3 Validation method via color-magnitude diagrams

From the g and r matched catalogs we excluded obvious stars (stellarity index >0.95) and then selected a box of $\sim$300 pixels in size (corresponding to a typical core cluster diameter of $\sim$750 kpc at $z \sim 0.2$), centered on the approximate cluster center and a second box of equal size located as far as possible from the cluster, to be used for the evaluation of the background contribution.

Our procedure is summarized in Fig. 5,

Figure 5: Complete set of plots for two confirmed (upper half) and two uncertain (lower half) cluster candidates. Each set of plots consists of color-magnitude diagrams for background + cluster box; color-magnitude diagrams for background box; color-magnitude diagrams for statistically corrected cluster objects; radial profiles and spatial distributions over the CCD field of the objects within a color strip around the early-type sequence. The four sets of plots refer respectively to: a) OV17_778, a typical rich nearby cluster ( $z \sim 0.2$); b) OV6_725, a poor cluster at redshift $z \sim 0.2$; c) OV21_694 and d) OV24_694, uncertain clusters, with less evidence for the early-type sequence in the color-magnitude diagrams, and for density peaks in the spatial distribution.

which shows the results for four sample candidates which are representative of the various morphologies encountered. For all candidates in our sample we first obtained the color-magnitude diagrams for both the cluster and background objects. Then, in order to enhance the early-type sequence, we performed the statistical subtraction of the background contribution by eliminating for each object in the background diagram the corresponding nearest galaxy in the cluster+background diagram. If we then isolate the objects contained within a narrow strip of the color-magnitude diagram centered around the early-type sequence, the galaxy overdensities become more evident in both the spatial distribution and in the number counts radial profile (Fig. 5; the radial profile was calculated by choosing as cluster center the barycenter of the density distribution). The plots in Fig. 5 can be used as a criterion to distinguish true clusters (candidates (a) and (b)), even if they are difficult to detect. In some cases (usually candidates which are either too distant or too poor), despite the presence of an apparent sequence in the color-magnitude diagram, the objects do not form a physical overdensity, but turn out to be uniformly distributed on the sky. In these cases it is more difficult to reach any definite conclusion about the physical nature of the candidate.

3.1 Color-magnitude diagrams for the calibration cluster sample

We chose as templates a sample of X-ray clusters for which, at least in principle, the early-type sequence in the color-magnitude diagrams should be easily detectable. This sample was also used to investigate whether or not it was possible to derive an acceptable estimate of the redshift from the g-r color of the early-type sequences. In Fig. 6 we plot the color-magnitude diagrams for the 8 clusters in the X-ray sample including only the cluster contribution (i.e., after the statistical subtraction of the background).

Figure 6: Color-magnitude diagrams after statistical background subtraction for the X-ray cluster sample. According to Gioia & Luppino (1994), MS1401 is a loose cluster, without a dominant galaxy; MS1426 contains spirals and possibly interacting systems, and moreover may be two clusters in projection. A Seyfert galaxy at z=0.074 is present in the foreground of the MS1532 field. Abell 2033 is of Bautz-Morgan type III and richness class 0.

It is quite evident that some of the early-type sequences are only broadly outlined (MS1401, MS1426, MS1532), which may be caused either by the intrinsic faintness of the cluster members or by cluster structural features (poorness, looseness and presence of interacting systems; see the comments in Gioia & Luppino 1994 about these three clusters). For each cluster we derived a median g-r color using only the 5 brightest galaxies after the background subtraction (continuous line), from which we also estimated the redshift. The crosses represent the g-r colors corresponding to the literature redshifts.

3.2 Photometric redshift estimate

Some techniques for deriving redshifts from broadband photometry consist of matching observed elliptical galaxy colors with those predicted from the Spectral Energy Distributions (SEDs) (Visvanathan & Sandage 1977) of a template elliptical galaxy at zero-redshift and corrected according to the redshift: since ellipticals become redder as their redshift increases and since the redshift dependent correction (k-correction), is monotonically increasing in the near and intermediate redshift Universe, colors can be used to infer the cluster redshift. There is no agreement in the literature for the g-r color of ellipticals at zero-redshift: $0.47^{\rm m}$, according to Schneider et al. (1983); 0.38 mag for Frei & Gunn (1994); $0.40^{\rm m}$ to $0.49^{\rm m}$ according to Fukugita et al. (1995). Differences in these values likely depend on the galaxy spectrum template adopted for the ellipticals and on the use of a synthetic or an observed spectrum for the standard stars defining the photometric system. To a lesser extent, differences are due to the variations in the actual shape of the Gunn g and r filters (convolved with the atmosphere, mirror and glass transmissions, CCD quantum efficiency, etc.) and possibly also to the way in which the colors are computed. In the absence of a definite value, we left the zero-redshift color of ellipticals as the unique free parameter and constrained it with our own observations by (robustly) fitting the relation between color and redshift. Figure 7 shows (filled dots) the observed colors from the color-magnitude relation vs. known spectroscopic redshift for our X-ray cluster sample.

Figure 7: The observed colors from the color-magnitude relation and their errors for the X-ray cluster sample (filled circles) are plotted, compared to the expected color of ellipticals (continuous line) as a function of spectroscopic redshift.

The expected color of ellipticals (continous line) were computed using the Schneider et al. (1983) k-correction curve and our own determination of the elliptical colors. The average g-rcolor of ellipticals of zero redshift turns out to be $0.44^{\rm m}$, i.e. the average of the four previously quoted literature values. Errors on the colors are given as one third of the interquartile range, which roughly corresponds, for a Gaussian distribution of five points to the error on the mean. We prefer these to the standard error since they are more robustly determined. Figure 7 shows that all points are compatible with the curve within $1\sigma$, excluding two points, which are within $2\sigma$. The agreement is good, provided that there is only one free parameter (the rest-frame elliptical color). Figure 8 compares the photometric redshift,

Figure 8: Photometric vs. spectroscopic redshift. The solid line is the bisector and is not derived from data fitting.

estimated from the color-magnitude diagrams and the spectroscopic redshift. The agreement is good, and the error (interquartile range) on the redshift is, on average, $\delta z = 0.01$, i.e. 3000 kms^-1. Table 3 lists the estimated photometric redshifts, with the errors computed as previously defined, for the putative clusters; since these clusters are fairly rich systems, this error is likely to be a lower limit.