Axisymmetric, Three-Integral Models of Galaxies: A Massive Black Hole in NGC 3379

Abstract

We fit axisymmetric three-integral dynamical models to NGC 3379 using the line-of-sight velocity distribution obtained from Hubble Space Telescope FOS spectra of the galaxy center and ground-based long-slit spectroscopy along four position angles, with the light distribution constrained by WFPC2 and ground-based images. We have fitted models with inclinations from 29° (intrinsic galaxy type E5) to 90° (intrinsic E1) and black hole masses from 0 to 109 M⊙. The best-fit black hole masses range from 6 × 107 to 2 × 108 M⊙, depending on inclination. The preferred inclination is 90° (edge-on); however, the constraints on allowed inclination are not very strong, owing to our assumption of constant M/LV. The velocity ellipsoid of the best model is not consistent with either isotropy or a two-integral distribution function. Along the major axis, the velocity ellipsoid becomes tangential at the innermost bin, radial in the midrange radii, and tangential again at the outermost bins. The rotation rises quickly at small radii owing to the presence of the black hole. For the acceptable models, the radial-to-tangential [(σ + σ)/2] dispersion in the midrange radii ranges over 1.1 < σr/σt < 1.7, with the smaller black holes requiring larger radial anisotropy. Compared with these three-integral models, two-integral isotropic models overestimate the black hole mass since they cannot provide adequate radial motion. However, the models presented in this paper still contain restrictive assumptions—namely, assumptions of constant M/LV and spheroidal symmetry—requiring yet more models to study black hole properties in complete generality.