Drag on a satellite moving across a spherical galaxy. I. Tidal and frictional forces in shortlived encounters

Abstract

We derive a formalism, within the theory of linear response, for the analysis of the interaction of a satellite (the perturber) with a spherical galaxy whose equilibrium is described by a one-particle distribution function. We compute the formal expression of the force on the satellite including the self-gravity of the stars and the shift of the stellar center of mass. We apply the perturbative technique to the case of a satellite moving at high speed across a stellar system and find a natural decomposition of the force into a global component resulting from the tidal interaction and a component that is related to dynamical friction. When the satellite orbits outside the galaxy, we derive the force in the impulse approximation. In penetrating shortlived encounters, the wake excited in the density field is responsible for most of the deceleration. We find that dynamical friction rises from a memory effect involving only those stars perturbed along the path. The force can be written in terms of an effective Coulomb logarithm which now depends on the dynamical history. It is derived for two simple equilibrium density distributions. In the case of a homogeneous cloud, we compute the total energy loss: Tides excited by the satellite in the galaxy reduce the value of the energy loss by friction.