Gravitational lensing by damped Ly-α absorbers

Abstract

Assuming that (i) damped Ly-α absorbers (DLAs) arise in present-day-like spiral galaxies which are immersed in isothermal dark matter halos, (ii) that these galaxies obey the Tully-Fisher σ σ ∗ = ( L L ∗ ) 1 α TF and the Holmberg R L R ∗ = ( L L ∗ ) α H relations, and (iii) that they follow the Schechter luminosity distribution, we describe how their observed number density ( dN dz ), distribution of column density ( f( N)) as well as inferred cosmological density of HI ( ω HI derived from DLA surveys are affected by gravitational lensing (GL). The ‘by-pass’ effect causes the lines-of-sight (LOSs) towards background QSOs to avoid the central parts of galaxies and reduces their effective cross-section for absorption; the ‘amplification bias’ leads observers to select QSOs whose LOSs preferentially cross galaxies close to their Einstein radius. As a consequence, the determination of the quantities dN dz , f( N) and ω HI from DLA surveys does not only depend on the redshift z and luminosity L of galaxies responsible for the absorbers but also on the column density profile of HI within the galaxies and on the redshift z q and magnitude b q of the background QSOs. For most of the existing surveys using b q ≲ 19 QSOs, the amplification bias dominates the combined effect resulting in a slight overestimate of dN dz , f( N) and ω HI. We mainly find that observational strategies presently used to produce high- z DLA surveys result in avoiding the signature of significant GL effects: following our model, we determine that an overestimate of ω HI by more than 10% is unlikely for the z ⋍ 1.7 existing surveys, but may reach ⋍ 35% for the low redshift ones. However, we show that, in the absence of extinction by dust and micro-lensing effects, surveys ideally designed to enhance GL effects, i.e. to search for DLAs at z ∼ 0.5 in front of very bright ( b q ⋍ 16 ), high- z ( z q > 1) QSOs, may lead 1) to overestimate by up to ⋍90% the number of DLAs per unit redshift; 2) to bias the survey towards high HI column density systems so that it could contain up to 4 times as many such systems, thus 3) to overestimate by up to ⋍170% the cosmological density of gas associated with those DLAs. Identification of the galaxies responsible for the DLAs may be severely biased towards luminous galaxies if 2 α TF − α H > 0 ; this latter effect is greatly increased for log N HI > 21 DLAs.