Dynamical friction for dark halo satellites: effects of tidal mass loss and growing host potential

Motivated by observations of inner halo satellite remnants like the Sgr stream and omega Centauri, we develop fully analytical models to study the orbital decay and tidal mass loss of satellites on eccentric orbits in an isothermal potential of a host galaxy halo. The orbital decay rate is often severely overestimated if applying Chandrasekhar's formula without correcting for (i) the evaporation and tidal loss of the satellite, and (ii) the contraction of satellite orbits due to adiabatic growth of the host galaxy potential over the Hubble time. As a satellite migrates inwards, the increasing halo density affects the dynamical friction in two opposite ways: (1) it boosts the number of halo particles swept in the gravitational 'wake' of the satellite, hence increasing the drag on the satellite, and (2) it boosts the tide which 'peels off' the satellite, and reduces the amplitude of the wake. These competing processes can be modelled analytically for a satellite with the help of an empirical formula for the mass-loss history. The analytical model agrees with more traditional numerical simulations of tidal mass loss and dynamical friction. Rapid mass loss due to increasing tides at smaller and smaller radius makes it less likely for streams or remnants of infalling satellites to intrude into the inner halo (like the Sgr stream and Centauri) than to stay in the outer halo (like the Magellanic stream), hence any intermediate-mass central black holes of the satellites are also probably 'hung up' at large distances as well. It is difficult for the black holes of the satellites to come close enough to merge into the supermassive black hole in the centre of the host potential unless the satellites started with (i) pericentres much smaller than the typical distances to present-day observed satellites, and (ii) central density much higher than in the often seen finite-density cores of observed satellites.