Mapping out peaks in the spectra of highly eccentric orbits of EMRI gravitational wave signals for LISA

Equatorial orbits of extreme mass ratio inspirals (EMRIs) are a potential source for LISA, the proposed gravitational wave detector. This project aims to find the shape of the gravitational wave (GW) spectrum from such sources. This is done by implementing a frequency domain, Teukolsky based code that can calculate the highly eccentric orbits from the capture of compact objects by a SMBH. In order to save on expensive computation time, it is important to anticipate the frequencies which need to be calculated to accurately characterize each spectrum. Previous studies have shown that peaks of the radial harmonic mode should follow a predictable pattern. We systematically explore the parameter space to predict where the peak mode (kmax) is going to be so that negligible modes can be skipped.