Gravitational Waves from Nonlinear Couplings of Radial and Polar Nonradial Modes in Relativistic Stars

TL;DR

This paper investigates how nonlinear interactions between radial and polar nonradial oscillation modes in relativistic stars produce combination frequencies that could generate detectable gravitational waves in supernova events.

Contribution

It introduces a gauge-invariant perturbative formalism to analyze nonlinear mode couplings and predicts potential gravitational wave signals from combination frequencies.

Findings

Combination frequencies can reach detectable amplitudes in galactic supernovae.

Nonlinear mode couplings significantly influence gravitational wave emission.

Detectability depends on energy distribution among oscillation modes.

Abstract

The post-bounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wide-band resonant detectors.