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

¹ CNR-ISC, Via Madonna del Piano 17, 50022 Sesto Fiorentino, Italy
² INAF-Osservatorio Astronomico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
³ Dipartimento di Fisica e Astronomia, Università di Firenze & INFN-Sezione di Firenze, Via Sansone 1, 50022 Sesto Fiorentino, Italy
⁴ Dipartimento di Fisica ”Giuseppe Occhialini”, Università di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
e-mail: federico.re@unimib.it
⁵ INFN-Sezione di Milano, Via Celoria 15, 20133 Milano, Italy
⁶ Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/A, 41125 Modena, Italy
e-mail: caterina.chiari@unimore.it
⁷ CNR-NANO, Via Campi 213/A, 41125 Modena, Italy

Received: 29 April 2024
Accepted: 19 June 2024

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 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.