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The statistical rejection removes on average 43–55 per cent of the objects that are kept as probable cluster members on the basis of their photometric redshifts, down to the magnitude limit I= 25. Note that this fraction is in good agreement with the residual contamination fraction that can be estimated from Fig. 5.5, suggesting that the performance of the technique is reasonably good.

6.4 The colour–magnitude relation

Fig. 6.2 shows the V-I vs I diagram for the 3 clusters used in this analysis. At the clusters redshifts, V₋I approximatively samples the rest–frame U₋V colour. It is therefore very sensitive to any recent or ongoing episode of star formation. A red se- quence is clearly visible in the CM diagram of each cluster, together with a significant population of blue galaxies that are known to populate clusters at high redshift. The solid thick line is a bi-weight linear fit (Beers et al. 1990) to the spectroscopically confirmed members with absorption–line spectra. As explained in Sec. 5.6.1, this algorithm gives higher weight to points that are closer to the centre of the distribu- tion and is then insensitive to the presence of outliers. The dashed lines correspond to _±3σ from the best fit line, where σ is the dispersion of the objects used for the fit and is, in all 3 clusters _∼ 0.1. Thin solid lines correspond to the 3 and 5σ de- tection limits in the V–band. Empty symbols represent galaxies retained as cluster members after using the photometric redshift and one Monte Carlo realization of the statistical subtraction. Filled circles are spectroscopically confirmed members with absorption–line spectra, while crosses represents spectroscopically confirmed mem- bers with emission–lines.

For comparison, Fig. 6.3 shows the colour–magnitude relation for the Coma cluster using all the objects in the photometric catalogue by Terlevich et al. (2001), who give observed U and V photometry in different apertures. We use the magnitudes in 25.2 arcsec diameter aperture that, at the redshift of Coma (0.023), corresponds to a physical size of 11.71 kpc. We do not apply any further aperture correction to account for the fact that our apertures are slightly larger that the one used for Coma. Observed magnitudes are converted to absolute magnitudes using the distance modulus of Coma (35.16) and observed colours are converted to rest–frame colours using the tabulated K–correction2 _{given by Poggianti (1997). According to these} tables, the K–correction to apply amounts to 0.033 for E type galaxies, 0.033 for Sa and 0.038 for Sc. We apply a single correction of 0.035 to all the objects in the photometric catalogue.

2

The K correction “corrects” for the fact that sources observed at different redshifts are, in general, compared with other objects or each other at different rest-frame wavelengths. It simply arises from the relation between the emitted or rest–frame absolute magnitude of a source in one broad photometric bandpass to the observed–frame apparent magnitude of the same source in another broad bandpass.

Figure 6.2: Colour–magnitude diagrams for the 3 EDisCS clusters under analysis. The solid thick line marks the best fit relation, the dashed lines correspond to±3σ

from the best fit line (σ is the dispersion of the objects used for the fit). Thin solid lines correspond to the 3 and 5σdetection limits in the V–band. Filled circles are spectroscopically confirmed members with absorption–line spectra, while crosses

6.4 The colour–magnitude relation

Figure 6.3: Colour–magnitude relation of Coma for all the galaxies in the catalogue

by Terlevich et al. (2001). Observed magnitudes have been converted to absolute magnitudes using the distance modulus of Coma (35.16) and observed colours were converted to rest–frame colours using tabulated K–corrections (Poggianti 1997). Solid and dashed lines have the same meaning as in Fig. 6.2. Coloured symbols represent two families of models (see text for details).

The coloured points in Fig. 6.2 show the location of galaxy models with two dif- ferent star formation histories: a single burst occurred at z = 3 (green points) and a 1 Gyr exponentially declining SFR beginning at z = 3 (red points), calculated with the population synthesis code by Bruzual & Charlot (2003). For each one of these two star formation histories, three different metallicities are shown: 0.02 (so- lar), 0.008 and 0.004, going from the brighter to the fainter objects. The relation between metallicity and luminosity in these models has been calibrated by requiring that they reproduce the observed colour–magnitude relation in Coma (see Fig. 6.3). (Note, in fact, that population synthesis models need to be normalised to a certain

Cluster Slope error Zero–point error Dispersion error

cl1054–1146 ₋0.07 0.05 4.01 1.00 0.11 0.03

cl1054–1245 ₋0.07 0.05 4.18 1.10 0.11 0.04

cl1216–1201 ₋0.11 0.03 5.04 0.68 0.11 0.02

Table 6.1: Coefficients and corresponding errors for the best fit relation obtained

for each of the clusters used in this analysis.

mass since they usually give magnitudes for a stellar population of a total mass equal to 1 M_¯). This calibration has been found a posteriori to be in good agreement with the metallicity–luminosity relation derived from spectral indices of Coma galax- ies (Poggianti et al. 2001). When these models are evolved back in time, the single burst models provide a remarkably good fit to the red sequence observed in the high redshift clusters, thus confirming that the location of the CM sequence observed in distant clusters requires high redshifts of formation, and that the slope is consistent with a correlation between galaxy metal content and luminosity.

The coefficients of the fit and the corresponding errors are determined using a bootstrap method over 100 Monte Carlo realizations. Both the slope and the zero– point are allowed to vary. In Table 6.1 we report the values of the coefficients and the corresponding errors obtained for each of the clusters used in this analysis. Although the number of objects used to fit the CMR is in general not high, and therefore the uncertainties on the coefficients are quite large, the agreement between the values obtained for the different clusters is remarkable. We have shown in Sec. 5.7 that the clusters used in this analysis exhibit a wide range of structures and cover a wide range of masses. Our analysis shows that the average colour of early–type galaxies is nearly the same in these clusters. In addition, the scatter about the CMRs also remains approximatively constant, although the uncertainties are too large to make more quantitative comparisons. This result, already pointed out by Stanford et al. (1998), suggests that the evolution of the bulk of the early–type population does not depend on cluster richness or on the degree of the concentration of the cluster itself. This is already an important result, given the fact that so far there is only one cluster at this redshift studied at this level of detail (van Dokkum et al. 2000). One cluster is obviously not enough to disentangle different formation scenarios for the formation and evolution of elliptical galaxies in clusters.

Note also that the dispersion we find around the red–sequence is larger than the canonical values found for closer clusters, although a quantitative comparison is ham- pered by the fact that we are not using objects that aremorphologically classified as elliptical galaxies, as is usually done in the literature. In future, we will have HST images of EDisCS clusters, that will allow us to undertake an analysis of the CMR as a function of the morphological type. Preliminary results, obtained using bulge/disc