Evidence for a massive black hole in the S0 galaxy NGC 4342

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 constr uct simple two-integral Jeans models as well as fully general, three-integr al models. The latter are built using a modified version of Schwarzschild's orbit-superposition technique developed by Rix et al. and Cretton et al. T hese models allow us to reproduce the full line-of-sight velocity distribut ions, or "velocity profiles" (VPs), which we parameterize by a Gauss-Hermit e series. The modeling takes seeing convolution and pixel binning into acco unt. The two-integral Jeans models suggest a black hole (BH) mass between 3 and 6 x 10(8) M-., depending on the data set used to constrain the model, but they fail to fit the details of the observed kinematics. The three-inte gral 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 confid ence level of better than 99.73%. We determine a BH mass of 3.0(-1.0)(+1.7) x 10(8) 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 d istribution function. They have rather complex dynamical structures: the ve locity anisotropies are strong functions of radius reflecting the multicomp onent structure of this galaxy. When no central BH is included, the best-fi t 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 m easured with the HST can be fit only when a massive BH is included in the m odels.