Central cusp caused by a supermassive black hole in axisymmetric models ofelliptical galaxies

We use numerical simulations to investigate the cusp at the centre of ellip tical galaxies caused by the slow growth of a supermassive black hole. We s tudy this problem for axisymmetric models of galaxies with or without rotat ion. The numerical simulations are based on the 'perturbation particles' me thod, and use GRAPEs to compute the force arising from the cusp. We study t he way in which the density cusp is affected by the initial flattening of t he model, as well as the role played by initial rotation. The logarithmic s lope of the density cusp is found to be very much insensitive to flattening ; as a consequence, we deduce that tangential velocity anisotropy - which s upports the flattening - is also of little influence on the final cusp. We investigate, via two different kinds of rotating models, the efficiency wit h which a rotation velocity component builds within the cusp. A cusp in rot ation develops only for models where a net rotation component is initially present at high energy levels. The eventual observation of a central rotati onal velocity peak in elliptical galaxies has, therefore, some implications for the galaxy dynamical history.