Gravitational Magnus effect from a massive scalar field

The Magnus effect, in the context of fluid dynamics, is a force on a spinning object moving in a surrounding fluid that is perpendicular to its motion. In general relativity, an analogous force is also present on a spinning compact object that interacts gravitationally with a massive "cloud" of surrounding matter. This "gravitational Magnus effect" can be astrophysically relevant since it can affect the gravitational wave signals from extreme mass-ratio inspirals when the secondary spinning black hole moves in the presence of a dark matter cloud. We consider a scalar field dark matter model and simulate numerically the motion of spinning black hole immersed within a massive scalar field cloud using the GRChombo code. We extract the gravitational Magnus force backreaction on the black hole by tracking the momentum change of the scalar field. We find that this gravitational Magnus force scales linearly with the spin parameter a of the black hole up to a = 0.99, and that it also scales linearly with the speed v of the black hole up to v = 0.55. These results are consistent with previous theoretical calculations in the post-Newtonian framework. Future simulations with better relaxation schemes could be used to probe the v > 0.55 region of the parameter space, where deviations from the linear relation between the Magnus force and v may occur.