Reality or Mirage? Observational Test and Implications for the Claimed Extremely Magnified Quasar at $z=6.3$

In the last two decades, approximately 200 quasars have been discovered at $z>6$, hosting active super-massive black holes with masses $M_{\bullet} \gtrsim 10^9 M_{\odot}$. 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, $M_{\bullet }\approx 1.2\times {10}^{10}{M}_{\odot }$) 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 $\beta \ge 3.7$ for the intrinsic quasar luminosity function, $\mathrm{\Phi }(L)\propto L^{-\beta }$. Commonly used values of $\beta \sim 2.8$ 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 $\gtrsim 25\mathrm{\%}$ 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 $\sim 4\mathrm{\%}$. 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 solving the open problem of the growth of the brightest $z\sim 7$ quasars.