ENVIRONMENTAL-EFFECT ON THE ASSOCIATIONS OF BACKGROUND QUASARS WITH FOREGROUND OBJECTS .1. ANALYTIC INVESTIGATION

The associations of the angular positions of background quasars with f oreground galaxies, clusters of galaxies, and quasars are often attrib uted to statistical lensing by gravitational potentials of the matter along the lines of sight, although it is known that the presence of no ne of the individual objects (galaxies, clusters, or quasars) is suffi cient to explain fully the reported amplitudes of the quasar number en hancements. This probably arises from the fact that the gravitational lensing effect of the environmental matter surrounding these objects h as been ignored. In this paper we conduct an extensive study of the in fluence of the environmental matter on the prediction of the quasar en hancement factor by employing a spatial two-point correlation function . Assuming a singular isothermal sphere for the mass density profile i n galaxies and cluster of galaxies, we estimate the average surface ma ss density <(Sigma)over bar> around galaxies, clusters, and quasars fr om the galaxy-galaxy, cluster-cluster, cluster-galaxy, and quasar-gala xy correlations. Our results show that the <(Sigma)over bar> induced q uasar number enhancement in the scenario of gravitational magnificatio n depends critically on the mass density parameters of galaxies (Omega (g)) and clusters of galaxies (Omega(c)) in the universe. For a flat c osmological model with Omega(0) = 1 the environmental matter can indee d play an important role in the lensing origin of the quasar-quasar an d quasar-galaxy associations if Omega(g) similar to Omega(c) similar t o Omega(0) while it is unlikely that <(Sigma)over bar> is sufficient t o account for the reported quasar overdensity behind quasars/ galaxies if galaxies and clusters of galaxies contribute no more than 25% to t he matter of the universe. Nonetheless, the recently observed quasar-c luster associations on a scale of similar to 10' cannot be the result of gravitational lensing by the cluster environmental matter even if O mega(g) = Omega(c) = Omega(0).