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Astron. Astrophys. 361, 415-428 (2000)

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5. Depletion effect in the cluster MS1008-1224

We have applied our simulations to the cluster MS1008-1224 ([FORMULA], Lewis et al. (1999)) which is one cluster of the Einstein Observatory Extended Medium Sensitivity Survey (Gioia & Luppino, 1994). It is a very rich galaxy cluster, slightly extended in X-rays, and it is also part of the Canadian Network for Observational Cosmology Survey (Carlberg et al., 1996). Its galaxy distribution is quite circular, surrounding a North-South elongated core. There is a secondary clump of galaxies to the North. The X-ray luminosity is LX(0.3-3.5 keV)[FORMULA] erg.s-1 (Gioia & Luppino, 1994), the X-ray temperature inferred from ASCA observations is TX=7.3 keV (Mushotzky & Scharf, 1997) and the radio flux at 6 cm is lower than 0.8 mJy (Gioia & Luppino, 1994). Some gravitationally lensed arcs to the North and to the East of the field have been reported by Le Fèvre et al. (1994) as well as by Athreya et al. (2000).

5.1. The observations

Data were obtained during very deep observations with FORS and ISAAC during the science verification phase of the VLT-ANTU (UT1) at Cerro Paranal (http://www.eso.org/science/ut1sv ). Multicolor photometry was obtained in the B, V, R and I bands with FORS1 (field-of-view [FORMULA]) and in the J and Ks bands with ISAAC (field-of-view [FORMULA]) with sub-arcsecond seeing in all cases. The total exposure times are respectively 2880 seconds in J, 3600 seconds in Ks, 4050 seconds in I, 4950 seconds in B, 5400 seconds in V and R. We used the SExtractor software (Bertin & Arnouts, 1996) to construct our photometric catalogue. The completeness magnitudes are respectively [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA]. Our values are identical to those of Athreya et al. (2000) concerning the FORS observations but they are one magnitude deeper concerning the ISAAC ones. In practice, we used only the FORS data which extend to a larger distance and are more suited to our study.

In order to remove part of the contamination by cluster members, we identified the elliptical galaxies by their position on the color-magnitude diagram (Fig. 10). So background sources were selected by removing this sequence, essentially valid at relatively bright magnitudes. This statistical correction is not fully reliable as it does not eliminate bluer cluster members or foreground sources. But it partly removes one cause of contamination, especially significant close to the cluster center. Our counts may also present an over-density of objects in the inner part of the cluster ([FORMULA]) due to the non-correction of the surface of cluster elliptical galaxies we have removed, effect which is more sensitive in the inner part of the cluster where these galaxies are dominant. But as it is not in the most interesting region of the depletion area, we did not try to improve the measures there.

In addition, due to the presence of two 11 magnitude stars in the northern part of the FORS field, two occulting masks were put to avoid excessive bleeding and scattered light. We took into account this partial occultation of the observed surface for the radial counts above a distance of 130" (see Fig. 9). This may possibly induce some additional errors in the last two points of the curves, which are probably underestimated, because of the difficulty to estimate the surface of the masks and some edge effects at the limit of the field.

[FIGURE] Fig. 9. VLT FORS1 image of MS1008-1224 in the B band. North is up, East is left. The field-of-view is [FORMULA]. Note the two occulting masks hiding the brightest stars in the field.

[FIGURE] Fig. 10. Color-magnitude diagram R-I versus R of MS1008-1224. The two horizontal lines delimit the sequence of the cluster elliptical galaxies, which has been removed from our catalogue.

5.2. Depletion curves and mass density profile

The first step would be to locate the cluster center. Its position is rather difficult to estimate directly from the distribution of the number density of background sources, although in principle one should be able to identify it as the barycenter of the points with the lower density around the cluster. We did not attempt to fit it and preferred to fix it 15" North of the cD, following both the X-ray center position (Lewis et al., 1999) or the weak lensing center (Athreya et al., 2000).

The radial counts were performed in a range of 3 magnitudes up to the completeness magnitude in the B, V, R and I bands and up to a radial distance of 210" from the center, which covers the entire FORS field. The count step was fixed to 30 pixels (6") in the innermost 80" and for the rest of the field we adopted a count step of 60 pixels (12") to reduce the statistical error bars. These values are a good balance between statistical errors in each bin which increase for small steps and a reasonable spatial resolution in the radial curve, limited by the bin size. The depletion curves obtained in the B, V, R and I bands are shown on Fig. 11. At some small limiting radius ([FORMULA]), the ratio between the area of the count rings and the area covered by the cluster galaxies is close to unity. For this reason, we exclude the measures obtained in these innermost rings for any study of depletion effects (shaded regions on Fig. 11).

