Dynamical stability of N - body models for M 32 with a central black hole

We study the stability of stellar dynamical equilibrium models for M32. Kinematic observations show that M32 has a central dark mass of ∼ 3 × 106 M⊙, most likely a black hole, and a phase-space distribution function that is close to the ‘two-integral’ form f = f(E,Lz). 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. This is the first stability analysis of two-integral models that have both a central density cusp and a nuclear black hole. Particle realizations with N = 512,000 were generated from distribution functions that fit the photometric and kinematic data of M32. We constructed equal-mass particle realizations, and also realizations with a mass spectrum to improve the central resolution. Models 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,Lz) models has shown that the bar-mode is the only possibly unstable mode for systems rounder than q ≈ 0.3 (i.e., E7), and that the likelihood for this mode to be unstable increases with flattening and rotation rate. The f(E,Lz) models studied for M32 are stable, and M32 has a higher rotation rate than nearly all other elliptical galaxies. This suggests that f(E,Lz) models constructed to fit data for real elliptical galaxies will generally be stable, at least for systems rounder than q ∼> 0.55, and possibly for flatter systems as well. Subject headings: black hole physics — galaxies: elliptical and lenticular, cD — galaxies: individual (M32) — galaxies: kinematics and dynamics — galaxies: nuclei — galaxies: structure.