Dynamical friction from scalar dark matter in the relativistic regime

TL;DR

This paper investigates the relativistic dynamical friction exerted by scalar dark matter on black holes, providing numerical results that could impact gravitational wave signal analysis during black hole inspirals.

Contribution

It offers the first numerical study of relativistic dynamical friction from scalar dark matter, including complex and real scalar fields, with implications for gravitational wave dephasing.

Findings

Relativistic scaling of dynamical friction is similar to that in supersonic fluids.

Complex scalars produce a time-averaged force, while real scalars cause oscillating forces.

Results can inform estimates of gravitational wave dephasing in black hole inspirals.

Abstract

Light bosonic scalars (e.g. axions) may form clouds around black holes via superradiant instabilities, or via accretion if they form some component of the dark matter. It has been suggested that their presence may lead to a distinctive dephasing of the gravitational wave signal when a small compact object spirals into a larger black hole. Motivated by this, we study numerically the dynamical friction force on a black hole moving at relativistic velocities in a background scalar field with an asymptotically homogeneous energy density. We show that the relativistic scaling is analogous to that found for supersonic collisional fluids, assuming an approximate expression for the pressure correction which depends on the velocity and scalar mass. While we focus on a complex scalar field, our results confirm the expectation that real scalars would exert a force which oscillates between positive and negative values in time with a frequency set by the scalar mass. The complex field describes the time averaged value of this force, but in a real scalar the rapid force oscillations could in principle leave an imprint on the trajectory. The approximation we obtain can be used to inform estimates of dephasing in the final stages of an extreme mass ratio inspiral.