Power spectrum of gravitational waves from unbound compact binaries

Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity {\epsilon} = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large {\epsilon} limit with the formula given by Turner.