Resonant Mode Coupling in δ Scuti Stars

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-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 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 14 delta Sct models that span the instability strip. For each model, we calculate the frequency detunings and nonlinear coupling strengths of similar to 10(4) unique combinations of mode triplets. We find that all the models contain at least similar to 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.