Dynamical friction for dark halo satellites: effects of tidal massloss   and growing host potential
  How fast a satellite decays its orbit depends on how slowly its mass is lost by tide. Motivated by inner halo satellite remnants like the Sgr and Omega Cen, we develop fully analytical models to study the orbital decay and tidal massloss of satellites. The orbital decay rate is often severely overestimated if applying the ChandraSekhar's formula without correcting for (a) the evaporation and tidal loss of the satellite and (b) 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 satellite's gravitational "wake", 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 modeled analytically for a satellite with the help of an empirical formula for the massloss history. The analytical model agrees with more numerical simulations of tidal massloss and dynamical friction. Rapid massloss due to increasing tides at ever smaller radius makes it less likely for streams or remnants of infalling satellites to intrude the inner halo (as the Sgr stream and oCen) than to stay in the outer halo (Magellanic stream), hence any intermediate-mass central black holes of the satellites are also likely "hung up" at large distances as well. To avoid "hung-up" the satellites might start with (i) pericenters much smaller than the typical distances to present-day observed satellites and with (ii) central density much higher than in the often seen finite density cores of observed satellites. 
HongSheng Zhao