# Equation-of-state insensitive relations after GW170817

## TL;DR

This paper improves the robustness of neutron star property relations derived from gravitational wave data by reducing equation-of-state variability, thereby decreasing systematic uncertainties in future measurements.

## Contribution

It introduces a method to reduce equation-of-state variability in neutron star relations by applying priors from GW170817 data, enhancing the reliability of gravitational wave inferences.

## Key findings

- Reduced equation-of-state variability by over 50%.
- Improved insensitivity of neutron star relations to the equation of state.
- Systematic uncertainties in tidal deformability extraction are decreased.

## Abstract

The thermodynamic relation between pressure and density (i.e. the equation of state) of cold supranuclear matter is critical in describing neutron stars, yet it remains one of the largest uncertainties in nuclear physics. The extraction of tidal deformabilities from the gravitational waves emitted in the coalescence of neutron star binaries, such as GW170817, is a promising tool to probe this thermodynamic relation. Equation-of-state insensitive relations between symmetric and antisymmetric combinations of individual tidal deformabilities, the so-called "binary Love relations", have proven important to infer the radius of neutron stars, and thus constrain the equation of state, from such gravitational waves. A similar set of relations between the moment of inertia, the tidal deformability, the quadrupole moment, and the compactness of neutron stars, the so-called `I-Love-Q' and `C-Love' relations, allow for future tests of General Relativity in the extreme gravity regime. But even the most insensitive of such relations still presents some degree of equation-of-state variability that could introduce systematic uncertainties in parameter extraction and in model selection. We here reduce this variability by more than 50% by imposing a prior on the allowed set of equations of state, derived from the posteriors generated from the analysis of GW170817. The resulting increase in insensitivity reduces systematic uncertainties in the extraction of the tidal deformability from future gravitational wave observations, although statistical uncertainties currently dominate the error budget, and will continue to do so until the era of Voyager-class detectors.