Abstract
The quest for high-redshift quasars has led to a series of record-breaking
sources, with the current record holder at $z=7.642$. Here, we show how future
detections of $z>8$ quasars impact the constraints on the parameters for black
hole growth and seed models. Using broad flat priors on the growth parameters
(Eddington ratio $\,f_Edd$, duty cycle $D$, seed mass $M_\rm
\bullet, seed$ and radiative efficiency $\epsilon$), we show that the large
uncertainties in their determination decrease by a factor $5$ when a
quasar's detection redshift goes from $z=9$ to $z=12$. In this high-redshift
regime, $\epsilon$ tends to the lowest value allowed, and the distribution for
$M_\bullet, seed$ peaks well inside the heavy seed domain. Remarkably,
two quasars detected at $z > 7$ with low accretion rates (J1243+0100 and
J0313-1806) already tighten the available parameter space, requiring $M_\rm
\bullet, seed > 10^3.5 \,M_ødot$ and $< 0.1$. The radiative
efficiency is a crucial unknown, with factor $2$ changes able to modify
the predicted mass by $3$ orders of magnitude already at $z9$. The
competing roles of inefficient accretion (decreasing $\epsilon$) and black hole
spin-up (increasing $\epsilon$) significantly impact growth models. Finally, we
suggest that yields currently predicted by upcoming quasar surveys (e.g.,
Euclid) will be instrumental for determining the most-likely seed mass regime.
For example, assuming thin-disk accretion, a detection of a quasar with
$M_10^10 \,M_ødot$ by $z9-10$ would exclude the
entire parameter space available for light seeds and dramatically reduce the
one for heavy seeds.
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