Black Hole-Neutron Star Binaries near Neutron Star Disruption Limit in the Mass Regime of Event GW230529

Technical Summary: Black Hole-Neutron Star Binaries near Neutron Star Disruption Limit in the Mass Regime of Event GW230529

Problem Statement
The detection of the gravitational wave event GW230529 by the LIGO–Virgo–KAGRA (LVK) Collaboration marked the first likely black hole–neutron star (BHNS) merger with a significant potential for producing electromagnetic (EM) counterparts. This event involves a primary black hole (BH) of 2.5–4.5 $M_\odot$ and a secondary compact object of 1.2–2.0 $M_\odot$, placing it in a mass regime where the neutron star (NS) may be tidally disrupted rather than plunging directly into the BH. Tidal disruption is a prerequisite for generating observable EM signals, such as kilonovae and compact-binary gamma-ray bursts (cbGRBs), which require the formation of an accretion disk and the ejection of neutron-rich matter.

However, predicting whether a specific BHNS merger will result in disruption relies heavily on analytical fitting formulas, such as the FNH18 model (Foucart et al. 2018), which estimates the mass of the post-merger remnant disk. These models were primarily calibrated on simulations with mass ratios $q \gtrsim 3$ and spins far from the critical threshold required for disruption. Consequently, there is a lack of high-fidelity numerical relativity (NR) data for systems near the disruption limit, particularly for the mass and spin parameters consistent with GW230529. This gap limits the ability to accurately predict the prevalence of EM signals and to constrain the neutron star equation of state (EOS) from EM observations.

Methodology
The authors utilize the Spectral Einstein Code (SpEC) to perform high-resolution numerical simulations of BHNS mergers. The study focuses on a mass ratio of $q=3$ and a neutron star mass of $M_{NS} = 1.35 M_\odot$, parameters consistent with the GW230529 event. Two distinct equations of state are employed to test different levels of neutron star compactness:

1. SFHo: A softer EOS with a radius $R_{NS} \approx 11.9$ km.
2. DD2: A stiffer EOS with a radius $R_{NS} \approx 13.2$ km.

The simulations vary the black hole spin magnitude ($\chi_{BH}$) to probe the region immediately surrounding the critical spin ($\chi_{crit}$) predicted by the FNH18 model for tidal disruption. For SFHo, $\chi_{crit} \approx 0.037$; for DD2, $\chi_{crit} \approx -0.23$. The study includes simulations with spins both slightly below and above these critical thresholds.

Key methodological features include:

• Monte Carlo Neutrino Transport: This marks the first application of Monte Carlo neutrino radiation transport in BHNS merger simulations. Unlike leakage models, this method tracks neutrino trajectories in position and momentum space to accurately model absorption, emission, and scattering. This is crucial for determining the composition (electron fraction, $Y_e$) of the post-merger remnant and outflows, which dictates the potential for r-process nucleosynthesis.
• Resolution Studies: Convergence tests were performed for the SFHo case at three resolutions to quantify numerical uncertainties.
• Initial Conditions: Initial data were generated using the Spells solver, with orbital eccentricities reduced to $e \lesssim 0.009$.

Key Results

1. Disk Mass vs. Analytical Predictions:

   • SFHo EOS: The numerical results for total remnant mass generally fall within the expected modeling errors of the FNH18 formula. However, the simulations consistently show slightly higher remnant masses than the model predicts.
   • DD2 EOS: A significant discrepancy is observed. For spins near the disruption limit, the FNH18 model underpredicts the remnant disk mass by a factor that exceeds the model's stated error margins. For example, at $\chi_{BH} = -0.030$, the model predicts a remnant mass of $\sim 0.012 M_\odot$, while the simulation yields $\sim 0.049 M_\odot$.
   • Critical Spin Threshold: Despite the mass discrepancies, the critical spin value required to trigger disruption (where the remnant mass transitions from zero to non-zero) is found to be consistent between the analytical model and the simulations. The primary difference lies in the slope of the remnant mass curve ($dM_{rem}/d\chi_{BH}$) near the threshold; simulations show a steeper rise than the model.

2. Emergence of Low-Mass Disks:

   • The simulations reveal the formation of non-zero accretion disks even for spins slightly below the predicted disruption limit (e.g., the SFHo case with $\chi_{BH} = -0.0130$). While these disks are low mass ($\sim 10^{-3} M_\odot$), they are potentially sufficient to power short cbGRBs, as suggested by previous studies (e.g., Gottlieb et al.).

3. Mass Ejection and Composition:

   • Dynamical Ejecta: The amount of mass ejected dynamically during the merger is very low, typically $\lesssim 0.004 M_\odot$. For the lowest spin configurations, the unbound mass is near the limits of numerical resolution, with uncertainties potentially reaching $\sim 100\%$.
   • Disk Winds: The study suggests that for these systems, the total mass ejected via later-time disk winds (viscous and magnetically driven) will likely dominate over the initial dynamical ejecta.
   • Electron Fraction ($Y_e$): The dynamical ejecta is highly neutron-rich ($Y_e < 0.1$). However, the outflows and disk material show a broader range of $Y_e$ (up to $\sim 0.3$) due to weak interactions (neutrino heating). The DD2 EOS produces more neutron-rich ejecta compared to SFHo.

4. Observational Implications:

   • Any kilonova signal from these specific GW230529-like mergers is predicted to be dim, likely dominated by the optical emission from disk wind outflows rather than the infrared emission from dynamical ejecta.
   • The total ejecta mass available for r-process nucleosynthesis is $\lesssim 0.02 M_\odot$.

Significance and Claims
The paper claims that while the FNH18 analytical model remains broadly reliable for predicting the existence of a disruption threshold (the critical spin), it systematically underestimates the mass of the resulting remnant disk, particularly for stiffer equations of state (DD2) near the disruption limit.

The authors emphasize that their results highlight the limits of current calibration when applied to BHNS mergers close to the disruption threshold. Specifically:

• The model's assumption of a "zero" remnant mass below the critical spin is not strictly accurate; low-mass disks can form even below the predicted limit.
• These low-mass disks are physically significant as potential progenitors for short gamma-ray bursts, even if they do not produce bright kilonovae.
• The findings suggest that a modest recalibration of the fitting formula may be necessary as more simulations in the low-mass-ratio, near-critical-spin regime become available.

The study does not claim to definitively alter the LVK's probability assessment for GW230529 being a disrupting merger, noting that the differences observed are unlikely to qualitatively change the results of the LVK analysis. However, it provides a more rigorous numerical foundation for understanding the behavior of BHNS binaries in this specific, observationally critical parameter space.