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

TL;DR

This paper derives and tests formulas for dynamical friction in Quasi-linear Modified Newtonian Dynamics (QuMOND), showing it is stronger than in Newtonian gravity and providing numerical validation of the theoretical predictions.

Contribution

It introduces a simple and a more rigorous integral formula for dynamical friction in QuMOND, extending previous work and enabling numerical evaluation.

Findings

Dynamical friction is stronger in MOND than in Newtonian systems with the same mass.

The Coulomb logarithm correction involves extra terms proportional to the MOND radius.

Numerical experiments confirm the theoretical predictions of increased dynamical friction in MOND.

Abstract

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 derive 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 obtain a more rigorous (though in integral form) dynamical friction formula that can be evaluated numerically for a given choice of the QuMOND interpolation function. Results. Consistently with previous work, we observe that 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 extra terms 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 work on MOND.