Precise analysis of gravitational waves from binary neutron star coalescence using Hilbert–Huang transform based on Akima spline interpolation

Abstract

Abstract The equation of state (EOS) information of neutron stars (NSs) can be obtained by analyzing the post-merger phases of gravitational waves resulting from the coalescence of NS binaries. In a previous study, we proposed a method to discriminate the EOS using the Hilbert–Huang transform (HHT). The HHT comprises empirical mode decomposition (EMD) and Hilbert spectrum analysis. An essential aspect of the EMD involves the generation of envelopes through interpolating extrema values. The original EMD (used in the previous study) utilizes cubic spline (CS) interpolation. However, the CS occasionally produces pseudo oscillations and overshoots that may decrease the performance of the EMD. In this study, we propose an extended version of the HHT by substituting Akima spline interpolation for the CS. We compared the ability of the original HHT (based on the CS) and the proposed HHT (based on the Akima spline) to discriminate the EOS. The results reveal that the proposed HHT yields a more precise analysis than the original HHT. With the proposed HHT, the number of events for discriminating the EOS is enhanced by a factor of 11.4.