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Astron. Astrophys. 326, L9-L11 (1997)

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1. Introduction

It is indeed not a novel idea to suggest that all the distant objects may be affected by the gravitational lensing of the matter clumps between the sources and the observer. Three decades ago, Barnothy and Barnothy (1968) proposed that all the quasars were nothing but the gravitationally magnified images of Seyfert galactic nuclei. Press and Gunn (1973) showed that the probability of the occurrence of gravitational lensing in an [FORMULA] universe is nearly unity. Unlike the previous speculations for which there was apparently a lack of both convincing observational and theoretical supports, the current argument is based on the numerous and unprecedented deep galaxy surveys which have revealed a considerably large population of faint galaxies (Metcalfe et al. 1996; references therein). Using the surface number density of faint galaxies down to [FORMULA], [FORMULA], Fried (1997) derived a projected mean distance between galaxies to be [FORMULA], which led him to the conclusion that all the high redshift ([FORMULA]) objects are moderately magnified by a factor of 1.1-1.5 due to gravitational lensing by the intervening galaxies. Indeed, this was a natural and plausible consequence, provided that all the faint galaxies were at [FORMULA] and had a mean velocity dispersion [FORMULA] -300 km s-1.

Nonetheless, spectroscopic redshifts have not been available for most of the faint galaxies to date. Namely, we do not yet know where these faint galaxies are. For instance, the faint blue galaxies might be the star-forming galaxies at moderate redshift of [FORMULA] (e.g. Broadhurst et al. 1992) or at high redshifts of [FORMULA] (Metcalfe et al. 1996). While the dispute regarding the merging rate has existed for several years, it is generally agreed that galaxy mergers may play an important role in the formation and evolution of galaxies. At least, the merging model provides a good fit to the faint galaxy number counts. It is particularly noted that the merging alters significantly the redshift and velocity dispersion distributions of galaxies. What is the optical depth due to gravitational lensing for a distant source if the redshift and velocity dispersion information for the faint galaxies according to the prediction of galaxy merging is employed ? Can the sky be fully covered by the lensing cross-sections of galaxies if faint galaxies are neither peaked at [FORMULA] nor distributed randomly in redshift space ? We would like to answer these questions by modeling the galaxy matter distribution as the simplest singular isothermal sphere and the galaxy evolution as merging. Rix et al. (1994) and Mao & Kochanek (1994) have presented a sophisticated treatment of how galaxy mergers affect the various aspects of statistical lensing. Here we focus on the specific issue of the lensing covering of galaxies over the sky.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998