A Linear and Quadratic Time-Frequency Analysis of Gravitational Waves from Core-collapse Supernovae

Recent core-collapse supernova (CCSN) simulations have predicted several distinct features in gravitational-wave (GW) spectrograms, including a ramp-up signature due to the g-mode oscillation of the protoneutron star (PNS) and an excess in the low-frequency domain (100 to ∼300 Hz) potentially induced by the standing accretion shock instability (SASI). These predictions motivated us to perform a sophisticated time-frequency analysis (TFA) of the GW signals, aimed at preparation for future observations. By reanalyzing a gravitational waveform obtained in a three-dimensional general-relativistic CCSN simulation, we show that both the spectrogram with an adequate window and the quadratic TFA separate the multimodal GW signatures much more clearly compared with a previous analysis. We find that the observed low-frequency excess during the SASI active phase is divided into two components, a stronger one at 130 Hz and an overtone at 260 Hz, both of which evolve quasistatically during the simulation time. We also identify a new mode with frequency varying from 700 to 600 Hz. Furthermore, we develop the quadratic TFA for the Stokes I, Q, U, and V parameters as a new tool to investigate the circular polarization of GWs. We demonstrate that the polarization states that randomly change with time after bounce are associated with the PNS g-mode oscillation, whereas a slowly changing polarization state in the low-frequency domain is connected to the PNS core oscillation. This study demonstrates the capability of sophisticated TFA to diagnose polarized CCSN GWs in order to explore their complex nature.