Examining the effects of dark matter spikes on eccentric intermediate mass ratio inspirals using N-body simulations

Recent studies suggest that dark matter (DM) spikes around intermediate-mass black holes could cause observable dephasing in gravitational wave (GW) signals from Intermediate Mass Ratio Inspirals (IMRIs). Previous research primarily used non-self-consistent analytic methods to estimate the impact of DM spikes on eccentric IMRIs. Our study provides the first self-consistent treatment of this phenomenon using $N$-body simulations, incorporating Post-Newtonian effects up to the 2.5 order for accurate and robust results. Contrary to prior works, which posited that the cumulative effect of two-body encounters (dynamical friction; DF) is the primary mechanism for energy dissipation, we reveal that a three-body effect (slingshot mechanism) plays a more significant role in driving the binary system's energy loss and consequent orbital shrinkage. We find that binaries counter-rotating with respect to the DM spike merge faster, while co-rotating binaries merge slower, contrary to expectations from the DF theory. Using Fokker-Planck methods, we also assess the presence and detectability of spikes in realistic environments. When interacting with surrounding materials, DM spikes can have shallower slopes and lower densities than previously considered, leading to smaller signals and lower detection prospects via dephasing. Our results suggest that `deshifting' rather than dephasing might be a more optimistic signature, as it is more robust even in low-density environments.