Nonlinear radial oscillations of neutron stars

TL;DR

This paper introduces a numerical scheme to study nonlinear radial oscillations in neutron stars, revealing mode coupling, resonance, shock formation, and stabilization effects in highly accurate simulations.

Contribution

A novel numerical method based on deviations from equilibrium for analyzing nonlinear oscillations in neutron stars.

Findings

Mode coupling due to nonlinear interactions

Resonance phenomena observed in oscillations

Shock formation near the stellar surface

Abstract

The effects of nonlinear oscillations in compact stars are attracting considerable current interest. In order to study such phenomena in the framework of fully nonlinear general relativity, highly accurate numerical studies are required. We present a numerical scheme specifically tailored for studies, based on formulating the time evolution in terms of deviations from a stationary equilibrium configuration. Using this technique, we investigate nonlinear effects associated with radial oscillations of neutron stars for a wide range of amplitudes. In particular, we discuss mode coupling due to nonlinear interactions, the occurrence of resonance phenomena, shock formation near the stellar surface as well as the capacity of nonlinearities to stabilize perturbatively unstable neutron star models.