The anti‐hierarchical growth of supermassive black holes

I present a new method to unveil the history of cosmic accretion and the build‐up of supermassive black holes (SMBHs) in the nuclei of galaxies, based on observations of the evolving radio and (hard) X‐ray luminosity functions of active galactic nuclei (AGN). The fundamental plane of black hole activity discovered by Merloni, Heinz & Di Matteo, which defines a universal correlation among black hole mass ( M ), 2–10 keV X‐ray luminosity and 5‐GHz radio luminosity is used as a mass and accretion rate estimator, provided a specific functional form for the dependency of the X‐ray luminosity on the dimensionless accretion rate &#x006d;̇ is assumed. I adopt the local black hole mass function (BHMF) as derived from the velocity dispersion (σ) distributions of nearby galaxies coupled with the M −σ relation as a boundary condition to integrate backwards in time the continuity equation for the evolution of SMBH, neglecting the role of mergers in shaping up the BHMF. Under the most general assumption that, independently on M , black hole accretion proceeds in a radiatively efficient way above a certain rate, and in a radiatively inefficient way below it, the redshift evolution of the BHMF and the black hole accretion rate (BHAR) function (i.e. the distribution of the Eddington scaled accretion rates for objects of any given mass) are calculated self‐consistently. The only tunable parameters are the overall efficiency of extracting gravitational energy from the accreting gas, ε, and the critical ratio of the X‐ray to Eddington luminosity, L 2‐10 keV,cr / L Edd ≡ x cr , at which the transition between accretion modes takes place. For fiducial values of these parameters ( ε= 0.1 and x cr = 10 −3 ), I found that half (∼85 per cent) of the local black hole mass density was accumulated at redshift z < 1 ( z < 3 ), mostly in radiatively efficient episodes of accretion. The evolution of the BHMF between z = 0 and z ∼ 3 shows clear signs of an anti‐hierarchical behaviour: while the majority of the most massive objects ( M ≳ 10 9 ) were already in place at z ∼ 3 , lower mass ones mainly grew at progressively lower redshift, so that the average black hole mass increases with increasing redshift. In addition, the average accretion rate decreases towards lower redshift. Consequently, sources in the radiatively inefficient regime of accretion only begin to dominate the comoving accretion energy density in the Universe at z < 1 (with the exact value of z depending on x cr ), while at the peak of the BHAR history, radiatively efficient accretion dominates by almost an order of magnitude. I will discuss the implications of these results for the efficiency of accretion on to SMBH, the lifetimes of quasars and duty cycles, the history of AGN feedback in the form of mechanical energy output and, more generally, for the cosmological models of structure formation in the Universe.