Short- and long-term evolution of a stellar disc around a massive black hole: the role of the cusp, stellar evolution and binaries

We study the dynamical evolution of a stellar disc orbiting a massive black hole. We explore the role of two-body relaxation, mass segregation, stellar evolution and binary-heating in affecting the disc evolution and consider the impact of the nuclear cluster properties and the stellar-disc mass-function. We use analytic arguments and apply them to study the evolution of a the velocity dispersion of stars in a Galatic Centre (GC) - like stellar disc on both short (few million years) and longer (100 Myr) evolutionary time-scales. The dominant processes affecting the disc evolution are two-body relaxation and mass-stratification, where the massive stars play a key role in kinematically heating lower mass stars; binary-heating has only a little contribution. In particular, models with realistic mass-functions show the disc structure to be mass-stratified. The number of massive stars in the disc decrease due to stellar evolution, consequently leading to slower relaxation. At these later evolutionary stages, dynamical heating by the nuclear cluster plays a progressively more important role. Given these findings, it is likely that two-body relaxation alone could not produce the observed configuration of the stellar disc in the GC and other collective processes might have played an important role. Such processes are less likely to produce mass-stratification in the disc and therefore a detailed study of the mass-stratification of the GC disc may provide a handle on the processes that dominate its evolution. Finally, two-body relaxation would leave a stellar disc in a relatively thin configuration even after 100 Myr and therefore earlier discs, now containing only older, lower mass stars, might still be observed in the GC, unless destroyed/smeared by other processes.