Radiative Transfer in a Clumpy Universe: III. The Nature of Cosmological   Ionizing Sources
  The history of the transition from a neutral intergalactic medium (IGM) to one that is almost fully ionized can reveal the character of cosmological ionizing sources. We study the evolution of the volume filling factor of HII and HeIII regions in a clumpy IGM, and discuss the implications for rival reionization scenarios of the rapid decline in the space density of radio-loud quasars and of the large population of star-forming galaxies recently observed at z>3. The hydrogen component in a highly inhomogeneous universe is completely reionized when the number of photons emitted above 1 ryd in one recombination time equals the mean number of hydrogen atoms. If stellar sources are responsible for keeping the IGM ionized at z=5, the rate of star formation at this epoch must be comparable or greater than the one inferred from optical observations of galaxies at z=3, and the mean metallicity per baryon in the universe of order 1/500 solar. An early generation of stars in dark matter halos with circular velocities v_circ=50 km/s, possibly one of the main source of UV photons at high-z, could be detectable with the Next Generation Space Telescope. Models in which the quasar emissivity declines rapidly at z>3 predict a late HeII reionization epoch, a feature that could explain the recent detection of patchy HeII Lyman-alpha at z=2.9 by Reimers et al. (1997) and the abrupt change observed by Songaila (1998) at about the same epoch of the SiIV/CIV ratio, but appear unable to provide the required number of hydrogen-ionizing photons at z=5. 
Piero Madau, Francesco Haardt, Martin J. Rees