Toward precise constraints on growth of massive black holes

TL;DR

This paper uses an extended Soltan argument with recent survey data to constrain the growth history and luminosity evolution of massive black holes and quasars, revealing a two-phase growth pattern and implications for black hole demographics.

Contribution

It introduces a robust two-phase luminosity evolution model for QSOs, combining optical and X-ray survey data to refine black hole growth constraints.

Findings

QSO luminosity evolution involves an initial exponential increase followed by a power-law decline.

Most black hole mass growth occurs during a 2-3 x 10^8 year high-luminosity phase.

Mass-to-energy conversion efficiency is approximately 0.16, with uncertainties due to obscured AGNs.

Abstract

Growth of massive black holes (MBHs) in galactic centers comes mainly from gas accretion during their QSO/AGN phases. In this paper we apply an extended Soltan argument, connecting the local MBH mass function with the time-integral of the QSO luminosity function, to the demography of MBHs and QSOs from recent optical and X-ray surveys, and obtain robust constraints on the luminosity evolution (or mass growth history) of individual QSOs (or MBHs). We find that the luminosity evolution probably involves two phases: an initial exponentially increasing phase set by the Eddington limit and a following phase in which the luminosity declines with time as a power law (with a slope of -1.2--1.3) set by a self-similar long-term evolution of disk accretion. Neither an evolution involving only the increasing phase with a single Eddington ratio nor an exponentially declining pattern in the second phase is likely. The period of a QSO radiating at a luminosity higher than 10% of its peak value is about (2-3)x10^8 yr, during which the MBH obtains ~80% of its mass. The mass-to-energy conversion efficiency is $0.16\pm0.04 ^{+0.05}_{-0}$, with the latter error accounting for the maximum uncertainty due to Compton-thick AGNs. The expected Eddington ratios in QSOs from the constrained luminosity evolution cluster around a single value close to 0.5-1 for high-luminosity QSOs and extend to a wide range of lower values for low-luminosity ones. The Eddington ratios for high luminosity QSOs appear to conflict with those estimated from observations (~0.25) by using some virial mass estimators for MBHs in QSOs unless the estimators systematically over-estimate MBH masses by a factor of 2-4. We also infer the fraction of optically obscured QSOs ~60-80%. Further applications of the luminosity evolution of individual QSOs are also discussed.