1999ApJ...514..704C

We present axisymmetric dynamical models of the edge-on S0 galaxy NGC 4342. This small low-luminosity galaxy harbors, in addition to its outer disk, a bright nuclear stellar disk. A combination of observations from the ground and with the Hubble Space Telescope (HST) has shown that NGC 4342 rotates rapidly and has a strong central increase in velocity dispersion. We construct simple two-integral Jeans models as well as fully general, three-integral models. The latter are built using a modified version of Schwarzschild's orbit-superposition technique developed by Rix et al. and Cretton et al. These models allow us to reproduce the full line-of-sight velocity distributions, or ``velocity profiles'' (VPs), which we parameterize by a Gauss-Hermite series. The modeling takes seeing convolution and pixel binning into account. The two-integral Jeans models suggest a black hole (BH) mass between 3 and 6x10⁸ M_☉, depending on the data set used to constrain the model, but they fail to fit the details of the observed kinematics. The three-integral models can fit all ground-based and HST data simultaneously, but only when a central BH is included. Models without BHs are ruled out to a confidence level of better than 99.73%. We determine a BH mass of 3.0^+1.7_–1.0x10⁸ M_☉, where the errors are the formal 68.3% confidence levels. This corresponds to 2.6% of the total mass of the bulge, making NGC 4342 one of the galaxies with the highest BH mass to bulge mass ratio currently known. The models that best fit the data do not have a two-integral phase-space distribution function. They have rather complex dynamical structures: the velocity anisotropies are strong functions of radius reflecting the multicomponent structure of this galaxy. When no central BH is included, the best-fit model tries to fit the high central velocity dispersion by placing stars on radial orbits. The high rotation velocities measured, however, restrict the amount of radial anisotropy such that the central velocity dispersion measured with the HST can be fit only when a massive BH is included in the models.