From kinematics to dynamics in thin galactic discs

We present a method for recovering the distribution functions of edge-on th in axisymmetric discs directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the l ine-of-sight velocity distributions of the stars at different projected rad ii along the galaxy. If the gravitational potential is known, then the gene ral two-integral distribution function can be reconstructed using the shape s of the high-velocity tails of these line-of-sight distributions. If the w rong gravitational potential is adopted, then a distribution function can s till be constructed using this technique, but the low-velocity parts of the observed velocity distributions will not be reproduced by the derived dyna mical model. Thus, the gravitational potential is also tightly constrained by the observed kinematics.