A semi-analytic dynamical friction model for cored galaxies

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We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density cores being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts et al. (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc << 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.