DYNAMIC FRICTION FROM FLUCTUATIONS IN STELLAR DYNAMIC-SYSTEMS

A test particle traveling through a collisionless gravitating background suffers a dissipative drag force known as dynamical friction. As with other dissipative forces, this friction must be related to fluctuations in the underlying medium (fluctuation-dissipation theorem). However, this long recognized aspect of the force did not easily yield to analysis until now, and Chandrasekhar's celebrated formula was obtained by considering momentum exchanges resulting from encounters between a test particle and field particles which were idealized as occurring sequentially. In this paper we return to the underlying basic physics and develop a theory of the interaction of the test particle with the stochastic force of the background. This enables us to derive in a unified way the Chandrasekhar formula for the friction (for the full range of m/M) and the heating of the particle by background fluctuations. This new approach shows that dynamical friction fits into the generic fluctuation-dissipation relation. It also readily suggests the modifications that would be required to treat dynamical friction and heating in an inhomogeneous background, as well as in the presence of initial correlations between background particles.