Mapping stationary axisymmetric phase-space distribution functions by orbit libraries

This is the first of a series of papers dedicated to unveil 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. (in preparation). 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 on to the library we show that the resulting line-of-sight velocity distributions and internal velocity moments of the library match those directly derived from the DF to a precision better than that of present day observational errors. Second, by fitting libraries to the projected kinematics of the same DFs we show that the distribution function 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 achieved accuracy allows us to implement effective entropy-based regularisation to fit real, noisy and spatially incomplete data.