THE DYNAMIC EVOLUTION OF DENSE STAR-CLUSTERS IN GALACTIC NUCLEI

We present the results of numerical Fokker-Planck calculations of the dynamical evolution of dense, spherical star clusters in galactic nuclei. Our calculations include the effects of two-body gravitational relaxation, stellar collisions and mergers, stellar evolution and the formation of new stars from gas liberated by stellar evolution, and interactions between hard binaries and single stars. The clusters initially contain solar-mass, main-sequence stars at densities and velocity dispersions similar to those observed in dense but otherwise normal galactic nuclei (p ≃ 106-108 M⊙ pc-3, vrms ≃ 100-400 km s-1). In clusters with initial relaxation time scales tr ≲ 108 yr, stars of mass greater than ≃ 100 M⊙ easily form through multiple stellar mergers at the cluster center. The massive stars form before there is a significant rise in the central velocity dispersion, unlike in earlier calculations that didn't include the effects of mass segregation. These massive stars can undergo further mergers and collapse to form the seed black holes (≃102-103 M⊙) that have been assumed as initial data in simulations of active galactic nuclei and quasars. Stellar mergers followed by supernovae can lead to dense clusters of compact stellar remnants in galactic nuclei, especially if star formation favors stars more massive than 1 M⊙ and if stars of mass greater than ∼15 M⊙ leave black-hole remnants (rather than less-massive, neutron-star remnants) at the end of their main-sequence lifetime. These clusters are important sources of gravitational radiation because of the frequent binary mergers that occur.