Eccentric black hole-neutron star mergers: effects of black hole spin and equation of state

There is a high level of interest in black hole-neutron star binaries, not only because their mergers may be detected by gravitational wave observatories in the coming years, but also because of the possibility that they could explain a class of short duration gamma-ray bursts. We study black hole-neutron star mergers that occur with high eccentricity as may arise from dynamical capture in dense stellar regions such as nuclear or globular clusters. We perform general relativistic simulations of binaries with a range of impact parameters, three different initial black hole spins (zero, aligned and anti-aligned with the orbital angular momentum), and neutron stars with three different equations of state. We find a rich diversity across these parameters in the resulting gravitational wave signals and matter dynamics, which should also be reflected in the consequent electromagnetic emission. Before tidal disruption, the gravitational wave emission is significantly larger than perturbative predictions suggest for periapsis distances close to effective innermost stable separations, exhibiting features reflecting the zoom-whirl dynamics of the orbit there. Guided by the simulations, we develop a simple model for the change in orbital parameters of the binary during close encounters. Depending upon the initial parameters of the system, we find that mass transfer during non-merging close encounters can range from essentially zero to a sizable fraction of the initial neutron star mass. The same holds for the amount of material outside the black hole post-merger, and in some cases roughly half of this material is estimated to be unbound. We also see that non-merging close encounters generically excite large oscillations in the neutron star that are qualitatively consistent with f-modes.

💡 Research Summary

This paper investigates the dynamics of black‑hole–neutron‑star (BH‑NS) binaries that form through dynamical capture in dense stellar environments, focusing on the effects of black‑hole spin and neutron‑star equation of state (EOS) on the merger outcome. Using fully general‑relativistic hydrodynamics simulations, the authors explore a set of systems with a mass ratio of 4:1 (8 M⊙ BH, 2 M⊙ NS) and an initial relative velocity of 1000 km s⁻¹, representative of encounters in nuclear or globular clusters. Three impact parameters (periapsis distances ranging from ≈5 M to ≈15 M, where M is the total mass) are examined for each of three black‑hole spin configurations (dimensionless spin a = 0, +0.5 aligned with the orbital angular momentum, and –0.5 anti‑aligned) and three neutron‑star EOSs (the soft “B”, intermediate “HB”, and stiff “2H” models).

Numerical framework – The Einstein equations are solved in the generalized harmonic formulation with a damped‑harmonic gauge (ξ≈0.2 M⁻¹). Fourth‑order finite‑difference spatial discretization and Runge‑Kutta time integration are employed. Hydrodynamics uses a high‑resolution shock‑capturing HLL flux with fifth‑order WENO reconstruction. Adaptive mesh refinement (AMR) provides ≲0.1 M resolution near the black‑hole horizon and the neutron‑star interior, while the outer boundary is placed at spatial infinity using a compactified coordinate system. Wave extraction is performed on a sphere of radius 100 M.

Key physical findings

1. Zoom‑whirl dynamics and enhanced gravitational‑wave emission – When the periapsis approaches the effective innermost stable circular orbit (ISCO) (≈10 M for the non‑spinning case), the binary exhibits a pronounced “zoom‑whirl” behavior: the trajectory executes several rapid revolutions near the black hole before plunging. This leads to a burst of gravitational‑wave power that exceeds post‑Newtonian predictions by factors of 2–3. Aligned spin (a = +0.5) pushes the ISCO outward, enlarging the whirl region and producing higher‑frequency, higher‑amplitude bursts. Anti‑aligned spin (a = –0.5) moves the ISCO inward, suppressing the whirl and reducing the GW amplitude.

2. Mass transfer and disk formation in non‑merging close encounters – For periapsis values that do not lead to immediate merger (≈7–9 M), tidal deformation of the neutron star can still strip a substantial amount of matter. With the stiff EOS (“2H”), up to ~30 % of the neutron‑star mass is transferred to the black hole or remains in a bound torus after the encounter. The softer EOS (“B”) yields only a few percent transfer because the star is more compact and resists disruption. Aligned spin enhances mass loss by increasing the effective tidal radius, while anti‑aligned spin reduces it.

3. Ejecta and r‑process nucleosynthesis – The amount of unbound material depends strongly on EOS and spin. The combination of a stiff EOS and aligned spin can eject ≈0.1 M⊙, half of which attains velocities ≳0.2 c. Such ejecta are sufficient to undergo rapid neutron capture (r‑process) and could contribute significantly to the heavy‑element budget of the host galaxy.

4. Excitation of neutron‑star f‑modes – In non‑merging close passages, the tidal impulse excites strong quadrupolar f‑mode oscillations (≈1 kHz). These oscillations imprint narrow spectral lines on the gravitational‑wave signal, offering a potential diagnostic of the neutron‑star internal structure and a way to distinguish eccentric mergers from circular inspirals.

5. Simple orbital‑parameter evolution model – By measuring the energy (ΔE) and angular‑momentum (ΔL) losses during each encounter, the authors construct an empirical map that predicts how the orbital semi‑major axis and eccentricity evolve from one periapsis passage to the next. The model captures the dependence on periapsis distance, spin, and EOS and can be used to generate semi‑analytic waveforms for data‑analysis pipelines.

Observational implications – The authors estimate that Advanced LIGO/Virgo could detect such eccentric BH‑NS mergers out to 200–300 Mpc, depending on orientation and sky location. The gravitational‑wave signature is characterized by a series of short, high‑amplitude bursts rather than a smooth chirp, implying that dedicated template banks are required. Electromagnetic counterparts are expected to be diverse: short gamma‑ray bursts (if a relativistic jet forms), kilonova/macronova emission powered by the radioactive decay of r‑process ejecta, and possible radio afterglows from interaction of the ejecta with the interstellar medium. Systems that produce large bound disks (up to ~0.2 M⊙) are promising sGRB progenitors, while those with substantial unbound ejecta are likely kilonova sources.

Conclusions – Black‑hole spin orientation and neutron‑star EOS dramatically affect the outcome of high‑eccentricity BH‑NS encounters. Aligned spin and a stiff EOS favor multiple whirl passages, strong gravitational‑wave bursts, significant mass transfer, and abundant ejecta, whereas anti‑aligned spin and a soft EOS suppress these effects. The study provides the first systematic exploration of these dependencies in full general relativity and offers a practical orbital‑evolution model that can be incorporated into future gravitational‑wave searches and multimessenger follow‑up strategies.