Faraday resonance in dynamical bar instability of differentially rotating stars

TL;DR

This paper explores the nonlinear dynamics of differentially rotating stars, revealing a potential gravitational wave signature of Faraday resonance caused by bar mode instabilities.

Contribution

It demonstrates the occurrence of Faraday resonance in gravitational waves from unstable rotating stars, a novel observation in astrophysical fluid dynamics.

Findings

Oscillation along the rotation axis is induced during bar mode growth.

The oscillation frequency is twice that of the bar mode.

Faraday resonance may be observable in gravitational wave signals.

Abstract

We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.