The cosmogony of supermassive black holes

We report calculations of the evolution, under Reynolds viscosity, of the massive gaseous accretion discs thought to form in the centres of galaxies as a result of major galactic mergers at early epochs. Starting with the formation of such a disc and the postulated existence of a low-mass 'seed' black hole, we focus on the mass accretion rate, and hence luminosity, L_GC, of a putative supermassive black hole (SMBH) in the galactic centre. Our computations cover a range of initial disc mass, M_{d, 0}, and outer radius, s_{max, 0}, and have been carried out under the assumption that cannot exceed the Eddington limit and that any excess mass supplied from the disc is lost from the system. Our purpose is to understand the extent to which such a model can account for the evolution with redshift of the observed properties of active galactic nuclei (AGNs). We show that within this framework: (i) the initial mass supply rate from the disc increases with M_{d, 0} and compactness, adjusts rapidly (on a viscous time-scale) to its peak value and decreases steadily thereafter; (ii) peak SMBH mass accretion rate and hence luminosity occurs when the (decreasing) disc flow rate equals the (increasing) black hole (BH) Eddington rate and is proportional to the BH mass, M^Edd_BH, at that juncture; (iii) the fractional disc mass lost during the Eddington-limited phase increases with M_{d, 0} and compactness so strongly that, for given (large) M_{d, 0}, the peak BH luminosity and corresponding mass occurs for some intermediate value of s_{max, 0} so that M^Edd_BH declines for more compact initial discs; (iv) SMBHs with mass M_BH≥ 10⁹M_⊙ and luminosity L_GC≥ 3 × 10¹³L_⊙ can form in a time t < 10⁹ yr as required by the most luminous high-redshift quasi-stellar objects but the Eddington-induced mass-loss renders unlikely the creation of BHs of comparable or greater mass or luminosity in significantly shorter times; (v) the most luminous quasars form and die at the earliest epochs while those of lower luminosity occur over successively longer periods ranging up to the present time; (vi) in general, AGNs that are at an early evolutionary phase accrete at or close to their Eddington rate but evolve into the sub-Eddington regime later on. The proposed scenario appears capable of accounting for many of the features of the observed quasar and AGN luminosity distribution with redshift and seems to be a natural consequence of the formation of massive central discs following major galaxy mergers.