Visualization of time-frequency structures in gravitational wave signals

Abstract

The gravitational wave signals produced by the coalescence of compact binaries progress through three stages: inspiral, merger, and postmerger. The evolution of their frequency follows a slow build up during the inspiral that peaks at merger, forming the characteristic "chirp" pattern in the signal's time-frequency map. Herein we introduce a framework for localizing further characteristic structures in the time-frequency space of gravitational wave signals using the continuous wavelet transform. We consider two example cases where there are specific patterns in the postmerger stage of the signal that are rich with information on the physical nature of the source: highly-inclined black hole binaries with asymmetric mass ratio, and neutron star binaries with postmerger remnant oscillations. It is demonstrated that the choice of quality factor $Q$ plays a central role in distinguishing the postmerger features from that of the inspiral, with black hole systems preferring lower $Q$ and neutron star systems preferring higher $Q$. Furthermore, we demonstrate the use of chirplets as the wavelet transform basis, which allow for manipulation of structure in the time-frequency map.