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

TL;DR

This paper uses gravitational wave data and universal relations to constrain pressure anisotropy in neutron stars, showing that anisotropy can be limited to order unity with current and future observations, largely independent of the equation of state.

Contribution

It introduces an anisotropy-dependent universal relation between neutron star tidal deformability and oscillation frequency, enabling constraints on pressure anisotropy from gravitational wave observations.

Findings

Anisotropy parameter constrained to order unity with current data.

Universal relation remains insensitive to equation of state variations.

Constraints are comparable for current and future gravitational wave detectors.

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.