On the Stability of Anisotropic Neutron Stars

TL;DR

This work investigates how pressure anisotropy, implemented via Horvat, Bowers–Liang, and Covariant models, affects the dynamical stability and gravitational-wave phenomenology of neutron stars across three generalized EOS (SLy4, GM1Y6, QHC21). Using a fully nonlinear relativistic code, the authors map stability through the fundamental radial mode frequency $\omega^2$, identify a neutral-stability line, and quantify how anisotropy shifts the maximum stable mass up to $\sim 30\%$ higher than the isotropic case. They find turning-point stability is not universally predictive for anisotropic stars, with BL and Covariant models becoming unstable at lower central densities than the isotropic maximum-mass point, while Horvat behaves more like the isotropic case. In addition, they probe GW echoes and show that no physically viable anisotropic NSs produce echoes, implying echoes are not a generic signature of such objects and depend sensitively on internal structure and EOS. Overall, the results constrain models of anisotropic NSs and inform interpretations of compactness, collapse times, and potential GW signals.

Abstract

We model anisotropic neutron stars using three distinct prescriptions for pressure anisotropy, the Horvat, Bowers-Liang, and Covariant models, and three equations of state with different particle compositions, each described by a piecewise polytropic parametrization with continuous sound speed. The stability of these configurations is assessed through their dynamical evolution using a fully non-linear relativistic code. For stable configurations, we compute the oscillation spectrum and identify the fundamental mode frequency. We found that, while the isotropic and Horvat models become unstable close to the maximum-mass point, the Bowers-Liang and Covariant models become unstable at lower central densities, indicating that the standard turning-point criterion may not reliably predict the onset of dynamical instability in anisotropic stars. Based on our results, we also determine the neutral-stability line and verify that configurations lying to the right of this line are indeed unstable under radial perturbations and collapse. Overall, given an equation of state, pressure anisotropy can increase the maximum mass of an stable configuration by up to ~30 % compared to the isotropic case. It also allows for more compact stable configurations that may collapse on longer timescales once they become unstable. Finally, we show that these compact stars could initially mimic a black hole's gravitational-wave ringdown. However, the production of subsequent echoes is not guaranteed by high compactness; instead, it depends critically on the star's specific internal structure and equation of state.

Figures (11)

• Figure 1: Squared frequency of the fundamental mode as a function of the star’s central rest-mass density for the Horvat (top panel), Bowers–Liang (middle panel), and Covariant (bottom panel) anisotropy models, using the QHC21 EOS. Colored dots represent results from non-linear simulations, while solid colored lines correspond to the linear stability analysis. The dashed lines correspond to a fourth-order polynomial fit to the colored data points. The color scale indicates the value of the anisotropy parameter in each model.
• Figure 2: Critical density as a function of the anisotropy parameter at which the fundamental mode frequency vanishes, shown for the Horvat (left), Bowers–Liang (center), and covariant (right) anisotropy models. Solid lines correspond to the semi-analytical results from the linear formalism. Dots are obtained from the numerical simulations, while the dashed line represents the analytical fit given by equation (\ref{['eq:rhoc_fit']}). The shaded regions indicate the corresponding uncertainties.
• Figure 3: Gravitational mass of anisotropic spherical configurations as a function of the central rest-mass density, for the three anisotropy models: Horvart (upper panel), Bowers-Liang (middle panel ), and Covariant model (bottom panel); and three NS EOS: QHC21, GM1Y6, and SLy4 EOS. Star-shaped points to the configuration with vanishing frequency of the fundamental mode as computed from the linear stability analisys, circular markers corresponds to the analytical fit given in equation (\ref{['eq:rhoc_fit']}) and obtained from the numerical simulations, and cross markers denote the point at which the star reaches its maximum mass. Dash gray lines enclose the corresponding uncertainties of the analytical fit. The color scale corresponds to the value of the anisotropic parameter.
• Figure 4: Radial profiles of the metric functions $\alpha$ (top panel) and $a$ (bottom panel) for an $2.17~M_\odot$ unstable isotropic configuration using the QHC21 EOS. The color scale corresponds to different time steps.
• Figure 5: Upper: Compactness of anisotropic spherical configurations as function of the central rest-mass density for the Horvart anisotropy model and the SLy4 EOS. Bottom: Central density time evolution