Neutron-Star–Black-Hole and Binary-Neutron-Star Observations

Binaries containing neutron stars add matter response to the compact-binary waveform. Inspiral tides probe deformability; an NSBH merger may disrupt the star; a BNS merger may form a hot remnant with kilohertz emission; and multiple events can constrain a shared equation of state. Yet matter effects are small, late, and model dependent. The chapter therefore distinguishes what the detector likelihood constrains from the stellar and microphysical interpretation supplied by Relativistic Matter and Compact Objects.

Helpful background. Compact-Binary Parameter Estimation develops mass, spin, distance, and waveform systematics. Compact-Star Binaries and Tidal Dynamics supplies stellar response, merger outcomes, and dense-matter interfaces.

Enter the matter-inference chain

For a tide varying slowly compared with the star’s internal response time, the induced quadrupole is

$$Q_{ij}=-\lambda\mathcal E_{ij}, \qquad \Lambda=\frac{\lambda}{G^4m^5}.$$

Binary phasing measures mainly the mass-weighted combination $\widetilde\Lambda$. A stellar-structure model maps $\Lambda(m)$ to radius and pressure. Close to merger, mass ratio, compactness, and black-hole spin decide whether an NSBH disrupts. After BNS contact, finite-temperature, composition, neutrino, magnetic, and transport physics shape the remnant.

This is a sequence of forward models, not one direct EOS measurement.

The route through the chapter

Tidal Signatures in the Inspiral derives the leading response and its fifth-post-Newtonian phase entry. It explains why high-frequency information, the point-particle baseline, spin, and waveform choice control the result.

Neutron-Star–Black-Hole Disruption compares the tidal and plunge scales. Low mass ratio, low neutron-star compactness, and prograde black-hole spin favor matter outside the remnant, but a counterpart also requires emission physics and adequate observations.

Binary-Neutron-Star Inspiral Inference follows the mass-ratio–spin–tide degeneracy through priors, frequency cutoffs, calibration, and common-star relations. It separates a measured $\widetilde\Lambda$ from an EOS-constrained radius.

Postmerger Gravitational-Wave Signals develops prompt-collapse and oscillating-remnant morphologies. Simulation-calibrated frequency correlations are promising, while current ground-based observations provide upper limits rather than a resolved postmerger spectrum.

Equation-of-State Inference builds the hierarchical map from pressure to TOV solutions, $\Lambda(M)$, and multiple event likelihoods. Smooth, phase-transition, and nonparametric EOS families encode different function priors.

Matter-Binary Catalog Status closes with the dated observational sample. It separates astrophysical significance from BNS/NSBH/BBH class probabilities and explains why mass, tides, counterparts, and population priors support different levels of classification.

Two reading routes

For an inspiral route, read tidal signatures, BNS inference, and EOS inference. This path follows one phase correction into a shared dense-matter relation.

For a merger and multimessenger route, read NSBH disruption, postmerger signals, and catalog status, then continue to Multimessenger Events, Standard Sirens, and Open Data.

What current results establish

GW170817 remains the central public example: a long BNS inspiral, matter-sensitive likelihood, and securely associated electromagnetic counterpart. GW190425 expands the BNS mass context; GW200105 and GW200115 establish NSBH observations under stated population assumptions; GW230529 probes the lower compact-object mass interval while retaining object-type ambiguity.

At the cutoff 2026-08-18, the cumulative GWTC-5.0 release adds no new confidently neutron-star-containing event from O4b LVK 2026, observations §§1 and 3. Consequently, exact EOS bands, rate intervals, and class odds remain sensitive to a small number of earlier events and their reanalyses. This page freezes the evidence date rather than treating a mutable catalog as evergreen.

Central distinctions

Tidal response versus EOS. $\widetilde\Lambda$ is in the waveform; pressure versus density enters through stellar equilibrium and shared-EOS assumptions.

Disruption versus counterpart. Matter outside a remnant is necessary for many electromagnetic models but not sufficient for a detected transient.

Postmerger prediction versus detection. Simulations robustly predict kHz morphology; current non-detections mainly reflect sensitivity.

Mass classification versus matter measurement. A neutron-star-like mass can strongly favor a class without resolving nonzero tides.

Common physics versus common parameterization. Assuming all stars share an EOS is physical; choosing one smooth basis can still exclude viable phase structure.

A common validation ladder

Every matter claim should survive: realistic selected injections; point-particle and tidal waveform alternatives; high-frequency cutoff, PSD, calibration, and glitch changes; low and broad spin priors; independent versus EOS-linked deformabilities; parameterization changes; and an explicit connection to numerical-relativity or electromagnetic models.

For frontier claims, add the strongest null: a black-hole or zero-tide waveform, nondisruptive NSBH fit, noise-only postmerger background, smooth EOS, or alternative compact-object class. A result is strongest when the data distinguish that null in detector-facing observables.

Review the chapter

1. Order the matter layers. Put these in order from closest to strain to most model dependent: $\widetilde\Lambda$, neutron-star radius, tidal phase shift, pressure at several times nuclear density.

Solution

The detector likelihood first responds to the tidal phase shift. It parameterizes that mainly by $\widetilde\Lambda$. A stellar-structure relation maps deformability and mass to radius. An EOS parameterization and TOV solution then infer pressure at high density. Each later step inherits uncertainty and adds assumptions.

2. A low-mass secondary. An event has a secondary mass compatible with known neutron stars but no tidal information. What can be said?

Solution

A neutron-star classification may be favored under stated maximum-mass and population priors. The event has not directly measured matter response, so a low-mass black hole or another compact object may remain possible depending on those priors. Report class odds and their sensitivity rather than declaring composition from mass alone.

References

• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog.” arXiv:2605.27225 (2026). Open PDF.

Further reading

• Baiotti, Luca. “Gravitational Waves from Neutron Star Mergers and Their Relation to the Nuclear Equation of State.” Progress in Particle and Nuclear Physics 109 (2019): 103714. DOI. Open PDF.
• LIGO Scientific Collaboration and Virgo Collaboration. “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral.” Physical Review Letters 119 (2017): 161101. DOI. Open PDF.