Cycle dependence of helioseismic oscillations above the acoustic cut-off frequency

ABSTRACT Helioseismic and recent asteroseismic observations reveal fine structure in the power spectrum with alternating peaks and troughs above the acoustic cut-off frequency. This structure is interpreted as the interference patterns of high-frequency acoustic waves excited in the solar interior and propagating into the atmosphere, known as pseudo-modes. Pseudo-modes exhibit clear solar-cycle variability, with frequency shifts that occur predominantly in anti-phase with the activity cycle, although the underlying mechanism remains uncertain. This work investigates how the subsurface excitation source location and the photospheric acoustic cut-off frequency influence the formation, frequency distribution, and solar-cycle variability of pseudo-modes. We employ an analytical Klein–Gordon subsurface cavity model, which is shown to act as an effective Fabry–Pérot interferometer for high-frequency waves that experience constructive and destructive interference between the source location and the lower turning point. We derive an effective dispersion relation isolating the effects of the source location and photospheric cut-off on the pseudo-mode frequency. The model reproduces the observed peak-trough pseudo-mode spectrum for reasonable parameter values constrained by Bayesian Markov chain Monte Carlo best-fitting to Global Oscillation Network Group observations. We also find that solar-cycle-associated 11-year modulations of the source location result in anti-phase pseudo-mode frequency shifts, whereas similar cyclic variations in the cut-off frequency produce harmonic-dependent behaviour, yielding both in-phase and anti-phase shifts. As the acoustic cut-off and mode excitation relate to stratification and flows in the solar interior, the results highlight pseudo-modes as a powerful diagnostic tool for changes in subsurface solar and stellar structure through the solar cycle.