SIMBAD references

We investigate the black hole mass function (BHMF) and Eddington-ratio distribution function (ERDF) of broad-line active galactic nuclei (AGNs) at z = 4, based on a sample of 52 quasars with i < 23.2 at 3.50 ≤ z ≤ 4.25 from the Hyper Suprime-Cam Subaru Strategic Program S16A-Wide2 data set, and 1462 quasars with i < 20.2 in the same redshift range from the Sloan Digital Sky Survey data release 7 quasar catalog. Virial black hole (BH) masses of quasars are estimated using the width of the C_IV 1549 Å line and the continuum luminosity at 1350 Å. To obtain the intrinsic broad-line AGN BHMF and ERDF, we correct for the incompleteness in the low-mass and/or low-Eddington-ratio ranges caused by the flux-limited selection. The resulting BHMF is constrained down to $\mathrm{log}{M}_{\mathrm{BH}}/{M}_{\odot }\sim 7.5$. In comparison with broad-line AGN BHMFs at z ∼ 2 in the literature, we find that the number density of massive SMBHs peaks at higher redshifts, consistent with the downsizing evolutionary scenario. Additionally, the resulting ERDF shows a negative dependence on BH mass, suggesting more massive SMBHs tend to accrete at lower-Eddington ratios at z = 4. With the derived intrinsic broad-line AGN BHMF, we also evaluate the active fraction of broad-line AGNs among the entire SMBH population at z = 4. The resulting active fraction may suggest a positive dependence on BH mass. Finally, we examine the time evolution of broad-line AGN BHMF between z = 4 and 6 through solving the continuity equation. The results suggest that the broad-line AGN BHMFs at z = 4-6 only show evolution in their normalization, but with no significant changes in their shape.