Gravitational waves from pulsating stars: Evolving the perturbation equations for a relativistic star

TL;DR

This paper formulates and numerically evolves perturbation equations for relativistic stars, demonstrating that gravitational waves carry signatures of various pulsation modes, which could inform neutron star properties through future detections.

Contribution

It develops a detailed initial-value formulation and numerical evolution of perturbations in relativistic stars, highlighting the presence of multiple pulsation modes in gravitational wave signals.

Findings

Gravitational waves from pulsating stars show multiple mode signatures.

The dominant modes include fluid f- and p-modes and the gravitational w-mode.

Results can serve as benchmarks for nonlinear simulations and aid future gravitational wave observations.

Abstract

We consider the perturbations of a relativistic star as an initial-value problem. Having discussed the formulation of the problem (the perturbation equations and the appropriate boundary conditions at the centre and the surface of the star) in detail we evolve the equations numerically from several different sets of initial data. In all the considered cases we find that the resulting gravitational waves carry the signature of several of the star's pulsation modes. Typically, the fluid $f$-mode, the first two $p$-modes and the slowest damped gravitational $w$-mode are present in the signal. This indicates that the pulsation modes may be an interesting source for detectable gravitational waves from colliding neutron stars or supernovae. We also survey the literature and find several indications of mode presence in numerical simulations of rotating core collapse and coalescing neutron stars. If such mode-signals can be detected by future gravitational-wave antennae one can hope to infer detailed information about neutron stars. Since a perturbation evolution should adequately describe the late time behaviour of a dynamically excited neutron star, the present work can also be used as a bench-mark test for future fully nonlinear simulations.