Probing the halo of Centaurus A: a merger dynamical model for the PN population

Photometry and kinematics of the giant elliptical galaxy NGC~5128 (Centaurus~A) based on planetary nebulae observations (Hui~\etal 1995) are used to build dynamical models which allow us to infer the presence of a dark matter halo. To this end, we apply a Quadratic Programming method. Constant mass-to-light ratio models fail to reproduce the major axis velocity dispersion measurements at large radii: the profile of this kind of models falls off too steeply when compared to the observations, clearly suggesting the necessity of including a dark component in the halo. By assuming a mass-to-light ratio which is increasing with radius, the model satisfactorily matches the observations. The total mass for the best fit model is $\sim4\times10^{11}M_\odot$ of which about 50\% is dark matter. However, models with different total masses and dark halos are also consistent with the data; we estimate that the total mass of Cen~A within 50~kpc may vary between $3\times10^{11}M_\odot$ and $5\times10^{11}M_\odot$. The best fit model consists of 75\% of stars rotating around the short axis $z$ and 25\% of stars rotating around the long axis $x$. Finally, the morphology of the projected velocity field is analyzed using Statler's classification criteria (Statler 1991). We find that the appearance of our velocity field is compatible with a type 'Nn' or 'Nd'.