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Numerical tests of dynamical friction in gravitational inhomogeneous systems

In this paper, I test by numerical simulations the results of Del Popolo & Gambera (1998),dealing with the extension of Chandrasekhar and von Neumann's analysis of the statistics of the gravitational field to systems in which particles (e.g., stars, galaxies) are inhomogeneously distributed. The paper is an extension of that of Ahmad & Cohen (1974), in which the authors tested some results of the stochastic theory of dynamical friction developed by Chandrasekhar & von Neumann (1943) in the case of homogeneous gravitational systems. It is also a continuation of the work developed in Del Popolo (1996a,b), which extended the results of Ahmad & Cohen (1973), (dealing with the study of the probability distribution of the stochastic force in homogeneous gravitational systems) to inhomogeneous gravitational systems. Similarly to what was done by Ahmad & Cohen (1974) in the case of homogeneous systems, I test, by means of the evolution of an inhomogeneous system of particles, that the theoretical rate of force fluctuation d F/dt describes correctly the experimental one, I find that the stochastic force distribution obtained for the evolved system is in good agreement with the Del Popolo & Gambera (1998) theory. Moreover, in an inhomogeneous background the friction force is actually enhanced relative to the homogeneous case.