The Luminosity Function of bright QSOs at z~4 and implications for the cosmic ionizing background

Based on results by recent surveys, the number of bright quasars at redshifts z>3 is being constantly revised upwards. Current consensus is that at bright magnitudes ($M_{1450}\le -27$) the number densities of such sources could have been underestimated by a factor of 30-40%. In the framework of the QUBRICS survey, we identified 58 bright QSOs at 3.6$\le z \le$4.2, with magnitudes $i_{psf}\le$18, in an area of 12400$deg^{2}$. The uniqueness of our survey is underlined by the fact that it allows us, for the first time, to extend the sampled absolute magnitude range up to $M_{1450}= -29.5$. We derived a bright-end slope of $\beta=-4.025$ and a space density at $<M_{1450}>=-28.75$ of 2.61$\times 10^{-10} Mpc^{-3}$ comoving, after taking into account the estimated incompleteness of our observations. Taking into account the results of fainter surveys, AGN brighter than $M_{1450}=-23$ could produce at least half of the ionizing emissivity at z$\sim$4. Considering a mean escape fraction of 0.7 for the QSO and AGN population, combined with a mean free path of 41.3 proper Mpc at $z=3.9$, we derive a photoionization rate of $Log(\Gamma [s^{-1}])=-12.17^{+0.13}_{-0.07}$, produced by AGN at M$_{1450}<-18$, i.e. ~100% of the measured ionizing background at z~4.