Constraining the ratio of median pixel optical depth profile around z ∼ 4 quasars using the longitudinal proximity effect

Abstract

ABSTRACT We present a detailed study of the longitudinal proximity effect using a sample of 85 quasars spanning an emission redshift range of 3.5 ≤ zem ≤ 4.5 and Lyman continuum luminosity (L912) ranging from 1.06 × 1031 to 2.24 × 1032 erg s−1 Hz−1. We use the high-quality spectra of these quasars obtained at a spectral resolution of R ∼ 5100 and S/N ∼ 30 using X-SHOOTER spectrograph mounted on the Very Large Telescope (VLT). In our analysis, we compared the transmitted flux and pixel optical depth of the Ly α absorption originating from the vicinity of quasars to those from the general intergalactic medium (IGM) by using a redshift-matched control sample. The longitudinal proximity effect is found up to r ≤ 12 Mpc (proper) from quasars. By appropriately scaling up the pixel optical depth in the vicinity of quasars to account for the excess ionization by quasars, we constrain the ratio of median H i optical depth in the vicinity of the quasar to that of the IGM (Rτ(r)). The Rτ(r) is found to be significantly higher than unity up to 6 Mpc from the quasar with a typical radial profile of the form Rτ(r) = 1 + A × exp(− r/r0) with A = 9.16 ± 0.68 and r0 = 1.27 ± 0.08 Mpc. The integrated value of the scaled pixel optical depth over the radial bin of 0–6 Mpc is found to be higher by a factor of 2.55 ± 0.17 than the corresponding integrated value of the median pixel optical depth of the IGM. We also found Rτ(r) to be luminosity dependent.