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

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2. Galaxy lenses as a result of merging

Following the idea of Broadhurst et al.(1992), we assume that the galaxy merging only increases the galaxy number with increasing lookback time, whilst maintaining the proportion of different types (E, S0, S) of galaxies, their respective K-corrections and luminosity function shapes. Under these hypotheses, the present-day galaxy luminosity function can be written as


where i indicates the [FORMULA] th morphological type of galaxies: i =(E, S0, S). The luminosity function at redshift z in the merging model is thus


Here [FORMULA] is representative of the time-dependence of evolution of the luminosity function, Q is the merging rate and [FORMULA] is the ratio of the Hubble time [FORMULA] to the age of the universe. The galaxy luminosity L at z is relevant to both the mering rate and the history of the star formation rate. For a matter dominated flat universe of [FORMULA], [FORMULA], while matching the galaxy number counts gives roughly [FORMULA]. This scenario of galaxy merging can account for both the redshift distribution and the number counts of galaxies at optical and near-infrared wavelengths (Broadhurst et al. 1992). If we further model the galactic halo by an isothermal sphere which is characterized solely by its velocity dispersion [FORMULA], [FORMULA] at z will be reduced by a factor of [FORMULA] with respect to its present-day value [FORMULA] since the galaxy mass as a result of merging would decrease with lookback time. In particular, [FORMULA] is close to [FORMULA] (Rix et al. 1994).

The surface number density of faint galaxies to [FORMULA] obtained by Fried (1997) from the deep observations of the fields around three quasars is [FORMULA], in good agreement with the previous surveys(e.g. Metcalfe et al. 1996). This yields a mean alignment distance of [FORMULA] between the line-of-sight and the faint galaxies, i.e. 7.3 [FORMULA] kpc in linear size if the galaxy is at [FORMULA], where h is the Hubble constant in unit of 100 km/s/Mpc. Indeed, assuming that the faint galaxies seen at [FORMULA] have a mean velocity dispersion of 200 km/s and are located at [FORMULA], we can easily estimate that any background sources at [FORMULA] will be gravitationally magnified by a factor of [FORMULA]. So, Fried (1997) argued that it is a purely observational fact that the distant objects must be lensed by foreground galaxies.

Using the empirical formula between the luminosity [FORMULA] and central velocity dispersion [FORMULA] of local galaxies [FORMULA] with [FORMULA] km/s and [FORMULA] for [FORMULA] galaxies (see Fukugita & Turner 1991), we can compute from eq.(1) the morphological composition { [FORMULA] } of galaxies by requiring [FORMULA] km/s. It turns out that [FORMULA], i.e., the galaxies with [FORMULA] km/s following the Schechter luminosity function eq.(1) are mainly composed of the E/S0 populations. As numerous surveys have shown that the spirals are in the majority in the universe ([FORMULA]), the oversimple assumption of Fried (1997) regarding the velocity dispersion ([FORMULA] km/s) for all the faint galaxies has overestimated their contributions to gravitational lensing. Furthermore, the velocity dispersion of distant galaxies becomes smaller relative to that of local galaxies in terms of galaxy merging, which also leads to a decrease of lensing magnification. As a consequence, if the faint galaxies observed by Fried (1997) are [FORMULA] spirals at [FORMULA], the lensing magnification of a background source at [FORMULA] would reduce to [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998