3 Joint radio-optical cluster selection

The cluster finding method we adopted is based on optical counts of galaxies in cells, followed by a smoothing of these counts with a Gaussian function and by the definition of a detection threshold for the selection of significative excesses in the surface galaxy density. The density peaks that are found near an optically identified NVSS radio source are included in the cluster sample.

Both to keep in evidence any possible inhomogeneities in optical counts and to make the data handling easier, we divided the EDSGC galaxies brighter than $b_{\rm J} =20.5$ in 21 adjacent sky maps corresponding to the $5\hbox {$^\circ $ }\times 5\hbox {$^\circ $ }$ central regions of the UKST plates that cover the radio source catalogue area.

The detection threshold is built in terms of the mode and rms of galaxy counts over each of these sky regions. Despite the possibility of small intra-plate variations in the photometric accuracy of the optical data, we considered the choice of a "local'' threshold for each plate preferable to a "global'' one, over the whole sky region, as the latter choice would introduce in the cluster sample incompleteness effects that depend on the cluster location in the sky.

The optical count matrix for each $5\hbox {$^\circ $ }\times 5\hbox {$^\circ $ }$ sky region has been built by defining a regular grid of $600 \times 600$ cells and by counting galaxies in these cells. The size of each cell has been chosen to be $30\hbox{$^{\prime\prime}$ }\times 30\hbox{$^{\prime\prime}$ }$, to optimize the statistics of galaxy counts as well as to point out the presence of structure in the spatial distribution of galaxies.

Since radiogalaxies tend to reside in different environments - from groups of galaxies to rich clusters - depending on their Faranoff-Riley morphological classification (Zirbel 1997), a careful choice of the size for the smoothing function is needed to avoid selection effects in favour of a particular environment. Too large a size could translate into a lack of detections of distant clusters, whose angular sizes are small. A small size could resolve a nearby cluster in many substructures, thus leading to the spurious detection of many candidates relative to the actual cluster, or, if the optical surface density excess in each substructure is less than the selected threshold (see below), could lead to a lack of detections. This last case is the most likely for clusters at moderate z having irregular morphologies, like the Abell I types (Abell 1958), where subclumps in the galaxy distribution are seen. Given the redshift range we expect to cover with our cluster sample, we decided to adopt, for the smoothing of the optical counts, a circular Gaussian function of ${\it FWHM} = 2\hbox{$^\prime$ }$, which is about half an Abell radius at z=0.4.

Figure 1: Smoothed matrix of the optical counts corresponding to the $5\hbox {$^\circ $ }\times 5\hbox {$^\circ $ }$ sky region of the UKST plate 412. Different grey levels correspond to regions of high galaxy density; superimposed contours are given as $2,3,...\,\sigma _{\rm gal}$ above $m_{\rm gal}$. On this plate there are 13 candidate clusters matching the selection criteria described in Sect. 3, marked with solid circles. The 44 NVSS radio sources optically identified in this sky region are marked with diamonds, except for the 2 residing in candidates associated with clusters known from the literature (A2878 and E536), that are marked with asterisks. Big dashed circles, with radius equal to one Abell radius, show ACO/Abell clusters on this plate, while the dotted circle marks the cluster EDCC 536.

We then looked for significative excesses in the optical surface galaxy density: for each smoothed matrix, we determined the mode $m_{\rm gal}$ and rms $\sigma_{\rm gal}$ of the optical surface density.

The threshold we adopted for the detection of density excesses is defined on each smoothed plate in terms of $m_{\rm gal}$ and $\sigma_{\rm gal}$ as $n_{\rm threshold} = m_{\rm gal} + 3\sigma_{\rm gal}$, that is we consider significative only those peaks where the galaxy surface density exceeds by at least $3\sigma_{\rm gal}$ the value of the mode determined over the whole plate. This choice can introduce selection effects in favour of "core-dominated'', regular clusters, and against irregular ones, where galaxies are less concentrated in the cluster core itself.

Finally, from this list of significant peaks we selected only those for which a radiogalaxy belonging to the considered smoothed matrix is found at a maximum distance of $4\hbox{$^\prime$ }$ from the density peak position. To determine the list of density peaks, no constraint has been set on the number of connected cells above the threshold. Radiogalaxies themselves are not required to belong to pixels whose optical surface density is above $n_{\rm threshold}$. Given the definition of the Abell radius, $R_{\rm A} = {1.7\hbox{$^\prime$ }\over z}$, this search distance corresponds to the Abell radius of a cluster at $z \sim 0.45$.

In the case of nearer clusters, this choice will favour the selection of those candidates where the radiogalaxy is located in the central region of the cluster. A larger value of the search distance would however increase the probability of detecting spurious associations between density peaks and radiogalaxies.

In Fig. 1 we show as an example the smoothed matrix relative to the UKST plate 412: regions with higher surface galaxy density are represented by increasing grey levels; the superimposed contours are given as $2,3,...\,\times\, \sigma_{\rm gal}$ above $m_{\rm gal}$. The 44 radiogalaxies having $17.5 \le b_{\rm J} \le 20.0$ and $d_{\rm r-o} \le 7\hbox{$^{\prime\prime}$ }$ present in this sky region are shown as well, marked with diamonds, except for the two associated with a known candidate cluster (see Sect. 4), that are marked with an asterisk. The 13 radio-optically selected cluster candidates are marked as small circles around the position of the associated radiogalaxy. For clarity, only the ACO/Abell and EDCC clusters found in this sky region are plotted in Fig. 1: they are marked with big circles, whose radius is equal to the cluster Abell radius. The fact that the clusters A2878, 2904 and E536 do not seem very conspicuous in this galaxy density map can be explained in terms of the different optical data set and the different scale used by Abell et al. (1989) and Lumsden et al. (1992) to look for overdensities in the galaxy distribution.

Figure 2: Sky distribution of the candidate clusters in our sample over the region defined by the NVSS catalogue ($\approx$550 sq degrees). Empty symbols refer to 76 candidates associated to clusters known in the literature, for which the name is marked; circles refer to known clusters with estimated redshift, while squares mark known clusters with measured redshift. Filled symbols refer to the 95 previously unknown candidates.