Gravitational-Wave Constraints on Neutron-Star Pressure Anisotropy via Universal Relations

TL;DR

Addressing how neutron-star interior pressure anisotropy, encoded by the single parameter $\beta$, modifies gravitational-wave observables. It develops a quasi-local anisotropy model and derives an anisotropy-dependent $f$-Love universal relation between the dimensionless tidal deformability $\bar{\Lambda}$ and the $f$-mode frequency. The relation is EOS-insensitive for fixed $\beta$, enabling Bayesian inference of $\beta$ from GW170817 and future CE/ET observations. They find upper bounds of order unity on $\beta$ (approximately $\beta \lesssim 2.2$ today and $\beta \lesssim 2.4$ with next-generation detectors), demonstrating that gravitational waves can probe NS interior physics in a way that is largely independent of the high-density EOS.

Abstract

Neutron stars may exhibit pressure anisotropy arising from various physical mechanisms, such as elasticity, magnetic fields, viscosity, and superfluidity. We compute the tidal deformability and the $f$-mode oscillation frequency of anisotropic neutron stars using a phenomenological quasi-local model characterized by a single dimensionless anisotropy parameter. We find that while the relation between the tidal deformability and the $f$-mode frequency depends on the degree of anisotropy, it remains largely insensitive to variations in the equation of state (the relation between radial pressure and energy density) for a fixed anisotropy parameter, similar to the isotropic case. Leveraging this anisotropy-dependent universal relation within a statistical framework, we place constraints on the anisotropy parameter using both the gravitational wave observation of GW170817 and simulated data for a GW170817-like event observed by a future network of detectors. We find that the anisotropy parameter can be constrained to order unity with current data, and the bounds remain comparable with future detector sensitivities. Importantly, these constraints are only weakly affected by uncertainties in the neutron-star equation of state.

Figures (4)

• Figure 1: Relation between the mass $M$ and the following quantities: radius $R$ (top left), dimensionless tidal deformability $\bar{\Lambda}$ (top right), $f$-mode frequency $f=\textrm{Re}(\omega)/2\pi$ (bottom left), and $f$-mode damping time $\tau=1/\textrm{Im}(\omega)$ (bottom right). We show results for three EOSs (WFF1, MPA1, and MS1) and five values for $\beta$ ($-10$, $-5$, $0$, $5$, and $10$). We show results for $M>0.5$ M$_{\odot}$ and for physical models, i.e. those that do not violate the conditions in eqs. \ref{['wec']}$-$\ref{['causality']}.
• Figure 2: (Top) $f$-Love relation for anisotropic NSs with different choices of the anisotropy parameter $\beta$: the dimensionless real (left panel) and imaginary (right panel) part of the $f$-mode complex frequency (see Eq. \ref{['omega_bar']}) against the dimensionless tidal deformability $\bar{\Lambda}$ (see Eq. \ref{['Lambda_bar']}). (Bottom) The absolute relative error, defined as $|1 - y_{\rm num}/y_{\rm fit}|$, where $y_{\rm num}$ is the numerical result and $y_{\rm fit}$ is the fit result obtained from Eq. \ref{['fit']} for each $\beta$. Note that the $f$-Love relation depends on $\beta$ and it remains EOS-universal for a fixed $\beta$. Note that the EOS universality is stronger for positive $\beta$.
• Figure 3: (Left) Posterior distributions on $\bar{\Lambda}$ and $\bar{\Omega}$ for GW170817 from Pratten:2019sed (top) and for a GW170817-like event detected by a future CE/ET network from Williams:2022vct (bottom). The solid and dashed lines represent the $50\%$ and $90\%$ credible contours, respectively. We overlay the anisotropic $f$-Love relations for various $\beta$. (Right) Posterior distributions on $\beta$ for the primary and secondary stars, as well as the joint analysis. The dotted vertical lines represent the $90\%$ upper bounds on $\beta$. Note that the upper bounds on $\beta$ are similar for current and future simulated data.
• Figure 4: Squared frequency of the fundamental radial mode of anisotropic NSs for the anisotropy model in Eq. \ref{['ansatz']} for various $\beta$. Each panel shows the result for one EOS. Each sequence in grey stops at the maximum mass while we highlight physically-viable stellar configurations satisfying the conditions in Eqs. \ref{['wec']}$-$\ref{['causality']} in color. This figure confirms that these models satisfy the maximum-mass criterion for the radial stability of anisotropic NSs, since $F^{2}_{0}(M)\rightarrow0$ as $M\rightarrow{M_{\rm max}}$.