Detecting dark matter halos with extreme mass-ratio inspirals

Abstract Extreme mass ratio inspirals (EMRIs), where a small compact object inspirals into a supermassive black hole, are excellent sources for the space-based laser interferometer gravitational wave (GW) detectors. The presence of the dark matter (DM) halo surrounding the supermassive black hole will influence the orbital evolution and emitted gravitational waveform of the binary. By direct observation of GW signals, we assess the detector's capability to detect whether an EMRI is immersed in a DM halo and to measure its characteristic spatial scale a 0 and mass M halo . Apart from the GW emission, the dynamical friction and accretion caused by the DM halo can also affect the dynamics of an EMRI, leaving detectable signatures in the emitted gravitational signal. We perform a Fisher-matrix error analysis to estimate the errors of parameters a 0 and M halo , as well as their correlation. The results show that the highly correlated parameters a 0 and M halo deteriorate the detector's ability to measure DM halo even though the dephasing and mismatch between signals with and without DM indicate much difference. The effects of the dynamical friction and accretion can break possible degeneracy between parameters a 0 and M halo , thus greatly decreasing the uncertainty by about one order of magnitude.