The Assembly of Black Hole Mass and Luminosity Functions of High-redshift Quasars via Multiple Accretion Episodes

TL;DR

This paper presents a semi-analytical model for the early growth of supermassive black holes, explaining the observed quasar luminosity and black hole mass functions at high redshift through multiple accretion episodes, including super-Eddington phases.

Contribution

It introduces a new model incorporating multiple accretion bursts with super-Eddington episodes to explain high-redshift quasar properties and their evolution.

Findings

Several super-Eddington accretion episodes last for 20-30 Myr.

Duty cycle of super-Eddington phases is about 15% for massive black holes.

Predicted rapid decline in quasar number and black hole mass density beyond redshift 6.

Abstract

The early evolution of the quasar luminosity function (QLF) and black hole mass function (BHMF) encodes key information on the physics determining the radiative and accretion processes of supermassive black holes (BHs) in high-$z$ quasars. Although the QLF shape has been constrained by recent observations, it remains challenging to develop a theoretical model that explains its redshift evolution associated with BH growth self-consistently. In this study, based on a semi-analytical model for the BH formation and growth, we construct the QLF and BHMF of the early BH population that experiences multiple accretion bursts, in each of which a constant Eddington ratio is assigned following a Schechter distribution function. Our best-fit model to reproduce the observed QLF and BHMF at $z\simeq 6$ suggests that several episodes of moderate super-Eddington accretion occur and each of them lasts for $\tau \simeq 20-30$ Myr. The average duty cycle in super-Eddington phases is $\simeq 15\%$ for massive BHs that reach $\gtrsim 10^8~M_\odot$ by $z\simeq 6$, which is nearly twice that of the entire population. We also find that the observed Eddington-ratio distribution function is skewed to a log-normal shape owing to detection limits of quasar surveys. The predicted redshift evolution of the QLF and BHMF suggests a rapid decay of their number and mass density in a cosmic volume toward $z\gtrsim 6$. These results will be unveiled by future deep and wide surveys with the James Webb Space Telescope, Roman Space Telescope, and Euclid.