On Constraining the Growth History of Massive Black Holes via Their Distribution on the Spin–Mass Plane

Abstract

The spin distribution of massive black holes (MBHs) contains rich information on the MBH growth history. In this paper, we investigate the spin evolution of MBHs by assuming that each MBH experiences two-phase accretion, with an initial phase of coherent-accretion via either the standard thin disc or super-Eddington disc, followed by a chaotic-accretion phase composed of many episodes with different disc orientations. If the chaotic-phase is significant to the growth of an MBH, the MBH spin quickly reaches the maximum value because of the initial coherent-accretion, then changes to a quasi-equilibrium state and fluctuates around a value mainly determined by the mean ratio of the disc to the MBH mass (M • ) in the chaotic-accretion episodes, and further declines due to late chaoticaccretion if M • (1 − 3) × 10 8 M ⊙ . The turning point to this decline is determined by the equality of the disc warp radius and disc size. By matching the currently available spin measurements with mock samples generated from the two-phase model(s) on the spin-mass plane, we find that MBHs must experience significant chaotic-accretion phase with many episodes and the mass accreted in each episode is roughly 1-2 percent of M • or less. MBHs with M • 10 8 M ⊙ appear to have intermediate-tohigh spins (∼ 0.5 − 1), while lighter MBHs have higher spins ( 0.8). The best matches also infer that (1) the radiative efficiencies (η) of those active MBHs appear to slightly decrease with M • ; however, the correlation between η and M • , if any, is weak; (2) the mean radiative efficiency of active MBHs is η ∼ 0.09 − 0.15, consistent with the global constraints.

Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering

“…This yields a mean radiative efficiency a factor of ∼ 2 − 3 higher than previous estimates solely based on observed/biased black hole scaling relations 5,36 . Our results would support black hole spin parameters 2 a 0.7, which are consistent with a number of direct measurements performed via X-ray reflection analysis 40 or spectral energy distribution fits 41,42 . Hints for relatively high mean radiative efficiencies are also present in some previous works 43,44 .…”

Probing black hole accretion tracks, scaling relations, and radiative efficiencies from stacked X-ray active galactic nuclei

“…Using Shankar et al (2016a)'s de-biased M bh -Mstar relation, or the relation inferred from AGN black hole mass estimates by Reines & Volonteri (2015), we find a mean radiative efficiency ε ∼ 0.15, in good agreement with theoretical expectations for accretion onto black holes with spin parameters a ∼ 0.5 − 1. The red solid line in Figure 7 shows the monotonic dependence of the spin parameter on radiative efficiency, obtained by integrating the specific energy and orbital angular momentum equations in the limit (Bardeen et al 1972;Zhang & Lu 2019) of no kinetic loss ε = 1 − E(Risco), with E(Risco) the specific orbital energy at the innermost stable circular orbit with radius Risco. This model suggests that values of a 0.5 would correspond to radiative efficiencies greater than ε 0.1 (black arrows in Figure 7), which would be in line with the limits on ε obtained in this work when comparing with the de-biased M bh -Mstar relations (purple area in the upper right of Figure 7), but in tension with the allowed ranges of ε required by the match to the raw M bh -Mstar relations (cyan area in the bottom left of Figure 7).…”

Observational Constraints on Black Hole Spin

“…The predominance of rapid-spinners in the lowmass SMBH population suggests growth via coherent accretion events, whereas the more modest spins of the more massive SMBHs (M > 3 × 10 7 M ) suggests the growing importance of SMBH-SMBH major mergers and/or incoherent accretion (Volonteri et al 2005). Indeed, this exact mass dependence of SMBH-spins is seen in semi-analytic (Sesana et al 2014, Zhang & Lu 2019 and full cosmological-hydrodynamic (Bustamante & Springel 2019) models of hierarchal galaxy formation.…”