Gravitational waves from extreme mass ratio inspirals around rotating black holes surrounded by dark matter halo

Abstract

Dark matter (DM) has become one of the biggest mysteries in the universe. The next generation gravitatinal wave (GW) detector is designed to detect low-frequency GWs emanating from extreme-mass-ratio-inspiral systems (EMRIs), this provides possibilities to detect DM with low-frequency GWs. In this paper, we calculate the GWs emanating from EMRIs with central SBH being rotating BH surrounded by DM halo (DMBH) and study the effects of DM on the waveforms of GW. We give the orbit of the secondary body by Hamilton-Jacobi (HJ) method, and calculate GWs with numerical Kludge (NK) method. By comparing the waveforms of GWs of DMBH and that of Kerr BH, we find there exist dephasing between the two waveforms. Through calculating mismatch of the two waveforms it's found mismatch increases with the DM parameter $c_q$ but decreases with the DM parameter ${\omega }_q$. As $c_q$ increases or ${\omega }_q$ decreases, the indistinguishable lower bound may be exceeded, then the gravitational waveforms of DMBH and that of Kerr BH are distinguishable. This allows to distinguish the GWs of DMBH from that of Kerr BH and constrain DM parameters with the observation data of the next generation GW detectors. In addition, the dephasing of the two waveforms is found to increase with the eccentricity of orbit, so more eccentric orbits will help to constrain the DM parameters further.