The evolution of a globular cluster is dominated
by the gravitational interaction between the component stars in the
cluster. The overall structure of the cluster as well as the
dynamics of most of the stars in the cluster are determined by
simple -body gravitational dynamics. However, the
evolutionary time scales of stellar evolution are comparable to the
relaxation time and core collapse time of the cluster.
Consequently, stellar evolution affects the masses of the component
stars of the cluster, which affects the dynamical state of the
cluster. Thus, the dynamical evolution of the cluster is coupled to
the evolutionary state of the stars. Also, as we have seen in the
previous section, stellar evolution governs the state of the binary
evolution and binaries provide a means of support against core
collapse. Thus, the details of binary evolution as coupled with
stellar evolution must also be incorporated into any realistic
model of the dynamical evolution of globular clusters. To close the
loop, the dynamical evolution of the globular cluster affects the
distribution and population of the binary systems in the cluster.
In our case, we are interested in the end products of binary
evolution, which are tied both to stellar evolution and to the
dynamical evolution of the globular cluster. To synthesize the
population of relativistic binaries, we need to look at the
dynamical evolution of the globular cluster as well as the
evolution of the binaries in the cluster.
General approaches to this problem involve
solving the -body problem for the component stars in
the cluster and introducing binary and stellar evolution when
appropriate to modify the
-body evolution. There are
two fundamental approaches to tackling this problem - direct
integration of the equations of motion for all
bodies in the system and large-
techniques, such as Fokker-Planck approximations
coupled with Monte Carlo treatments of binaries (see Heggie et al. [71] for a comparison
of these techniques). In the next two subsections, we discuss the
basics of each approach and their successes and shortfalls. We
conclude this section with a discussion of the recent relativistic
binary population syntheses generated by dynamical simulations.