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We provide a family of action-based distribution functions (DFs) for thedouble-power law family of densities often used to model galaxies. The DFitself is a double-power law in combinations of the actions, and reduces to theknown limits in the case of a pure power-law at small and large radii. Ourmethod enables the velocity anisotropy of the model to be tuned, and so theanisotropy in the inner and outer parts can be specified for the application inhand. We provide self-consistent DFs for the Hernquist and Jaffe models - bothwith everywhere isotropic velocity dispersions, and with kinematics thatgradually becomes more radially anisotropic on moving outwards. We also carryout this exercise for a cored dark-matter model. These are tailored torepresent dark haloes and elliptical galaxies respectively with kinematicproperties inferred from simulations or observational data. Finally, we relax acored luminous component within a dark matter halo to provide a self-consistentmodel of a dwarf spheroidal embedded in dark matter. The DFs provide us withnon-rotating spherical stellar systems, but one of the virtues of working withactions is the relative ease with which such models can be converted intoaxisymmetry and triaxiality.

Made-to-Measure Dark Matter Haloes, Elliptical Galaxies and Dwarf Galaxies in Action Coordinates