On black hole evolution in active galactic nuclei

We study the evolution of supermassive black holes in active galactic nuclei (AGNs), taking into account both accretion of matter on to the black hole, and extraction of the black hole energy via the Blandford-Znajek mechanism within the framework of the Shakura-Sunyaev accretion disc model. We show that for high accretion rates, the black hole spin evolves quickly from its initial value to the equilibrium value as determined by a balance between the rate of spinning up by an accretion disc and the rate of spinning down by the Blandford-Znajek mechanism. For accretion rates close to the Eddington rate, the equilibrium spin is close to the maximum value for black holes and, according to the 'spin paradigm', quasars hosting black holes with such spins should be radio loud. The equilibrium spins are shown to decrease with decreasing accretion rate. However, initially fast-spinning black holes can reach low spins on sub-Hubble timescales only for very small viscosity parameters, alpha < 0.03. The optimal conditions for black hole deceleration are for accretion rates, M similar to 0.001 M(Edd), for which innermost parts of an accretion disc are still dominated by radiation pressure. This is because the rate of electromagnetic extraction of black hole angular momentum is proportional to the total pressure in a disc, which in radiation pressure dominated discs does not depend on the accretion rate. For lower accretion rates, M < 0.001 M(Edd), where the accretion discs are totally dominated by gas pressure, the angular momentum extraction rate is proportional to M(4/5). Therefore, for very low accretion rates, M much less than 0.001 M(Edd), the time-scale of deceleration becomes much longer than the Hubble time, unless alpha much less than 0.03. We discuss our results in the context of different quasar accretion histories, and investigate whether higher accretion rates during low activity periods in quasars hosted by spiral galaxies (as compared to quasars hosted by elliptical galaxies) can eventually lead to the observed radio-loud-radio-quiet dichotomy of quasars.