The slope, the hill, the drop, and the swoosh: Learning about the nuclear matter equation of state from the binary Love relations

TL;DR

This paper demonstrates that the slope of binary Love relations reveals the variation of the nuclear matter speed of sound at sub-saturation densities, with unique features indicating twin star configurations.

Contribution

It introduces a novel connection between the slope of binary Love relations and the nuclear matter speed of sound, including the effects of twin stars on these relations.

Findings

Slope encodes the change in nuclear matter speed of sound.

Twin stars produce distinctive 'hill', 'drop', and 'swoosh' features.

New description needed for relations involving twin stars.

Abstract

Analyses that connect astrophysical observations of neutron stars with nuclear matter properties sometimes rely on equation-of-state insensitive relations. We show that the slope of the binary Love relations (i.e.~between the tidal deformabilities of binary neutron stars) encodes the rate of change of the nuclear matter speed of sound below three times nuclear saturation density. Twin stars lead to relations that present a signature ''hill'', ''drop'', and ''swoosh'' due to the second (mass-radius) stable branch, requiring a new description of the binary love relations.