Made-to-measure dark matter haloes, elliptical galaxies and dwarf galaxies in action coordinates

We provide a family of action-based distribution functions (DFs) for the double power-law family of densities often used to model galaxies. The DF itself is a double power law in combinations of the actions, and reduces to the pure power-law case at small and large radii. Our method enables the velocity anisotropy of the model to be tuned, and so the anisotropy in the inner and outer parts can be specified for the application in hand. We provide self-consistent DFs for the Hernquist and Jaffe models - both with everywhere isotropic velocity dispersions, and with kinematics that gradually become more radially anisotropic on moving outwards. We also carry out this exercise for a cored dark matter model. These are tailored to represent dark haloes and elliptical galaxies, respectively, with kinematic properties inferred from simulations or observational data. Finally, we relax a cored luminous component within a dark matter halo to provide a self-consistent model of a dwarf spheroidal embedded in dark matter. The DFs provide us with non-rotating spherical stellar systems, but one of the virtues of working with actions is the relative ease with which such models can be converted into axisymmetry and triaxiality.