In this note I will report the general character of all scale-free solutions of the collisionless Boltzmann and Poisson equations for a specific shape. In this case, the density falls as r−2 along any radial ray, the potential is logarithmic with oblate spheroidal level surfaces, and the flattening corresponds to an E5 or E6 density distribution (see Richstone 1980, hereafter Paper I). Schwarzschild's (1979) method was used. Toomre (1982) has recently discussed the properties of scale free models of this sort with distribution functions dependent on only the two classical isolating integrals. The method used here automatically incorporates the third integral.

It is well known by now that models of elliptical galaxies based on Jeans theorem require the inclusion of a third integral in the distribution function.

For a number of years the Geneva Observatory stellar dynamics group has undertaken numerical investigations of stellar orbital behaviour in conservative dynamical systems with three degrees of freedom. Compared to results for 3-D axisymmetrical models (2 degrees of freedom), this work displayed the advent of several new phenomena which may appear in rotating or non-rotating stellar systems with three unequal axes (ellipticals, bulges, bars). Some of these phenomena deserve particular attention.

Giant elliptical galaxies are now known to be supported by anisotropic pressure rather than by rotation (cf. Binney, 1981). This anisotropy can be derived from observable quantities for spherical systems as was shown by Binney and Mamon (1982) in their study of M87. We investigate here the velocity anisotropy of the El galaxy NGC 3379, a giant elliptical whose surface brightness constitutes an excellent illustration of the r1/4 law.

This contribution concentrates on the properties of the large gas structures in elliptical galaxies, those seen in dust and HI. The distribution and kinematics of ionized gas, which is generally confined to a small region in the center of the galaxy, are discussed at this conference by Illingworth and by Ulrich.

Do elliptical and SO galaxies in which type I supernovae (SNI) were detected contain more gas than those without SNI detections? Thirteen E and SO galaxies in the Virgo and Pegasus I clusters, seven with SNI detections and six without, were mapped well beyond the optical image at the 21-cm neutral hydrogen line. No HI was detected. In Virgo, the upper limit to MMI/LB is between 0.0005 and 0.0024.

In this note we report the detection and mapping of neutral hydrogen in two dwarf elliptical galaxies NGC 185 and NGC 205. Both are companions to M 31 and both are classified as peculiar owing to the presence of obscurring dust patches near their nuclei. Both galaxies also contain a small population of blue, presumably young stars (Hodge 1963, 1973).

It has been known for several decades that about 15% of elliptical galaries contain ionized gas yet very little data is available in the literature on the properties of this gas such as spatial distribution, velocity field, and abundances. The properties of this gas are related to current problems about elliptical galaxies: (1) origin of the gas (stellar mass loss vs. accretion from a nearby gas-rich galaxy or an intergalactic cloud); (2) structure of the galaxy itself, because the locus of the stationary orbits of the gas depends on whether the galaxy is prolate or oblate and on whether the galaxy is rotating or not; (3) the relationship between the presence of gas in elliptical galaxies and their radio properties.

Since the time it became evident that ellipticals are not rotationally supported, there has been an increasing interest on their dynamical properties, and new models have been formulated. However, the spectroscopic, as well as the photometric and morphological observations, do not provide yet a clear understanding of the structure of these objects, just proving that they are much more complicated than thought before. An obvious way to attack the problem seems to look at the motions of the gaseous component in those few cases where it is present, because of the different response to the same potential field of the gas and star components.

Recent spectroscopic measurements of 5 strong radio galaxies showed that approximately 50% of these objects had internal gas velocities which were notably non-circular. To investigate this, more detailed observations were done for the galaxies in question. Examination of these results suggests that the non-circular velocities tend to fall into a pattern. All of the objects have one kinematical component which fits the classical picture of “circular rotation”. This occurs in BOTH the stellar and ionized gas and displays MUCH HIGHER peak velocities than are found in E galaxies. In addition, all of the objects studied possess a second ionized gas system at a different velocity from that of the rotating gas. Finally, at least one of the objects has an envelope of stars which is either not rotating or has a very different kinematic major axis from that of the stellar population in its inner regions.

There are many reasons to consider the dynamics of triaxial galaxies. Elliptical galaxies are not rotationally flattened (Illingworth, this conference) and their isophotal profiles are often twisted. N-body simulations of collapse have produced a number of final state figures which are triaxial. Even those still skeptical will have to grant that barred spirals (a category which seems to include the Galaxy) are certainly not axisymmetric.

Theory has long suggested that dynamical friction between colliding galaxies must lead to mergers. The problem for observers has been to find which galaxies are mergers. I shall first review the available evidence for mergers in various kinds of galaxies, then propose a tentative classification scheme for mergers, and finally discuss mergers in giant ellipticals and their relation to the evolution and perhaps even the formation of ellipticals.

Using TAURUS – an Imaging Fabry Perot system in conjunction with the IPCS on the AAT, we have studied the velocity field of the Ha emission line at a spatial resolution of 1.7″ over the dark lane structure of Centaurus A. The derived velocity field is quite symmetrical and strongly suggests that the emission line material is orbiting the elliptical component, as a warped disc.

Recently Marcelin et al (1982) published some results of Fabry-Perrot interferometry of NGC 5128. We would like here to draw attention to several more aspects of this enigmatic galaxy.

The last few years have seen a considerable amount of effort devoted to the problem of simulating the coalescence of galaxies. After a discussion of the merits and limitations of the N-body techniques that have been used, I summarise the insight this research gives into the mechanisms driving strong interactions in galaxy collisions and into the structure of the remnants such collisions produce.

Sharp shell-like structures around elliptical galaxies can be modelled by the phase wrapping of a cold disk of stars in the fixed potential of a massive elliptical galaxy. Such structures can then be used as probes of the potential field of ellipticals and a diagnostic of the merger event.

The velocities of escape of colliding galaxies obtained under the impulsive approximation are compared to those obtained from N-body simulations.

This study is part of a program to investigate consequences to a galaxy of its orbiting within a cluster of galaxies. Numerical experiments have been conducted to study the tidal influences on the internal dynamics of a galaxy (Miller and Smith 1982). The present first cut at the general problem treats effects of the cluster's tidal potential on the pattern motion and observable properties of a galaxy (shape, density contours, velocity fields, velocity dispersions) for a fixed external potential. The first-order cluster force field is balanced by the galaxy's acceleration in the real cluster, leaving tidal terms as the leading terms in a Taylor series expansion of the cluster force field about the center of the galaxy. The cluster tidal force field is usually stretching along a line toward the cluster center and compressive at right angles.

Collisions between disk galaxies embedded in massive halos have been studied by means of numerical experiments. The large three-dimensional n-body programs used for numerical experiments in the dynamics of galaxies and galaxy collisions (Miller 1978; Miller and Smith 1980) have been used in this investigation of the collision and merging of galaxies. The use of the large n-body code is important in a systematic study of the physical processes involved. There are enough particles (105) and the detail in the force field is sufficient to give the necessary resolution. Dynamical and relaxation time scales are well separated. This is particularly important in investigations of the merging process and of the nature of the merger product.

Numerical simulations of merging galaxies do not include a disc component due to bar instability modes. Analytic work is based upon the impulsive approximation which leads to energy loss by the perturber. However, for the perturber to become bound we need consider parabolic encounters. Here we present an analytic technique suitable for all types of encounters.