Abstract
In the last two decades $200$ quasars have been discovered at $z>6$,
hosting active super-massive black holes with masses $M_\bullet 10^9
\,M_ødot$. While these sources reflect only the tip of the iceberg of
the black hole mass distribution, their detection challenges standard growth
models. The most massive $z>6$ black hole that was inferred thus far
(J0100+2802, $M_\bullet 1.210^10 \,M_ødot$) was
recently claimed to be lensed, with a magnification factor $\mu=450$. Here we
perform a consistency check of this claim, finding that the detection of such
source requires a bright-end slope $3.6$ for the intrinsic quasar
luminosity function, $\Phi(L) L^-\beta$. Commonly used values of
$2.8$ are rejected at $>3\sigma$. If the claim is confirmed, it is
very unlikely that all the remaining $51$ sources in the SDSS sample are not
magnified. Furthermore, it suffices that $25\%$ of the remaining
sources are lensed for the intrinsic luminosity function to differ
significantly (i.e., $>3\sigma$) from the observed one. The presence of
additional extremely magnified sources in the sample would lower the
requirement to $4\%$. Our results urge the community to perform more
extended multi-wavelength searches targeting $z>6$ lensed quasars, also among
known samples. This effort could vitally contribute to solve the open problem
of the growth of the brightest $z7$ quasars.
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