The density structure around quasars from optical depth statistics

We present a method for studying the proximity effect and the density structure around redshift z=2-3 quasars. It is based on the probability distribution of Lyman-alpha pixel optical depths and its evolution with redshift. We validate the method using mock spectra obtained from hydrodynamical simulations, and then apply it to a sample of 12 bright quasars at redshifts 2-3 observed with UVES at the VLT-UT2 Kueyen ESO telescope. These quasars do not show signatures of associated absorption and have a mean monochromatic luminosity of 5.4 10^{31} h^{-2} erg/s/Hz at the Lyman limit. The observed distribution of optical depth within 10 Mpc/h from the QSO is statistically different from that measured in the general intergalactic medium at the same redshift. Such a change will result from the combined effects of the increase in photoionisation rate above the mean UV-background due to the extra ionizing photons from the quasar radiation (proximity effect), and the higher density of the IGM if the quasars reside in overdense regions (as expected from biased galaxy formation). The first factor decreases the optical depth whereas the second one increases the optical depth, but our measurement cannot distinguish a high background from a low overdensity. An overdensity of the order of a few is required if we use the amplitude of the UV-background inferred from the mean Lyman-$\alpha$ opacity. If no overdensity is present, then we require the UV-background to be higher, and consistent with the existing measurements based on standard analysis of the proximity effect.