2015ApJ...804...45L

Warped accretion disks have attracted intense attention because of their critical role in shaping the spin of supermassive massive black holes (SMBHs) through the Bardeen-Petterson effect, a general relativistic effect that leads to final alignments or anti-alignments between black holes and warped accretion disks. We study such alignment processes by explicitly taking into account the finite sizes of accretion disks and the episodic lifetimes of active galactic nuclei (AGNs) that delineate the duration of gas fueling onto accretion disks. We employ an approximate global model to simulate the evolution of accretion disks, allowing us to determine the gravitomagnetic torque that drives the alignments in a simple way. We then track down the evolutionary paths for mass and spin of black holes both in a single activity episode and over a series of episodes. Given with randomly and isotropically oriented gas fueling over episodes, we calculate the spin evolution with different episodic lifetimes and find that it is quite sensitive to the lifetimes. We therefore propose that the spin distribution of SMBHs can place constraints on the episodic lifetimes of AGNs and vice versa. The applications of our results on the observed spin distributions of SMBHs and the observed episodic lifetimes of AGNs are discussed, although both measurements at present are too ambiguous for us to draw a firm conclusion. Our prescription can be easily incorporated into semi-analytic models for black hole growth and spin evolution.