Internal dynamics of highly flattened spheroidal systems

Schwarzschild's method has been employed to estimate the fraction of stars in retrograde orbits and the nature of the velocity ellipsoids in three well-observed galaxies, NGC 720, NGC 7785, and NGC 3115. It is assumed that the galaxies are oblate spheroids with r exp -2 radial mass density profiles but self-similar r exp -3 emission profiles. This method forces the projected velocity moments on the principal axes, normalized to the circular velocity, in the model to match corresponding observed quantities of real galaxies (except for NGC 3115, where the velocity moments on the major axis are replaced by those at 30 deg to the major axis to avoid contamination from the disk). This method also provides information on the circular velocity and M/R in these cases. All but one of the models built for these galaxies are dominated by orbit families with large amounts of angular momentum. The meridional velocity dispersion tensors are isotropic in most cases. The model for NGC 3115 requires that the circular velocity be 340 km/s, which is consistent with the value derived from observations of the stellar disk. For the presented model of NGC 720, more than 42 percent of the stars must be in retrograde orbits.