Frequency domain analysis of the gravitational wave energy loss in hyperbolic encounters

The energy radiated (without the 1.5PN tail contribution which requires a different treatment) by binary system of compact objects moving in hyperboliclike orbit is computed frequency domain through second post-Newtonian level as an expansion large-eccentricity parameter up to next-to-next-to-leading order, completing time corresponding information (fully known closed form at accuracy). spectrum contains quadratic products modified Bessel functions first kind (Bessel $K$ functions) with frequency-dependent order (and argument) already Newtonian level, so preventing direct evaluation Fourier integrals. However, tends zero for large eccentricities, allows analytical computation beyond lowest order.