Resonant Mode Coupling in δ Scuti Stars

Delta Scuti (δ Sct) variables are intermediate-mass stars that lie at the intersection of the main sequence and the instability strip on the Hertzsprung-Russell 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 δ 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 14 δ Sct models that span the instability strip. For each model, we calculate the frequency detunings and nonlinear coupling strengths of ~10⁴ unique combinations of mode triplets. We find that all the models contain at least ~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 δ Sct stars and may explain why many exhibit rapid changes in amplitude and oscillation period.