Dynamical Friction in presence of a mass spectrum

The analytical generalization of the classical dynamical friction formula (derived under the assumption that all the field particles have the same mass) to the case in which the masses of the field particles are distributed with a mass spectrum is presented. Two extreme cases are considered: in the first, energy equipartition is assumed, in the second all the field particles have the same (Maxwellian) velocity distribution. Three different mass spectra are studied in detail, namely the exponential, discrete (two components), and power-law cases. It is found that the dynamical friction deceleration can be significantly stronger than in the equivalent classical case, with the largest differences (up to a factor of 10 or more in extreme cases) arising for test particle velocities comparable to the mass-averaged velocity dispersion of the field particles. The present results are relevant to our understanding of the dynamical evolution of globular clusters, in particular in the modelization of mass segregation and sedimentation of Blue Straggler stars and Neutron stars, and for the study of binary black holes in galactic nuclei.