On the Radiative Efficiencies, Eddington Ratios, and Duty Cycles of Luminous High-Redshift Quasars

Abstract

We investigate the characteristic radiative efficiency , Eddington ratio λ, and duty cycle P 0 of high-redshift active galactic nuclei (AGNs), drawing on measurements of the AGN luminosity function at z = 3-6 and, especially, on recent measurements of quasar clustering at z = 3-4.5 from the Sloan Digital Sky Survey. The free parameters of our models are , λ, and the normalization, scatter, and redshift evolution of the relation between black hole (BH) mass M BH and halo virial velocity V vir . We compute the luminosity function from the implied growth of the BH mass function and the quasar correlation length from the bias of the host halos. We test our adopted formulae for the halo mass function and halo bias against measurements from the large N-body simulation developed by the MICE collaboration. The strong clustering of AGNs observed at z = 3 and, especially, at z = 4 implies that massive BHs reside in rare, massive dark matter halos. Reproducing the observed luminosity function then requires high efficiency and/or low Eddington ratio λ, with a lower limit (based on 2σ agreement with the measured z = 4 correlation length)0.7λ/(1 + 0.7λ), implying 0.17 for λ > 0.25. Successful models predict high duty cycles, P 0 ∼ 0.2, 0.5, and 0.9 at z = 3.1, 4.5, and 6, respectively, and they require that the fraction of halo baryons locked in the central BH is much larger than the locally observed value. The rapid drop in the abundance of the massive and rare host halos at z > 7 implies a proportionally rapid decline in the number density of luminous quasars, much stronger than simple extrapolations of the z = 3-6 luminosity function would predict. For example, our most successful model predicts that the highest redshift quasar in the sky with true bolometric luminosity L > 10 47.5 erg s −1 should be at z ∼ 7.5, and that all quasars with higher apparent luminosities would have to be magnified by lensing.

Faint high-redshift AGN in theChandradeep field south: the evolution of the AGN luminosity function and black hole demography

“…The main advantage of approaching AGN modeling through this simplified technique is that not being part of a specific SAM, they can explore easily and quickly a large space of parameters and physical recipes to trigger AGN. Here we follow the models presented in the preliminary work of Shankar (2010a) with the same parameters as in Shen (2009). A more comprehensive and detailed analysis of AGN merger models, that provides predictions for SMBH scaling relations and AGN clustering (Shankar et al 2010a,b) is beyond the scope of the present paper and will be discussed elsewhere (Shankar et al, in prep.).…”

Black holes in pseudobulges: demography and models

“…Thus, the number of outliers in the BH-galaxy classical relations could be very high, impacting the demography of local BHs by severely reducing the expected number density of low mass BHs in the local Universe (similar thoughts were also put forward by Gadotti & Kauffmann 2009;Greene et al 2010). This in turn could have a non-negligible repercussion on accretion and merging models that try to tune parameters such as the radiative efficiency and Eddington ratio distributions by matching the full shape of the local BH mass function (e.g., Marulli et al 2008;Shankar et al 2012b). …”

“…Recent estimates of the local BH mass function (e.g., Vika et al 2009) claim even lower number densities of low mass BHs that would further exacerbate the tension with model predictions. The shape of the local BH mass function at low masses is essential to properly constrain the total amount of sub-Eddington accretion that characterized the cosmic evolution of BHs (Shankar et al 2012b). …”

Cosmological Evolution of Supermassive Black Holes: Mass Functions and Spins

“…As mentioned above, previous studies show that mass accretion dominates over mergers in determining the mass growth and spin distribution of black holes (Berti & Volonteri 2008;King et al 2008). Shankar et al (2009Shankar et al ( , 2010, using theoretically predicted merger rates from hierarchical structure formation models, also conclude that the effect of mergers is minor compared with mass accretion. However, based on a semi-analytic model of hierarchical galaxy formation and evolution incorporating black hole growth, Fanidakis et al (2011b) recently showed that mergers do contribute significantly to the final black hole mass for high-mass black holes (e.g., M • 10 9 M ⊙ ).…”

“…As in most previous works (e.g., Small & Blandford 1992;Yu & Tremaine 2002;Marconi et al 2004), we neglect black hole mergers, setting S(t, M • ) = 0. Shankar et al (2009Shankar et al ( , 2010 investigated the importance of black hole mergers on the evolution of the SMBH mass function and concluded that the effect of mergers is minor compared with mass accretion. Numerical simulations by Volonteri et al (2005) and Berti & Volonteri (2008) also verified that mass accretion dominates over mergers in determining the mass growth and spin distribution of black holes.…”