Faint Active Galactic Nuclei and the Ionizing Background

We determine the evolution of the faint, high-redshift, optical luminosityfunction (LF) of AGN implied by several observationally-motivated models of theionizing background. Our results depend crucially on whether we use the totalionizing rate measured by the proximity effect technique or the lowerdetermination from the flux decrement distribution of Ly alpha forest lines.Assuming a faint-end LF slope of 1.58 and the SDSS estimates of the bright-endslope 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 stellarcontribution to the background. The break must occur at M_B*=-20.6,-18.7, -18.7for the proximity effect background estimate. These values brighten by as muchas ~2 mag if high-z galaxies contribute to the background with an escapefraction of ionizing photons consistent with recent estimates: f_e=0.16. Bycomparing to faint AGN searches, we find that the typically-quoted proximityeffect estimates of the background imply an over-abundance of faint AGN (evenwith f_e=1). Even adopting the lower bound on proximity effect measurements,the stellar escape fraction must be high: f_e>0.2. Conversely, the lower flux-decrement-derived background requires a limited stellar contribution: f_e<0.05.Our derived LFs together with the locally-estimated black hole density suggestthat the efficiency of converting mass to light in optically-unobscured AGN issomewhat lower than expected, <0.05. Comparison with similar estimates based onX-ray counts suggests that more than half of all AGN are obscured in theUV/optical. We also derive lower limits on typical AGN lifetimes and obtain>10^7 yrs for favored cases.Comment: 19 pages, 16 figures. Accepted by Astrophysical Journa