Convective stability analysis of massive neutron stars formed in binary mergers

TL;DR

The paper tackles convective stability in hot, differentially rotating neutron-star remnants formed in binary mergers by deriving and applying a relativistic Solberg–Høiland criterion that includes buoyancy and rotational restoring forces. Using fully general-relativistic hydrodynamics simulations with piecewise polytropic EOSs (APR4, SLy4, MPA1) and a fixed thermal index $\Gamma_{ m th}=1.8$, the authors find no evidence for large-scale convection and show that rotation stabilizes the remnant against buoyancy-driven instability; inertial modes are not excited to observable levels after the main $f$-mode damps. An $m=1$ one-armed mode appears post-merger but its growth correlates with linear momentum violations, raising concerns about a numerical origin rather than a physical instability. The study discusses limitations, including the neglect of microphysics and magnetic fields, and highlights the need to incorporate neutrino transport and MHD effects in future work to fully assess convective behavior in merger remnants.

Abstract

We perform fully general-relativistic hydrodynamics simulations of binary neutron star mergers over $100\,\rm ms$ post-merger to investigate the dynamics of remnant massive neutron stars (NSs). Our focus is mainly on the analysis of convective stability and mode characteristics of the massive NSs. We derive stability criteria for hot, differentially rotating relativistic stars that account for both buoyant and rotational restoring forces, and apply them for the first time to the post-merger massive NSs. Our results show no evidence of large-scale convective instability, as both angle-averaged specific entropy and specific angular momentum increase outward within the massive NSs. Rotational effects significantly enhance stability for local regions that would be otherwise unstable by the Schwarzschild criterion. Additionally, our mode analysis of matter fields and gravitational waves reveals no excitation of observable inertial modes after the damping of quadrupolar $f$-modes in the massive NSs, contrasting with previous studies. As in many previous works, we observe the excitation of an $m=1$ one-armed mode. However, we also find that the growth of the $m=1$ mode amplitude after the merger may correlate strongly with the violation of linear momentum conservation, indicating that we cannot reject the possibility that the excitation of the one-armed mode has a numerical origin.

Figures (18)

• Figure 1: The distribution of rest-mass density (top), the thermal contribution to the specific internal energy (middle), and the fluid rotational frequency (bottom) in the equatorial $x$-$y$ plane is presented for the APR4-135135 binary system at different post-merger times (see the top of the figure). The isocontours for the rest-mass density are plotted at ${\rm log}_{10}{[{\rho/(\rm g\,cm^{-3})}]}=\{12,13,14,15\}$, while those for the rotational frequency are shown at $\Omega/{(2\pi\,\rm kHz)}=\{0.5,1,1.5,2\}$. Note that the rotational frequency is not monotonic in the radial direction.
• Figure 2: The angle-averaged rotational frequency $\bar{\Omega}/2\pi$ and thermal energy $k_{\rm B}\bar{T}$ for the APR4-135135, MPA1-135135, and SLy4-128128 binaries at different after-merger times. The three subplots share a common set of labels displayed in the middle panel, with the ticks representing the post-merger time corresponding to the plotted curves.
• Figure 3: The time evolution of the angle-averaged radial component of the Schwarzschild criterion $\bar{A}_{\varpi}$ (top), the angle-averaged specific angular momentum $\ell$ (middle), and the angle-averaged radial component of the orientation vector $\theta_{\varpi}$ (bottom) on the equatorial plane for three different binary models. The horizontal gray line in the top panel indicates the place where $\bar{A}_{\varpi}=0$. The three subplots share a common set of labels displayed in the middle panel, with the ticks representing the post-merger times corresponding to the plotted curves.
• Figure 4: The time evolution of the angle-averaged Schwarzschild criterion, the Rayleigh-Solberg criterion, and the Criterion I on the equatorial plane for the three numerical models. The horizontal grey lines mark the place where the quantities are equal to zero. The three subplots share a common set of labels displayed in the middle panel, with the ticks representing the post-merger times corresponding to the plotted curves.
• Figure 5: The snapshot of the Schwarzschild criterion value (first column), the Reyleigh-Solberg criterion value (second column), and the Criterion I value (third column) in the $x$-$z$ (first row) and $x$-$y$ (second row) planes for the model APR4-135135 at post-merger time $t = 75.9\,\rm ms$. The black dashed curve marks the place where the criterion value equals to zero. The black solid enclosed curve represents the density contour at rest mass density $\rho =10^{12}\,\rm g\,cm^{-3}$.