Statistical evidence for linear combination frequencies in γ Doradus stars being nonlinear resonant modes

Abstract: The quest for the origin of linear combination frequencies in pulsating stars is critical for mode identification and subsequent seismic modeling. Hybrid γ Doradus (Dor) stars provide a crucial testbed for such investigations due to their rich frequency content in both gravity (g) and pressure (p) modes. Here, we performed a comprehensive survey of 608 Kepler γ Dor stars, detecting 81,265 frequencies, and identifying 1,895 harmonics and 45,968 combinations involving two parent frequencies. Our results suggest that the proportion of linear combinations increases with the frequency number in each γ Dor star, leveling off at approximately 75%. The majority of the parent-to-child amplitude ratios are distributed between 100 and 10,000, peaking between 2,000 and 4,000. Moreover, the amplitude ratios, involving two g-mode parents, are found to escalate with increasing combination frequency. These values are at least an order of magnitude higher than those predicted by nonlinearity distortion of the light curve, whereas they align well with those of nonlinear resonant coupling. Our findings suggest that a significant portion of combination frequencies are likely intrinsic modes under resonant conditions rather than products of surface geometric distortions, offering new insights that warrant systematic investigations across other types of pulsating star.