In a previous publication (1975) we showed that it is possible to determine the maximum diameters of galaxies on photographic plates by means of the photographic equidensity method. This method was applied especially to 235 members of the Coma cluster. On Tautenburg plates it was possible to determine for these objects equidensitometric angular diameters down to 10 arc sec.

I will confine this brief review to just two examples of galaxies that seem to have interacted recently with impressive consequences: (1) the well-known Messier 51 system NGC 5194/5 = deservedly VV 1, and (2) the so-called Cartwheel, a ring within a ring, separated by vaguely spokelike features and accompanied by two smaller galaxies.

We established M51 systems as a class of interacting pairs of galaxies in 1959. in 1975 I showed that among 160 systems with this appearance the ratio of luminosities (and hence masses) of the components varies from 1:1 to 1:0.01. in the latter case, the companion is comparable in mass and dimension to an isolated H II region. the number of such M51-type systems increases as the luminosity of the companion decreases. Small companions cannot draw spiral arms from the primary companions by means of tides. Yet, they are observed at the tips of spiral arms. Thus, they must originate at the same time as the spiral or form within them. in some cases, these companions emanate from the spiral arm, as is shown by comparison of observations and calculations.

A survey of ring galaxies which were discovered in 1960 by B. Vorontsov-Velyaminov has been carried out using the Morphological Catalogue of Galaxies. Clusters of galaxies were also included. Such galaxies without spiral arms constitute 0.7% of all galaxies down to 15m.0, and are 100 times less frequent than spiral galaxies. This percentage is the same for clusters, but there are fields where ring galaxies are 3–5 times more frequent than the average. the probability of nearly central chance collisions of galaxies as proposed by some theories has been calculated. It was assumed that a ring galaxy is formed from the encounter of a spiral galaxy with another galaxy if its mass or luminosity is not less than 1% of that of the principal galaxy. the minimum separation of their centres was taken to be less than 2.7 kpc, but the angles between the vectors of the relative velocity and the planes of galaxies were not restricted. the lifetime of the rings once they are formed was assumed to be 109 years and the distribution of the galactic velocities was calculated according to a Maxwellian distribution. the number of galaxies of given absolute magnitude per unit volume was taken from Holmberg (Stars and Stellar Systems, 9, 123). the curvature of the trajectories was taken into account. So conditions were chosen to be most favourable for nearly central collisions.

We have studied hyperbolic encounters of spherical galaxies by self-consistent N-body simulations. Each galaxy is represented by a Plummer model. A galaxy contains up to 250 “particles”. the force between the particles is properly softened in order to avoid an unrealistic internal evolution due to close encounters of the particles. the results of these numerical experiments, carried out by R.W., are compared with theoretical predictions based on the impulsive approximation, made by P.B. in order to facilitate the assessment of such a comparison, the passing galaxy is here represented by a rigid gravitational field, moving on a straight line. in the table given below, we compare the relative mass loss, ΔM/M, and the relative change in the total internal energy of a galaxy, ΔE/E, for two cases. Both galaxies are of equal mass and size; the impact parameter is equal to the median radius of a galaxy (containing 50% of its mass in projection); the initial relative velocity would correspond to the orbital excentricity e as given, if the galaxies were mass points. While the agreement is fair with respect to the energy transfer ΔE, the theory predicts a mass loss of more than 10% (or 25 particles) in cases where no mass loss is observed in the N-body simulations the probable reason for this discrepancy is the failure of the impulsive approximation in these cases. A mass loss of the order of 1% or less cannot be ruled out in the N-body calculations, because of the limited number of particles. the significant increase of the internal energy of a galaxy during an encounter leads to an expansion of the outer parts of the galaxy. This expansion may finally lead to a mass loss as soon as the outer parts have expanded beyond the tidal radius of the galaxy caused by its cluster environment. the inelasticity of galactic encounters has implications for the dynamical evolution of groups and clusters of galaxies. the groups and clusters will shrink in radius because of the loss of orbital energy which is used to expand the individual galaxies. the final amount of collapse of the group or cluster is governed by the relative amount of the internal binding energies stored initially in the individual galaxies and released during the galactic encounters, in comparison to the binding energy of the group or cluster.

