# Role of crustal physics in the tidal deformation of a neutron star

## TL;DR

This paper investigates how realistic crustal physics, including shear modulus, influences the tidal deformability of neutron stars during inspiral, finding small but potentially detectable corrections to gravitational wave signals.

## Contribution

It introduces a fully general relativistic model incorporating realistic crust equations of state and shear modulus, quantifying their impact on neutron star tidal deformability.

## Key findings

- Realistic crust EOSs cause about 1% correction in the second Love number.
- Crustal shear effects on magnetic-type Love number are negligible.
- Corrections are subdominant for current detectors but relevant for third-generation observatories.

## Abstract

In the late inspiral phase, gravitational waves from binary neutron star mergers carry the imprint of the equation of state due to the tidally deformed structure of the components. If the stars contain solid crusts, then their shear modulus can affect the deformability of the star and, thereby, modify the emitted signal. Here, we investigate the effect of realistic equations of state (EOSs) of the crustal matter, with a realistic model for the shear modulus of the stellar crust in a fully general relativistic framework. This allows us to systematically study the deviations that are expected from fluid models. In particular, we use unified EOSs, both relativistic and non-relativistic, in our calculations. We find that realistic EOSs of crusts cause a small correction, of $\sim 1\%$, in the second Love number. This correction will likely be subdominant to the statistical error expected in LIGO-Virgo observations at their respective advanced design sensitivities, but rival that error in third generation detectors. For completeness, we also study the effect of crustal shear on the magnetic-type Love number and find it to be much smaller.