Dynamic and Thermodynamic Stability of Superconducting-superfluid Stars

TL;DR

This paper analyzes the dynamic and thermodynamic stability of neutron stars with superconducting-superfluid mixtures, establishing conditions under which these stabilities are equivalent and providing a comprehensive theoretical framework.

Contribution

It introduces a unified formalism linking dynamic and thermodynamic stability of superconducting-superfluid neutron stars using the Iyer-Wald approach.

Findings

Dynamic stability is equivalent to non-negativity of canonical energy.

Axisymmetric stability implies all perturbation stability.

Thermodynamic stability requires positivity of canonical energy on all axisymmetric perturbations.

Abstract

We give a comprehensive analysis of the dynamic and thermodynamic stability of neutron stars composed of superconducting-superfluid mixtures within the Iyer-Wald formalism. We derive the first law of thermodynamics and the necessary and sufficient condition under which dynamic equilibrium implies thermodynamic equilibrium. By constructing the phase space and canonical energy, we show that the dynamic stability for perturbations, restricted in symplectic complement of trivial perturbations with the ADM 3-momentum unchanged, is equivalent to the non-negativity of the canonical energy. Furthermore, dynamic stability against restricted axisymmetric perturbations guarantees the dynamic stability against all axisymmetric perturbations. We also prove that the positivity of canonical energy on all axisymmetric perturbations within the Lagrangian displacement framework with fixed angular momentum is necessary for thermodynamic stability. In particular, the equivalence of dynamic and thermodynamic stability for spherically symmetric perturbations of static, spherically symmetric isentropic configurations is established.