Equation of State Classification of Core-Collapse Supernovae with a Network of Gravitational-Wave Detectors

Author(s)

Akhmetali, A., Abylkairov, Y.S., Font, J.A., Zanolin, M., Abdikamalov, E.

Abstract

Gravitational waves from core-collapse supernovae may provide a unique probe of the equation of state (EOS) of dense nuclear matter. In previous work, we assessed the potential of machine-learning methods for EOS classification for rapidly rotating supernovae using individual gravitational-wave detectors. Here, we extend the framework to detector networks and investigate the impact of detector configuration, source distance, arrival time, and sky location on the classification. Using convolutional neural networks, we perform 10-class EOS classification directly from noisy detector data for both second- and third-generation observatories. We find that detector geometry strongly influences classification performance. For Galactic events, current detector networks can achieve promising classification performance, but the reach depends sensitively on the detector network antenna response. Adding detectors improves time-averaged performance and produces more uniform classification across the sky. Third-generation observatories extend the classification reach to 100 kpc for favorable source orientations but do not remove the dependence on detector geometry.

Figures

Amplitude spectral densities as a function of frequency for the ground-based gravitational-wave detectors considered in this study.
Caption Amplitude spectral densities as a function of frequency for the ground-based gravitational-wave detectors considered in this study.
Classification accuracy as a function of the source distance for different 2G detector network configurations. The left and right panels correspond to favourable and unfavourable GW arrival times, respectively (see Table~\ref{tab:antenna_cases} and the main text for details). Each curve corresponds to a different \x{detector} network configuration: HL, HLV, HLVK, HLVA, and HLVKA, as indicated in the legend. The gray horizontal dashed line at 0.7 indicates the threshold adopted for reasonably accurate classification performance. The vertical dashed lines mark the distances to the Galactic Center (8.2 kpc) and the Large Magellanic Cloud (LMC; 49.8 kpc).
Caption Classification accuracy as a function of the source distance for different 2G detector network configurations. The left and right panels correspond to favourable and unfavourable GW arrival times, respectively (see Table~\ref{tab:antenna_cases} and the main text for details). Each curve corresponds to a different \x{detector} network configuration: HL, HLV, HLVK, HLVA, and HLVKA, as indicated in the legend. The gray horizontal dashed line at 0.7 indicates the threshold adopted for reasonably accurate classification performance. The vertical dashed lines mark the distances to the Galactic Center (8.2 kpc) and the Large Magellanic Cloud (LMC; 49.8 kpc).
Classification accuracy as a function of the GW arrival time over a 24-hour period for different 2G detector-network configurations. Each curve corresponds to a different \x{detector} network configuration: HL, HLV, HLVK, HLVA, and HLVKA, as indicated in the legend.
Caption Classification accuracy as a function of the GW arrival time over a 24-hour period for different 2G detector-network configurations. Each curve corresponds to a different \x{detector} network configuration: HL, HLV, HLVK, HLVA, and HLVKA, as indicated in the legend.
Sky maps of the accuracy score for different \x{detector} network configurations of 2G detectors. Titles correspond to the detector networks, while colors indicate the classification performance, with warmer colors representing lower accuracy values and cooler colors representing higher accuracy values.
Caption Sky maps of the accuracy score for different \x{detector} network configurations of 2G detectors. Titles correspond to the detector networks, while colors indicate the classification performance, with warmer colors representing lower accuracy values and cooler colors representing higher accuracy values.
Sky coverage as a function of the classification accuracy threshold for different 2G detector network configurations. Different colors denote the HL, HLV, HLVK, and HLVKA \x{detector} networks. The gray vertical dashed line at an accuracy of 0.7 marks the adopted threshold for accurate classification and provides a reference for comparing the sky coverage achieved by each detector network.
Caption Sky coverage as a function of the classification accuracy threshold for different 2G detector network configurations. Different colors denote the HL, HLV, HLVK, and HLVKA \x{detector} networks. The gray vertical dashed line at an accuracy of 0.7 marks the adopted threshold for accurate classification and provides a reference for comparing the sky coverage achieved by each detector network.
Classification accuracy as a function of the source distance for different 3G detector network configurations. The left and right panels correspond to favourable and unfavourable GW arrival times, respectively. Each curve corresponds to a different \x{detector} network configuration, as indicated in the legend. The gray horizontal dashed line at 0.7 indicates the threshold adopted for reasonably accurate classification performance. The vertical dashed lines mark the distances to the Galactic Center (8.2 kpc) and the LMC (49.8 kpc).
Caption Classification accuracy as a function of the source distance for different 3G detector network configurations. The left and right panels correspond to favourable and unfavourable GW arrival times, respectively. Each curve corresponds to a different \x{detector} network configuration, as indicated in the legend. The gray horizontal dashed line at 0.7 indicates the threshold adopted for reasonably accurate classification performance. The vertical dashed lines mark the distances to the Galactic Center (8.2 kpc) and the LMC (49.8 kpc).
Training and validation loss and accuracy as a function of epoch for a representative CNN training run.
Caption Training and validation loss and accuracy as a function of epoch for a representative CNN training run.
Confusion matrix for the 10-EOS classification for the HL network at a source distance of 2~kpc, favourable case and a Galactic Center sky location. Classification accuracy is 94\%.
Caption Confusion matrix for the 10-EOS classification for the HL network at a source distance of 2~kpc, favourable case and a Galactic Center sky location. Classification accuracy is 94\%.
Confusion matrix for the reduced 7-EOS classification after excluding HSTM1, GShenNL3, and LS220, which show the strongest mutual confusions in the full classification. Classification accuracy is 99\%.
Caption Confusion matrix for the reduced 7-EOS classification after excluding HSTM1, GShenNL3, and LS220, which show the strongest mutual confusions in the full classification. Classification accuracy is 99\%.
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