Echoes of Self-Interacting Dark Matter from Binary Black Hole Mergers

Abstract: 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, we show that SIDM models with a massive force mediator can support dense enough DM spikes, significantly affecting BH mergers and producing a distinct GW dephasing. Using ${N}$-body simulations, we analyze GW dephasing in binary BH inspirals within CDM and SIDM spikes. By tracking the binary's motion in different SIDM environments, we show that the Laser Interferometer Space Antenna (LISA) can distinguish DM profiles shaped by varying DM interaction strengths, revealing detailed properties of SIDM.