Asymmetry in the tidal tails of open star clusters from direct N-body integrations in Milgrom-law dynamics

Helmholtz-Institut für Strahlen- und Kernphysik, Nussallee 14-16, 53115 Bonn, Germany

^★ Corresponding author; jpa@hiskp.uni-bonn.de

Received: 24 August 2023
Accepted: 12 November 2024

Abstract

Context. Numerical simulations of star clusters in quasilinear modified Newtonian dynamics (QUMOND) orbiting in a Galactic disk potential show that the leading tidal arm of open star clusters typically contain more members than the trailing arm. However, these type of simulations are performed by solving the field equations of QUMOND and have already proven impractical for star cluster masses of around 5000 M_⊙. Nearby star clusters exhibit (maximum) masses of 1000 M_⊙ (or ≈1000 particles) and cannot be simulated reliably in field-theoretical formulations of modified Newtonian dynamics (MOND) at present.

Aims. Differences in the formation and evolution of tidal tails of open star clusters in the Newtonian and in the MONDian context are explored in the case of an equal-mass n = 400 particle cluster (M_tot = 200 M_⊙).

Methods. To handle particle numbers below the QUMOND-limit, we simulated the star cluster in Milgrom-law dynamics (MLD). Milgrom’s law 𝑔_N = µ(|a_M|/a₀)a_M has been postulated to be valid for discrete systems in vectorial form, while MLD resembles QUMOND in that the acceleration of a particle outside any isolated mass concentration scales inversely with the distance. However, in MLD, an internally Newtonian binary will follow a Newtonian rather than a MONDian path around the Galactic centre. To suppress the New- tonisation of compact subsystems in the star cluster, the gravitational force is softened below particle distances of 0.001 pc ≈ 206 AU. Thus, MLD can only be considered as an approximation of a full MOND-theoretical description of discrete systems that are internally in the MOND regime. The MLD equations of motion are integrated by the standard Hermite scheme that is generally applied to Newtonian N-body systems. In this work, we have extended this scheme to solve for the accelerations and jerks associated with Milgrom’s law.

Results. We found that the tidal tails of a low-mass star cluster are populated asymmetrically in the MLD treatment, similarly to what is seen in QUMOND simulations of higher mass star clusters. In the MLD simulations, the leading tail hosts up to twice as many members than the trailing arm, while the low-mass open star cluster dissolves approximately 25% faster than in the respective Newtonian case. Furthermore, the numerical simulations show that the Newtonian integrals of motion are not conserved in MLD. However, the case of an isolated binary in the deep MOND limit can be handled analytically. The velocity of the Newtonian centre of mass does not increase continuously, but instead it wobbles around the constantly moving MLD centre of mass.