Gravitational wave energy spectrum of a parabolic encounter

We derive an analytic expression for the energy spectrum of gravitational waves from a parabolic Keplerian binary by taking the limit of the Peters and Mathews spectrum for eccentric orbits. This demonstrates that the location of the peak of the energy spectrum depends primarily on the orbital periapse rather than the eccentricity. We compare this weak-field result to strong-field calculations and find it is reasonably accurate (∼10%) provided that the azimuthal and radial orbital frequencies do not differ by more than ∼10%. For equatorial orbits in the Kerr spacetime, this corresponds to periapse radii of r_p?20M. These results can be used to model radiation bursts from compact objects on highly eccentric orbits about massive black holes in the local Universe, which could be detected by the Laser Interferometer Space Antenna (LISA).