Eddington accreting Black Holes in the Epoch of Reionization

Abstract: The evolution of the luminosity function (LF) of Active Galactic Nuclei (AGNs) at $z \gtrsim 5$ represents a key constraint to understand their contribution to the ionizing photon budget necessary to trigger the last phase transition in the Universe, i.e. the epoch of Reionization. Recent searches for bright high-z AGNs suggest that the space densities of this population at $z>4$ has to be revised upwards, and sparks new questions about their evolutionary paths. Gas accretion is the key physical mechanism to understand both the distribution of luminous sources and the growth of central Super-Massive Black Holes (SMBHs). In this work, we model the high-z AGN-LF assuming that high-z luminous AGN shine at their Eddington limit: we derive the expected evolution as a function of the ``duty-cycle'' ($f_{\rm dc}$), i.e. the fraction of life-time that a given SMBH spends accreting at the Eddington rate. Our results show that intermediate values ($f_{\rm dc} \simeq 0.1$) predict the best agreement with the ionizing background and photoionization rate, but do not provide enough ionizing photons to account for the observed evolution of the hydrogen neutral fraction. Smaller values ($f_{\rm dc} \lesssim 0.05$) are required for AGNs to be the dominant population responsible for Hydrogen reionization in the Early Universe. We then show that this low-$f_{\rm dc}$ evolution can be reconciled with the current constraints on Helium reionization, although it implies a relatively large number of inactive SMBHs at $z\gtrsim5$, in tension with SMBH growth models based on heavy seeding.