Environmental Effect on the Associations of Background Quasars with Foreground Objects. I. Analytic Investigation

The associations of the angular positions of background quasars withforeground galaxies, clusters of galaxies and quasars are often attributed tothe statistical lensing by gravitational potentials of the matter along thelines of sight, although it has been known that none of the individual objects(galaxies, clusters or quasars) are able to fully explain the reportedamplitudes of the quasar number enhancements. This probably arises from thefact that the gravitational lensing effect by the environmental mattersurrounding these objects has been ignored. In this paper we conduct anextensive study of the influence of the environmental matter on the predictionof quasar enhancement factor by employing the spatial two-point correlationfunction. Assuming a singular isothermal sphere for mass density profile ingalaxy and cluster of galaxies, we estimate the average surface mass density$\overline{\Sigma}$ around galaxies, clusters and quasars from thegalaxy-galaxy, cluster-cluster, cluster-galaxy and quasar-galaxy correlations.Our results show that the $\overline{\Sigma}$ induced quasar number enhancementin the scenario of gravitational magnification depends critically on the massdensity parameters of galaxies ($\Omega_g$) and clusters of galaxies($\Omega_c$) in the universe. For a flat cosmological model of $\Omega_0=1$ theenvironmental matter can indeed play an important role in the lensing origin ofthe quasar-quasar and quasar-galaxy associations if$\Omega_g\sim\Omega_c\sim\Omega_0$, while it is unlikely that$\overline{\Sigma}$ is sufficient to account for the reported quasaroverdensity behind quasars/galaxies if galaxies and clusters of galaxiescontribute no more than $25\%$ to the matter of the universe. Nonetheless, theComment: 25 pages, AASTEX, ApJ in pres