4. Influence of background galaxies on depletion curves
In this section, we use a unique model for the lens, i.e. a SIS profile with a velocity dispersion of 1500 km s-1 for a cluster located at , to avoid effects due to the lens.
4.1. Effect of the lens on the magnitude-redshift distribution of background populations
Fig. 7 shows the distortion of the magnitude-redshift distribution in the B band along the curve. The results are qualitatively the same in the others bands. Near the cluster center, where the effects of the gravitational magnification are stronger, objects located just behind the lens show a gain in magnitude larger than 1. In the minimum area of the curve, the competition between gravitational magnification and dilatation is more favorable to high z objects (). In the outer part of the cluster, the effects of the gravitational magnification decrease and one finds again the distribution in empty field (asymptotic limit of the depletion curves).
4.2. Differential effects in several filters
We first studied the evolution of the depletion area with the redshift distribution of the background population by considering several filters. We tried to determine some characteristics of the redshift distribution of background population which could be connected to typical features of the depletion area (Fig. 8). The magnitude limits of the simulations correspond to a typical observation time of about 2 hours on an 8-meter telescope with good imaging facilities. The contamination by foreground objects in the 3 filters is weak ( in the I and K bands and in the B band for which the counts are deeper).
The evolution of the position of the minimum of the depletion area reflects the evolution of the mean redshift of the different populations ( for the K band, for the B band and for the I band), but with a weak effect. The variation of the intensity of the minimum of the depletion area is connected for one part to the fraction of foreground objects and for the other part to the slope of the luminosity function. As this slope decreases from I band to B band with the magnitude thresholds we have chosen, the intensity of the minimum of the depletion area decreases in the same way from I band () to B band (). Both features of the depletion curves are in fact weakly dependent on the choice of the filter and may be difficult to distinguish with real data, at least while the variation of the redshift distribution with wavelength is rather smooth.
On the contrary, the half width at half minimum of the depletion curve is affected by the redshift distribution of background populations in a more sensitive way. The increase of the half width at half minimum from B band to K band is anti-correlated with the fraction of objects at high redshift () for these populations which also decreases in the same way from B band () to K band () and seems to reflect essentially the bulk of galaxies at redshift around 1.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000