# Impact of the neutron star crust on the tidal polarizability

## TL;DR

This paper investigates how the neutron star crust influences the tidal Love number k2 and the tidal polarizability, highlighting the crust's significant impact on these quantities and their implications for constraining neutron star properties.

## Contribution

It provides a detailed analysis of the crust's role in determining the tidal Love number k2 and the tidal polarizability, emphasizing the sensitivity to the crustal component of the EOS.

## Key findings

- k2 is highly sensitive to the crustal EOS component
- A universal relation exists between tidal polarizability and compactness
- Future observations can constrain neutron star mass-radius relations

## Abstract

The first detection of a binary neutron star merger has opened the brand new era of multimessenger astronomy. This historic detection has been instrumental in providing constraints on the tidal polarizability of neutron stars. In turn, the tidal polarizability has been used to impose limits on stellar radii and ultimately on the equation of state (EOS). The tidal polarizability is also sensitive to the second tidal Love number k2. It is the main purpose of this work to perform a detailed study of k2 which, for a given compactness parameter, encodes the entire sensitivity of the tidal polarizability to the EOS. In particular, we examine the role that the crustal component of the EOS plays in the determination of k2. A set of realistic models of the equation of state that yield an accurate description of the properties of finite nuclei and support neutron stars of two solar masses is used. Given that the tidal polarizability scales as the fifth power of the compactness parameter, a universal relation exists among the tidal polarizability and the compactness parameter that is highly insensitive to the underlying EOS. Thus, besides an extraction of the tidal polarizabilities, a measurement of the individual stellar masses is also required to impact the mass-radius relation. However, we observe a strong sensitivity of k2 to the EOS, particularly to the contribution from the inner crust. Although by itself the tidal polarizability can not contribute to the determination of the mass-radius relation, future detections of binary neutron star mergers are poised to provide significant constraints on both the tidal polarizabilities and masses of the individual stars, and thus ultimately on the mass-radius relation. Yet, subleading corrections to the tidal polarizability are encoded in the second Love number k2 which displays a large sensitivity to the entire (crust-plus-core) EOS.