Cosmological evolution of massive black holes: effects of Eddington ratio distribution and quasar lifetime

TL;DR

This paper models the evolution of massive black holes using a power-law Eddington ratio distribution and quasar lifetime, successfully matching observed black hole mass functions and constraining AGN duty cycles.

Contribution

It introduces a model incorporating a power-law Eddington ratio distribution and quasar lifetime to explain black hole growth and relic mass functions.

Findings

The black hole mass function at z=0 aligns with observations under certain efficiency and distribution parameters.

AGN duty cycle must be less than one, implying quasar lifetimes over 0.5 billion years.

The model supports a self-regulated growth scenario for AGNs.

Abstract

A power-law time-dependent lightcurve for active galactic nuclei (AGNs) is expected by the self-regulated black hole growth scenario, in which the feedback of AGNs expels gas and shut down accretion. This is also supported by the observed power-law Eddington ratio distribution of AGNs. At high redshifts, the AGN life timescale is comparable with (or even shorter than) the age of the universe, which set a constraint on the minimal Eddington ratio for AGNs on the assumption of a power-law AGN lightcurve. The black hole mass function (BHMF) of AGN relics is calculated by integrating the continuity equation of massive black hole number density on the assumption of the growth of massive black holes being dominated by mass accretion with a power-law Eddington ratio distribution for AGNs. The derived BHMF of AGN relics at z=0 can fit the measured local mass function of the massive black holes in galaxies quite well, provided the radiative efficiency ~0.1 and a suitable power-law index for the Eddington ratio distribution are adopted. In our calculations of the black hole evolution, the duty cycle of AGN should be less than unity, which requires the quasar life timescale >0.5 giga-years.