Resonant Mode Coupling in $\delta$ Scuti Stars

TL;DR

This paper investigates nonlinear resonant mode interactions in delta Scuti stars using three-mode coupling theory, revealing that such interactions are common and may explain observed amplitude and period variations.

Contribution

It provides a comprehensive analysis of mode triplet interactions across multiple delta Scuti models, demonstrating their potential significance in stellar oscillation behavior.

Findings

All models contain numerous well-coupled triplets consistent with observations.

Resonant mode interactions are prevalent and may cause amplitude and period variability.

The study supports the role of nonlinear mode coupling in delta Scuti star oscillations.

Abstract

Delta Scuti ($\delta$ Sct) variables are intermediate mass stars that lie at the intersection of the main sequence and the instability strip on the Hertzsprung-Russel diagram. Various lines of evidence indicate that nonlinear mode interactions shape their oscillation spectra, including the particularly compelling detection of resonantly interacting mode triplets in the $\delta$ Sct star KIC 8054146. Motivated by these observations, we use the theory of three-mode coupling to study the strength and prevalence of nonlinear mode interactions in fourteen $\delta$ Sct models that span the instability strip. For each model, we calculate the frequency detunings and nonlinear coupling strengths of $\sim 10^4$ unique combinations of mode triplets. We find that all the models contain at least $\sim 100$ well-coupled triplets whose detunings and coupling strengths are consistent with the triplets identified in KIC 8054146. Our results suggest that resonant mode interactions can be significant in $\delta$ Sct stars and may explain why many exhibit rapid changes in amplitude and oscillation period.