The Search for the Farthest Quasar: Consequences for Black Hole Growth
  and Seed Models
  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 $\,f_{\rm Edd}$, duty cycle ${\cal D}$, seed mass $M_{\rm
\bullet, seed}$ and radiative efficiency $\epsilon$), we show that the large
uncertainties in their determination decrease by a factor $\sim 5$ 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
$M_{\rm \bullet, seed}$ 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 $M_{\rm
\bullet, seed} > 10^{3.5} \,{\rm M_\odot}$ and $\epsilon < 0.1$. The radiative
efficiency is a crucial unknown, with factor $\sim 2$ changes able to modify
the predicted mass by $\sim 3$ orders of magnitude already at $z\sim 9$. 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
$M_\bullet \sim 10^{10} \,{\rm M_\odot}$ by $z\sim 9-10$ would exclude the
entire parameter space available for light seeds and dramatically reduce the
one for heavy seeds.
