Using Equation of State Constraints to Classify Low-Mass Compact Binary Mergers

TL;DR

This work tackles the challenge of classifying subsolar-mass compact binaries detected by ground-based GW observatories by combining tidal information with dense-matter equation-of-state (EOS) constraints. The authors develop a Bayesian framework that marginalizes over EOS posteriors $\pi(\epsilon|d_{\rm aux})$ to compute odds for source-type hypotheses (NS-NS, NS-BH, BH-BH) using tidal deformabilities $\Lambda$ and their mass dependence $\Lambda(m)$. Through simulations at high and moderate SNR, they show that subsolar-mass NSs exhibit large tides ($\tilde{\Lambda}$) that are inconsistent with $\Lambda=0$ for BHs, enabling robust classification in favorable cases (e.g., BBH vs BNS) and giving quantifiable odds for HasNS and HasBH. The study highlights a practical path to identifying extreme-physics objects (including primordial BHs or exotic NSs) in GW data and emphasizes labeling ambiguities between components, which could be mitigated by tide-based ordering. Overall, EOS-informed tidal classification substantially enhances our ability to distinguish NS and BH content in low-mass binaries and informs future waveform modeling and EOS constraints.

Abstract

Compact objects observed via gravitational waves are classified as black holes or neutron stars primarily based on their inferred mass with respect to stellar evolution expectations. However, astrophysical expectations for the lowest mass range, $\lesssim 1.2 \,M_\odot$, are uncertain. If such low-mass compact objects exist, ground-based gravitational wave detectors may observe them in binary mergers. Lacking astrophysical expectations for classifying such observations, we go beyond the mass and explore the role of tidal effects. We evaluate how combined mass and tidal inference can inform whether each binary component is a black hole or a neutron star based on consistency with the supranuclear-density equation of state. Low-mass neutron stars experience a large tidal deformation; its observational identification (or lack thereof) can therefore aid in determining the nature of the binary components. Using simulated data, we find that the presence of a sub-solar mass neutron star (black hole) can be established with odds $\sim 100:1$ when two neutron stars (black holes) merge and emit gravitational waves at signal-to-noise ratio $\sim 20$. For the same systems, the absence of a black hole (neutron star) can be established with odds $\sim 10:1$. For mixed neutron star-black hole binaries, we can establish that the system contains a neutron star with odds $\gtrsim 5:1$. Establishing the presence of a black hole in mixed neutron star-black hole binaries is more challenging, except for the case of a $\lesssim 1\,M_{\odot}$ black hole with a $\gtrsim 1\,M_{\odot}$ neutron star companion. On the other hand, classifying each individual binary component suffers from an inherent labeling ambiguity.

Figures (9)

• Figure 1: The $m-\Lambda$ relation for draws from the EoS posterior from Legred21 (gray lines). A red dashed line denotes the SLY9 EoS. An orange solid line indicates the $\Lambda \propto m^{-6}$ trend. The posteriors of the masses and tidal deformabilties of the primary and secondary component of a BBH simulated signal are shown in light blue and dark blue, respectively. Despite poorer tidal constraints, the secondary is less consistent with the EoSs, suggestive of a BH. While this demonstration does not capture the full 4-dimensional mass-$\Lambda$ correlations, it sketches the main classification idea.
• Figure 2: Relevant frequencies for late-inspiral signals: merger (peak strain, tan) and contact (orbital separation corresponding to objects touching, light blue) of NSs in equal-mass systems as a function of component mass. Shaded regions correspond to marginalization over the EoS posterior from Legred21. Colored lines correspond to the SLy9 EoS Douchin:2001svGulminelli15, which we use to simulate data. Lastly, we display an approximation for the plunge frequency of a comparable mass BBH $f_{6M}$ with a black dash-dot line.
• Figure 3: One- and two-dimensional marginalized source-frame mass posteriors for the $q \equiv m_2/m_1 = 1$ signals. Same-color lines denote systems with varying total mass $M$ with true values marked. For a given mass, varying line styles denote BBH, NSBH, and BNS systems. Contours represent two-dimensional 2-$\sigma$ regions. Given a simulated mass, similar posteriors across source types shows the subdominant effect of tides on the inferred masses.
• Figure 4: Two dimensional marginal posteriors for select parameters for systems with $q = 1$, with each column referring to a different simulated total mass. Blue, yellow, and magenta lines outline the 2-$\sigma$ contours of the posterior for the BBH, NSBH, and BNS systems, respectively. We omit the BHNS configuration as it is identical to NSBH for equal-mass simulations. The left (right) halves of the third row plots are the posterior of the primary (secondary), and include draws from the EoS distribution Legred21 for reference. A decreasing total mass increases the tidal signature and correspondingly affects all posteriors.
• Figure 5: Similar to Fig. \ref{['fig:q1_comparisons']} but for systems with the same simulated total mass $M = 2\,M_\odot$, with each column referring to a different simulated the mass ratio. When relevant, we also include BHNS configurations in green. The posteriors of all parameters are, weakly sensitive to the true mass ratio, with the exception of the BHNS cases.