Application of the Hilbert-Huang transform for analyzing standing-accretion-shock-instability induced gravitational waves in a core-collapse supernova

Abstract

Through numerical simulations, it is predicted that the gravitational waves (GWs) reflect the characteristics of the core-collapse supernova (CCSN) explosion mechanism. There are multiple GW excitation processes that occur inside a star before its explosion, and it is suggested that the GWs originating from the CCSN have a mode for each excitation process in terms of time-frequency representation. Therefore, we propose an application of the Hilbert-Huang Transform (HHT), which is a high-resolution time-frequency analysis method, to analyze these GW modes for theoretically probing and increasing our understanding of the explosion mechanism. The HHT defines frequency as a function of time, and is not bound by the trade-off between time and frequency resolutions.In this study, we analyze a gravitational waveform obtained from a three-dimensional generalrelativistic CCSN model that showed a vigorous activity of the standing-accretion-shock-instability (SASI). We succeed in extracting the SASI induced GWs with high resolution on a time-frequency representation using the HHT and we examine their instantaneous frequencies.

Core-collapse supernova simulations and the formation of neutron stars, hybrid stars, and black holes

“…In the late post bounce phase t pb 600 ms, the spectrogram shows a wide band emission ranging from 300 Hz to a few kHz. Since we use a simple short time Fourier analysis to obtain the spectrogram, we need to apply sophisticated analysis methods, such as S-method (Kawahara et al 2018), the Hilbert-Huang transform (Takeda et al 2021), or non-harmonic analysis (Yanagisawa et al 2019) to determine more detailed peak frequency.…”