The faint end of the quasar luminosity function at z ∼ 4: Implications for ionization of the intergalactic medium and cosmic downsizing

We present an updated determination of the z ∼ 4 QSO luminosity function (QLF), improving the quality of the determination of the faint end of the QLF presented by Glikman et al. (2010). We have observed an additional 43 candidates from our survey sample, yielding one additional QSO at z = 4.23 and increasing the completeness of our spectroscopic follow-up to 48% for candidates brighter than R = 24 over our survey area of 3.76 deg². We study the effect of using K-corrections to compute the rest-frame absolute magnitude at 1450 Å compared with measuring M₁₄₅₀ directly from the object spectra. We find a luminosity-dependent bias: template-based K-corrections overestimate the luminosity of low-luminosity QSOs, likely due to their reliance on templates derived from higher luminosity QSOs. Combining our sample with bright quasars from the Sloan Digital Sky Survey and using spectrum-based M ₁₄₅₀ for all the quasars, we fit a double power law to the binned QLF. Our best fit has a bright-end slope, α = 3.3 ± 0.2, and faint-end slope, β = 1.6^+0.8_0.6. Our new data revise the faint-end slope of the QLF down to flatter values similar to those measured at z ∼ 3. The break luminosity, though poorly constrained, is at M ^* = -24.1^+0.7_-1.9, approximately 1-1.5 mag fainter than at z ∼ 3. This QLF implies that QSOs account for about half the radiation needed to ionize the intergalactic medium at these redshifts.