Beating and coupling in pulsating stars: A unified Fourier description and observational diagnostics
Context. Long-term amplitude and phase variations in pulsating stars produce side peaks or multiplets in the Fourier spectrum of the light curves around the pulsation frequency and its harmonics. Such structures are often attributed to modulation, although linear beating and the non-linear coupling of close oscillations can also produce similar patterns. Aims. We developed a unified analytical Fourier description of these alternatives and identify observational relations that retain discriminatory power when their frequency patterns overlap. Methods. We represented the signal as a dominant, non-sinusoidal oscillation plus one or more secondary oscillations close to it, and analytically derived the frequencies, complex amplitudes, and phases resulting from linear superposition, quadratic coupling, and general non-linear coupling. Synthetic light curves illustrate these results. Results. We implemented freqdiag, which compares modulation with primary–secondary quadratic coupling models a