[FIGURE] Fig. 11. Depletion curves measured in MS1008-1224 in several spectral bands up to the completeness magnitude of the catalogues. For each plot, the best fit by the three models described in text are given. Error bars correspond to Poisson statistical noise. The shaded area on each plot corresponds to regions where the study of the depletion does not make sense (see text for more details).

We fitted the observed depletion curve in the I-band with three of the mass models discussed above, namely a singular isothermal sphere, a power-law density profile and a NFW profile, and with the galaxy distribution described in Sect. 2.3.2. For each model, a [FORMULA] minimization was introduced to derive the best fits and their related parameters (Table 2). The first fit included all the data points ([FORMULA]) and gave poor results with a reduced [FORMULA] always close to or larger than 2. A second fit was done after removing some clear deviant points ([FORMULA]): the last two points probably poorly corrected from edge effects, and those associated to the overdensity seen at [FORMULA]. This bump is easily identifiable in the V, R and I curves, and can be partly explained by the presence of a background cluster lensed by MS1008-1224 and identified by Athreya et al. (2000). Nevertheless, even if we remove from our data all the lower right quadrant of the field where this structure is located, the bump is still there although significantly reduced. This suggests that it may be more extended behind the cluster center than initially suspected. This second fit gave more satisfying results. So we will consider the parameters associated with the best fit of each model as our best results.

  • The velocity dispersion derived from the SIS model ([FORMULA] km s-1) is in good agreement with the value measured by Carlberg et al. (1996) ([FORMULA] km s-1) but is more discordant with the value of 900 km s-1 inferred from the shear analysis of Athreya et al. (2000).

  • The slope of the potential fit with a power-law density profile is close to an isothermal one ([FORMULA]), although slightly shallower.

  • For a NFW profile, we find a virial radius ([FORMULA] Mpc) and a concentration parameter ([FORMULA]) quite in good agreement with those of Athreya et al. (2000) derived from weak lensing measures.

  • The comparison between the 3 fits favors a NFW profile as the best fit of our depletion curves (Table 2), also in agreement with the shear results for this cluster.


Table 2. Results of the fit of the model parameters with a [FORMULA] minimization. The errors are given at the 99.9% confidence level.

Note however that we did not use the B-band data in the fit because the depletion effect is less obvious and much noisier than in the 3 other filters. This is due to the fact that for this magnitude range the logarithmic slope of the counts is close to the critical value 0.4 and the depletion effect is strongly attenuated. Probing fainter objects in this band ([FORMULA]), even beyond the completeness limit, strengthens the depletion signal again, as it is shown in Fig. 12. In addition this deeper magnitude range may be used to scan a different redshift distribution with a higher density of high redshift objects. This is one of the future prospects of the depletion curve analysis to perform a multi-wavelength analysis to try to disentangle lensing effects from the statistical distribution of the sources.

[FIGURE] Fig. 12. Top: Depletion curve obtained for [FORMULA]. The fits by the three models described in text are given. Bottom: Redshift distribution of background objects which corresponds to the best fit of the above depletion curve.

5.3. Ellipticity and orientation of the mass distribution

We have also used the depletion effect to determine the orientation of the main axis and the ellipticity of MS1008-1224. For this purpose, we divided the area of the FORS field into four quadrants where quadrants 1 and 2 are in opposition, and we performed the counts for radial distances from the cluster center to 130" (Fig. 9). The positions of the four quadrants are marked by [FORMULA], the clockwise angle between the North-South axis and the median of quadrant 1. We then computed the depletion curves corresponding to the counts in quadrants 1+2 and 3+4. We varied [FORMULA] and followed the shift of the minimum position of the depletion area of the two curves. We can measure the orientation of the two main axis when the shift between the two minima is maximum. For this value of [FORMULA], the relative positions of the two minima give the main axis ratio and consequently the ellipticity. The results, obtained from I-band data only, are similar in the others bands. From the I-band data only, we found [FORMULA] and an ellipticity of [FORMULA] (Fig. 13). These results agree well with the mass map orientation derived from weak lensing as well as the galaxy number density map (Athreya et al., 2000). A small discrepancy arrises with the X-ray gas distribution which orientation is shifted a few 10 to 20 degrees West from our measure (Lewis et al., 1999). But globally, all these results are consistent within each other.

[FIGURE] Fig. 13. Depletion curves obtained in the I band for [FORMULA] (top), [FORMULA] (middle) and [FORMULA] (bottom). The radial step has been reduced to 6" only for a more accurate localisation of the minima

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Online publication: October 2, 2000