The Magellanic stream has been fitted with high accuracy in both position and velocity by the tidal tearing of a Magellanic Cloud. To get the good fit to the high velocity at the stream's tip at a suitable distance from the Galaxy we need either a large mass for the Galaxy, or a large circular velocity for the Sun, or both. An extragalactic method of determining the circular velocity yields the high value of Vc = 294 ± 42 km/sec and an orbit of poor accuracy for the relative motion of the Galaxy and the Andromeda nebula. Very large masses are needed if Andromeda and the Galaxy were formed together. A new direct determination of Hubble's constant from the “superluminal” expansion observed in VLB radio sources gives an age of the Universe of 9 billion years. Either larger masses still or smaller distances within the local group are necessary to bring Andromeda back towards us in so short a time.

The problem of the Magellanic Stream (MS) is re-examined considering also stellar systems (globular clusters and dwarf spheroidal galaxies) lying between 25 and 250 kpc from the Galactic center (Kunkel and Demers 1976). the distribution of these systems is shown to be non-random, with a planar component whose inclination to the Local Group is 43°, and to the local supergalaxy exceeds 60°. the velocity distribution of members of the group shows a symmetry typical of debris associated with a disruptive event at perigalacticon of a victim moving in an elliptical orbit.

Dr Erkes and I, of Dudley Observatory, and Dr Ken Turner, of the Carnegie Institution of Washington, used the 300 foot radio telescope at the National Radio Astronomical Observatory, Greenbank, West Virginia in March of 1977 to measure neutral hydrogen at 21 cm in three 2° strips across positions indicated by Mathewson, Cleary, and Murray (1974, Astrophys. J., 190, 291) as being part of the Magellanic Stream. in region “A” (centred at α = 22h44m, δ = +24 0.5) no hydrogen was found above the background (3 × 1019 H atoms cm−2). in a revised map Mathewson and Schwarz (1976, Mon. Not. R. astr. Soc., 176, 47P) show that this region is not occupied by the stream. in regions “B” and “C” (centred at α = 23h10m, δ = +11° and α = 0h00m, δ = −17°) hydrogen was detected at the velocities found by Mathewson and Schwarz. Maps of the structure found in these regions are shown in Figure 1.

A photoelectric search is presented for light from a smooth intergalactic background in the Coma cluster of galaxies.

Since the early 60's the association of some radio sources with rich clusters of galaxies was noted (Mills, 1960; van den Bergh, 1961) and subsequent investigations concentrated mostly on the radio properties of clusters in the Abell catalogue. This paper is confined to this subject, although one should bear in mind the importance of associations with other scales of clustering which do not appear as entries of that catalogue. in this paper we shall use HO = 100 km sec−1 and the radio power P in WHz−1 at 408 MHz.

The “head-tail” class of radio galaxies (e.g. Ryle and Windram, 1968 and Miley et al., 1972) are of particular interest in the context of this symposium since they provide some of the clearest evidence for a diffuse medium.

Whether galaxy clusters, in addition to a number of radio sources associated with individual cluster members, have an extended radio emitting region designated as cluster halo is in an interesting way related to several questions concerning cluster characteristics:

The existence of ‘haloes’ in clusters of galaxies was deduced by Ryle and Windram (1968) for the Perseus cluster and by Willson (1970) for the Coma cluster at 408 MHz by comparing total flux measured by a single dish with the sum of fluxes of radio sources found in the field. A direct measurement of the extended source Coma C was made by Jaffe et al. (1976) at 610 MHz. the failure to detect the halo of Coma at higher frequencies is attributed by all authors to a steep spectrum of this extended component.

The question of whether or not our and other normal galaxies have some sort of halo - an extended region containing, in particular, cosmic rays - has been discussed for no less than 25 years. Such a “cosmic ray halo” (CRH) appears as a radio-halo, although the absence of the latter is not evidence against the presence of CRH. the point is that the relativistic electrons responsible for the radio emission from the radio-halo undergo synchrotron and Compton losses which are practically absent in the case of the cosmic-ray proton-nuclear component. Possibly because the discussion concerning the existence of the radio-halo in the Galaxy has lasted for years it has acquired a particular character. the latter is clearly reflected in the report by Baldwin (1976) who emphasized that: ȜIn this discussion so far I have avoided the use of the phrase Ȝradio-haloȝ. It arouses antagonism in otherwise placid astronomers and many sought to deny its existence …ȝ Such a situation evidently reflects the difficulties that arise in detecting the radio-halo of our own Galaxy when account is taken of other confusing galactic sources as well as of the metagalactic background.

