Orbital decay of satellite galaxies in spherical systems

The orbital-decay rate of a dwarf satellite moving in a spherical parent galaxy is considered on the basis of a theory of dynamical friction applicable to spherical systems, in which the orbits are determined exactly in a given spherical potential U(r). The spherical theory avoids the drag-force divergence that exists in Chandrasekhar's theory (CT), and the results may be regarded as determining the logarithimic factor appearing in CT. For a dwarf galaxy modeled by a Plummer law with a core radius gamma(rs) moving in a circular orbit in a singular isothermal sphere at radius rs, the logarithmic factor is ln Lambda = ln (0.75/gamma), corresponding to p-max = 1.2(rs). The response density of the sphere to the satellite (the satellite wake) is computed and compared with the wake in the infinite homogeneous case.