An investigation of solar and stellar pseudo-modes

Acoustic oscillations (p modes) are trapped within the interior of the Sun and solar-like stars if their frequencies are below the acoustic cut-off frequency. Above this frequency, acoustic modes are not confined to the stellar interior and are free to propagate into the atmosphere. Known as pseudo-modes, they are observed as a regular repeating peak-like structure in frequency-power spectra, and are the focus of our investigation. In the Sun, variations in solar pseudo-mode frequencies are known to be anti-correlated with the 11-year sunspot cycle. Therefore, utilising 22 years of spatially resolved GONG data, we investigated whether any latitudinal dependence exists in the pseudo-mode frequencies, as there does with sunspot emergence and progression. By cross-correlating realisations of Lomb- Scargle periodograms generated from overlapping, successive 216-day segments in time (the resampled periodogram approach), we were able to determine temporal frequency shifts and the uncertainties. We identified morphological differences in the pseudo-mode shifts below 15◦ compared to all latitudes above 15◦, which was most pronounced during the rise to solar maximum. Additionally, wavelet analysis was used to identify a statistically significant periodicity of around four years, which was present at all latitudes. Our investigation was also extended to a sample of 91 Kepler stars, with the aim of detecting the presence of the pseudo-modes and searching for temporal frequency shifts. To detect the signal of the pseudo-modes, we generated a power spectrum from the power spectrum of the pseudo-mode region (PSxPS), and used bootstrapping to quantify whether the peak at maximum PSxPS power was statistically significant. Pseudo-modes were identified in 51 stars, which were then analysed by the resampled periodogram approach to search for frequency variations with time. For 16% of the sample, pseudo-mode frequency shifts were significantly anti-correlated with stellar p-mode shifts (as is the case for the Sun). However, pseudo-mode and p-mode shifts were significantly correlated in-phase for 8% of the sample. The magnitude of pseudo-mode frequency variation was found to be greater for cooler and slower rotating stars (in opposition to p-modes). Temporal changes to pseudo-mode frequencies may be attributable to stellar magnetic activity cycles, and can therefore contribute to our understanding of stellar magnetism.