The structure of a globular cluster—the spatial distribution and random velocities of its stars—changes slowly with time as a result of simple dynamical principles. In much of this dynamical evolution, the changes in the cluster are a consequence of Newton’s laws of motion and of gravitation as applied to an assembly of mass points. The theory of such changes is the general topic of this book.

The following sections in this first chapter present the observational and theoretical background for the later chapters. Relevant observations on globular clusters, especially data on the structure, age and mass of these...

The relative motions of the stars in a globular cluster produce continual fluctuations in the gravitational field, and these fluctuations produce, in turn, changes in the magnitude and direction of each stellar velocity. Thus the energyEof a star and its angular momentumJ(both measured per unit mass) will gradually change with time, perturbing the zero-order solutions discussed in the first chapter. In this chapter we discuss the rate at which these changes occur. The stars are treated as point gravitating masses, and hence direct physical collisions, which are generally very infrequent, are ignored. The gravitational interactions considered...

The simplified models presented here provide an opportunity to explore a number of physical processes which are important in the dynamical evolution of clusters. In a real cluster or in a realistic model several of these processes will usually occur simultaneously. The idealized models discussed in this chapter make it possible to isolate a number of specific processes and to gain some understanding of the particular effects involved.

These four models, each of which considers some process leading to a cataclysmic fate for the cluster, embody quite different methods of analysis. Evaporation from an isolated cluster, considered in §3.1, is...

We discuss now the detailed dynamical evolution which the velocity perturbations of chapter 2 produce in the zero-order steady solutions of §1.2. The three basic approximations of §1.2 are, of course, retained for the zero-order solutions; i.e., (A) a smooth gravitational potential, averaged over the granularity of the stellar distribution, (B) a quasi-steady state for the cluster, withf(r,v) and other physical properties changing slowly as the cluster evolves through a succession of essentially steady states, and (C) complete spherical symmetry in r, with f(r,v_r,v_t) independent of the direction of the transverse velocity vt.

The first section below discusses the...

A conspicuous lack of realism in the standard model is its neglect of the galactic gravitational field. The tidal force associated with this field makes it possible for individual stars to escape from the cluster if their energy suffices to take them beyond some critical distance from the cluster center. In addition, variations in the galactic field, as experienced by a cluster moving about the Galaxy, provide a time-dependent gravitational potential, when expressed relative to the center of the cluster, and can produce important changes in the random kinetic energies of some cluster stars.

These effects are discussed in the...

Binary star systems can provide an important source of energy for globular clusters. The binding energy of such a system can be increased during an encounter with a single star; this decrease in binary energy is matched by a corresponding increase in the kinetic energy of relative motion of the single star with respect to the binary. Under some conditions, the resultant increase of internal kinetic energy of the cluster, computed with each binary regarded as a mass point, can have important dynamical consequences on the cluster’s evolution. Some binaries may be primordial; i.e., they may have formed at the...

As the core of a cluster collapses, the rapid increase in central density accelerates the rate of binary formation and also the rate at which binaries harden. At the same time, the heavier stars become more and more concentrated within the core, while the core mass steadily decreases. In addition, the granularity of the gravitational potential becomes progressively more and more important, with the gravitational force of the nearest neighbor becoming comparable with the force produced by the inner stars; the relative effect of close encounters steadily increases and the Fokker-Planck approach becomes less accurate. If stars of normal radii...