Detectability of hyperbolic encounters of compact stars with ground-based gravitational waves detectors

Gravitational wave (GW) astronomy promises to observe different kinds of astrophysical sources. Here we explore the possibility of detection of GWs from hyperbolic interactions of compact stars with ground-based interferometric detectors and estimate detection rates for such events. It is believed that a closed cluster, such as a globular cluster, can be a primary source for these interactions. While a rigorous rate estimation calls for more extensive relativistic studies, here, for a reasonable set of parameters well within the astrophysical realm, and considering local geometry within the cluster for such interactions as well as realistic initial conditions, our conservative estimates show that these events may be detectable by the present (with ongoing upgrades) and next-generation ground-based observatories. Some of the implications pertaining to this formalism are represented along with comparisons with the existing literature. In practice, actual detection rates can significantly surpass the estimated average rates, since the chances of finding outliers in a very large population can be high. Such observations (or, no observation) will provide an estimate of isolated compact stars in the universe, which cannot be directly estimated from the observations of binary mergers, taking us one step closer to address a fundamental question, how many black holes and neutron stars are there in the observable universe.