Quasar‐Galaxy Associations from Gravitational Lensing: Revisited

The theoretically expected amplitude of the associations of backgroundquasars with foreground galaxies as a result of gravitational lensing has beenupdated in this paper. Since the galactic matter alone yields an amplitude ofquasar overdensity smaller than that observed, a special attention has beenpaid to the examination or re-examination of the uncertainties in the estimateof the quasar enhancement factor arising from the cosmic evolution of galaxies,the core radius and velocity bias of galactic matter distributions, theclusters of galaxies, the obstruction effect by galactic disks, the non-zerocosmological constant, etc. Unfortunately, none of these factors has been shownto be able to significantly improve the situation, although a combination ofsome effects may provide a result that marginally agrees with observations. Itis concluded that the quasar-galaxy association still remains to be an unsolvedpuzzle in today's astronomy, if the reported quasar-galaxy associations are notdue to the statistical variations and/or the observed quasar number counts as awhole have not been seriously contaminated by gravitational lensing.Comment: 21 pages, uses aastex, ApJ in pres