Assessing the Distance for Probing the Nuclear Equation of State with Supernova Gravitational Waves

TL;DR

Gravitational waves from rotating core-collapse supernovae encode information about the high-density nuclear EOS, motivating methods to extract EOS constraints from observed signals. The authors train a linear support vector machine on a catalog of $\sim$1070 bounce-phase waveforms from $18$ EOS models with rotation in $0.02 < T/|W| < 0.18$, injecting detector noise and controlling the signal-to-noise ratio to evaluate EOS distinguishability. They report horizon-like distances: for optimally oriented sources, Advanced LIGO A+ can probe the EOS within $\sim$20 kpc, while ET and CE extend to the Galaxy’s outskirts ($\sim$80–100 kpc) with high accuracy; for randomly oriented sources, only ET and CE retain substantial discrimination power. The study reveals that accuracy is sensitive to rotation and EOS low-density treatment, with higher confusion among EOS sharing similar low-density physics; it also notes major limitations — a single progenitor mass, bounce-focused analysis, a limited EOS set, and simplified noise — implying these horizons are optimistic upper limits and guiding future, more comprehensive investigations. $T/|W|$, $SNR$, and horizon estimates are central to interpreting the practical potential of GW observations to constrain dense matter.

Abstract

Gravitational waves from core-collapse supernovae provide a unique probe of the equation of state (EOS) of high density matter. In this work, we focus on the bounce signal from numerical simulations of rotating supernovae and explore its potential for EOS inference. We employ a support vector machine, previously shown to perform best among tested methods, to classify GW signals simulated for 18 EOS models. For optimally oriented sources, we estimate that the Advanced LIGO A+ detector can probe the EOS for Galactic events, while third-generation observatories such as the Einstein Telescope and Cosmic Explorer can reach substantially farther. For randomly oriented sources, only these next-generation detectors are expected to have sufficient sensitivity. These results represent the potential observational range for probing the nuclear EOS, although, due to the simplifying assumptions adopted, they should be regarded as approximate upper limits.

Figures (9)

• Figure 1: Fourier transformed gravitational wave signals for the SFHo EOS at a distance of 10 kpc, scaled by $\sqrt{f}$, for $0.02 < T/|W| < 0.18$ (shown in grey). The purple curve corresponds to the signal at $T/|W| \approx 0.07$. The blue, orange, and green curves represent the sensitivity curves of Advanced LIGO A+, the Einstein Telescope, and the Cosmic Explorer, respectively.
• Figure 2: Signal-to-noise ratio at 10 kpc as a function of $T/|W|$ for all 18 EOS waveforms with different detector sensitivities: Advanced LIGO A+ (blue), Einstein Telescope (orange), and Cosmic Explorer (green).
• Figure 3: Confusion matrix for the classification of 18 EOS models without added noise, using signals with $0.02 < T/|W| < 0.18$. EOS numerical labels correspond to those listed in Table \ref{['Table:EOS_GR_ML']}. The overall classification accuracy, averaged over 100 runs, is $39.8\% \pm 3.1\%$.
• Figure 4: Classification accuracy as a function of the maximum $T/|W|$ value included in the dataset, evaluated using clean (noise-free) signals.
• Figure 5: Confusion matrices for EOSs with the same (left) and distinct (right) treatments of low-density matter for $T/|W| < 0.10$. The corresponding classification accuracies are $95.6\% \pm 5.5\%$ and $98.3\% \pm 3.1\%$, respectively. The EOS labels are provided in Table \ref{['Table:EOS_GR_ML']}.