Modelling strains and stresses in continuously stratified rotating neutron stars

TL;DR

This paper develops a Newtonian model to study how stratification and variations in the adiabatic index affect deformations and strains in rotating neutron stars, with implications for understanding starquakes and pulsar glitches.

Contribution

It introduces a new framework for modeling neutron star deformations considering stratification and non-equilibrium adiabatic indices, challenging previous assumptions about starquake triggers.

Findings

Small changes in the adiabatic index cause large strains.

Crust breaking thresholds are not reached during typical glitches.

Starquakes may require incomplete relaxation of the crust after glitches.

Abstract

We introduce a Newtonian model for the deformations of a compressible, autogravitating, and continuously stratified neutron star. The present framework can be applied to a number of astrophysical scenarios as it allows us to account for a great variety of loading forces. In this first analysis, the model is used to study the impact of a frozen adiabatic index in the estimate of rotation-induced deformations: we assume a polytropic equation of state for the matter at equilibrium but, since chemical reactions may be slow, the perturbations with respect to the unstressed configuration are modelled by using a different adiabatic index. We quantify the impact of a departure of the adiabatic index from its equilibrium value on the stressed stellar configuration and we find that a small perturbation can cause large variations both in displacements and strains. As a first practical application, we estimate the strain developed between two large glitches in the Vela pulsar showing that, starting from an initial unstressed configuration, it is not possible to reach the breaking threshold of the crust, namely to trigger a starquake. In this sense, the hypothesis that starquakes could trigger the unpinning of superfluid vortices is challenged and, for the quake to be a possible trigger, the solid crust must never fully relax after a glitch, making the sequence of starquakes in a neutron star an history-dependent process.