GROWTH OF EARLY SUPERMASSIVE BLACK HOLES AND THE HIGH-REDSHIFT EDDINGTON RATIO DISTRIBUTION

Using a new large-scale (∼ 0.75 Gpc)3 hydrodynamic cosmological simulation, we investigate the growth rate of supermassive black holes (BHs) in the early universe (z ≳ 4.75). Remarkably we find a clear peak in the typical Eddington ratio (λ) at BH masses of (4–8) × 107 M☉ (typically in halos of ∼7 × 1011 to 1 × 1012 M☉, close to their shock heating scale), independent of redshift and indicative that most BH growth occurs in the cold-flow-dominated regime. BH growth is enhanced at high-z and by and large regulated by the cosmological evolution of gas density, with λ scaling simply as (1 + z)3. The peak in λ is caused by the competition between increased gas density available in more massive hosts, and a decrease due to active galactic nucleus feedback that becomes effective above the shock heating halo mass scale and at high BH masses. We show that the distribution of λ among both mass-selected and luminosity-selected samples is approximately lognormal. We combine these findings into a single lognormal fitting formula for the distribution of Eddington ratios as a function of (MBH, z). This formula can be used in analytic and semianalytic models for evolving BH populations, predicting BH masses of observed quasars, and, in conjunction with the observed distribution of Eddington ratios, can be used to constrain the BH mass function.