasars and stars
  Observations on the high-redshift galaxies at $z>6$ imply that their ionizing
emissivity is unable to fully reionize the Universe at $z\sim 6$. Either a high
escape fraction of ionizing photons from these galaxies or a large population
of faint galaxies below the detection limit are required. However, these
requirements are somewhat in tension with present observations. In this work,
we explored the combined contribution of mini-quasars and stars to the
reionization of cosmic hydrogen and helium. Our model is roughly consistent
with: (1) the low escape fractions of ionizing photons from the observed
galaxies, (2) the optical depth of Cosmic Microwave Background (CMB) measured
by the WMAP-7, and (3) the redshift of the end of hydrogen and helium
reionization at $z\approx 6$ and $z\approx 3$, respectively. Neither an
extremely high escape fraction nor a large population of fainter galaxies is
required in this scenario. In our most optimistic model, more than $\sim20\%$
of the cosmic helium is reionized by $z\sim6$, and the ionized fraction of
cosmic helium rapidly climbs to more than $50\%$ by $z\sim5$. These results may
imply that better measurements of helium reionization, especially at high
redshifts, could be helpful in constraining the growth of intermediate-mass
black holes (IMBHs) in the early Universe, which would shed some light on the
puzzles concerning the formation of supermassive black holes (SMBHs).
