Resonant Mode Coupling in δ-Scuti Stars

The δ Scuti variables are intermediate mass stars on or near the main sequence that exhibit pulsations excited by the κ mechanism. Over half of the approximately one thousand δ Scuti stars detected by the Kepler space telescope exhibit pulsation modes that vary significantly in amplitude over the four year mission (Bowman et al. 2016). It has been suggested that at least some of these amplitude variations are due to nonlinear mode coupling between linearly unstable parent modes and resonant daughter modes. We use the stellar evolution code MESA to construct models of δ-Scuti stars across the instability strip and the oscillation code GYRE to compute their eigenmodes. For each stellar model, we calculate the nonlinear coupling coefficients and frequency detunings for ~104 unique combinations of parent-daughter triplets. We find that a large fraction of the stellar models contain at least a few triplets with significant coupling and especially small detunings. Our results are consistent with the fraction of δ Scuti stars showing significant nonlinear amplitude modulations and with the observationally inferred strengths of the parent-daughter couplings.