Relic of quadrupole deformation produced in a hot neutron star era

TL;DR

This paper investigates the evolution of quadrupole deformation in newly born neutron stars during crust formation, estimating residual ellipticity and its implications for gravitational-wave detection.

Contribution

It is the first to model the deformation decay during crust solidification, linking early neutron star deformation to potential gravitational-wave signals.

Findings

Residual ellipticity is a few percent of the initial deformation.

Elastic shear in the crust retains some deformation after solidification.

The deformation profile is imprinted in the crust's elastic shear.

Abstract

A newly born neutron star is expected to exhibit significant deviations from spherical symmetry, which decay with time. Determining how much deformation remains at present is crucial for gravitational-wave astronomy. This study is the first investigation into the evolution of quadrupole deformation during the solid crust formation phase to obtain a plausible value at present. The equilibrium structure before solidification is modeled using a fluid description, and the deformation is introduced through an assumed driving force. As the star cools, this force weakens, leading to a gradual decay of the deformation. Eventually, the deformation vanishes in the fluid region but partially remains in the crust, sustained by elastic forces, after solidification. By comparing the equilibrium models before and after solidification, we estimate the residual ellipticity and demonstrate that the spatial profile of the elastic shear is imprinted in the crust. The relic ellipticity is only a few percent of the original value, with its absolute magnitude depending on the deformation mechanism during the hot era, which cannot be specified owing to the lack of elaborate models. This work provides a first step toward linking early neutron star deformation with future gravitational-wave observations.