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

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 semianalytical 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 ≃ 6 suggests that several episodes of moderate super-Eddington accretion occur and each of them lasts for τ ≃ 20–30 Myr. The average duty cycle in super-Eddington phases is ≃15% for massive BHs that reach ≳108 M ⊙ by z ≃ 6, which is nearly twice that of the entire population. We find that the observed Eddington ratio distribution function is skewed to a lognormal 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 ≳ 6. These results will be unveiled by future deep and wide surveys with the James Webb Space Telescope, Roman Space Telescope, and Euclid.

Black Hole Mass and Eddington-ratio Distributions of Less-luminous Quasars at z ∼ 4 in the Subaru Hyper Suprime-Cam Wide Field

“…They show constant values with a mean at 0.01 ∼ 0.15 over a wide BH mass range of M M 7.5 log 9 BH  < < , implying the phase of active accretion is occurring throughout the less-massive SMBH population without preferences on the BH mass. That active fractions are consistent with the values evaluated with the X-ray-selected AGNs in the deep survey fields (e.g., Bongiorno et al 2012Bongiorno et al , 2016Georgakakis et al 2017), and with the semianalytical model for the BH formation and growth (e.g., Li et al 2022). Again, the increase beyond M M log 9 BH  > is highly uncertain because the total BHMFs are evaluated with the extrapolated M BH -M Bulge or M BH -M star relations.…”

Hidden Little Monsters: Spectroscopic Identification of Low-mass, Broad-line AGNs at z > 5 with CEERS

“…The virial BH mass estimate we present above now shows that this low-luminosity AGN is by far the least massive BH known in the Universe at the end of cosmic reionization. The modest Eddington ratio of CEERS 2782 suggests that this AGN has been identified after its rapid accretion mode has ended, although it is possible that the system will experience future bursts of heavy accretion (Li et al 2023).…”

“…These ultrarare systems, which formed in biased regions of the early Universe, place limited constraints on the BH seed population, as they would have undergone sustained episodes of exponential growth, even for the most massive predicted seeds, thereby erasing the imprint of the initial seed mass distribution (e.g., Tanaka & Haiman 2009;Volonteri 2010). A complementary approach is to search for lower-luminosity quasars hosting SMBHs with masses closer to the predicted seed mass range at the earliest epochs possible (Somerville et al 2008;Valiante et al 2016;Ricarte & Natarajan 2018;Yung et al 2021;Li et al 2023). Several deep optical surveys have attempted to do this by reaching a dex fainter in luminosity (e.g., Willott et al 2007Willott et al , 2010Matsuoka et al 2016Matsuoka et al , 2022Kim et al 2018Kim et al , 2020Fujimoto et al 2022); however, these samples are still far more luminous than what is observed in the nearby Universe (L bol ∼ 10 43 −10 44 erg s −1 ; e.g., Greene & Ho 2007;Liu et al 2018Liu et al , 2019, biasing our understanding of early SMBHs toward the most massive and active populations (however, see also Mezcua et al 2018).…”

Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6

“…For example, by assuming that the feedback is inefficient at z ∼ 6 while it becomes more efficient until z ∼ 4, an evolution model that the bias keeps low until z ∼ 4 and increases rapidly to z ∼ 6 does not conflict with our observational result. Alternatively, it could be explained by intermittent black hole growth (Inayoshi et al 2022;Li et al 2023). To further restrict the models, the measurement of the bias parameter at z ∼ 5 is a key.…”