Augmented analytic kludge waveform with quadrupole moment correction

Abstract: One of the most important sources for future space-borne gravitational wave detectors such as TianQin and LISA is EMRI. It happens when a stellar orgin compact object orbiting around a massive black hole(MBH) in the center of galaxies and has many benefits in the study of astrophysics and fundamental theories. One of the most important objectives is to test the no-hair theorem by measuring the quadrupole moment of the MBH. This requires us to estimate the parameters of an EMRI system accurately enough, which means we also need an accurate waveform templet for this process. Based on the fast and fiducial augmented analytic kludge (AAK) waveform for the standard Kerr black hole, we develop a waveform model for a metric with non-Kerr quadrupole moment. We also analyze the accuracy of parameter estimation for different sources and detectors.