Refining dynamical-friction feedback on dark-matter distributions surrounding intermediate mass-ratio inspirals

Massive black holes can grow within dark-matter distributions to create dense dark-matter spikes. When a lighter black hole inspirals around the massive black hole with dark matter, the binary's dynamics and gravitational wave signal will deviate from those of a vacuum inspiral. The effects of the dark-matter distribution will be imprinted on the gravitational-wave signal during the binary's inspiral, and the dark-matter distribution will evolve during the inspiral; thus, the binary and dark matter are coupled and must be jointly evolved. Prior work has formulated a feedback prescription and demonstrated that feedback onto the dark matter from dynamical friction can be significant. However, the feedback formalism was not proven to satisfy energy conservation (namely, the energy losses from dynamical friction on the binary are balanced by an equal and opposite energy gain in the dark-matter distribution). In this talk, I will present modifications to the feedback formalism that allow energy conservation to be verified, and which can speed up the coupled evolution of the binary and dark matter.