Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

TL;DR

This paper investigates how certain azimuthal modes with odd wave numbers are amplified during the nonlinear growth of the bar-mode instability in differentially rotating stars, highlighting the importance of mode coupling.

Contribution

It demonstrates that mode coupling significantly amplifies odd azimuthal modes during bar-mode growth, using both simplified models and realistic simulations.

Findings

Odd azimuthal modes are amplified through coupling with even modes.

Non-zero initial odd modes grow substantially during instability.

Mode coupling affects late-time dynamics of rotating stars.

Abstract

Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.