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

We study the dynamical evolution of a stellar disk orbiting a massive black hole. We explore the role of two-body relaxation, mass segregation, stellar evolution and binary heating in affecting the disk evolution, and consider the impact of the nuclear cluster structure and the stellar-disk mass-function. We use analytic arguments and numerical calculations, and apply them to study the evolution of a stellar disk (similar to that observed in the Galactic center; GC), both on the short (few Myr) and longer (100 Myr) evolutionary timescales. We find the dominant processes affecting the disk evolution are two-body relaxation and mass segregation where as binary heating have only a little contribution. Massive stars play a dominant role in kinematically heating low mass stars, and driving them to high eccentricities/inclinations. Multi-mass models with realistic mass-functions for the disk stars show the disk structure to be mass stratified, with the most massive stars residing in thinner structures. Stellar evolution plays an important role in decreasing the number of massive stars with time, thereby leading to slower relaxation, where the remnant compact objects of these stars are excited to higher eccentricities/inclinations. At these later evolutionary stages dynamical heating by the nuclear cluster plays a progressively more important role. We conclude that the high eccentricities of the disk-stars in the Galactic Center suggest that the disk formed with initially high eccentricities, or that collective or secular processes dominate the disk evolution. Finally, we find that the disk structure is expected to keep a thin structure even after 100 Myrs. It therefore suggests earlier disks now containing only older, lower mass stars might still be observed in the Galactic center, unless destroyed/smeared by other non-two-body relaxation processes.