Einasto et al. (1976d) investigated in detail the dynamics of aggregates of galaxies and their relation to the dynamics of member galaxies, in particular to the dynamics of main galaxies. We calculated the mean velocity dispersion of members of aggregates for various distances from the primary (main) galaxy. Results of our calculations are shown in Fig. 7.16. We see that in the inner regions of aggregates the velocity dispersion of galaxies is higher than the mean dispersion. This suggests that galaxies in this region are in their peri-cluster parts of orbits around the center of the system. With increasing distance the velocity dispersion decreases slowly. Internal velocity dispersions of satellite galaxies also decrease with increasing distance from the system center, see the right panel of Fig. 7.16.
Fig. 7.16 Left: the velocity dispersions of companion galaxies, s(α) = [σr(α)/σcomp]2, as a function of the distance from the main galaxy, α = R/a0, where a0 is the harmonic mean radius of the group or cluster. The full line represents the adopted mean s(α) while the broken line is the upper envelope of the internal velocity dispersion of companion galaxies g(α), shown in the right panel. Filled circles show data on companion galaxies in the Coma cluster, filled squares are mean data on groups with a giant E galaxy as the main galaxy, open spheres show mean data on groups with a giant S galaxy, and open squares with a medium bright S galaxy as the main galaxy. Right: internal velocity dispersion of companion galaxies, g(α) = (σ/σmain)2 (in units of the dispersion of the main galaxy), at various distance from the main galaxy. The straight line is the upper envelope. Symbols are: filled circles — M87 and other members of the Virgo cluster; open circles — members of the M94 group; squares — members of the M81 group; triangles — members of the M31 subgroup (hypergalaxy); crosses — members of the Galaxy subgroup (hypergalaxy) (Einasto et al., 1976d).
Data available in 1975 suggested that velocity dispersions of main galaxies are approximately equal to the mean velocity dispersions of galaxies in the system. More accurate velocity dispersion measurements by Faber & Jackson (1976) showed that velocity dispersions of main galaxies are actually lower. This result is expected since otherwise stars of the main galaxy would have orbits covering the whole cluster. More accurate data suggest that the broken line in the left panel of Fig. 7.16 should lie lower than shown in the Figure.
The close link between dynamical properties of galaxies and systems they belong to suggests a common origin of galaxies in groups/clusters.
One of the principal functions which characterises physical properties and the evolutionary stage of galaxies is the luminosity function. Einasto et al. (1974a) studied the luminosity function of galaxies in systems of various richness from hypergalaxies (groups with one bright galaxy and dwarf companion galaxies) to rich clusters of galaxies. We found that main galaxies of hypergalaxies have a definite lower limit of the luminosity. Member galaxies can be divided into dwarf and giant galaxies, and there is a gap in the luminosity between giant and dwarf members. These data suggest that the formation mechanism of giant and dwarf galaxies can be different. The reason for such a difference was investigated in detail by Dekel & Silk (1986).
In the mid 1970’s data were available only for nearby groups and clusters, thus the above results can be considered as preliminary. Recently large and deep redshift data became available, and we resumed the study of the luminosity function of galaxies. First we investigated the luminosity function of the 2dF Galaxy Redshift Survey. I made the preliminary analysis myself, while the principal author of the final version is our young collaborator Elmo Tempel (Tempel et al., 2009).
Here we had several problems to elaborate, both technical and principal. The technical problem was to calculate total luminosities of groups of galaxies on the basis of data available in the visibility window of the survey. As discussed above, we corrected the observed luminosities to take into account galaxies which are too faint to be visible in the observational window of apparent magnitudes. Our check indicates that mean corrected luminosities of groups are independent of the distance from the observer. This shows that statistically our method to find expected total luminosities of groups is correct.
