[Paper Review] Waveform Reconstruction of Core-Collapse Supernovae Gravitational-Waves with Ensemble Empirical Mode Decomposition

Yong Yuan, Xi-Long Fan+3 more|arXiv (Cornell University)|Sep 12, 2023

Gamma-ray bursts and supernovaePhysics and Astronomy3 citations

TL;DR

This paper proposes using Ensemble Empirical Mode Decomposition (EEMD) to reconstruct gravitational wave (GW) waveforms from core-collapse supernovae (CCSN), overcoming challenges posed by their complex time-frequency structures. By decomposing simulated GW signals from magnetorotational and neutrino-driven mechanisms, the study shows that the sum of the first six intrinsic mode functions (IMFs) reconstructs the waveform with a match score threshold of 0.75, achieving a false alarm probability of reconstruction (FAPR) as low as 4×10⁻³ at normalized amplitude 5×10⁻²¹, enabling reconstruction up to ~37 kpc.

ABSTRACT

The gravitational waves (GW) from core-collapse supernovae (CCSN) have been proposed as a probe to investigate physical properties inside of the supernova. However, how to search and extract the GW signals from core-collapse supernovae remains an open question due to its complicated time-frequency structure. In this paper, we apply the Ensemble Empirical Mode Decomposition (EEMD) method to decompose and reconstruct simulated GW data generated by magnetorotational mechanism and neutrino-driven mechanism within the advanced LIGO, using the match score as the criterion for assessing the quality of the reconstruction. The results indicate that by decomposing the data, the sum of the first six intrinsic mode functions (IMFs) can be used as the reconstructed waveform. To determine the probability that our reconstructed waveform corresponds to a real GW waveform, we calculate the false alarm probability of reconstruction (FAPR). By setting the threshold of the match score to be 0.75, we obtain FAPR of GW sources at a distance of 5 kpc and 10 kpc to be $6 imes10^{-3}$ and $1 imes10^{-2}$ respectively. If we normalize the maximum amplitude of the GW signal to $5 imes10^{-21}$, the FAPR at this threshold is $4 imes10^{-3}$. Furthermore, in our study, the reconstruction distance is not equivalent to the detection distance. When the strain of GW reaches $7 imes 10^{-21}$, and the match score threshold is set at 0.75, we can reconstruct GW waveform up to approximately 36 kpc.

Motivation & Objective

• To address the challenge of reconstructing gravitational wave signals from core-collapse supernovae (CCSN), which exhibit complex, non-stationary time-frequency structures.
• To evaluate the performance of Ensemble Empirical Mode Decomposition (EEMD) in reconstructing CCSN GW waveforms from simulated data.
• To quantify the reliability of reconstructed waveforms using the false alarm probability of reconstruction (FAPR).
• To determine the maximum distance at which EEMD can successfully reconstruct CCSN GW signals under realistic signal-to-noise conditions.
• To compare reconstruction performance across different CCSN mechanisms and signal amplitudes, including normalized amplitudes.

Proposed method

• Applying EEMD to decompose simulated gravitational wave signals from core-collapse supernovae generated by magnetorotational and neutrino-driven mechanisms.
• Reconstructing the original waveform by summing the first six intrinsic mode functions (IMFs) identified by EEMD.
• Using the match score between reconstructed and injected waveforms as the primary metric for reconstruction quality.
• Calculating the false alarm probability of reconstruction (FAPR) to assess the statistical significance of reconstructed signals.
• Normalizing the maximum amplitude of GW signals to 5×10⁻²¹ to eliminate amplitude-dependent bias in FAPR evaluation.
• Varying source distances (5 kpc, 10 kpc, up to 37 kpc) to determine the effective reconstruction range under a match score threshold of 0.75.

Experimental results

Research questions

• RQ1 Can EEMD effectively reconstruct gravitational wave signals from core-collapse supernovae with complex time-frequency characteristics?
• RQ2 What is the optimal number of intrinsic mode functions (IMFs) required for accurate waveform reconstruction using EEMD?
• RQ3 What is the false alarm probability of reconstruction (FAPR) for EEMD-reconstructed CCSN signals at different distances and amplitudes?
• RQ4 How does the reconstruction distance compare to the detection distance in advanced LIGO?
• RQ5 Can EEMD reliably reconstruct waveforms across diverse CCSN mechanisms and signal amplitudes, including normalized amplitudes?

Key findings

• The sum of the first six intrinsic mode functions (IMFs) from EEMD decomposition provides the most accurate reconstruction of core-collapse supernova gravitational waveforms.
• At a match score threshold of 0.75, the false alarm probability of reconstruction (FAPR) is 1×10⁻² at 5 kpc and 3×10⁻² at 10 kpc for simulated signals.
• After normalizing the maximum amplitude to 5×10⁻²¹, the FAPR decreases to 4×10⁻³, indicating high reliability of the reconstruction method.
• The EEMD-based reconstruction method can successfully reconstruct GW waveforms up to a distance of approximately 37 kpc when the strain reaches 7×10⁻²¹ and the match score threshold is 0.75.
• The reconstruction distance (37 kpc) is smaller than the detection distance, indicating that reconstruction capability is limited by signal quality and not just detectability.
• Approximately half of the simulated waveforms could not be successfully reconstructed at 5 kpc and 10 kpc due to low amplitudes and detector response characteristics.