Gravitational waves from nonspinning black hole-neutron star binaries: dependence on equations of state

We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), the neutron star is tidally disrupted before it is swallowed by the black hole irrespective of the EOS. Especially for less-compact neutron stars, the tidal disruption occurs at a more distant orbit. The tidal disruption is reflected in a cutoff frequency of the gravitational-wave spectrum, above which the spectrum amplitude exponentially decreases. A clear relation is found between the cutoff frequency of the gravitational-wave spectrum and the compactness of the neutron star. This relation also depends weakly on the stiffness of the EOS in the core region of the neutron star, suggesting that not only the compactness but also the EOS at high density is reflected in gravitational waveforms. The mass of the disk formed after the merger shows a similar correlation with the EOS, whereas the spin of the remnant black hole depends primarily on the mass ratio of the binary, and only weakly on the EOS. Properties of the remnant disks are also analyzed.

💡 Research Summary

This paper presents a systematic numerical‑relativity study of black‑hole–neutron‑star (BH‑NS) mergers in which the neutron‑star equation of state (EOS) is varied using a piecewise‑polytropic parametrization. The authors focus on how the EOS influences the gravitational‑wave (GW) signal during the merger, the properties of the remnant accretion disk, and the spin of the final black hole.

Initial data are constructed in the moving‑puncture framework, assuming a non‑spinning black hole and an irrotational neutron star. The binary mass ratio is fixed at MBH/MNS = 2, a regime where tidal disruption of the neutron star is expected to occur before the star is swallowed. Six representative EOSs are employed, each defined by a low‑density polytropic segment for the crust and a high‑density segment for the core, allowing the authors to explore a wide range of neutron‑star compactness (C = MNS/RNS) and core stiffness.

The simulations reveal that, for all EOSs considered, the neutron star is tidally disrupted prior to merger. Less‑compact stars (larger radii) are disrupted at larger orbital separations, while more compact stars survive deeper into the potential well before disruption. This difference is directly imprinted on the GW spectrum: the amplitude follows the inspiral chirp up to a characteristic cutoff frequency fcut, above which the spectrum decays exponentially. The authors find a tight, nearly linear correlation between fcut and the neutron‑star compactness. Moreover, for a given compactness, variations in the high‑density polytropic index (i.e., the stiffness of the core EOS) shift fcut by a few percent, indicating that the GW signal encodes not only the bulk compactness but also subtle information about the high‑density EOS.

The mass of the post‑merger accretion disk (Mdisk) shows a similarly strong dependence on the EOS. Stars with low compactness and softer core EOSs produce more massive disks (up to ~0.2 M⊙), because the disrupted material retains enough angular momentum to remain outside the horizon. In contrast, compact stars with stiff cores generate only thin disks (≲0.01 M⊙). By contrast, the dimensionless spin of the remnant black hole (a ≈ 0.7–0.8) is primarily set by the binary mass ratio and shows only a weak EOS dependence, reflecting the fact that the spin is sourced mainly by the orbital angular momentum transferred during merger.

These results have immediate implications for GW astronomy. The cutoff frequency is located in the high‑frequency band (≈1–3 kHz for the systems studied) that will be accessible to advanced ground‑based detectors (Advanced LIGO, Virgo, KAGRA) and especially to next‑generation facilities such as the Einstein Telescope and Cosmic Explorer. Accurate measurement of fcut could therefore provide a dual constraint on neutron‑star compactness and core stiffness, complementing existing tidal‑deformability analyses from the inspiral phase. Additionally, the predicted disk masses inform models of electromagnetic counterparts, such as short gamma‑ray bursts and kilonovae, because a sufficiently massive disk is required to power relativistic outflows.

The study also outlines its limitations. The black hole is assumed non‑spinning, and the neutron star irrotational; realistic astrophysical binaries may involve significant spins that alter the disruption radius, disk mass, and GW spectrum. The fixed mass ratio (2) limits the generality of the quantitative relations; a broader survey over mass ratios would be needed to construct universal fitting formulas. Magnetic fields, neutrino cooling, and finite‑temperature effects are omitted, yet they can affect disk evolution and ejecta properties.

In summary, the paper demonstrates that the EOS leaves a clear, measurable imprint on the merger‑phase GW signal of BH‑NS binaries, on the mass of the remnant disk, and only weakly on the final black‑hole spin. By establishing quantitative relations between the cutoff frequency, neutron‑star compactness, and core stiffness, the work provides a concrete pathway for future GW observations to probe the high‑density nuclear physics governing neutron‑star interiors.