### Abstract

We study the stability of stellar dynamical equilibrium models for M32. Kinematic observations show that M32 has a central dark mass of ∼3 × 10^{6} M_{⊙}, most likely a black hole, 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. This is the first stability analysis of twointegral 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, L_{z}) models has shown that the bar mode is the most common 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, L_{z}) models studied for M32 are not barunstable, 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, at least for systems rounder than q ≳ 0.55, and possibly for flatter systems as well.

Original language | English (US) |
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Pages (from-to) | 153-162 |

Number of pages | 10 |

Journal | Astrophysical Journal |

Volume | 487 |

Issue number | 1 PART I |

DOIs | |

State | Published - 1997 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*487*(1 PART I), 153-162. https://doi.org/10.1086/304605