Dynamical constant mass-to-light ratio models of NGC 5128

Context. The existence and amount of dark matter in early-type galaxies remains a hotly debated topic. We study dynamical models of NGC 5128, which do not include dark matter, to test the predictions of different constant mass-to-light models. Aims. We use the measurements of the radial velocities of the planetary nebulae in NGC 5128 to test the predictions of Newtonian constant mass-to-light ratio models and we also extend our study to different MOND models. Methods. The planetary nebulae of NGC 5128 were used as a tracer of the galaxy's gravitational potential. The Jeans equation was calculated for both the Newtonian mass-follows-light and the MOND approaches. Spherical symmetry is assumed and the calculations are performed for both isotropic and anisotropic cases. Results. We solved the Jeans equation in spherical approximation and found that the isotropic Newtonian mass-follows-light models without dark matter may provide successful fits out to 6.4R(e); to obtain a good fit in the outermost region (similar to 10.7R(e)) one needs either dark matter or tangential anisotropies. Concerning MOND models we found that no isotropic MOND model without dark matter can provide a successful fit interior to similar to 6.4R(e); for the anisotropic MOND models interior to similar to 40 arcmin only standard MOND model with tangential anisotropies can provide a successful fit of the observed velocity dispersion without the need of dark matter.