The influence of mass-loss from a star cluster on its dynamical friction - I. Clusters without internal evolution

Many Local Group dwarf spheroidal galaxies are found in the Galactic halo along great circles in the sky. Some of these stellar systems are thought to be the fragments of larger parent galaxies which have once intruded into and were torn apart by the tide of the Galaxy. Supporting evidence for tidal disruption is found in the form of stellar tidal bridges and tails along the orbits of some dwarf galaxies and globular clusters. In this study, we investigate the influence of mass-loss from star clusters or dwarf galaxies on the rate of their orbit decay due to the effect of dynamical friction. Using a series of numerical N-body simulations, we show that stars, which become unbound from their host systems, but remain in their vicinity and share their orbits, still contribute to the mass responsible for the dynamical friction. As a rule-of-thumb, the magnitude of dynamical friction at any instance can be approximated by the bound mass plus half of the mass which has already become unbound during the proceeding Galactic orbit. Based on these results, we suggest the tidal disruption of relatively massive satellite stellar systems may be more abrupt than previously estimated.