Dynamical friction in constant density cores: a failure of the Chandrasekhar formula

Using analytic calculations and N-body simulations we show that in constant density (harmonic) cores, sinking satellites undergo an initial phase of very rapid (super-Chandrasekhar) dynamical friction, after which they experience no dynamical friction at all. For density profiles with a central power law profile of log-slope, $-\alpha$, the infalling satellite heats the background and causes $\alpha$ to decrease. For $\alpha < 0.5$ initially, the satellite generates a small central constant density core and stalls as in the $\alpha = 0$ case. We discuss some astrophysical applications of our results to decaying satellite orbits, galactic bars and mergers of supermassive black hole binaries. In a companion paper we show that a central constant density core can provide a natural solution to the timing problem for Fornax's globular clusters.