Modelling strains and stresses in continuously stratified rotating neutron stars

Abstract

We introduce a Newtonian model for the deformations of a compressible, auto-gravitating and continuously stratified neutron star. The present framework can be applied to a number of astrophysical scenarios as it allows 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 modeled 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.

Incompressible analytical models for spinning-down pulsars

“…Finally, since the two-density model gives typically larger and differently shaped strains with respect to the FLE one (e.g. the maximum strain can be at the poles), the study of a realistic stratification, without the assumption of incompressible medium, seems to be the obvious choice for future studies (see Giliberti et al 2018).…”

“…If matter is at equilibrium, the crustal composition can be thought as a function of the total density , and thus . However, continuous stratification introduces a considerable complication that can be dealt with the more refined approach proposed in Giliberti et al (2018), which has to be solved numerically (see also Ushomirsky et al 2000; Cutler et al 2003). Therefore, in order to obtain exactly solvable analytic models, in the following we will study only idealised incompressible stellar structures with homogeneous layers, implying also constant shear modulus, as sketched in Figure 1.…”

“…Detailed derivation of the model and of the main equations are summarised in Appendix A, while more technical details can be found in Sabadini et al (2016) and in the recent description of a class of more realistic (i.e. continuously stratified and auto-gravitating) NS models (Giliberti et al 2018).…”

“…The important effects due to the finite compressibility and stratification of matter, not included in these models, are considered in the more general approach described in Giliberti et al (2018). However, compressible and self-gravitating models are considerably more complex and need a certain amount of numerical work to be solved, so that the kind of two-density models studied here represent an improvement of the approach pioneered by Baym & Pines (1971), without losing the possibility to obtain closed solutions for the displacement field ready to be used for astrophysical estimates.…”

Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect

“…The assumption of Hall and Ohmic evolution as formulated in [10] is valid for NSs whose magnetic field is moderately strong. NSs with very strong magnetic fields are susceptible to crust failure, as deformations beyond the crust elastic limit lead to permanent deformation [69][70][71][72][73][74][75][76][77]. Thus, the assumption of a rigid crust that can absorb the stresses induced by the magnetic field and maintain its equilibrium does not hold any more.…”