Gravitational Wave Imprints of Dark MatterAnnihilation: Probing Halo Structures throughEMRI Signals

Gravitational waves, as potential probes of dark matter halos, have received much attention recently. This paper investigates how the annihilation channels of dark matter particles — namely s-wave, p-wave, and d-wave — influence the spatial distribution characteristics of dark matter halos, thereby leaving observable imprints on the gravitational wave signals from Extreme Mass Ratio Inspiral (EMRI) systems. We construct dark matter halo density distribution models incorporating s-wave, p-wave, and d-wave annihilation channels. We derive the phase corrections to the frequency-domain gravitational waveforms by combining these models with the orbital evolution equations of EMRI systems. Our study reveals that s-wave annihilation leads to the formation of a flattened density region in the dark matter halo, while p-wave and d-wave annihilation primarily modify smaller-scale structures within the halo. These distinct dark matter halo configurations induce significantly different phase shifts in the gravitational waveforms, providing a new observational window to distinguish the scattering properties of dark matter particles. Future space-based gravitational wave detectors, such as LISA, are expected to provide constraints on small-scale dark matter halos and the fundamental properties of dark matter particles by accurately measuring the gravitational wave signal of EMRI systems. These findings not only offer new insights into the gravitational wave signatures of dark matter annihilation, but also have potential implications for indirect dark matter detection via gamma-ray or cosmic-ray observations, as the modified halo profiles may affect the expected annihilation signals in the electromagnetic spectrum.