2014ApJ...792L..13W

A tight relation between the size of the broad-line region (BLR) and optical luminosity has been established in about 50 active galactic nuclei studied through reverberation mapping of the broad Hβ emission line. The R_BLR-L relation arises from simple photoionization considerations. Using a general relativistic model of an optically thick, geometrically thin accretion disk, we show that the ionizing luminosity jointly depends on black hole mass, accretion rate, and spin. The non-monotonic relation between the ionizing and optical luminosity gives rise to a complicated relation between the BLR size and the optical luminosity. We show that the reverberation lag of Hβ to the varying continuum depends very sensitively on black hole spin. For retrograde spins, the disk is so cold that there is a deficit of ionizing photons in the BLR, resulting in shrinkage of the hydrogen ionization front with increasing optical luminosity, and hence shortened Hβ lags. This effect is specially striking for luminous quasars undergoing retrograde accretion, manifesting in strong deviations from the canonical R_BLR-L relation. This could lead to a method to estimate black hole spins of quasars and to study their cosmic evolution. At the same time, the small scatter of the observed R_BLR-L relation for the current sample of reverberation-mapped active galaxies implies that the majority of these sources have rapidly spinning black holes.