SELF-CONSISTENT MODELS OF THE AGN AND BLACK HOLE POPULATIONS: DUTY CYCLES, ACCRETION RATES, AND THE MEAN RADIATIVE EFFICIENCY

By Francesco Shankar, D. Weinberg, J. Miralda-Escudé. 2007

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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 109M☉ 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.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/518f1d7f84a4bd10e2d29023d0628595deeeefaa

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Citations in the corpus

What drives the growth of black holes (2011, background): “…(e.g., BH mass density and distribution, evolving AGN luminosity functions, X-ray background spectrum; e.g., Marconi et al. 2004; Merloni 2004; Shankar et al. 2004, 2009; Hopkins et al. 2006a, 2008; Malbon et al. 2007; Di Matteo et al. 2008; Somerville et al. 2008; Fanidakis et al. 2011,…”
Galaxy luminosities, stellar masses, sizes, velocity dispersions as a function of morphological type (2009, background): “Section 6 shows that the morphological dependence of this relation means it is sensitive to how the ‘early-type’ sample was selected, potentially resolving a discrepancy in the recent literature (Shankar & Bernardi 2009; van der Wel et al. 2009; Shankar et al. 2009d).”
THE NON-CAUSAL ORIGIN OF THE BLACK-HOLE–GALAXY SCALING RELATIONS (2010, background): “…this subject either explicitly include AGN feedback (e.g. Croton et al. 2006; Robertson et al. 2006; Booth & Schaye 2009; Johansson et al. 2009; Shankar et al. 2009) or couple the merging scenario with a self regulation prescription for BH growth (e.g. Kauffmann & Haehnelt 2000; Volonteri &…”
AGN wind scaling relations and the co-evolution of black holes and galaxies (2017, background): “It has been already emphasised in the literature that the average SMBH accretion rate density has a redshift dependence morphologically similar to the cosmological SFR density (Marconi et al. 2004; Merloni et al. 2004; Silverman et al. 2008; Zheng et al. 2009; Shankar et al. 2009).”
Bolometric luminosities and Eddington ratios of X-ray selected active galactic nuclei in the XMM-COSMOS survey (2012, background): “In fact all accretion models, that also include mergers, fail in reproducing the high mass end of the local black hole mass function (see Shankar et al. 2009).”
A CATALOG OF QUASAR PROPERTIES FROM SLOAN DIGITAL SKY SURVEY DATA RELEASE 7 (2010, background): “…evolution of the SMBH population within the concordanceΛCDM paradigm (Kauffmann & Haehnelt 2000; Wyithe & Loeb 2003; Hopkins et al. 2006, 2008; Shankar et al. 2009; Shen 2009), where the key observational components include quasar clustering, the luminosity function (LF), the BH mass…”
Cosmological simulations of black hole growth: AGN luminosities and downsizing (2013, result): “5, the present-day BH mass function of the 500 Mpc/hr run (red line) is compared to observations from Marconi et al. (2004), Shankar et al. (2004, 2009) (black lines and symbols and grey shaded areas) and is found to be in reasonably good agreement for a BH mass range of 7.5 < log (M•/M ) < 9.5.”
TOWARD THE STANDARD POPULATION SYNTHESIS MODEL OF THE X-RAY BACKGROUND: EVOLUTION OF X-RAY LUMINOSITY AND ABSORPTION FUNCTIONS OF ACTIVE GALACTIC NUCLEI INCLUDING COMPTON-THICK POPULATIONS (2014, background): “…by many authors (e.g., Small & Blandford 1992; Yu & Tremeine 2012; Marconi et al. 2004; Shankar et al. 2004; Tamura et al. 2006; Cao & Li 2008; Shankar et al. 2009; Li et al. 2012; Shankar et al. 2013), it is also possible to trace the cosmological evolution of the mass function (MF) of all…”
Selection bias in dynamically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation (2016, methodology): “…black hole accretion models (e.g., Marconi et al. 2004; Merloni 2004; Granato et al. 2006; Lapi et al. 2006; Zheng et al. 2009; Silverman et al. 2008; Shankar et al. 2009b; Mullaney et al. 2012; Lapi et al. 2014) suggest some degree of correlation between black hole growth and large-scale star…”
The cosmic evolution of massive black holes in the Horizon-AGN simulation (2016, methodology): “We choose here the functional form proposed by Hopkins et al. (2007), which at the redshifts of interest falls between those proposed by Ueda et al. (2014) and Shankar et al. (2009), thus marking a ‘middle ground’.”
PRIMUS: THE DEPENDENCE OF AGN ACCRETION ON HOST STELLAR MASS AND COLOR (2011, background): “The evolution of the XLF is driven by this shift in accretion rate rather than the downsizing of black hole growth (see also Shankar et al. 2009).”
AN ALTERNATIVE APPROACH TO MEASURING REVERBERATION LAGS IN ACTIVE GALACTIC NUCLEI (2010, neutral): “This allows us to explore BH properties and evolution with redshift (e.g., Kollmeier et al. 2006; Peng et al. 2006; Hopkins & Hernquist 2006; Shankar et al. 2009; Steinhardt & Elvis 2010; Kelly et al. 2010), thus providing valuable insights into the mystery of black hole growth and its connection…”
CLUSTERING OF LOW-REDSHIFT (z ⩽ 2.2) QUASARS FROM THE SLOAN DIGITAL SKY SURVEY (2008, background): “This information, combined with the quasar luminosity function (QLF), constrains η, the fraction of the Eddington luminosity at which quasars shine, and their duty cycle (Wyithe & Loeb 2005; Shankar et al. 2007).”
EDDINGTON-LIMITED ACCRETION AND THE BLACK HOLE MASS FUNCTION AT REDSHIFT 6 (2010, methodology): “Therefore we see that the differences in duty cycle, accretion efficiency, Eddington ratio and luminosity functions cause the differences between our results and those of Shankar et al. (2009).”
THE RADIATIVE EFFICIENCY OF ACCRETION FLOWS IN INDIVIDUAL ACTIVE GALACTIC NUCLEI (2010, methodology): “This method has also been used to estimate the time and luminosity dependence of ηav through more detailed modeling (e.g. Hopkins et al. 2006; Shankar et al. 2009; Wang et al. 2009; Raimundo & Fabian 2009), but the derived values are significantly uncertain.”
Supermassive black holes and their feedback effects in the IllustrisTNG simulation (2017, background): “First, the luminosity function, which can be measured up to high redshift, gives insights about the mass growth via gas accretion over cosmic time (Hopkins et al. 2007; Shankar et al. 2009; Ueda et al. 2014; Lacy et al. 2015).”