4. Results

For a dynamical analysis of the velocity data in Tables 2-4, allowance must be made for the fact that, even when velocity information is available, there is a certain degree of ambiguity about cluster membership. Thus, velocity dispersions were calculated by rejecting galaxies with a too high velocity relative to the mean, using the 3- clipping procedure of Yahil & Vidal (1977). Then the method described by Danese et al. (1980) was applied, in order to determine the 68% confidence uncertainties for cluster redshifts and velocity dispersions. This method assumes a Gaussian velocity distribution.

For our two best-studied clusters, Cl 0053-37 and A 3889, we collected 21 and 24 cluster galaxy spectra respectively, with negligible contamination from stars and background or foreground galaxies. Our estimates of mean velocity, velocity dispersion and virial mass are therefore not affected by undersampling (see Girardi et al. 1993).

Table 5 summarizes the global dynamical information derived from our analysis. Column 1 gives the cluster name, Col. 2 gives the number of cluster members with measured redshifts, Col. 3 gives the weighted mean heliocentric velocity. The mean redshifts referred to the Local Group (Yahil et al. 1977), , are listed in Col. 4, while Col. 5 gives the radial velocity dispersion . Estimates of the cluster total velocity dispersions and virial masses are given in Cols. 6 and 7, and discussed below.

 

Cluster N <V>

Cl 0053-37 21  49265 1144 _-145 ⁺²³⁴ 1982 _-317 ⁺⁴⁵⁰

A 3889 24  75354 1119 _-134 ⁺²¹⁰ 1939 _-292 ⁺⁴⁰⁵

A 3663  5  71861 -- -- --

 

Whenever the velocity distribution is not well-matched by a Gaussian, one of the robust techniques described by Beers et al. (1990) is preferable. To have a feeling of the influence of the Gaussian hypothesis on our results, for all clusters we calculated the median velocity, the biweight location estimator, equivalent to the mean velocity of the Gaussian distribution, and the biweight scale estimator, equivalent to the velocity dispersion (, , respectively in the notation of Beers et al. 1990). Table 6 gives the values of some robust estimators, assuming the same weight for all redshift measures: median velocity (Col. 2), biweight estimate (Col. 3), and biweight velocity dispersion (Col. 4). Errors are estimated from the standard deviation of 100 bootstrap samples. There is a very good agreement between the standard and the robust estimates for these two clusters; the difference
between median, biweight and mean velocity is
300 km s for Cl 0053-37 and 400 km s for A 3889, while the standard and biweight estimates of the velocity dispersion agree within 100 km s.

 

Cl 0053-37 49555

A 3889 74947

A 3663 72886

 

We now give a short description of our results for individual clusters. For Cl 0053-37, we measured the redshifts of 22 galaxies in the frame: only one turned out to be a background galaxy with the [OII] 3727 Å emission line, at a redshift of 0.27, the remaining 21 spectra passing the 3- clipping test. None of them shows emission lines.

The velocity histogram, shown in Fig. 4 (click here)a, appears quite symmetric. The mean heliocentric velocity of this cluster is v = 49265 km s, and the redshift relative to the Local Group is . The radial velocity dispersion is , and the total velocity dispersion (for an isotropic velocity distribution) is km s. It is clear that Cl 0053-37 cannot be part of S0102, unless the distance of the latter was underestimated by Abell et al. (1989). We will discuss this issue in the following section.

For A 3889, 24 of the 26 observed galaxies turned out to be true members of the cluster, passing the 3- clipping test; the remaining two are foreground galaxies (presumably belonging to a group) at . The mean observed velocity of the cluster is 75354 km s, and the redshift is . The measured radial velocity dispersion is 1119 _-134 ⁺²¹⁰ km s, while the total velocity dispersion is 1939 _-292 ⁺⁴⁰⁵ km s, consistent with values determined for nearby rich clusters. The brightest galaxy (No. 12) has a velocity of -694 km s relative to the cluster mean velocity, but its velocity relative to the median velocity of the cluster is -287 km s. Indeed, the velocity histogram (Fig. 4 (click here)b) shows two main peaks. Since no apparent segregation is found across the field, if the peaks correspond to two real subclusters, they are mainly along the line-of-sight. The foreground peak is centered at  km s, and the background one at  km s.

  
Figure 4: a) Velocity histogram of cluster Cl 0053-37; b) velocity histogram of cluster A 3889

We estimated the masses of these two clusters using the virial theorem (see Bahcall & Tremaine 1981; Malumuth et al. 1992). Assuming isotropic orbits and spherical symmetry,

where D is the angular diameter distance of the cluster, v_r,i is the difference between the velocity of galaxy i and cluster (mean) velocity, is the angular separation between galaxy i and galaxy j, N is the total number of galaxies and is the statistical weight of galaxy i. Giving the same weight (1/N) to all galaxies, we obtain for Cl 0053-37, and for A 3889, quite typical of rich clusters, even if these values can only be considered as rough estimates of the real mass.

More limited velocity data are available for the third cluster. A 3663 was observed in not very good weather conditions, and we lost some spectra because of their low signal-to-noise ratio. The small number of measured velocities does not allow a precise determination of the cluster redshift, especially because the spread is quite large: this is apparent in the difference between the median and the mean radial velocity of the cluster, km s, while the biweight estimate gives an intermediate value (cf. Table 6 (click here)). The standard deviation of the 5 measured radial velocities, divided by , gives km s; the biweight estimator gives a velocity dispersion km s. These values may represent an overestimate of the true radial velocity dispersion, and are only indicative. It is possible that these galaxies belong to different groups or subclusters, and more redshifts are needed to provide an answer. We also note that 2 out of the 5 observed galaxies have emission lines.

Our new results offer the opportunity to test the precision of redshift estimates (obtained from a relation between cluster redshift and magnitude of the tenth brightest galaxy, or a combination of the magnitudes of the first, third, and tenth brightest galaxies, with a possible correction for the cluster richness) at high distances. Using the relation given by Scaramella et al. (1991; their Eq. (1)), we find estimated luminosity distances equal to 860  Mpc  for A 3889 and 920  Mpc  for A 3663, while the luminosity distances calculated from our measured redshifts are respectively 797  Mpc  and 757  Mpc. There is a well-defined relation between estimated and measured distances in the Abell and ACO catalogs, and our results confirm that, for the ACO catalog, such a relation can give reasonable results even at .