Effects of dust on gravitational lensing by spiral galaxies

Gravitational lensing of an optical QSO by a spiral galaxy is often counteracted by dust obscuration, since the line of sight to the QSO passes close to the center of the galactic disk. The dust in the lens is likely to be correlated with neutral hydrogen, which in turn should leave an Lyα absorption signature on the QSO spectrum. We use the estimated dust-to-gas ratio of the Milky Way galaxy as a mean and allow a spread in its values to calculate the effects of dust on lensing by low-redshift spiral galaxies. Using a no-evolution model for spirals at z ≲ 0.8, we find, in Λ = 0 cosmologies, that the magnification bias due to lensing is stronger than dust obscuration for QSO samples with a magnitude limit of B ≲ 16. The density parameter of neutral hydrogen, Ω_{H I} is overestimated in such samples and is underestimated for fainter QSOs.