Eccentric Black Hole-Neutron Star Mergers

Within the next few years gravitational waves (GWs) from merging black holes (BHs) and neutron stars (NSs) may be directly detected, making a thorough theoretical understanding of these systems a high priority. As an additional motivation, these systems may represent a subset of short-duration gamma-ray burst (sGRB) progenitors. BH-NS mergers are expected to result from primordial, quasi-circular inspiral as well as dynamically formed capture binaries. The latter channel allows mergers with high eccentricity, resulting in a richer variety of outcomes. We perform general relativistic simulations of BH-NS interactions with a range of impact parameters, and find significant variation in the properties of these events that have potentially observable consequences, namely the GW signature, remnant accretion disk mass, and amount of unbound material.

💡 Research Summary

This paper presents the first fully general‑relativistic simulations of black‑hole–neutron‑star (BH‑NS) encounters that start on hyperbolic or highly eccentric trajectories, a scenario expected for dynamically formed binaries in dense stellar environments such as galactic nuclear clusters or globular clusters. The authors explore a suite of impact parameters, parameterized by the periapsis distance (r_{p}) measured in units of the total mass (M) of the system, ranging from (r_{p}/M = 5) to (15) (approximately 50–150 km for a 4 M⊙ + 1 M⊙ binary). All simulations use a 4:1 mass ratio, non‑spinning components, and a piecewise‑Γ‑law “HB” equation of state for the neutron star (mass = 1.35 M⊙, radius ≈ 11.6 km). The initial relative velocity at infinity is set to 1000 km s⁻¹, representative of the velocity dispersion in nuclear clusters.

The numerical infrastructure combines a fourth‑order finite‑difference implementation of the generalized harmonic formulation of Einstein’s equations with Berger‑Oliger adaptive mesh refinement (seven refinement levels). Hydrodynamics is treated with high‑resolution shock‑capturing schemes (HLL fluxes and WENO‑5 reconstruction). Convergence tests at low, medium, and high resolutions (≈ 80³, 100³, 150³ cells covering each compact object) confirm that key observables (disk mass, unbound mass, gravitational‑wave (GW) energy loss) converge to within ~10 %.

The outcomes fall into three distinct dynamical classes:

1. Direct plunge ((r_{p}=5.0, 5.83, 6.67, 6.81)): The neutron star is swallowed with minimal tidal disruption. Less than 1 % of the neutron‑star rest mass remains in a bound accretion disk, and the GW energy radiated amounts to 0.7–1.7 % of the total mass‑energy. The GW signal consists of a single, relatively weak burst.

2. Single‑orbit plunge ((r_{p}=6.95, 7.22, 7.50)): After the first periapsis passage the system executes one highly eccentric orbit before merging. The first encounter produces a strong “whirl” phase—an extended near‑circular motion around an unstable circular orbit—resulting in a pronounced GW pulse. Tidal forces stretch the neutron star into a long tail, leaving a substantial bound remnant: 10–12 % of the original neutron‑star mass forms a disk. GW energy loss peaks for the transitional case (r_{p}=6.95), reflecting the combined effect of the whirl pulse and the final merger burst.

3. Multiple‑orbit encounters ((r_{p}=8.75, 10.0, 12.5, 15.0)): The neutron star survives the first periapsis passage and continues on a series of increasingly circular, precessing ellipses. Because of computational cost the simulations stop after the first passage, but the emitted GW waveform already shows a clear “fly‑by” burst that matches the Newtonian quadrupole approximation (NQA) in shape while exhibiting up to ~30 % larger amplitude for the smallest (r_{p}) in this group. The GW energy loss follows a smooth trend that departs from the NQA prediction for (r_{p}\lesssim 10,M), consistent with the onset of zoom‑whirl dynamics.

A key quantitative result is the strong, non‑monotonic dependence of the post‑merger disk mass on (r_{p}). Near the transition around (r_{p}\approx 6.9,M) the system switches from negligible disks to disks containing up to (\sim0.3,M_{\odot}). The authors interpret this behavior through the lens of unstable circular orbits: when the periapsis lies just outside the radius (r_{c}) of the effective unstable orbit, the binary can linger in a whirl phase, extracting orbital energy efficiently via GW emission and tidal heating. If (\delta r_{p}=r_{p}-r_{c}) is negative, the whirl collapses directly into a plunge; if slightly positive, a brief separation follows before the next periapsis, which is typically already inside the unstable region, leading to a rapid final plunge.

The fallback accretion rate of bound material onto the remnant black hole follows the classic (t^{-5/3}) power law, with normalization set by the disk mass. For the most massive disk case ((r_{p}=6.81)), the fallback luminosity at 100 s after merger would be only (\sim2\times10^{42}) erg s⁻¹ (assuming 10 % radiative efficiency), far below the sustained emission observed in some short GRBs. Consequently, while high‑disk‑mass eccentric mergers could power the prompt sGRB emission, they are unlikely to explain extended X‑ray plateaus without additional energy sources.

Overall, the study demonstrates that eccentric BH‑NS encounters produce a rich phenomenology absent in quasi‑circular mergers: (i) GW waveforms with distinct whirl‑pulse structures and amplitudes exceeding Newtonian estimates; (ii) a wide spread in remnant disk masses (0–0.3 M⊙); (iii) variable amounts of unbound ejecta. These signatures provide potential discriminants for future GW detections, especially for events that deviate from the canonical chirp‑like signal of circular inspirals. Moreover, the results suggest that a non‑negligible fraction (≈ 30 %) of dynamically formed BH‑NS encounters in nuclear clusters could lead to bound remnants, making them plausible contributors to the observed short‑GRB population, albeit with a possibly different electromagnetic afterglow behavior compared to primordial, low‑eccentricity mergers.