N BODY SIMULATIONS OF THE NUCLEUS OF M-31

We test through stellar N-body simulations some scenarios to explain t he dynamics of the peculiar nucleus of the Andromeda galaxy (M 31): al though HST observations reveal a double nucleus morphology, the rotati on field is almost symmetric around the bulge gravity centre and the v elocity dispersion is off-centred. We show that any m = 1 perturbation has a very short life-time (a few 10(5) yr). Assuming that the bright peak (P1) is a cold stellar cluster in falling into the nucleus, and that the large central velocity gradient is due to a central dark mass (in the range 7 10(7)-10(8) M.), we obtain a reasonably good fit to t he observations. However, if this cluster lies in the central 20 pc, w e estimate the life-time of the cluster to be less than 0.5 Myr. The d ynamical friction is more efficient than estimated by analytic formula e, and is essentially due to the deformation of the stellar cluster th rough the huge tidal forces provided by the black hole. We show that t he cluster cannot be on a circular orbit around the centre if the nucl eus hosts a massive black hole of a few 10(7) M., and finally provide some estimates of the kinematics as observed with HST.