Extreme mass ratio inspirals in galaxies with dark matter halos
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Using an analytic, static, and spherically symmetric metric for a Schwarzschild black hole immersed in a dark matter (DM) halo with the Hernquist-type profile, we derive analytic expressions for the orbital period and precession of eccentric extreme mass ratio inspirals (EMRIs) surrounded by DM halos, and we show how the precession rates decrease and even undergo a prograde-to-retrograde precession transition if the density of DM halo is large enough. The presence of local DM halos also retards the decrease of the semi-latus rectum and the eccentricity. The orbital evolution of EMRIs immersed in DM halos is then calculated numerically by considering the combined effects of gravitational radiation reaction, dynamical friction, and accretion. Comparing the number of orbital cycles accumulated over a one-year evolution for EMRIs with and without DM halos, we find that DM halos with compactness as small as $10^{-5}$ can be detected. From the mismatch between gravitational waveforms of EMRIs with and without DM halos, we show that EMRIs in galaxies can be used to probe the existence of DM halos and detect the compactness of DM halos as small as $10^{-5}$. Employing the Fisher information matrix method, we find that larger compactness and density values of DM halos help to reduce the estimation error of parameters and further break the degeneracy between the parameters.
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