Limits on the growth rate of supermassive black holes at early cosmic epochs

Abstract

The effect of AGN wind feedback on the accretion rate and mass evolution of supermassive black holes (SMBH) is considered. It is shown, under reasonable assumptions, that the rate at which gas can be supplied to a SMBH at the center of a young galaxy, is limited to $\sim 20 (\sigma/350~ {\rm km ~s^{-1}})^4~M_\odot/yr$ (where $\sigma$ is the velocity dispersion of the host bulge) by interaction of winds expelled from the innermost regions of the accretion flow with the gas in the bulge. This rate is independent of the black hole mass but is sensitive to the properties of the host bulge. It is further argued that the interaction of the wind and the inflowing gas in the bulge can strongly affect the structure of the accretion flow in the super-Eddington regime, potentially leading to highly super-Eddington accretion into the SMBH. About 300 Myr after the onset of the accretion phase, the AGN wind expels all the gas from the bulge and the accretion rate is strongly suppressed. This scenario is in remarkable agreement with recent observations, as it (i) reveals the origin of the maximal observed accretion rates, (ii) accounts for the inferred growth rate of SMBHs at high redshift (independent of their initial seeds masses), (iii) elucidates the decline in the accretion rate at lower redshifts, and (iv) explains the relation between $\sigma$ and the mass $M_{BH}$ of the central SMBH, measured in the local Universe.