High-redshift quasars and the supermassive black hole mass budget: constraints on quasar formation models

Abstract

We investigate the constraints on models of supermassive black hole (SMBH) and quasar formation obtainable from two recent observational developments: the discovery of luminous quasars at z∼ 6, and estimates of the local mass density of SMBHs. If ∼90 per cent of this mass was accreted at redshifts z≲ 3, as suggested by the observed quasar luminosity functions, these joint constraints pose a challenge for models, which must account for the observed luminous quasar population at z∼ 6 within a very limited ‘mass budget’. We investigate a class of models based within the hierarchical structure formation scenario, in which major mergers lead to black hole formation and fuelling, and the resulting quasars shine at their Eddington‐limited rate until their fuel is exhausted. We show that the simplest such model, in which a constant fraction of the gas within the halo is accreted in each major merger, cannot satisfy both constraints simultaneously. When this model is normalized to reproduce the number density of luminous quasars at z∼ 6, the mass budget is grossly exceeded owing to an overabundance of lower‐mass SMBHs. We explore a range of modifications to the simple model designed to overcome this problem. We show that both constraints can be satisfied if the gas accretion fraction scales as a function of the halo virial velocity. Similar scalings have been proposed in order to reproduce the local M•–σ relation. Successful models can also be constructed by restricting the formation of seed black holes to redshifts above zcrit∼ 11.5 or to haloes above a velocity threshold vcrit∼ 55 km s−1, or assuming that only a fraction of major mergers result in formation of a seed SMBH. We also briefly discuss the issue of trying to assume a ‘universal M•–σ relation’ within the framework of simple Press–Schechter models, and further show that a fixed universal relation between SMBH mass and host halo mass is unlikely.

Active Galactic Nuclei with Candidate Intermediate‐Mass Black Holes

“…However, there are few direct observational constraints on the nature of seed BHs, the path by which nuclear BHs grow, or the form of the BH mass function. The low end of the BH mass function, in particular, provides critical input to check theoretical models of quasar formation (e.g., Haehnelt et al 1998;Bromley et al 2004), and it affects predictions of future gravitational wave experiments such as the Laser Interferometer Space Antenna (Hughes 2002).…”

Four Quasars above Redshift 6 Discovered by the Canada-France High-zQuasar Survey

“…The high luminosities and broad line widths of the most distant quasars require black holes with masses greater than 10 9 M (Fan et al 2001;Willott et al 2003). Forming such massive black holes within the first billion years of the universe provides a challenge to models of galaxy formation, black hole formation, and black hole growth (Bromley et al 2004;Yoo & Miralda-Escudé 2004;Shapiro 2005;Volonteri & Rees 2005;King & Pringle 2006).…”

Observational Constraints on the Dependence of Radio‐Quiet Quasar X‐Ray Emission on Black Hole Mass and Accretion Rate

“…Investigations of how quasar X-ray parameters depend on black hole mass, M BH , and accretion rate relative to the Eddington rate,ṁ, offer important constraints on models of the disk/corona system. There have been attempts to link the evolution of SMBHs to analytic and semianalytic models of structure formation (e.g., Kauffmann & Haehnelt 2000;Hatziminaoglou et al 2003;Bromley et al 2004), where black holes grow by accreting gas funneled toward the center during a galaxy merger until feedback energy from the SMBH expels gas and shuts off the accretion process (e.g., Silk & Rees 1998;Fabian 1999;Wyithe & Loeb 2003;Begelman & Nath 2005). This self-regulated growth of black holes has recently been successfully applied in smoothed particle hydrodynamics simulations Springel et al 2005).…”