Accretion of a Satellite onto a Spherical Galaxy: Binary Evolution and Orbital Decay

We study the dynamical evolution of a satellite orbiting outside of acompanion spherical galaxy. The satellite is subject to a back-reaction forceresulting from the density fluctuations excited in the primary stellar system.We evaluate this force using the linear response theory developed in Colpi andPallavicini (1997). The force is computed in the reference frame comoving withthe primary galaxy and is expanded in multipoles. To capture the relevantfeatures of the physical process determining the evolution of the detachedbinary, we introduce in the Hamiltonian the harmonic potential as interactionpotential among stars. The dynamics of the satellite is computedself-consistently. We determine the conditions for tidal capture of a satellitefrom an asymptotic free state. If the binary comes to existence as a boundpair, stability against orbital decay is lost near resonance. The time scale ofbinary coalescence is computed as a function of the eccentricity and massratio. In a comparison with Weinberg's perturbative technique we demonstratethat pinning the center of mass of the galaxy would induce a much larger torqueon the satellite.Comment: 13 pages, Tex,+ 10 .ps figures Submitted to The Astrophysical Journa