Constraining the Properties of Black Hole Seeds from the Farthest Quasars

Abstract: Over 60 years after the discovery of the first quasar, more than $275$ such sources are identified in the epoch of reionization at $z>6$. JWST is now exploring higher redshifts ($z\gtrsim 8$) and lower mass ($ \lesssim 10^7 \Msun$) ranges. The discovery of progressively farther quasars is instrumental to constraining the properties of the first population of black holes (BHs), or BH seeds, formed at $z \sim 20-30$. For the first time, we use Bayesian analysis of the most comprehensive catalog of quasars at $z>6$ to constrain the distribution of BH seeds. We show that the mass distribution of BH seeds can be effectively described by combining a power law and a lognormal function tailored to the mass ranges associated with light and heavy seeds, assuming Eddington-limited growth and early seeding time. Our analysis reveals a power-law slope of $-0.70^{+0.46}_{-0.46}$ and a lognormal mean of $4.44^{+0.30}_{-0.30}$. The inferred values of the Eddington ratio, the duty cycle, and the mean radiative efficiency are $0.82^{+0.10}_{-0.10}$, $0.66^{+0.23}_{-0.23}$, and $0.06^{+0.02}_{-0.02}$, respectively. Models that solely incorporate a power law or a lognormal distribution within the specific mass range corresponding to light and heavy seeds are statistically strongly disfavored, unlike models not restricted to this specific range. Our results suggest that including both components is necessary to comprehensively account for the masses of high-redshift quasars, and that both light and heavy seeds formed in the early Universe and grew to form the population of quasars we observe.