On the significance of the excess number of strong Mg II absorbers observed toward gamma-ray bursts

The number of strong (equivalent width >1 Å) Mg II absorbers observed toward gamma-ray bursts (GRBs) has been found to be statistically larger than the number of strong absorbers toward quasi-stellar objects (QSOs). We formalize this "Mg II problem" and present a detailed explanation of the statistical tools required to assess the significance of the discrepancy. We find that the problem exists at the 4σ level for GRBs with high-resolution spectra. It has been suggested that the discrepancy can be resolved by the combination of a dust obscuration bias toward QSOs, and a strong gravitational lensing bias toward GRBs. We investigate one of the two most probable lensed GRBs that we presented in our previous work (GRB020405) and find that it is not strongly gravitationally lensed, constraining the percentage of lensed GRBs to be <35% (2σ). Dust obscuration of QSOs has been estimated to be a significant effect with dusty Mg II systems removing 20% of absorbed objects from flux-limited QSO samples. We find that if 30% of the strong Mg II systems toward QSOs are missing from the observed samples, then GRBs and QSOs would have comparable numbers of absorbers per unit redshift. Thus, strong gravitational lensing bias is likely to make only a modest contribution to solving the Mg II problem. However, if the dust obscuration bias has been slightly underestimated, the Mg II problem would no longer persist.