We calculate the distribution of HI within 750 proper kpc/h of a quasar, Lbol = 1.62e13 Lsun, powered by an SMBH, Mbh = 4.47e8 Msun, at z = 3. Our numerical model includes a cosmological hydrodynamic simulation that tracks the self consistent growth and thermal feedback of black holes calculated using GADGET-3 as well as a detailed post-processing ray tracing treatment of the non-uniform ionizing radiation field calculated using SPHRAY, which naturally accounts for the self shielding of optically thick systems. We show that the correct treatment of self shielding introduces a flattening feature into the neutral column density distribution around Log NHI = 20 and that regions with the lowest neutral fractions are not those with the highest density gas. For comparison, we solve a Ricatti equation which determines the equilibrium Hydrogen ionization fractions in the presence of a radiation field that falls off as 1/r^2 with regions above a given gas density threshold completely shielded from ionizing radiation. We demonstrate that these semi analytic models cannot reproduce the HI field calculated using SPHRAY. We conclude by comparing our models of this single proximity zone to observations by Hennawi and Prochaska of the absorption spectra of background quasars which are coincident on the sky with foreground quasars in their Quasars Probing Quasars (QPQ) series of papers. Compared to the QPQ sample, we find a factor of 3 fewer optically thick (Log NHI > 17.2) systems around our quasar, however the dark matter halo that hosts our simulated quasar, Mhalo = 5.25e12 Msun, is less massive than the typical QPQ host halo by a factor of four. Allowing for a linear scaling between halo mass, baryonic overdensity and number of absorbers, we estimate the typical host halo mass in the QPQ sample as 1.92e13 Msun.
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