6 Results

On the basis of the measured galaxy velocities for each candidate cluster, we verified in which cases the spectroscopic data confirm the presence of a cluster associated to a NVSS radiogalaxy. As can be noticed from Table 1, for the candidate 349N02 the few available spectroscopic data are not useful for a statistical analysis aimed to assess the presence of a cluster around the radio source.

Among the 11 fields for which we have sufficient data, in two cases (409N03 and 412N23) the radiogalaxy velocity is significantly different from all the other measured values and we conclude that the radiogalaxy is not associated to a cluster. In both cases the data suggest the presence of a group or cluster, but at a redshift different from that of the radiogalaxy.

For the 9 remaining candidates, we confirm the presence of a cluster around the radiogalaxy: this corresponds to a positive detection rate of $82\%$. For these 9 clusters we determined the mean velocity and velocity dispersion by means of the ROSTAT package (Robust Statistics, Beers et al. 1990), which allows robust estimates of central location and scale in data samples affected by the presence of "outliers''. When dealing with small data sets (n = 5-10) as in our case, the best estimators are the biweight $C_{\rm BI}$ (Tukey 1958) for the central location and the classical standard deviation $S_{\rm G}$ for the scale (Beers et al. 1990). The $C_{\rm BI}$ estimator is evaluated iteratively, by minimizing a function of the deviations of each observation from the estimate of the central location. It thus requires an additional estimate of this last quantity, which is generally given as the absolute value of the median of the differences between the data and the sample median.

The uncertainties associated to central location and scale have been estimated by the bootstrap method. This technique consists in the generation of a large number of samples, not independent from the original data set, and in the evaluation of the statistical parameters for each of these "bootstrapped'' samples.

In Fig. 4 we show the distributions of measured velocities for the 9 cluster candidates involved in this statistical analysis: the shadowed regions represent the data sets used as input for the ROSTAT package.

The results of the statistical analysis are shown in Table 2: mean cluster velocities vary from $40\,514~{\rm km~s^{-1}}$ to $90\,122~{\rm km~s^{-1}}$, corresponding to the redshift range $0.13 \le z \le 0.3$.

Despite the small number of available redshifts for each cluster, which reflects into rather large errors for both the central location and velocity dispersion, an interesting result arises from the velocity dispersions: they range from $210~{\rm km~s^{-1}}$ to $906~{\rm km~s^{-1}}$, that is from values typical of poor clusters or groups of galaxies to those typical of moderately rich clusters.

Figure 4: Measured velocities distributions for the 9 spectroscopically confirmed clusters. In black are shown the data sets used for the evaluation of cluster redshift and velocity dispersion (see Table 2).

Following the criteria in Abell (1958), we used the EDSGC catalog to get an estimate of the cluster richness for the 9 confirmed clusters: the background-subtracted galaxy counts in the magnitude range $m_3 \div m_3 +2$ within an Abell radius from the cluster centre range from a minimum of 6 to a maximum of 23. These galaxy counts are similar to those found for many of the ACO poor clusters (Abell et al. 1989), and suggest that our radio-optically selected clusters are poorer than Abell richness class 0. We stress however that these richness estimates must be viewed with caution: first, the values of m₃ +2 often fall near or below $b_{\rm J} =20.5$, where the EDSGC completeness drops significantly, thus seriously biasing the galaxy counts. Second, at our typical m₃ the number density of galaxies in the EDSGC is high, about 50 galaxies per square degree, thus the probability of selecting as the third member of the cluster a galaxy which is actually a background or foreground object seen in projection is not negligible, and this again can alter the richness estimate.

As shown in Fig. 5, there is no evident correlation between measured velocity dispersion and cluster redshift. The use of radio emission properties of galaxies seems thus a very efficient method to select new candidate clusters samples in a wide range of richness at any redshift.

 

 

Table 2: Mean velocity and velocity dispersion obtained from the package ROSTAT for the 9 spectroscopically confirmed clusters. Values for <v> are given by the biweight estimator of central location, while for $\sigma _{\rm v}$ the classical standard deviation is given: these are the most robust and efficient statistical estimators in the case of small data sets. The number of measured velocities used to obtain these results is given in Col. 4.

CLUSTER	Right Ascension (B1950)	Declination (B1950)	n	$<v> ~{\rm (km~s^{-1})}$	$\sigma_{\rm v} ~{\rm (km~s^{-1})}$
294N15	00 23 41.0	-39 37 15.0	6	90122  +519-589	906  +227-128
295N35	01 03 11.0	-38 47 15.0	4	79241  +130-270	429  +162-49
350N71	00 35 04.0	-34 49 15.0	5	70180  +293-138	373   +98 -44
352N47	01 14 13.0	-36 44 45.0	4	51969  +14-309	444  +179-123
352N63	01 19 50.0	-33 45 15.0	6	54844  +497-144	674  +254-127
352N75	01 21 11.0	-33 17 15.0	5	40712   +66-227	263   +73 -60
409N15	00 02 36.0	-28 20 15.0	5	45573  +96-254	210   +41 -16
409N44	23 51 13.0	-31 34 15.0	5	40514  +761-269	757  +184-108
475N50	01 15 13.0	-24 09 45.0	10	63266  +256-414	847  +182-121

If confirmed by future spectroscopic follow-up, this result could be of great interest as our sample would offer the possibility to investigate differences in cluster dynamical properties in a homogeneously selected sample of clusters which spans a wide range in richness, and to improve our knowledge of their number counts, as well as to study the radio emission properties of galaxies residing in different environments.