The Diversity of Environments Around Luminous Quasars at Redshift $z \sim 6$

Significant clustering around the rarest luminous quasars is a feature predicted by dark matter theory combined with number density matching arguments. However, this expectation is not reflected by observations of quasars residing in a diverse range of environments. Here, we assess the tension in the diverse clustering of visible $i$-band dropout galaxies around luminous $z\sim6$ quasars. Our approach uses a simple empirical method to derive the median luminosity to halo mass relation, $L_{c}(M_{h})$ for both quasars and galaxies under the assumption of log-normal luminosity scatter, $\Sigma_{Q}$ and $\Sigma_{G}$. We show that higher $\Sigma_{Q}$ reduces the average halo mass hosting a quasar of a given luminosity, thus introducing at least a partial reversion to the mean in the number count distribution of nearby Lyman-Break galaxies. We generate a large sample of mock Hubble Space Telescope fields-of-view centred across rare $z\sim6$ quasars by resampling pencil beams traced through the dark matter component of the BlueTides cosmological simulation. We find that diverse quasar environments are expected for $\Sigma_{Q}>0.4$, consistent with numerous observations and theoretical studies. However, we note that the average number of galaxies around the central quasar is primarily driven by galaxy evolutionary processes in neighbouring halos, as embodied by our parameter $\Sigma_{G}$, instead of a difference in the large scale structure around the central quasar host, embodied by $\Sigma_{Q}$. We conclude that models with $\Sigma_{G}>0.3$ are consistent with current observational constraints on high-z quasars, and that such a value is comparable to the scatter estimated from hydrodynamical simulations of galaxy formation.