Gravitational Wave Probes of Dark Matter Environments in Rotating Systems

Dark matter environments within extreme mass ratio inspiral systems are shown to impact GW emission significantly, mainly due to their effect on the geometry and through the dynamical friction effect felt by the secondary object. Such effects crucially depend on the density distribution of the dark matter environment, which has been shown to form local overdensity "spikes" near the central black hole. In astrophysical scenarios, the rotation of the central black hole also plays a key role in the formation and distribution of the spike. In our work, for the first time, we calculate the change in GWs due to dynamical friction felt by the secondary object moving through a DM spike sourced by rotating central supermassive black holes. We use a fully relativistic calculation to derive the spike profiles for various values of rotation parameter of the central BH and use the profiles to calculate resulting mismatch and dephasing in GW data using FastEMRIWaveform package for both prograde and retrograde motion. We also studied the effect of DF and rotation to look into the circularization of the orbits. As a part of this work, a weak field approximation is also employed to provide a semi-analytic treatment of the environment's impact on orbital dynamics.