One of the main goals of the study of the luminosity function was to find its dependence on galaxy properties and on the large-scale environment of galaxies. Earlier studies of many authors, including our own earlier work (Einasto & Einasto, 1987; Einasto, 1991), have shown that luminosities and morphological properties of galaxies depend on the environment. Using new and more complete data Tempel et al. (2009) calculated luminosity functions (LF) of 2dF galaxies for four different environment, defined by the global luminosity density found by smoothing with a kernel of radius 8 h−1 Mpc. Void, filament, supercluster, and supercluster core environments were defined by threshold densities 1.5, 4.6, and 7, and were designated as D1, D2, D3, and D4.
The second main goal of our study was to understand the nature of galaxies in various local (group/cluster) environments. For this purpose luminosity functions were found separately for first-ranked galaxies, second-ranked galaxies, all satellite galaxies, and isolated galaxies.
Our main results are shown in Fig. 7.17. The Figure shows that in voids, the bright end of LFs of all galaxy populations is shifted toward lower luminosities. LFs in filament and supercluster environments are rather similar; actually our supercluster environment corresponds to poor superclusters. The luminosity functions for supercluster cores are different from functions in all other environments: here all LFs have a well-defined lower luminosity limit, about 17 mag, which for first- ranked galaxies had been seen already in supercluster environment. Also, in supercluster cores the brightest first ranked galaxies are more luminous than the brightest first-ranked galaxies in other environments. This shows that the densest environment (supercluster cores) is different from other environments. Differences in less dense environments for galaxies of various types (local environment) are much smaller.
Fig. 7.17 Differential luminosity functions of the 2dF galaxy samples in different environments and for different galaxy populations. Top-left panel — void environment D1; top-right panel — filament environment D2; bottom-left panel — supercluster environment D3; bottom-right panel — supercluster core environment D4. Solid line shows first-ranked galaxies; dashed line — second-ranked galaxies; short-dashed line — satellite galaxies; dotted line — isolated galaxies (Tempel et al., 2009).
Of special interest is the LF of isolated galaxies. Figure 7.17 suggests that isolated galaxies may be a superposition of two populations: the bright end of their LF is close to that of the first-ranked galaxy LF, and the faint end of the LF is similar to the LF of satellite galaxies. This is compatible with the assumption that the brightest isolated galaxies in the sample are actually the brightest galaxies of invisible groups. This assumption is supported by results of our group shifting procedure: at large distance only the brightest member of the group falls into the visibility window of the survey.
To examine this possibility, Tempel et al. (2009) made the following test. A group has only one galaxy in the visibility window if its second-ranked galaxy (and all fainter group galaxies) are fainter than the faint limit of the luminosity window at the distance of the galaxy. Thus we calculated for each isolated galaxy the magnitude difference between the galaxy and the faint limit of the absolute magnitude of the sample at the distance of the galaxy. The distribution of magnitude differences was compared with the distribution of the actual magnitude differences between the first-ranked and second-ranked group galaxies. The distributions look rather similar.
Tempel et al. (2011) studied the morphology, luminosity, and environment in the SDSS Data Release 7 galaxy sample. The authors constructed the LFs separately for galaxies of different morphology (spiral and elliptical) and of different colours (red and blue) using data from the Sloan Digital Sky Survey (SDSS), correcting the luminosities for intrinsic absorption.
The results suggest that the evolution of spiral galaxies is slightly different for different
types (colours) of spirals. A possible interpretation of our results may lie in the fragility of spiral galaxies: they form and survive only in specific conditions (e.g. the preservation of the gas, the absence of major mergers) which are typical in low density regions, but to some extent can be present also in high density regions.
The derived LF of elliptical galaxies can be reconciled with hierarchical galaxy formation through mergers. The denser the environment, the brighter the galaxies that should reside there because of the increased merger rate. The difference between the LFs of elliptical galaxies in different environments is more notable for red galaxies, in accordance with their supposed merger origin. This interpretation agrees well also with the picture of hierarchical formation of galaxies: for blue galaxies, the evolution is more quiescent and major mergers are not so important; for red ellipticals, merging is the dominant factor of galaxy evolution. Since blue ellipticals are most likely S0-s or late-type ellipticals, they still have some gas available for star formation and therefore the evolution of blue ellipticals is closer to the evolution of spiral galaxies — the global environment is less important.
