Gravitational focusing and the association of distant quasars with foreground galaxies

The surface density of quasars brighter than a given threshold is enhanced near a galaxy by the gravitational focusing of light from those quasars that are nearly co-aligned with individual stars in the galaxy halo. The focusing can intensify and make detectable quasars which would otherwise have been below the threshold. If galaxies have massive haloes of macroscopic objects then the resulting enhancement could explain the apparent association between quasars and galaxies with discrepant redshifts found in a statistical analysis. Therefore, such quasar-galaxy associations need not require the abandonment of the cosmological interpretation of the redshift.