The dust obscuration bias in damped Lyman α systems

We present a new study of the effects of quasar obscuration on the statistics of Damped Ly a (DLA) systems. We show that the extinction of any Galactic or extragalactic Hi region, A(lambda), increases linearly with the column density of zinc, with a turning point theta A(lambda)/theta(log N-Zn) = 1, above which background sources are suddenly obscured. We derive a relation A(lambda) = A(lambda)(N-H, Z, z) between the extinction of a DLA system and its Hi column density, N-H, metallicity, Z, fraction of iron in dust, f(Fe)(Z), and redshift, z. From this relation we estimate the fraction of DLA systems missed as a consequence of their own extinction in magnitude-limited surveys. We derive a method for recovering the true frequency distributions of N-H and Z in DLAs, f(NH) and f(Z), using the biased distributions measured in the redshift range where the observations have sufficient statistics (1.8 = z = 3). By applying our method we find that the well-known empirical thresholds of DLA column densities, N-Zn less than or similar to 10(13.1) atoms cm(-2) and N-Hi less than or similar to 10(22) atoms cm(-2), can be successfully explained in terms of the obscuration effect without tuning of the local dust parameters. The obscuration has a modest effect on the distribution of quasar apparent magnitudes, but plays an important role in shaping the statistical distributions of DLAs. The exact estimate of the bias is still limited by the paucity of the data (similar or equal to 40 zinc measurements at 1.8 = z = 3). We find that the fraction of DLAs missed as a consequence of obscuration is similar to 30% to 50%, consistent with the results of surveys of radio-selected quasars. By modelling the metallicity distribution with a Schechter function we find that the mean metallicity can be similar to 5 to 6 times higher than the value commonly reported for DLAs at z similar to 2.3.