Super-Chandrasekhar dynamical friction in a constant-density spherical star system

N-body modelling of massive body motion in constant density-cores shows deviations in the dynamical friction force from Chandrasekhar's formula. When the body orbit falls within the core, the body experiences a stage of enhanced friction after which the friction force becomes very low or zero. This effect takes place for circular as well as radial and elliptic orbits of the massive perturber. Previously developed perturbative treatment of dynamical friction in spherical systems cannot be directly applied to constant density cores because of the importance of non-linear resonant effects in this case. This feature is caused by the full resonance of the moving body with all the stars in the harmonic potential. There has been a successful attempt at semi-analytical treatment of the problem, but there remains a lack of any analytical description of this phenomenon. We study the motion of a massive point-like object in a strictly constant density sphere analytically and obtain a formula for the energy decay rate of the object at the stage of super-Chandrasekhar friction. We show that the dynamical friction force at this stage is half an order in Mobject/Mcore stronger than in Chandrasekhar's case. Our numerical simulations for both circular and radial orbits of the perturber reveal the stage of enhanced friction and the stalling stage afterwards. Dependence of the decay time at the super-Chandrasekhar stage on the perturber mass confirms our analytical relationship. We compare our analytical formula with N-body results of other authors for the enhanced friction stage and find good agreement.