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

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4. Conclusion

The merging model provides an increasing galaxy number and a decreasing galaxy mass with lookback time, which can relatively easily account for the observed high surface number density and the redshift distribution of galaxies in the deep surveys (Broadhurst et al. 1992). At least, it works equally well as other models (see, for examples, Yoshii & Sato 1992; Metcalfe et al. 1996). In the scenario of galaxy mergers, the gravitational lensing of distant sources (e.g. quasars) by galaxies is affected by the following two factors: (1)There will be more galaxies as lenses as one goes back in time; (2)The galaxy masses, and equivalently the galaxy velocity dispersion, will decrease with lookback time. The first factor will alter significantly the galaxy redshift distributions and enhance the lensing amplitude, while the second one reduces the lensing cross-sections. A combination of these two factors gives rise to an optical depth to gravitational lensing that is roughly independent of the galaxy mergers [eqs.(4)-(6); see also Rix et al. 1994; Mao & Kochanek 1994].

As a consequence, despite the fact that a considerably high surface number density of faint galaxies is detected in the deep surveys, the total lensing cross-sections of galaxies towards a distant source are still rather small, and can never fully cover our sky up to [FORMULA]. The claim that all the high redshift ([FORMULA]) objects are moderately magnified by galaxies (Fried 1997) arises

from the oversimple assumptions about the galaxy redshifts and velocity dispersions ([FORMULA] km s-1) at high redshifts. We find that the maximum lensing covering by galaxies to [FORMULA] is only [FORMULA], and this number is likely to reduce to [FORMULA] for a more realistic galaxy distribution. Other more sophisticated models of galaxy evolution should be employed in order to give a better estimate of the lensing covering by the faint galaxies over the sky.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998