We present a comprehensive synthesis model for the AGN evolution and the growth of supermassive black hole in the Universe .
We assume that black holes accrete in just three distinct physical states , or “ modes ” : at low Eddington ratio , only a radiatively inefficient , kinetically dominated mode is allowed ( LK ) ; at high Eddington ratio , instead , AGN may display both a purely radiative ( radio quiet , HR ) , and a kinetic ( radio loud , HK ) mode .
We solve the continuity equation for the black hole mass function using the locally determined one as a boundary condition , and the hard X-ray luminosity function as tracer of the AGN growth rate distribution , supplemented with a luminosity-dependent bolometric correction and an absorbing column distribution .
Differently from most previous semi-analytic and numerical models for black hole growth , we do not assume any specific distribution of Eddington ratios , rather we determine it empirically by coupling the mass and luminosity functions and the set of fundamental relations between observables in the three accretion modes .
SMBH always show a very broad accretion rate distribution , and we discuss the profound consequences of this fact for our understanding of observed AGN fractions in galaxies , as well as for the empirical determination of SMBH mass functions with large surveys .
We confirm previous results and clearly demonstrate that , at least for z \la 1.5 , SMBH mass function evolves anti-hierarchically , i.e .
the most massive holes grew earlier and faster than less massive ones .
For the first time , we find hints of a reversal of such a downsizing behaviour at redshifts above the peak of the black hole accretion rate density ( z \approx 2 ) .
We also derive tight constraints on the ( mass weighted ) average radiative efficiency of AGN : under the simplifying assumption that the mass density of both high redshift ( z \sim 5 ) and “ wandering ” black holes ejected from galactic nuclei after merger events are negligible compared to the local mass density , we find that 0.065 < \xi _ { 0 } \langle \epsilon _ { rad } \rangle < 0.07 , where \xi _ { 0 } is the local SMBH mass density in units of 4.3 \times 10 ^ { 5 } M _ { \odot } Mpc ^ { -3 } .
We trace the cosmological evolution of the kinetic luminosity function of AGN , and find that the overall efficiency of SMBH in converting accreted rest mass energy into kinetic power , \epsilon _ { kin } , ranges between \epsilon _ { kin } \simeq 3 \div 5 \times 10 ^ { -3 } , depending on the choice of the radio core luminosity function .
Such a “ kinetic efficiency ” varies however strongly with SMBH mass and redshift , being maximal for very massive holes at late times , as required for the AGN feedback by many galaxy formation models in Cosmological contexts .