SIMBAD references

We investigate the black hole mass function at z ∼ 5 using XQz5, our recent sample of the most luminous quasars between the redshifts 4.5 < z < 5.3. We include 72 quasars with black hole masses estimated from velocity-broadened emission-line measurements and single-epoch virial prescriptions in the footprint of a highly complete parent survey. The sample mean Eddington ratio and standard deviation is log λ ≈ -0.20 ± 0.24. The completeness-corrected mass function is modelled as a double power law, and we constrain its evolution across redshift assuming accretion-dominated mass growth. We estimate the evolution of the mass function from z = 5-4, presenting joint constraints on accretion properties through a measured dimensionless e-folding parameter, k_ef ≡ 〈λ〉U(1 - ϵ)/ϵ = 1.79 ± 0.06, where 〈λ〉 is the mean Eddington ratio, U is the duty cycle, and ϵ is the radiative efficiency. If these supermassive black holes were to form from seeds smaller than $10^8\, {\rm M}_{\odot }$, the growth rate must have been considerably faster at z ≫ 5 than observed from z = 5-4. A growth rate exceeding 3 × the observed rate would reduce the initial heavy seed mass to $10^{5-6}\, {\rm M}_{\odot }$, aligning with supermassive star and/or direct collapse seed masses. Stellar mass ($10^2\, {\rm M}_{\odot }$) black hole seeds would require ≳4.5 × the observed growth rate at z ≫ 5 to reproduce the measured active black hole mass function. A possible pathway to produce the most extreme quasars is radiatively inefficient accretion flow, suggesting black holes with low angular momentum or photon trapping in supercritically accreting thick discs.