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A tight relation between the size of the broad-line region (BLR) and opticalluminosity has been established in about 50 active galactic nuclei studiedthrough reverberation mapping of the broad Hbeta emission line. The R_blr-Lrelation arises from simple photoionization considerations. Using a generalrelativistic model of an optically thick, geometrically thin accretion disk, weshow that the ionizing luminosity jointly depends on black hole mass, accretionrate, and spin. The non-monotonic relation between the ionizing and opticalluminosity gives rise to a complicated relation between the BLR size and theoptical luminosity. We show that the reverberation lag of Hbeta to the varyingcontinuum depends very sensitively to 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 opticalluminosity, and hence shortened Hbeta lags. This effect is specially strikingfor luminous quasars undergoing retrograde accretion, manifesting in strongdeviations from the canonical R_blr-L relation. This could lead to a method toestimate black hole spins of quasars and to study their cosmic evolution. Atthe same time, the small scatter of the observed R_blr-L relation for thecurrent sample of reverberation-mapped active galaxies implies that themajority of these sources have rapidly spinning black holes.

A New Approach to Constrain Black Hole Spins in Active Galaxies Using Optical Reverberation Mapping