Classification of the equation of state of neutron stars via sparse dictionary learning

TL;DR

This work demonstrates that sparse dictionary learning, implemented in the CLAWDIA pipeline, can classify neutron-star EOS using only post-merger GW signals from NR simulations, when signals are injected into third-generation detector noise. The dominant post-merger frequency $f_2$ emerges as the key discriminant across five EOS, with robust performance at moderate SNR and measurable generalisation to an unseen EOS. The study highlights detector-specific biases and the limited benefit of a shared dictionary in this context, while showing potential for EOS inference in realistic observational scenarios. This approach provides a data-driven path to extract EOS information from high-frequency post-merger signals, motivating extensions to more realistic noise, uncertainty quantification, and broader EOS coverage.

Abstract

The post-merger phase of binary neutron star (BNS) mergers encodes valuable information about the equation of state (EOS) of supranuclear matter. Extracting this information from the analysis of the post-merger waveforms remains challenging due to the high-frequency limitations of current detectors. Future third-generation observatories, such as the Einstein Telescope (ET) and NEMO, will have the sensitivity required to resolve post-merger signals with high fidelity. In this work, we apply CLAWDIA, our recently developed sparse dictionary learning (SDL) framework, to classify different EOS models using only the post-merger gravitational-wave emission of simulated BNS mergers available in the CoRe database. Our dataset comprises five EOS models representative of a broad range of neutron star properties. The SDL framework is optimised under realistic detection conditions by injecting signals into simulated noise matching the sensitivity curves of ET and NEMO. Our results show that classification is primarily driven by the dominant post-merger frequency, $f_2$, which encodes EOS-dependent information. At a modest signal-to-noise ratio of 5, our method achieves $F_1$ scores of $0.76$ for ET and $0.70$ for NEMO, with performance improving for higher signal-to-noise ratios. The reliability and generalisation capabilities of the model are assessed with additional tests, including the classification of an EOS not included in the training dataset and the analysis of detector-specific biases.

Figures (12)

• Figure 1: Mass-radius sequences of the EOS included in the dataset. Diamond-shaped markers correspond to the maximum mass for each EOS, whereas the circle-shaped ones show the radius $R_{1.4}$ for a 1.4 $M_\odot$ star. The color bands show the current mass constraints of GW190814 GW190814, PSR J0348+0432 Antoniadis:2013, and PSR J1614-2230 Arzoumanian:2018. The contour lines show the combined constraints of GW170817 GW170817, PSR J0740+6620 Riley:2021Miller:2021, and PSR J0030+0451 Riley:2019Miller:2019.
• Figure 2: Gravitational wave spectrograms from NR simulations of BNS mergers with different EOS models. Each panel shows the normalized power spectral density (PSD) on a logarithmic scale, covering the late inspiral, merger (centered at $t=0$), and post-merger phase. Solid curves represent instantaneous frequencies. $\Lambda$ denotes the dimensionless tidal deformability, while masses A and B correspond to individual neutron stars. The time-domain GW signals are overlaid at the top of each panel.
• Figure 3: Comparison of the design sensitivity curves (in ASD units) for several ground-based interferometric detectors: LIGO LIGO:2015 (red), Virgo Acernese:2014 (green), and KAGRA KAGRA:2020 (blue), along with the proposed next-generation detectors ET ET:D (purple) and NEMO NEMO (orange). The smoothed ASD of the GW170817 signal, as detected by the LIGO Livingston (L1) detector, is shown in black, with a frequency range between 20 Hz and 500 Hz to highlight the power excess from the merger.
• Figure 4: Confusion matrices for the training subset at the optimised configuration (Table \ref{['tab:eos-optimised-parameters']}) for the ET (\ref{['fig:bns-confusion-matrices-train-optim:ET']}) and NEMO (\ref{['fig:bns-confusion-matrices-train-optim:NEMO']}) detectors. In each matrix, rows correspond to the true EOS, and columns to the EOS predicted by our pipeline.
• Figure 5: Confusion matrices for the test subset at the optimised configuration for the ET (\ref{['fig:bns-confusion-matrices-test-5snr:ET']}) and NEMO (\ref{['fig:bns-confusion-matrices-test-5snr:NEMO']}) detectors. In each matrix, rows correspond to the true EOS, and columns correspond to the EOS predicted by the pipeline.