Ionization bias and the ghost proximity effect near $z\gtrsim6$ quasars
  in the shadow of proximate absorption systems
  The larger-than-expected scatter in the opacity of the Ly$\alpha$ forest
suggests that the metagalactic ionizing background is strongly fluctuating at
$z > 5.5$. Models for ionizing background fluctuations predict a strong
positive bias on large scales, so the environments of massive $>10^{12}\,{\rm
M}_\odot$ dark matter halos, e.g. $z\sim6$ quasar hosts, would be ideal
laboratories to constrain the sources of ionizing photons. While the quasars
themselves should overwhelm any plausible ionizing photon contribution from
neighboring galaxies, proximate damped Ly$\alpha$ absorbers (DLAs) have
recently been discovered in the foreground of $z\sim6$ quasars, and the
Ly$\alpha$ forest in the shadow of these DLAs could probe the local ionization
environment. Using Gpc$^3$ simulations of $z=6$ ionizing background
fluctuations, we show that while the Ly$\alpha$ forest signal from ionization
bias around a quasar host halo should be strong, it is likely suppressed by the
associated intergalactic matter overdensity. We also show that the quasar
itself may still overwhelm the clustering signal via a "ghost" of the proximity
effect from the quasar radiation causing a large-scale bias in the ionizing
photon mean free path. This ghost proximity effect is sensitive to the lifetime
and geometry of quasar emission, potentially unlocking a new avenue for
constraining these fundamental quasar properties. Finally, we present
observations of a $z\sim6$ quasar with a proximate DLA which shows a strong
excess in Ly$\alpha$ forest transmission at the predicted location of the ghost
proximity effect.
