Profiling Dark Matter Spikes with Gravitational Waves from Accelerated Binaries

TL;DR

This paper proposes using gravitational wave signals from binary mergers near supermassive black holes to precisely measure dark matter density spikes, offering a new way to probe dark matter distribution independent of particle physics assumptions.

Contribution

It introduces a novel gravitational wave observational method to measure dark matter spike profiles around supermassive black holes with high precision.

Findings

Future LISA/DECIGO observations can measure spike slope $ ho ightarrow r^{- ext{gamma}_{sp}}$ with a few-percent accuracy.

The method detects a secular modulation in gravitational wave signals caused by the spike-induced acceleration.

This approach is insensitive to astrophysical confounders and does not depend on dark matter particle physics.

Abstract

Dark matter halos can develop a density spike, e.g., around a galactic supermassive black hole, with the profile $\rho \propto r^{-\gamma_{\rm sp}}$ determined both by the galaxy's formation history and the microphysics of dark matter. We show that future LISA/DECIGO observations, of intermediate/stellar-mass binary mergers inside the spike around the supermassive black hole, can measure $\gamma_{\rm sp}$ at a few-percent--level precision. The spike induces a distinctive time-dependent acceleration along the non-circular orbit taken by the binary's center of mass, which is observable as a secular modulation of the gravitational wave signal. This method -- insensitive to confounding astrophysical effects (dynamical friction, tidal effects, etc.) and not reliant on unknown dark matter particle physics -- provides a clean diagnostic of density spikes and a new probe of dark matter.