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 the Ultraviolet and Visible Echelle Spectrograph (UVES) at the VLT-UT2 Kueyen European Southern Observatory telescope. These quasars do not show signatures of associated absorption and have a mean monochromatic luminosity of 5.4 x 10(31) h(-2) erg s(-1) Hz(-1) at the Lyman limit. The observed distribution of optical depth within 10 h(-1) Mpc from the quasi-stellar object 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 photoionization rate above the mean ultraviolet-background due to the extra ionizing photons from the quasar radiation (proximity effect), and the higher density of the intergalactic medium if the quasars reside in overdense regions (as expected from biased galaxy formation). The first factor decreases the optical depth whereas the second 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 ultraviolet-background inferred from the mean Lyman a opacity. If no overdensity is present, then we require the ultraviolet-background to be higher, and consistent with the existing measurements based on standard analysis of the proximity effect.