Neutron-Star–Black-Hole Disruption

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A neutron star in a neutron-star–black-hole binary can be torn apart outside the black hole, plunge nearly intact, or occupy a transitional regime. The outcome is controlled mainly by mass ratio, neutron-star compactness, and the black-hole spin component aligned with the orbit. Disruption can truncate the gravitational-wave signal and leave matter outside the remnant, but neither effect is guaranteed to be observable.

Helpful background. Merger and Remnant Classification develops relativistic matter dynamics and disruption outcomes. Tidal Signatures in the Inspiral supplies the detector-facing tidal parameters.

Tidal scale versus plunge scale

A Newtonian estimate equates the black hole’s tidal field across a star of radius $R_{\rm NS}$ with the star’s self-gravity:

r_{\rm tid} \sim R_{\rm NS} \left(\frac{M_{\rm BH}}{M_{\rm NS}}\right)^{1/3}.

Disruption must occur outside the relativistic plunge scale. Write the neutron-star compactness and black-hole mass ratio as

C=\frac{GM_{\rm NS}}{R_{\rm NS}}, \qquad Q=\frac{M_{\rm BH}}{M_{\rm NS}}\ge1.

Compare the tidal scale with $r_{\rm ISCO}=GM_{\rm BH}\widehat R_{\rm ISCO}$ :

\frac{r_{\rm tid}}{r_{\rm ISCO}} \sim\frac{1}{C\,Q^{2/3}\widehat R_{\rm ISCO}}.

This explains the otherwise counterintuitive mass-ratio trend. A more massive black hole produces a stronger tide at a fixed distance, but its plunge scale grows faster than the disruption distance. Larger $Q$ therefore generally makes observable disruption harder. Larger $C$ makes the star harder to disrupt. Prograde black-hole spin reduces the Kerr innermost-stable-orbit radius and can allow disruption closer to the hole; retrograde spin does the opposite. This comparison supplies trends, not an exact boundary, especially at comparable masses.

The Newtonian comparison is qualitative. Relativistic simulations calibrate fits for remnant mass outside the black hole using $C$ , symmetric mass ratio $\eta=Q/(1+Q)^2$ , and the dimensionless Kerr ISCO radius $\widehat R_{\rm ISCO}(\chi_{\rm BH})$ . A common structure is

\frac{M_{\rm out}}{M_{\rm NS}^{b}} =\left[ \max\!\left( \alpha\frac{1-2C}{\eta^{1/3}} -\beta\frac{C\widehat R_{\rm ISCO}}{\eta} +\gamma,0 \right) \right]^\delta,

Here $M_{\rm NS}^{b}$ is the initial baryonic mass. The Foucart–Hinderer–Nissanke fit uses

(\alpha,\beta,\gamma,\delta) =(0.406,\,0.139,\,0.255,\,1.761).

Its calibration simulations span $1\le Q\le7$ , $-0.5\le\chi_{\rm BH}\le0.97$ , and $0.13\le C\le0.182$ , with nonprecessing black-hole spin and negligible neutron-star spin and eccentricity. The fitted quantity is baryonic matter remaining outside the black hole shortly after merger, including bound and unbound material; it is not simply disk mass or ejecta mass Foucart et al. 2018, “Numerical simulations” and Eqs. (4)–(6). The zero is a fit boundary, not a sharp law of nature. Applying a fit to tilted spins by replacing spin with its aligned projection is an additional approximation.

For example, take $Q=5$ and $C=0.16$ , so $\eta=5/36$ . A nonspinning black hole has $\widehat R_{\rm ISCO}=6$ and the fit returns zero outside mass. At aligned spin $\chi_{\rm BH}=0.8$ , the Kerr value is $\widehat R_{\rm ISCO}\simeq2.907$ and the same fit gives $M_{\rm out}/M_{\rm NS}^{b}\simeq0.136$ . This controlled comparison shows how spin can change the outcome; it is a fit prediction within the calibration domain, not an observed remnant fraction or a counterpart probability.

What disruption could imprint

Gravitational waves. Disruption can suppress the late merger–ringdown amplitude and introduce matter-dependent cutoff structure. Detectability requires sufficient high-frequency signal-to-noise ratio and a waveform calibrated over the relevant $Q$ , spin, compactness, and equation-of-state domain.

Matter outside the remnant. Dynamical ejecta and an accretion disk can power a kilonova, jet, or other electromagnetic emission. The mapping from $M_{\rm out}$ to light is not one-to-one: ejecta geometry, composition, neutrino transport, magnetic fields, jet launching, viewing angle, host extinction, and observing coverage intervene.

Inspiral tides. A neutron star can have measurable deformability even if it ultimately plunges. Conversely, a weak inspiral tidal measurement does not prove a black-hole secondary; the detector may simply lack high-frequency information.

Current evidence and competing interpretations

GW200105 and GW200115 provided the first confident gravitational-wave observations of systems consistent with neutron-star–black-hole binaries. Their secondary classifications depend on mass and maximum-neutron-star-mass assumptions, and their data did not tightly measure secondary tides; no electromagnetic counterpart was identified LVK 2021, pp. 2–8.

At the cutoff 2026-08-18, GWTC-5.0 is the cumulative reference and reports no new confidently matter-containing O4b event LVK 2026, observations §§1 and 3. The broader catalog contains additional candidates whose NSBH classification can be sensitive to compact-object mass priors. Therefore:

Evidence line	Supported conclusion	Not established
Component masses and population priors favor an NSBH class	A matter-containing interpretation is plausible or strong	Direct tidal measurement of the secondary
Parameters fall in a disruption-favorable region under an EOS	Matter may remain outside the remnant	An electromagnetic counterpart must occur
No counterpart is found	No transient was identified to survey limits and coverage	The neutron star plunged intact
No resolved cutoff or tides	Matter effects are below current sensitivity	The compact object is certainly a black hole

Discriminating checks

A defensible disruption claim propagates the joint posterior in $M_{\rm BH}$ , $M_{\rm NS}$ , $\chi_{\rm BH}$ , and $\Lambda_{\rm NS}$ through more than one simulation-calibrated fit. It checks whether posterior support lies inside the fit domain and adds calibration uncertainty.

Waveform comparisons should include point-particle, inspiral-tidal, and disruptive NSBH models where valid. High-frequency results require alternate PSDs, calibration perturbations, and glitch treatment. Electromagnetic non-detections require sky coverage, depth, cadence, distance, viewing-angle, and emission-model marginalization.

An independent injection study places disruptive and nondisruptive numerical-relativity-informed signals in representative detector noise. It asks whether the claimed cutoff is recovered and whether a binary-black-hole model can mimic it. The conclusion should be reviewed after a new NSBH event, stronger counterpart limits, or an expanded simulation/waveform calibration.

Exercises

1. Direction of the trends. Holding neutron-star mass fixed, which changes favor disruption outside the plunge: larger radius, lower black-hole mass, or more prograde black-hole spin?

Solution

All three favor disruption. A larger radius lowers compactness and increases the tidal scale; a lower black-hole mass reduces $Q$ and the relative plunge scale; prograde spin reduces the Kerr ISCO radius. Quantitative boundaries require relativistic fits rather than multiplying these trends independently.

2. No kilonova. List two reasons a disrupted neutron star might yield no detected kilonova.