X-ray astronomy has, in the past year, seen the publication of the second Ariel (2A) and fourth Uhuru (4U) catalogues of X-ray sources. A number of new X-ray cluster identifications and the confirmation of several others has resulted. in this review I will briefly summarise the situation regarding identifications and, for the 2A clusters, discuss the luminosity function and the possible relationships between a number of cluster X-ray and optical properties. Superclusters have been tentatively proposed as a class of X-ray sources and I will comment briefly on recent observations of these objects. Cluster structure has been studied by the Copernicus and SAS-3 spacecraft and by a number of rocket observations with imaging X-ray telescopes undertaken by the Harvard Centre for Astrophysics. I will review the current situation regarding structural measurements. Finally I will discuss the present status of Iron line observations at 6.7 keV in cluster spectra and the estimates of Fe abundance that result from these data.

Gaseous matter almost certainly cannot account for a significant amount of the binding mass in the cores of rich clusters. Implications of the variety of upper limits are well known (Tarter and Silk 1974), and will not be described here. However intracluster gas provides important clues to the evolution of galaxy clusters, and the present review is devoted to elucidating its role.

The aim of the present work (performed in collaboration with J.R. Gott and E.L. Turner) is to account for the observed distribution of galaxies in terms of the gravitational instability picture. Specifically we assume that all the matter is contained in galaxies. the evolution of such a system can then be studied by N-body simulations once the initial conditions are specified. Our approach is essentially experimental; a variety of models are computed and the results are compared with observations.

A study of clusters is presented by means of the function Nm(θ), i.e. the total number N of members heavier than a limiting mass m, as a function of the limiting projected angular distance from the centre θ. As a rule such a function is found to possess a well-defined maximum change of slope - an apparent Ȝdeflectionȝ - if the limiting mass is large enough (see Figure 1 a-g). Some possible definitions of this deflection and the corresponding special Ȝcore radiusȝ of the cluster are described elsewhere (Astrofizika, 7, 435, 1971). the typical occurrence and rather regular behaviour (systematic temporal variations) of this deflection in a sample of 17 configurations simulated by S.J. Aarseth and S.D.M. White for different conditions prove this feature to be a natural consequence of the gravitational interaction of many bodies in a statistical sense; it is apparently a characteristic of core formation and the evolution of clusters. in the case of computer data the existence of such deflections cannot possibly be due to any observational error or uncertainty or erroneous personal judgement. the corresponding diagrams, Nm(θ) for clusters of galaxies (see also loc. cit.) are found to be practically indistinguishable from those of star clusters and simulated systems. They show the very same type of deflection, the same remarkably small dependence on the choice of the limiting mass, that of the Ȝcentreȝ, the field correction etc. As simulations give just the same diagrams as have been obtained observationally it is plausible to regard also these observational findings as dynamically necessary and not chance coincidences, unless the actual clusters of galaxies are stabilized by some continuously distributed intergalactic Ȝhidden matterȝ instead of the masses of observable discrete bodies themselves. However one can hardly accept a radically different explanation for the apparently identical phenomenon in the case of systems of galaxies on the one hand and those of stars on the other. Estimates of the crossing time tc of the systems together with morphological arguments and numerical experiments indicate that actual “rich” clusters of galaxies might typically be near a particular epoch of very rapid systematic cosmological evolution. A considerable decrease of the aforementioned “core radii” (a transition between two nearly constant values) with the other characteristic sizes of the systems almost unchanged (Figure 1 a-d). the corresponding phenomena were detected earlier observationally and consequently these empirical data, together with their consequences, now seem to be once again corroborated (see e.g. Astron. Nachrichten, 297, 311, 1976). These remarkable analogies suggest that a similar mechanism is responsible for the formation and evolution of conspicuous cores of clusters and a similar solution of the somewhat controversial situation with regard to mass segregation both for clusters of galaxies and open star clusters (e.g. by properly choosing the initial conditions).

I would like to present some preliminary results of an investigation of 50 clusters of galaxies. For studying the clusters, Schmidt plates taken with the 2-metre universal telescope at Tautenburg and the prints of the Palomar Sky Survey were used. For all the clusters we determined isopleths to obtain detailed information about the distribution of galaxies. We have found well isolated clusters, double clusters, multiple systems and rather complicated structures.

The mathematical theory of the description of the structure of point-sets in a plane or in space can be applied to the investigation of the distribution of different extragalactic objects. Mathematically we can define rigorously such ideas as cluster, nucleus of cluster, monoor polynuclear structure, background and so on. First we choose a critical distance that determines the scale on which we investigate the distribution of objects. the critical distance plays a similar role to the wavelength of radiation by means of which we investigate the internal structure of matter. It is obvious that the description is different for different critical distances. To obtain a complete picture we have to analyse the evolution of this description as the critical distance changes.