Magnitude‐Redshift Relation in Clusters, Groups and Pairs of Galaxies
Authors: Jaakkola T. 
Published: July 2007

AbstractMagnitude‐redshift (m, z) relation within systems of galaxies is studied in detail in several kinds of systems. The main data contains 17 clusters, 64 groups, 121 pairs and 14 systems with two measured members, altogether 1043 galaxies in 162 separate systems. In addition, another sample of nearby groups and pairs, recently published data on six clusters with 121 measured members, as well as 65 compact galaxies in four groups and 23 pairs are studied.In Section 2 the data and the method are described. The numerical results for the main data are given in Table 1. There exists a significant positive (m, z)‐relation in groups and pairs, but for clusters the same is valid only with a rather loose selection of members. The (m, z)‐relations are calculated separately for each morphological type, but systematic differences between the types are not found.In Section 3 some properties of the velocity (redshift) dispersion σV are discussed. The joint dispersion decreases significantly from the early to the late types. This may point to an early dynamical state of the systems but it is also quite possible that this result is due to a selection effect. The presence of a selection effect in some commonly used samples of systems is indicated by the increase of velocity dispersion σV with increasing distance (Section 4). This effect which was first found for clusters and groups by SCOTT is present also in the larger sample of these systems and in the sample of pairs. Implications of this feature are discussed. As one of them, it is concluded in Section 5 that there exists no separate Canes Venatici cluster of galaxies but the galaxies supposed to form it belong to the Ursa Major cloud of galaxies. Several independent arguments supporting this conclusion are pointed out. In the Ursa Major‐Canes Venatici complex of galaxies a distinct positive (m, z)‐relation is found.In Section 4 the distance‐dependence of the (m, z)‐relations is studied and it is found that positive relations are most common for nearby systems. This is natural if the effect is an intergalactic one, the redshift being dependent on the distance of the galaxy. The (m, z)‐relations is are studied as function of size of the systems in Section 6. It is found that σV, (m, z) regression coefficient bm, and parameter h which measures strength of redshift within the system, are largest in the systems with smallest radii. The result is opposite to that obtained using the virial theorem. In the Dopplerian context it would mean that the systems disperse the more rapidly the more dense these are. Dependence of the results on the number of data is studied in Section 7. As expected for a real effect, the frequency of positive relations increases with increasing number. The dispersion σV is usually larger in the central areas of the clusters than in the outskirts (Section 8). In these areas, σV is systematically larger for faint galaxies than for bright ones. The reason for large σV for faint galaxies projected on the centre is considered, studying in particular in the Coma cluster the velocity (redshift) distribution, colour‐redshirt relation and morphological features which might be used in localization of the galaxies along the line of sight. The results of these three kinds of tests point to the possibility that redshift increases along the line of sight, but the results refer to sparse data and are very uncertain. A similar effect is suggested independently by observations of the galaxies in the background of the clusters. If true, the effect must be non‐Dopplerian. In combination with brightness seggregation and preponderance of measured galaxies in the near side over those in the rear, this may cause the observed negative (m, z)‐relations for some clusters.In SANDAGE's and TAMMANN's sample of nearby groups and pairs redshift appears dependent on luminosity class. This points to intrinsic redshifts in faint galaxies (Section 9). A similar implication is valid for the positive (m, z)‐relations in the case of pairs and groups of compact galaxies (Section 10). Since there are indications of physical association in the latter case, the result cannot be explained by optical members.The present results are compared with previous ones in Section 11. This includes a study of redshifts with regard to brightness and surface brightness simultaneously, leading to a new statistical definition of relative compacity of galaxies belonging to the systems. Recent observations not included in the main data are viewed in Section 12. These show a positive (m, z)‐relation.Interpretation of the results is discussed in Sections 13 and 14. From the numerous ones, three main possibilities remain, i. e. projected galaxies, intrinsic redshifts in faint galaxies and non‐Dopplerian integalactic redshifts. There are several arguments suggesting that chance projections are not the principal explanation of the positive (m, z)‐relations. If so, intrinsic redshifts in faint galaxies give probably the main explanation for pairs and small groups and integralactic redshifts for larger systems. This is in accordance with the general view of the redshift phenomenon in other scales. However, definitive proof of this conclusion could not be obtained from the present data which, though considerably large in number, is too small regarding the complexity of the problem.