2011MNRAS.413.1495D

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, {img}, 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 {img} 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:

 {\listitem {\label (i)} {\par}the initial mass supply rate {img} from the disc increases with {\em M}_d, 0_ and compactness, adjusts rapidly (on a viscous time-scale) to its peak value and decreases steadily thereafter;} {\listitem {\label (ii)} {\par}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, {\em M}^Edd^_BH_, at that juncture;} {\listitem {\label (iii)} {\par}the fractional disc mass lost during the Eddington-limited phase increases with {\em M}_d, 0_ and compactness so strongly that, for given (large) {\em M}_d, 0_, the peak BH luminosity and corresponding mass occurs for some intermediate value of {\em s}_max, 0_ so that {\em M}^Edd^_BH_ declines for more compact initial discs;} {\listitem {\label (iv)} {\par}SMBHs with mass {\em M}_BH_ >=  10^9^ M_{sun}_ and luminosity {\em L}_GC_ >=  3 {x} 10^13^ L_{sun}_ can form in a time {\em t} < 10^9^ 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;} {\listitem {\label (v)} {\par}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;} {\listitem {\label (vi)} {\par}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.} {\par}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.