Numerical Solutions of the External Field Effect on the Radial Acceleration in Disk Galaxies

In modified Newtonian dynamics (MOND)-based theories, the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an external field effect (EFE). The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies, the EFE can induce warps and modify the rotational speeds. Due to the nonlinearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two nonrelativistic Lagrangian theories of MOND: the Aquadratic-Lagrangian theory (AQUAL) and Quasilinear MOND (QUMOND). For AQUAL, we consider only the axisymmetric field configurations with the external field along the disk axis, or a spherical galaxy with test-particle orbits inclined to the external field. For the more manageable QUMOND, we also calculate the three-dimensional field configurations, with the external field inclined to the disk axis. We investigate in particular to what degree an external field modifies the quasi-flat part of rotation curves. While our QUMOND results agree well with published numerical results in QUMOND, we find that AQUAL predicts weaker EFE than published AQUAL results. However, AQUAL still predicts stronger EFE than QUMOND, which demonstrates current theoretical uncertainties. We also illustrate how the MOND prediction on the rising part of the rotation curve, in the inner parts, depends largely on disk thickness but only weakly on a plausible external field for a fixed galaxy model. Finally, we summarize our results for the outer parts as an improved, approximate analytic expression.

Automated summary

In theories based on modified Newtonian dynamics (MOND), the strong equivalence principle is broken in a unique way, resulting in the action of an external field effect (EFE). Research shows that even a constant external field can affect the internal dynamics of a self-gravitating system, leading to changes in rotational speeds in disk galaxies. Numerical studies provide insights into how external fields modify the quasi-flat part of rotation curves.