On Schwarzschild's method for the construction of model galaxies

The method developed recently by Schwarzschild (1979, 1982) for the construction of model galaxies is formulated explicitly as a numerical method for the solution of the equations of galactic dynamics governing the equilibrium configurations of a stellar system. In this formulation, the method applies to systems in which the stellar orbits admit of three isolating integrals of the motion, and it provides numerical solutions for the distribution of stars in the phase space of a single star. The present version of Schwarzschild's method is illustrated with the construction of model galaxies with spherically symmetric mass distributions. In particular, a construction of Plummer's model tests the method on an exact solution of the equations of galactic dynamics. In spherical systems, many of the solutions of Schwarzshild's equations that are called basic solutions in the nomenclature of linear programming, can be interpreted as representing distribution functions in which the stars are confined to two-dimensional surfaces in the three-dimensional space of the isolating integrals.