Faint active galactic nuclei and the ionizing background

We determine the evolution of the faint, high-redshift, optical luminosity function (LF) of active galactic nuclei (AGNs) implied by several observationally motivated models of the ionizing background from 3 < z < 5. Our results depend crucially on whether we use the total ionizing rate measured by the proximity effect technique or the lower determination favored by the flux decrement distribution of Lyalpha forest lines. Assuming a faint-end LF slope of 1.58 and the SDSS estimates of the bright-end slope and normalization, we find that the LF must break at M-B* = -24.2, -22.3, -20.8 at z = 3, 4, 5 if we adopt the lower ionization rate and assume no stellar contribution to the background. The breaks must occur at M-B* = -20.6, 18.7, -18.7 for the proximity effect estimate. Since stars may also contribute to the background, these values are lower limits on the break luminosity, and they brighten by as much as similar to2 mag if the escape fraction of ionizing photons from high-z galaxies is consistent with recent estimates: f(esc) = 0.16. By comparing our expectations to faint AGN searches in the Hubble Deep Field and high-z galaxy fields, we find that typically quoted proximity effect estimates of the background imply an overabundance of AGNs compared to the faint counts ( even with f(esc) = 1). Even adopting the lower bound on proximity effect measurements, the stellar escape fraction must be high: f(esc) greater than or similar to 0.2. Conversely, the lower flux decrement-derived background requires a smaller number of ionizing sources, and faint AGN counts are consistent with this estimate only if there is a limited stellar contribution, f(esc) less than or similar to 0.05. Our derived LFs together with the locally estimated black hole density suggest that the effciency of converting mass to light in optically unobscured AGNs is somewhat lower than expected, epsilon less than or similar to 0.05 (all models). Comparison with similar estimates based on X-ray counts suggests that more than half of all AGNs are obscured in the UV/optical. We also derive lower limits on typical AGN lifetimes and obtain greater than or similar to 10(7) yr for favored cases.