Toward an Alternative Way of Looking at Elliptical Galaxies: Case Studies for NGC 4649 and NGC 7097

In this paper we consider three-integral axisymmetric models for NGC 4649 and NGC 7097, addressing the question of the presence of dark matter in these elliptical galaxies. The data for NGC 7097 can be modeled without a dark matter halo. The central region of NGC 4649 could be hosting a black hole. The kinematical data of NGC 4649 are not inconsistent with a constant mass-to-light ratio model, but a dynamical model with a moderate amount of dark matter better reproduces the observed anisotropy on the major axis. In addition, we look more closely at the issue of the classification of elliptical galaxies. Both galaxies can be placed in different families of elliptical galaxies based on the isophote shape. In this paper we set out to investigate whether the kinematic information can be used to specify a second classification parameter. We propose the use of normalized distribution functions, which are the three-integral distribution functions divided by the two-integral model (constructed from photometry alone), and argue why this is an efficient way of presenting the dynamics of elliptical galaxies. We show that they can be used to characterize the rotational state of a galaxy in a more specific way than merely indicating the amount of rotation or counterrotation. Furthermore, the distribution function for NGC 7097 suggests that the counterrotation is caused by stars spread over large radii in the galaxy, implying that this phenomenon is not related to a compact group of stars. Hence, the origin of the counterrotation should not be found in a recent merger in the first place. This shows that it is important to construct dynamic models with a distribution function. The distribution function is the tool used to visualize structure in phase space, which is the only stellar dynamic remnant of galaxy formation.