The effect of dust bias on the census of neutral gas and metals in the high-redshift Universe due to SDSS-II quasar colour selection

We present a systematic study of the impact of a dust bias on samples of damped Lyman-$\alpha$ absorbers (DLAs). This bias arises as an effect of the magnitude and colour criteria utilized in the Sloan Digital Sky Survey (SDSS) quasar target selection up until data release 7 (DR7). The bias has previously been quantified assuming only a contribution from the dust obscuration. In this work, we apply the full set of magnitude and colour criteria used up until SDSS DR7 in order to quantify the full impact of dust biasing against dusty and metal-rich DLAs. We apply the quasar target selection algorithm on a modelled population of intrinsic colours, and by exploring the parameter space consisting of redshift, ($z_{\rm QSO}$ and $z_{\rm abs}$), optical extinction, and HI column density, we demonstrate how the selection probability depends on these variables. We quantify the dust bias on the following properties derived for DLAs at z=3: the incidence rate, the mass density of neutral hydrogen and metals, the average metallicity. We find that all quantities are significantly affected. When considering all uncertainties, the mass density of neutral hydrogen is underestimated by 10 to 50%, and the mass density in metals is underestimated by 30 to 200%. Lastly, we find that the bias depends on redshift. At redshift z=2.2, the mass density of neutral hydrogen and metals might be underestimated by up to a factor of 2 and 5, respectively. Characterizing such a bias is crucial in order to accurately interpret and model the properties and metallicity evolution of absorption-selected galaxies.