2019ApJ...877..143Z

Accretion of tidally disrupted stars (TDSs) is expected to contribute significantly to the growth of massive black holes (MBHs) with mass ∼10⁶M_☉ in galactic centers. In this paper, we quantitatively investigate the effect of the TDS accretion on the spin evolution of these relatively small MBHs, by also considering the accretion of gas clouds with (many) chaotic episodes. We find that the accretion of TDSs can play an important role or even a dominant role in shaping the spin distribution of ∼10⁶M_☉ MBHs, depending on the contribution fraction (f_TDE) of the TDS accretion to the MBH growth. If f_TDE is as large as ≳0.9, most ∼10⁶M_☉ MBHs have low spins (| a| ≲0.3); if f_TDE is as small as ≲0.1, most ∼10⁶M_☉ MBHs have high spins (| a| ≳0.7). We also find that (1) the fraction of highly spinning ∼10⁶M_☉ MBHs in the TDS accretion states is smaller than that in the gas-cloud (active galactic nucleus [AGN]) accretion states, which is a consequence of more rapid spin decrease during the period of consecutive TDS accretion than the spin increase during the AGN periods when the spin is large; and (2) the fraction of retrograde-spin accretion in the TDS accretion states is almost the same as that of prograde-spin accretion, while it is negligible in the gas-cloud (AGN) accretion states. The current scarce sample of AGNs (∼10⁶M_☉) with spin measurements hints at an insignificant contribution from TDS accretion to MBH growth. Future measurements on spins of ∼10⁶M_☉ MBHs may provide stronger constraints on the importance of both AGN and TDS accretion states in their growth history.