Constraining the Gravitational Lensing of z ≳ 6 Quasars from Their Proximity Zones

Since their discovery 20 years ago, the observed luminosity function of z ≳ 6 quasars has been suspected to be biased by gravitational lensing. Apart from the recent discovery of UHS J0439+1634 at z ≈ 6.52, no other strongly lensed z ≳ 6 quasar has been conclusively identified. The hyperluminous z ≈ 6.33 quasar SDSS J0100+2802, believed to host a supermassive black hole of ∼10¹⁰ M _⊙, has recently been claimed to be lensed by a factor of ∼450, which would negate both its extreme luminosity and black hole mass. However, its Lyα-transparent proximity zone is the largest known at z > 6, suggesting an intrinsically extreme ionizing luminosity. Here we show that the lensing hypothesis of z ≳ 6 quasars can be quantitatively constrained by their proximity zones. We first show that our proximity zone analysis can recover the strongly lensed nature of UHS J0439+1634, with an estimated magnification $\mu ={28.0}_{-11.7}^{+18.4}{(}_{-18.3}^{+44.9})$ at 68% (95%) credibility that is consistent with previously published lensing models. We then show that the large proximity zone of SDSS J0100+2802 rules out lensing magnifications of μ > 4.9 at 95% probability, and conclusively rule out the proposed μ > 100 scenario. Future proximity zone analyses of existing z ≳ 6 quasar samples have the potential to identify promising strongly lensed candidates, constrain the distribution of z ≳ 6 quasar lensing, and improve our knowledge of the shape of the intrinsic quasar luminosity function.