  Context. Merging compact objects such as binary black holes provide a
promising probe for the physics of dark matter (DM). The gravitational waves
emitted during inspiral potentially allow to detect DM spikes around black
holes. This is because the dynamical friction force experienced by the
inspiraling black hole alters the orbital period and thus the gravitational
wave signal. Aims. The dynamical friction arising from DM can potentially
differ from the collisionless case when DM is subject to self-interactions.
This paper aims to understand how self-interactions impact dynamical friction.
Methods. To study the dynamical friction force, we use idealized N-body
simulations, where we include self-interacting dark matter. Results. We find
that the dynamical friction force for inspiraling black holes would be
typically enhanced by DM self-interactions compared to a collisionless medium
(ignoring differences in the DM density). At lower velocities below the sound
speed, we find that the dynamical friction force can be reduced by the presence
of self-interactions. Conclusions. DM self-interactions have a significant
effect on the dynamical friction for black hole mergers. Assuming the
Chandrasekhar formula may underpredict the deceleration due to dynamical
friction.
