Post-collapse evolution and gravothermal oscillation of globular clusters

Abstract

Post-collapse evolution of globular clusters is studied by means of a gaseous model. As a result of the gravothermal instability, cores of globular clusters have been thought to collapse within a finite time. It is shown that there exists a gravothermally unstable isothermal configuration with a central singularity of a definite functional form. Evolution towards such a configuration is computed numerically. Here, however, energy release through hardening of binary stars is taken into account. It is found that the globular cluster does not approach it monotonically but oscillatorily. The core oscillates between a state with a high-density cusp at the centre and another state having a regular isothermal core of moderate central density. Only a minute energy generation is necessary to drive this gravothermal oscillation. Such results will resolve a long-standing question; how the non-existence of the collapsed globular clusters can be reconciled with the theoretical prediction of the central singularity. Globular clusters pass recurrently through relatively short phases of high central densities and long phases of low central densities. Therefore, the probability of finding the cluster in low central density states is much higher than in high density states. Typical low central density states can be described by standard King models.