Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

TL;DR

This study investigates the critical phenomena in nonrotating neutron stars under small perturbations, confirming type-I critical behavior and providing insights into the nature of the critical solution as a fundamental F-mode spherical oscillation.

Contribution

The paper demonstrates the presence of type-I critical phenomena in nonrotating neutron stars using full general relativity and simple fluid models, extending previous findings to a more fundamental, spherical context.

Findings

Confirmed type-I critical behavior in nonrotating neutron stars

Identified the critical solution as a spherical F-mode oscillation

Showed how finite-size velocity perturbations influence criticality

Abstract

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].