Dynamical friction in the quasi-linear formulation of modified Newtonian dynamics (QuMOND)

Aims. We explore the dynamical friction on a test mass in gravitational systems in the quasi-linear formulation of modified Newtonian dynamics (QuMOND). Methods. Exploiting the quasi-linearity of QuMOND, we derived a simple expression for the dynamical friction in akin to its Newtonian counterpart in the standard Chandrasekhar derivation. Moreover, adopting a mean field approach based on the Liouville equation, we were able to obtain a more rigorous (albeit in integral form) dynamical friction formula that can be evaluated numerically for a given choice of the QuMOND interpolation function. Results. We find that our results are consistent with those of previous works. We observe that the dynamical friction is stronger in MOND with respect to a baryon-only Newtonian system with the same mass distribution. This amounts to a correction of the Coulomb logarithmic factor via additional terms that are proportional to the MOND radius of the system. Moreover, with the aid of simple numerical experiments, we confirm our theoretical predictions and those of previous works based on MOND.