Self-Interacting Dark Matter-Induced Dynamical Friction and Its Imprint on EMRI Gravitational Waves

Abstract

Extreme-mass-ratio inspirals (EMRIs) provide a promising probe of the dark matter environment surrounding massive black holes through their long-duration gravitational-wave signals. In this work, we investigate the influence of self-interacting dark matter (SIDM) on EMRI dynamics and gravitational-wave phase evolution. Motivated by the collisional Boltzmann description of SIDM, we construct a leading-order effective correction to the conventional Chandrasekhar dynamical-friction force, controlled by the momentum-transfer cross section $\sigma_T$ and the dimensionless collisionality parameter $n_\chi\sigma_T r=r/\lambda_{\rm mfp}$. We then compute the resulting orbital evolution, waveform modification, and accumulated gravitational-wave dephasing. In the enhanced-drag regime considered here, increasing the SIDM self-interaction strength increases the effective dynamical friction, accelerates the inspiral, and produces a progressively larger phase deviation relative to the collisionless dark matter case. We further distinguish the total dark-matter-induced dephasing relative to vacuum from the additional phase correction generated specifically by dark matter self-interactions. Our results demonstrate that the cumulative gravitational-wave phase of EMRIs can be sensitive to the microscopic momentum-transfer properties of dark matter, suggesting that future space-based detectors such as LISA may provide a complementary probe of SIDM in the vicinity of massive black holes.