Multiple quasars for multiple images

Three quasar pairs that have been identified as the products of gravitational lenses have no obvious visible lenses^1-3. They are: 1146+111 (redshift z=1.01; pair separation Δθ=157 arc s) ³, 1635+267 (z=1.96; Δθ=4 arc s)¹ and 2345+007 (z=2.15; Δθ=7 arc s)². An even number (two) of quasar images is observed in each case, although an odd number of images is produced by gravitational lenses with non-singular potentials⁴. The absence of a visible lens creates, in the lens hypothesis, a severe 'missing matter' problem. The missing lenses range in estimated mass^3,5 from >10¹²M_ȯ for 1635+267 (where M_ȯ is the mass of the Sun) to ∼10¹⁵M_ȯ for 1146+111. We investigate here the possibility that these qges are pairs of physically distinct quasars in galaxy associations. We show that, at the same redshifts as the quasars, only galaxy associations of exceptional richness would be identifiable in the existing data. Less prominent groups of galaxies, such as those known to be associated with nearby quasars⁶, would not be visible. We calculate the probability of pairs of quasars appearing in galaxy associations and find that physical pairs could appear with the observed frequency if, as expected, quasars are more common relative to galaxy associations at earlier epochs. We also discuss observations that can distinguish between the hypothesis of a gravitational lens and that of physical pairs.