Self-Consistent Models of the Agn and Black Hole Populations: Duty Cycles, Accretion Rates, and the Mean Radiative Efficiency

Abstract

We construct evolutionary models of the populations of active galactic nuclei (AGN) and supermassive black holes, in which the black hole mass function grows at the rate implied by the observed luminosity function, given assumptions about the radiative efficiency and the luminosity in Eddington units. We draw on a variety of recent X-ray and optical measurements to estimate the bolometric AGN luminosity function and compare to X-ray background data and the independent estimate of Hopkins et al. (2007) to assess remaining systematic uncertainties. The integrated AGN emissivity closely tracks the cosmic star formation history, suggesting that star formation and black hole growth are closely linked at all redshifts. We discuss observational uncertainties in the local black hole mass function, which remain substantial, with estimates of the integrated black hole mass density ρ • spanning the range 3 − 5.5 × 10 5 M ⊙ Mpc −3 . We find good agreement with estimates of the local mass function for a reference model where all active black holes have a fixed efficiency ǫ = 0.065 and L bol /L Edd ≈ 0.4 (shifting to ǫ = 0.09, L bol /L Edd ≈ 0.9 for the Hopkins et al. luminosity function). In our reference model, the duty cycle of 10 9 M ⊙ black holes declines from 0.07 at z = 3 to 0.004 at z = 1 and 10 −4 at z = 0. The decline is shallower for less massive black holes, a signature of "downsizing" evolution in which more massive black holes build their mass earlier. The predicted duty cycles and AGN clustering bias in this model are in reasonable accord with observational estimates. If the typical Eddington ratio declines at z < 2, then the "downsizing" of black hole growth is less pronounced. Models with reduced Eddington ratios at low redshift or black hole mass predict fewer low mass black holes (M • 10 8 M ⊙ ) in the local universe, while models with black hole mergers predict more black holes at M • > 10 9 M ⊙ . Matching the integrated AGN emissivity to the local black hole mass density implies ǫ = 0.075 × (ρ • /4.5 × 10 5 M ⊙ Mpc −3 ) −1 for our standard luminosity function estimate, or 25% higher for Hopkins et al.'s estimate. It is difficult to reconcile current observations with a model in which most black holes have the high efficiencies ǫ ≈ 0.16−0.20 predicted by MHD simulations of disk accretion. We provide electronic tabulations of our bolometric luminosity function and our reference model predictions for black hole mass functions and duty cycles as a function of redshift.

The cosmic growth of the active black hole population at 1 <z <2 in zCOSMOS, VVDS and SDSS

“…Our work strongly supports the picture of BH mass downsizing or 'anti-hierarchical' BH growth, suggested by previous studies (Merloni 2004;Heckman et al 2004;Shankar et al 2009;Vestergaard & Osmer 2009;Shen & Kelly 2012;Nobuta et al 2012). The downsizing in the AGN LF is driven by mass downsizing and by a change of the accretion rate distribution function with time, suggesting a complex process driving the cosmic evolution of BH growth.…”

Herschel Observed Stripe 82 Quasars and Their Host Galaxies: Connections Between Agn Activity and Host Galaxy Star Formation

“…Our results are comparable to Mullaney et al (2012), in which the SFR within 1 z < 2 bin is 3.5 times greater than within z < 1 bin, while the SFR when z > 2 is 10.3 times greater than when z < 1. Because the AGN activity and star formation are known to peak at z ∼ 2 (e.g., Shankar et al 2009;Behroozi et al 2013;Burgarella et al 2013;Delvecchio et al 2014), we then fit the SFR as a function to the redshift within z < 2 and z 2 separately. Besides the rapidly increasing SFR when z < 2, we also see a slight decrease toward higher redshifts at z > 2.…”

A Practical Guide to the Massive Black Hole Cosmic History

“…Subsequent mass measurements of the local nuclear MBHs suggested that the MBH mass density in the local Universe is consistent with the accreted mass inferred by integrating the quasar luminosity function at all redshifts assuming ≈ 0.1 [20,[87][88][89][90]. Therefore, the "quasar mode," in which large amount of gas are accreted in single coherent episodes via accretion disks shining close to the Eddington luminosity, appears to be principal path of MBH cosmic growth.…”

“…Different fits to the Kα line in MCG-6-30-15 gave a > 0.98 [167], a = 0.86±0.01 [165], and a = 0.49 +0. 20 −0.12 [164]. Even more problematic is the case of NGC 3783, for which different groups found a > 0.88 [168] and a < 0.32 [164].…”