Xray Constraints on the Growth of SMBH

The AGN luminosity function can be used to determine the masses of remnant black holes in galactic centers, using Soltan's continuity equation argument [80] and assuming a mass-to-energy conversion efficiency e. For a nonrotating Schwarzschild BH, e is expected to be 0.057, while for a maximally rotating Kerr BH, e can be as high as 0.29. The AGN demography predicted, that most normal galaxies contain supermassive black holes (BH) in their centers, which is now widely accepted. Recent determinations of the accreted mass from the optical QSO luminosity function are around 2e-11 • 105M0 Mpc-3 [8,96]. Probably the most reliable recent determination comes from an integration of the X-ray luminosity function. Using the Ueda et al. [88] hard X-ray luminosity function including a correction for

Compton-thick AGN normalized to the X-ray background, as well as an updated bolometric correction ignoring the IR dust emission, Marconi et al [51] derived Paccr ~ 3.5£0-1 • 105M0 Mpc-3.

The BH masses measured in local galaxies are tightly correlated to the galactic velocity dispersion [19] and less tightly to the luminosity of the host galaxy bulge. Using these correlations and galaxy luminosity (or velocity) functions, the total remnant black hole mass density in galactic bulges can be estimated. Scaled to the same assumption for the Hubble constant (H0 = 70kms-1 Mpc-1), recent papers arrive at different values, mainly depending on assumptions about the intrinsic scatter in the BH-galaxy correlations. The most recent estimate is pBH = (4.6+1 4) hj0 • 105M0 Mpc-3 [51]. The local dark remnant mass function is thus fully consistent with the above accreted mass function, if black holes accrete with an average energy conversion efficiency of £ = 0.1 [51], which is the classically assumed value and lies between the Schwarzschild and the extreme Kerr solution. However, taking also into account the widespread evidence for a significant kinetic AGN luminosity in the form of jets and winds, it is predicted that the average supermassive black hole should be rapidly spinning fast (see also [14,96]).

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