The higher concentration of stars in the center of the cluster increases the probability of an encounter, which, in turn, decreases the relaxation time. Thus, the relaxation time given in Equation (1) is an average over the whole cluster. The local relaxation time of the cluster is given in Meylan and Heggie  and can be described by[157, 172] and . Binney and Tremaine provide a range of values for from 10.1 in the center of the cluster to 12 at . Note that in the central regions of the cluster, the value of is much lower than the average relaxation time. This means that in the core of the cluster, where the more massive stars have concentrated, there are more encounters between these stars.
The concentration of massive stars in the core of the cluster will occur within a few relaxation times, . This time is longer than the lifetime of low metallicity stars with . Consequently, these stars will have evolved into carbon-oxygen (CO) and oxygen-neon (ONe) white dwarfs, neutron stars, and black holes. After a few more relaxation times, the average mass of a star in the globular cluster will be around and these degenerate objects will once again be the more massive objects in the cluster, despite having lost most of their mass during their evolution. Thus, the population in the core of the cluster will be enhanced in degenerate objects. Any binaries in the cluster that have a gravitational binding energy significantly greater than the average kinetic energy of a cluster star will act effectively as single objects with masses equal to their total mass. These objects, too, will segregate to the central regions of the globular cluster . The core will then be overabundant in binaries and degenerate objects.
The core would undergo what is known as core collapse within a few tens of relaxation times unless these binaries release some of their binding energy to the cluster. In core collapse, the central density increases to infinity as the core radius shrinks to zero. An example of core collapse can be seen in the comparison of two cluster evolution simulations shown in Figure 4 . Note the core collapse when the inner radius containing 1% of the total mass dramatically shrinks after . Since these evolution syntheses are single-mass Plummer models without binary interactions, the actual time of core collapse is not representative of a real globular cluster.
The static description of the structure of globular clusters using King–Michie or Plummer models provides a framework for describing the environment of relativistic binaries and their progenitors in globular clusters. The short-term interactions between stars and degenerate objects can be analyzed in the presence of this background. Over longer time scales (comparable to ), the dynamical evolution of the distribution function as well as population changes due to stellar evolution can alter the overall structure of the globular cluster. We will discuss the dynamical evolution and its impact on relativistic binaries in Section 5.
Before moving on to the dynamical models and population syntheses of relativistic binaries, we will first look at the observational evidence for these objects in globular clusters.
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