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Schwarzschild modelling of elliptical galaxies and their black holes

This article describes the Schwarzschild orbit superposition method. It is the state-of-the-art dynamical modelling tool for early-type galaxies. Tests with analytic models show that masses and orbital anisotropies of not too face-on galaxies can be recovered with about 15 percent accuracy from typical observational data. Applying Schwarzschild models to a sample of Coma galaxies their dark matter halos were found to be 13 times denser than those of spirals with the same stellar mass. Since denser halos assembled earlier, this result indicates that the formation redshift 1+z of ellipticals is about two times higher than of spirals. Roughly half of the sample galaxies have halo assembly redshifts in agreement with their stellar-population ages. Galaxies where stars appear younger than the halos show strong phase-space density gradients in their orbital structure, indicative for dissipational evolution and possibly connected with secondary star-formation after the main halo assembly epoch. The importance of considering dark-matter in dynamical models aimed to measure black-hole masses is briefly discussed.