Resonant Mode Coupling in $\delta$ Scuti Stars

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.

13 pages, 8 figures. Submitted to ApJ

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• Non-linear Three-mode Coupling of Gravity Modes in Rotating Slowly Pulsating B Stars: Stationary Solutions and Modeling Potential
• The extraordinary frequency pattern variation in δ Scuti stars
• KIC 10855535: An elegant Delta Scuti pulsator with Amplitude and Phase Modulation