Gravitational wave energy spectrum of a parabolic encounter

Understand

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 Matthews 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 rp > 20M.