Emission and detection of ultra high frequency gravitational waves from highly eccentric orbits of compact binary systems

The ultrahigh frequency emission of gravitational waves by binary systems of black holes has recently been investigated in details in the framework of new experimental ideas around resonant cavities. In this article, we consider the case of elliptic trajectories. At fixed masses and frequency, we conclude that the total amount of energy radiated by the system within the bandwidth of the detector can be significantly higher than for circular orbits. However, owing to subtle experimental effects, the signal-to-noise ratio is, overall, a decreasing function of the eccentricity. Limits on the maximum distance at which a merging system of black holes can be detected derived are therefore not improved by considering elliptic trajectories, when compared to the circular case. The article is written as pedagogically as possible so as to be accessible to the nonfamiliar reader and possibly useful beyond the ultrahigh frequency case.