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Self-consistent models of the AGN and black hole populations: duty cycles, accretion rates, and the mean radiative efficiency

Self-consistent models of the AGN and black hole populations: duty cycles, accretion rates, and the mean radiative efficiency
Self-consistent models of the AGN and black hole populations: duty cycles, accretion rates, and the mean radiative efficiency
We construct evolutionary models of the populations of active galactic nuclei (AGNs) 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. 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 × 105 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 ε = 0.065 and Lbol/LEdd ~ 0.4 (shifting to ε = 0.09, Lbol/LEdd ~ 0.9 for the Hopkins et al. luminosity function). In our reference model, the duty cycle of 109 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 ≲ 108 M) in the local universe, while models with black hole mergers predict more black holes at M > 109 M. Matching the integrated AGN emissivity to the local black hole mass density implies ε = 0.075 × (ρ/4.5 × 105 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 ε ~ 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
0004-637X
20-41
Shankar, Francesco
b10c91e4-85cd-4394-a18a-d4f049fd9cdb
Weinberg, David H.
40dbbb02-c823-48be-9de0-57567338db5b
Miralda-Escude, Jordi
188e00a5-e8df-4de2-be3d-9cb9cb0fe4bf
Shankar, Francesco
b10c91e4-85cd-4394-a18a-d4f049fd9cdb
Weinberg, David H.
40dbbb02-c823-48be-9de0-57567338db5b
Miralda-Escude, Jordi
188e00a5-e8df-4de2-be3d-9cb9cb0fe4bf

Shankar, Francesco, Weinberg, David H. and Miralda-Escude, Jordi (2009) Self-consistent models of the AGN and black hole populations: duty cycles, accretion rates, and the mean radiative efficiency. Astrophysical Journal, 690, 20-41. (doi:10.1088/0004-637X/690/1/20).

Record type: Article

Abstract

We construct evolutionary models of the populations of active galactic nuclei (AGNs) 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. 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 × 105 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 ε = 0.065 and Lbol/LEdd ~ 0.4 (shifting to ε = 0.09, Lbol/LEdd ~ 0.9 for the Hopkins et al. luminosity function). In our reference model, the duty cycle of 109 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 ≲ 108 M) in the local universe, while models with black hole mergers predict more black holes at M > 109 M. Matching the integrated AGN emissivity to the local black hole mass density implies ε = 0.075 × (ρ/4.5 × 105 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 ε ~ 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

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Published date: April 2009
Organisations: Physics & Astronomy

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Local EPrints ID: 357028
URI: http://eprints.soton.ac.uk/id/eprint/357028
ISSN: 0004-637X
PURE UUID: b963dbba-0b73-4973-8ed2-dac06eec3797

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Date deposited: 19 Sep 2013 10:23
Last modified: 25 Nov 2021 17:07

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Contributors

Author: David H. Weinberg
Author: Jordi Miralda-Escude

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