Love-C relations for elastic hybrid stars

TL;DR

This paper explores how a crystalline phase in hybrid star cores affects their mass-radius and Love-C relations, revealing potential deviations that could help identify phase transitions inside neutron stars, though current measurements are insufficient.

Contribution

It investigates the impact of a crystalline phase in hybrid star cores on their structural relations, highlighting how elastic properties influence observable deviations from fluid star models.

Findings

Deviations in Love-C relation can reach up to 60% due to elasticity.

Stiffer quark matter cores increase maximum mass and radius.

Current measurements are not sensitive enough to detect these deviations.

Abstract

Neutron stars (NSs) provide a unique laboratory to study matter under extreme densities. Recent observations from gravitational and electromagnetic waves have enabled constraints on NS properties, such as tidal deformability (related to the tidal Love number) and stellar compactness. Although each of these two NS observables depends strongly on the stellar internal structure, the relation between them (called the Love-C relation) is known to be equation-of-state insensitive. In this study, we investigate the effects of a possible crystalline phase in the core of hybrid stars (HSs) on the mass-radius and Love-C relations, where HSs are a subclass of NS models with a quark matter core and a nuclear matter envelope with a sharp phase transition in between. We find that both the maximum mass and the corresponding radius increase as one increases the stiffness of the quark matter core controlled by the speed of sound, while the density discontinuity at the nuclear-quark matter transition effectively softens the equations of state. Deviations of the Love-C relation for elastic HSs from that of fluid NSs become more pronounced with a larger shear modulus, lower transition pressure, and larger density gap and can be as large as 60%. These findings suggest a potential method for testing the existence of distinct phases within HSs, though deviations are not large enough to be detected with current measurements of the tidal deformability and compactness.