I-Love-Q anisotropically: Universal relations for compact stars with scalar pressure anisotropy

TL;DR

This study examines how pressure anisotropy in compact stars influences universal relations among their physical properties, finding that anisotropy weakly affects these relations and they remain useful for gravitational wave and X-ray observations.

Contribution

The paper demonstrates that pressure anisotropy only slightly weakens the universal relations in compact stars, supporting their continued use in astrophysical observations despite anisotropic effects.

Findings

Anisotropy increases variability in universal relations by a factor of 1.5-3.

Universal relations remain approximately 10% accurate despite anisotropy.

Pressure anisotropy does not prevent the application of universal relations in gravitational wave physics.

Abstract

Certain physical quantities that characterize neutron stars and quark stars (e.g. their mass, spin angular momentum and quadrupole moment) are interrelated in a way that is approximately insensitive to their internal structure. Such approximately universal relations are useful to break degeneracies in data analysis for future radio, X-ray and gravitational wave observations. Although the pressure inside compact stars is most likely nearly isotropic, certain scenarios have been put forth that suggest otherwise, for example due to phase transitions. We here investigate whether pressure anisotropy affects the approximate universal relations and whether it prevents their use in future observations. We achieve this by numerically constructing slowly-rotating and tidally-deformed, anisotropic, compact stars in General Relativity to third order in spin. We find that anisotropy affects the universal relations only weakly; the relations become less universal by a factor of 1.5-3 relative to the isotropic case, but remain approximately universal to 10%. We succeed in explaining this increase in variability as an increase in the eccentricity variation of isodensity contours, which provides further support for the emergent approximate symmetry explanation of universality. Anisotropy does not affect the universal relations to a sufficient level to prevent their use in gravitational wave astrophysics or in experimental relativity. We provide an explicit example of the latter in dynamical Chern-Simons gravity. The increase in variability of the universal relations due to pressure anisotropy could affect their use in future X-ray observations. Given expected observational uncertainties, however, the relations remain sufficiently universal for use in such observations if the anisotropic modifications to the moment of inertia and the quadrupole moment are less than 10% of their isotropic values.