Dynamical stability of N-body models for M32 with a central black hole

We study the stability of stellar dynamical equilibrium models for M32. Kinematic observations show that M32 has a central black hole of 3x10^6 solar masses, and a phase-space distribution function that is close to the `two-integral' form f=f(E,L_z). M32 is also rapidly rotating; 85-90% of the stars have the same sense of rotation around the symmetry axis. Previous work has shown that flattened, rapidly rotating two-integral models can be bar-unstable. We have performed N-body simulations to test whether this is the case for M32. Particle realizations with N=512,000 were studied for two representative inclinations, i=90 (edge-on) and i=55, corresponding to intrinsic axial ratios of q=0.73 and q=0.55, respectively. The time evolution of the models was calculated with a `self-consistent field' code on a Cray T3D parallel supercomputer. We find both models to be dynamically stable. This implies that they provide a physically meaningful description of M32, and that the inclination of M32 (and hence its intrinsic flattening) cannot be strongly constrained through stability arguments. Previous work on the stability of f(E,L_z) models has shown that the bar-mode is the only possibly unstable mode for systems rounder than q=0.3, and that the likelihood for this mode to be unstable increases with flattening and rotation rate. The f(E,L_z) models studied for M32 are stable, and M32 has a higher rotation rate than nearly all other elliptical galaxies. This suggests that f(E,L_z) models constructed to fit data for real elliptical galaxies will generally be stable for q>0.55, and possibly for flatter systems as well.