Mapping stationary axisymmetric phase-space distribution functions by orbit libraries

This is the first of a series of papers dedicated to unveiling the mass composition and dynamical structure of a sample of flattened early-type galaxies in the Coma cluster. We describe our modifications to the Schwarzschild code of Richstone et al. Applying a Voronoi tessellation in the surface of section, we are able to assign accurate phase-space volumes to individual orbits and to reconstruct the full three-integral phase-space distribution function (DF) of any axisymmetric orbit library. Two types of tests have been performed to check the accuracy with which DFs can be represented by appropriate orbit libraries. First, by mapping DFs of spherical gamma-models and flattened Plummer models onto the library, we show that the resulting line-of-sight velocity distributions and internal velocity moments of the library match those derived directly from the DF to a precision better than that of present-day observational errors. Secondly, by fitting libraries to the projected kinematics of the same DFs, we show that the DF reconstructed from the fitted library matches the input DF to a rms of about 15 per cent over a region in phase space covering 90 per cent of the mass of the library. The accuracy achieved allows us to implement effective entropy-based regularization to fit real, noisy and spatially incomplete data.