Echoes of self-interacting dark matter from binary black hole mergers

Dark matter (DM) environments around black holes (BHs) can influence their mergers through dynamical friction, causing gravitational wave (GW) dephasing during the inspiral phase. While this effect is well studied for collisionless dark matter (CDM), it remains unexplored for self-interacting dark matter (SIDM) due to the typically low DM density in SIDM halo cores. In this work, by considering BH mergers within SIDM spikes, which can arise from models with a massive force mediator, we show that the GWs emitted are dephased in a distinct manner. To incorporate the feedback of the BH orbital motion that can significantly modify the DM profiles, we use $N$-body simulations to analyze GW dephasing in binary BH inspirals within CDM and SIDM spikes. By tracking the binary's motion in different DM environments, we show that the Laser Interferometer Space Antenna (LISA) can observe GW dephasing arising from SIDM spikes in particular scenarios. Our results indicate that these observations offer a possibility of distinguishing between binary-BH inspirals in different DM environments.