Coupling of Radial and Axial non-Radial Oscillations of Compact Stars: Gravitational Waves from first-order Differential Rotation

TL;DR

This paper explores the non-linear coupling between radial and axial non-radial oscillations in neutron stars, revealing potential gravitational wave signatures and resonance phenomena that could be observed.

Contribution

It introduces a comprehensive perturbative framework for modeling non-linear oscillation coupling in neutron stars, focusing on axial modes and their gravitational wave implications.

Findings

Resonance phenomena occur when radial and axial mode frequencies align.

Simulation results show signal amplification due to non-linear coupling.

The framework enables time-domain evolution of coupled oscillations.

Abstract

We investigate the non-linear coupling between radial and non-radial oscillations of static spherically symmetric neutron stars as a possible mechanism for the generation of gravitational waves that may lead to observable signatures. In this paper we concentrate on the axial sector of the non-radial perturbations. By using a multi-parameter perturbative framework we introduce a complete description of the non-linear coupling between radial and axial non-radial oscillations; we study the gauge invariant character of the associated perturbative variables and develop a computational scheme to evolve the non-linear coupling perturbations in the time domain. We present results of simulations corresponding to different physical situations and discuss the dynamical behaviour of this non-linear coupling. Of particular interest is the occurrence of signal amplifications in the form of resonance phenomena when a frequency associated with the radial pulsations is close to a frequency associated with one of the axial w-modes of the star. Finally, we mention possible extensions of this work and improvements towards more astrophysically motivated scenarios.