BASIC FACTS RELATED TO THE KINEMATICS AND DYNAMICS OF GALACTIC SYSTEMS Our knowledge of galactic motions is confined to information on the radial velocities of about a thousand galaxies. We have no data at all concerning their tangential velocities. Nevertheless, the available data on the radial velocities (nearly all of which were obtained at the Mount Wilson, Palomar, and Lick Observatories) have posed some of the most difficult problems which astronomy has ever had to face.
The totality of observable galaxies constitutes a part of some vast system which we call the Metagalaxy. The concept of the Metagalaxy, by the way, is meaningful regardless of whether galaxies exist beyond this system or not. The most important consequence of our information on the radial velocities of the galaxies is the fact that the Metagalaxy is expanding.
Hubble's law, which was derived from empirical data, states that where is the radial velocity of the galaxy, H is a constant, and r is the distance to the galaxy. This law, which is valid within minor fluctuations for values of r up to almost 2 billion parsecs, indicates that the observed expansion is approximately uniform. All attempts to find an explanation for the red shift other than the Doppler effect have turned out to be artificial and futile. Consequently, whenever we consider any problems concerning the nature, and particularly the evolution, of the Metagalaxy, we have to take into account its expansion.
Clearly, Hubble's law is valid only as an average. In addition to the velocity defined by Hubble's formula, each galactic cluster has its own peculiar velocity, as does each galaxy with respect to the center of gravity of its cluster.
For instance, in the Local Group, where the distances between galaxies are small, the relative velocities are mainly determined by the peculiar motions of the individual members. However, even the nearest galactic clusters and the nearest outer groups are receding from us, indicating that the peculiar velocities of these clusters and groups are small compared with the systematic recession velocities given by Hubble's law.
It is important to know the value of the constant H, since this makes it possible to determine the distances of the remotest clusters. Unfortunately, this value is not precisely known, although probably it lies somewhere between the following limits: and it is a fair guess that it lies between the narrower limits: according to the measurements of Sandage (1958). It will not be advisable
to consider here the problems involved in determining H, but we should note that under any given conditions Hubble's law provides a good estimate of the relative distances.
Another important factor with respect to galactic motions is the existence of a certain dispersion of velocities within each galactic cluster, this being associated with internal motions in the clusters.
If a cluster is in a steady state, or if it is supposed to reach a steady state after a certain length of time, its total energy E must be negative: where T and U are the kinetic and potential energies of the system. If E>0, on the other hand, the system cannot reach a steady state, and at least some of its members must move off to infinity.
Recent investigations have shown that there are some groups and multiple systems for which the kinetic energy of internal motion (deter mined from the radial velocities) is many times higher than the probable absolute magnitude of the potential energy; the latter was calculated assuming that the main mass of the cluster is concentrated in its galaxies and that the mass-luminosity ration f= for a given type of galaxy is of the same order as in cases when this ratio could be determined by studying the galactic rotation. This gave rise to the conclusion that some groups and clusters have a positive energy and should immediately become scattered throughout space. Such a conclusion was reached, for instance, for the galactic clusters in Virgo and Hercules, and also for the relatively nearby group in Sculptor. The latter case, which was analyzed in detail by de Vaucouleurs, is a particularly striking example, because its kinetic energy apparently exceeds the calculated absolute potential energy by one and one half or two orders of magnitude. Since a positive energy must cause some members of the cluster to wander away, and sometimes even makes the whole cluster disperse, it could be assumed that there is something in common between unsteady-state processes in clusters, on the one hand, and the expansion of the Metagalaxy on the other.