We have recently written a new code to simulate the long term evolution of spherical clusters of stars. It is based on the pioneering Monte Carlo scheme proposed by Hénon in the 70's. Unlike other implementations of this numerical method which were successfully used to investigate the dynamics of globular clusters, our code has been devised in the specific goal to treat dense galactic nuclei. In a previous paper, we described the basic version of our code which includes 2-body relaxation as the only physical process. In the present work, we go on and include further physical ingredients that are mostly pertinent to galactic nuclei, namely the presence of a central (growing) black hole (BH) and collisions between (main sequence) stars. Stars that venture too close to the BH are destroyed by the tidal field. We took particular care of this process because of its importance, both as a channel to feed the BH and a way to produce accretion flares from otherwise quiescent galactic nuclei. Collisions between stars have often been proposed as another mechanism to drive stellar matter into the central BH. Furthermore, non disruptive collisions may create peculiar stellar populations which are of great observational interest in the case of the central cluster of our Galaxy. To get the best handle on the role of this process in galactic nuclei, we include it with unpreceded realism through the use of a set of more than 10 000 collision simulations carried out with a SPH (Smoothed Particle Hydrodynamics) code. Stellar evolution has also been introduced in a simple way, similar to what has been done in previous dynamical simulations of galactic nuclei. To ensure that this physics is correctly simulated, we realized a variety of tests whose results are reported here. This unique code, featuring most important physical processes, allows million particle simulations, spanning a Hubble time, in a few CPU days on standard personal computers and provides a wealth of data only rivalized by N-body simulations.
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