Fig. 7.18 The differential luminosity function of 2dF groups (shown by points). The solid line is the double-power-law fit and the dashed line is the Schechter function (Tempel et al., 2009).
Tempel et al. (2009) calculated also the LF for groups of galaxies, using the Tago et al. (2006) group catalogue. The differential LF of 2dF groups is shown in Fig. 7.18. For comparison Tempel et al. (2009) found also the best-fit model luminosity functions, applying the conventional Schechter (1976) function and the double-power-law function. A similar comparison was made for 2dF and SDSS galaxy luminosity functions. We note that the double-power-law function was used in the early 1970’s by many authors. In earlier applications a sharp transition between two power laws was made; in our case we made the transition smooth. Our analysis suggests that the double-power-law function represents galaxy and group luminosity functions better than the Schechter function, especially at the high-luminosity end.
7.3.2 Groups and clusters of galaxies
There exists a large number of studies of the structure and properties of groups and clusters of galaxies. We studied group properties in the 1970’s in relation to the dark matter problem, as discussed above. In recent years we resumed the study of groups of galaxies. We needed group catalogues to eliminate the Finger of God effect in the cosmic web, and to calculate the luminosity density field. As a byproduct we had the possibility of studying group and cluster properties, since they are principal building blocks of the web.
Here I shall discuss briefly only our recent study of morphological properties of clusters in our list of SDSS DR8 groups of galaxies by Tempel et al. (2012c). This list includes also rich clusters if found by our group finding algorithm. Einasto et al.(2012) searched for the presence of substructure, the non-Gaussian, asymmetrical velocity distribution of galaxies, and large peculiar velocities of the main galaxies in clusters with at least 50 member galaxies, drawn from this SDSS DR8 group catalogue; in total we found 109 clusters. Using various tests Einasto et al. (2012) found that 70–80% of the clusters in the sample have multiple components. The authors find that in about half of the multicomponent clusters the peculiar velocity of the main galaxy is larger than 250 km/s (0.5 of the normalised peculiar velocities). There is a clear difference between the median values of the peculiar velocities and the normalised peculiar velocities of the one-component and multicomponent clusters: these velocities are much larger in the multicomponent clusters.
Figure 7.19 shows the distance of the main galaxy from the cluster centre, both for the multicomponent and one-component clusters (in the plane of the sky). It is easily seen that in multicomponent clusters a large fraction of main galaxies are located far away from the cluster centre (grey dotted line). However, when looking at the components found by the 3D normal mixture modelling, we see that the main galaxies of clusters are preferentially located close to the centre of one of the components (solid line). The distribution of distances from the component centre for the brightest galaxies in the components shows that these galaxies are also located preferentially close to the component centre (dashed line).
Figure 7.19 (dark long-dashed line) shows that in one-component clusters in most cases the main galaxy lies close to the cluster centre. But there is also a substantial number of main galaxies, which are further away from the cluster centre. We calculated the minimum distance from the cluster centre for the three brightest galaxies in the one component clusters. As seen from Fig. 7.19 (light dotted-dashed line), one of the three brightest galaxies in clusters is always located close to the cluster centre. This shows that the central galaxy of a cluster is typically one of the most luminous galaxies, but not always the most luminous one.
Fig. 7.19 Distribution of the distance of the main galaxy from the cluster (subcluster or component) centre for various subsamples of galaxies. Multicomponent clusters: grey dotted line — the distance of the main galaxy from the cluster centre; solid line — the distance of the main galaxy from the (nearest) component centre; dashed line — the distance of the brightest galaxy in a component from the component centre. One-component clusters: dark long-dashed line — the distance from the cluster centre; light dotted-dashed line — the minimum distance of one of the three brightest galaxies from the cluster centre (Einasto et al., 2012).
