Stability Analysis of Magnetised Neutron Stars - A Semi-analytic Approach

TL;DR

This paper introduces a semi-analytic method for analyzing the stability of magnetized neutron stars, combining analytical and numerical techniques to explore realistic configurations and their stability properties.

Contribution

The authors develop a semi-analytic approach that improves stability analysis of neutron stars by considering realistic features and relaxing simplifying assumptions like the Cowling approximation.

Findings

Simple magnetized models are generally unstable.

Mixed magnetic fields and stratification tend to stabilize neutron stars.

The method extends previous analytical models by lifting simplifications.

Abstract

We implement a semi-analytic approach for stability analysis, addressing the ongoing uncertainty about stability and structure of neutron star magnetic fields. Applying the energy variational principle, a model system is displaced from its equilibrium state. The related energy density variation is set up analytically, whereas its volume integration is carried out numerically. This facilitates the consideration of more realistic neutron star characteristics within the model compared to analytical treatments. At the same time, our method retains the possibility to yield general information about neutron star magnetic field and composition structures that are likely to be stable. In contrast to numerical studies, classes of parametrized systems can be studied at once, finally constraining realistic configurations for interior neutron star magnetic fields. We apply the stability analysis scheme on polytropic and non-barotropic neutron stars with toroidal, poloidal and mixed fields testing their stability in a Newtonian framework. Furthermore, we provide the analytical scheme for dropping the Cowling approximation in an axisymmetric system and investigate its impact. Our results confirm the instability of simple magnetised neutron star models as well as a stabilisation tendency in the case of mixed fields and stratification. These findings agree with analytical studies whose spectrum of model systems we extend by lifting former simplifications.