Go to previous page Go up Go to next page

5 Dynamical Evolution

Simulations of the populations of relativistic binaries in globular clusters rely on the interplay between the evolution of individual stars in the progenitor systems and the evolution of globular clusters. The evolution of stars in the progenitor systems has been discussed in the previous Section 4 and we now turn to techniques for simulating the evolution of globular clusters.

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 N-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 may 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. MODEST (MOdeling DEnse STellar systems), a collaboration of various groups working stellar dynamics, maintains a website that provides the latest information about efforts to combine simulations of both the dynamical evolution of N-body systems and stellar evolution [151Jump To The Next Citation Point].

General approaches to this problem involve solving the N-body problem for the component stars in the cluster and introducing binary and stellar evolution when appropriate to modify the N-body evolution. There are two fundamental approaches to tackling this problem – direct integration of the equations of motion for all N bodies in the system and large-N techniques, such as Fokker–Planck approximations coupled with Monte Carlo treatments of binaries (see Heggie et al. [97] for a comparison of these techniques). For a recent review of progress in implementing these techniques, see the summary of the MODEST-2 meeting [220]. In the next two Sections 5.1 and 5.2, we discuss the basics of each approach and their successes and shortfalls. We conclude in Section 5.3 with a discussion of the recent relativistic binary population syntheses generated by dynamical simulations.

 5.1 N-body
 5.2 Fokker–Planck
 5.3 Population syntheses
  5.3.1 N-body simulations
  5.3.2 Monte Carlo simulations
  5.3.3 Encounter rate techniques
  5.3.4 Semi-empirical methods

  Go to previous page Go up Go to next page