The basic conclusion from this study is that the presence of substructure, large distances of main galaxies from the cluster centre, and their large peculiar velocities are signs of mergers and/or infall. This suggests that most clusters in our sample are not yet in dynamical equilibrium. The high frequency of such clusters indicates that mergers between groups and clusters are common — galaxy groups continue to grow and are still assembling. Unimodal clusters are examples of clusters which are probably already in dynamical equilibrium.
7.3.3 Chains, strings and filaments
Jõeveer & Einasto (1978) noticed that the Perseus–Pisces supercluster contains rich Abell clusters, less rich clusters and groups, and galaxies. Clusters, groups and most galaxies form a network of chains. The main chain of the supercluster has 7 high-density knots. 3 of them are Abell clusters, and all are Zwicky near clusters. Knots are fairly regularly spaced as pearls in a chain. One knot contains only one very bright peculiar galaxy NGC 315; it lies exactly on the place where a cluster should be. We discussed with Mihkel if this object should be included as a member of the chain. Then we decided that this very bright peculiar galaxy has probably ‘eaten’ all other members of the group via galaxy mergers (Toomre & Toomre, 1972; Toomre, 1977). This is an example of a fossil group, as they were later called.
Also we noticed that chains can be very different in richness. The main chain of the Perseus–Pisces supercluster contains clusters and groups as members. Some less rich chains join various superclusters to a connected netweork; such chains were mentioned by Jõeveer & Einasto (1978); Jõeveer et al. (1978) and in our more detailed analysis by Einasto et al. (1980a, 1984) and Tago et al. (1984). Even fainter chains consisting of galaxies only cross large voids; they are seen in our wedge diagrams Fig. 5.5 and 5.4. A detailed analysis of the distribution of galaxies around the main chain of the Perseus–Pisces supercluster and in chains crossing the large void between the Local, the Coma and the Hercules supercluster suggested that galaxy and cluster chains are essentially one-dimensional structures, surrounded by empty regions devoid of galaxies.
Zeldovich et al. (1982), Einasto & Miller (1983), and Einasto et al. (1984) analysed in more detail the shape of various systems of galaxies in and around the Virgo and Coma superclusters, see Fig. 7.20. Thin slices in supergalactic coordinates indicate that galaxy chains between the Local and the Coma superclusters are very narrow. For further analysis galaxies were collected into systems using the clustering Friends-of-Friends method. At small neighbourhood radius all systems are round; at this radius only high-density cores of clusters and groups
are combined into systems. At medium neighbourhood radii most systems become elongated and are mostly tri-axial. When one axis exceeds considerably two other axes, these systems can be called strings or filaments. If two shorter axes are approximately equal, they can be called sheets of galaxies. One sheet forms the main body of the central part of the Virgo supercluster, see Fig. 7.1. At still larger neighbourhood radii galaxy strings merge into a connected network, as seen in Figs. 5.5, 5.4, and 7.20. The respective radius is called the percolation radius, as discussed above.
Fig. 7.20 Slices through the Virgo and Coma superclusters in supergalactic rectangular coordinates. The Galaxy is at the centre, x = y = 0, the Virgo cluster at y = 20 Mpc, the Coma cluster at y = 120 Mpc, and the other rich cluster in the Coma supercluster, A1367, at y = 130, 2 = —10 Mpc. Galaxies brighter than —19.5 absolute magnitude have been plotted. All coordinates correspond to the Hubble constant h = 0.5 (Zeldovich et al., 1982).
Our analysis was questioned by Geller (1987) in her talk at the Vatican Conference on Theory and Observational Limits in Cosmology, July 1985. She cites our studies on this problem (Jõeveer et al., 1978; Einasto et al., 1980a; Zeldovich et al., 1982), but disagrees with our conclusion on the filamentary character of the distribution. On the basis of the first results the Second CfA redshift survey by de Lapparent et al. (1986) she argues that galaxies are located in shells which surround voids, and that filaments are just slices through walls in relatively thin observational wedges. According to her interpretation observations strongly favour the Ostriker & Cowie (1981) explosive scenario of structure formation.
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