Kavli Affiliate: Kohei Inayoshi
| First 5 Authors: Wenxiu Li, Kohei Inayoshi, Masafusa Onoue, Daisuke Toyouchi,
| Summary:
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 $zsimeq 6$ 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 $zsimeq 6$, 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 $zgtrsim 6$.
These results will be unveiled by future deep and wide surveys with the James
Webb Space Telescope, Roman Space Telescope, and Euclid.
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