Post-Collapse evolution of globular clusters

A number of globular clusters appear to have undergone core collapse, in the sense that their predicted collapse time is much shorter than their current age. Simulations using gas models and Fokker-Planck approximation have shown that the central density of a globular cluster after the collapse undergoes nonlinear oscillation with large amplitude (gravothermal oscillation). However, whether such an oscillation actually takes place in a real $N$-body system has remained unsolved, because an $N$-body simulation with a sufficiently high resolution would have required the computing resource of the order of several Gflops$\cdot$years. In the present paper, we report the result of such a simulation, performed on a dedicated special-purpose computer GRAPE-4. We simulated the evolution of isolated point-mass systems with up to 32,768 particles. The largest number of particles reported previously is 10,000. We confirmed that gravothermal oscillation takes place in an $N$-body system. The expansion phase shows all signatures that are considered as the evidences of the gravothermal nature of the oscillation. At the maximum expansion, the core radius is $\sim 1$\% of the half-mass radius for the run with 32,768 particles. The maximum core size $r_c$ depends on $N$, as $ \propto N^{-1/3}$.