Distinguishing dark matter halos with Extreme mass ratio inspirals

We study extreme mass-ratio inspirals (EMRIs) around a static, spherically symmetric massive black hole embedded in dark-matter (DM) halos with Hernquist, Burkert, and Navarro–Frenk–White (NFW) density profiles. The DM halo adds a gravitational force on the stellar-mass compact object (SCO), reducing the orbital period P; this reduction and the change in orbital precession depend on the combined parameter M/a₀² (halo mass M, scale length a0). The BH’s effective gravitational pull on the SCO is weakened only for the Hernquist model, slowing orbital motion, whereas Burkert and NFW halos accelerate evolution. In all three halo types the eccentricity decay is slowed. We compute the evolution of the semi-latus rectum and eccentricity, the number of orbital cycles, and GW waveform mismatches among the three halo types and against the vacuum case. Detectability thresholds are found at M_a0 > 10−5 for Hernquist, and M_a0 > 10−3 for both NFW and Burkert halos. Distinguishability between halo types requires M_a0 > 10−3 to separate NFW from Burkert, while NFW–Hernquist and Burkert–Hernquist can be distinguished at M_a0 > 10−5.