Investigation of oscillations above the acoustic cut-off frequency for a sample of <i>Kepler</i> stars. I. Methodology for detecting stellar pseudo-modes

ABSTRACT Stellar oscillations with frequencies below the acoustic cut-off frequency are confined within resonant cavities in the stellar interior. However, waves with frequencies above the cut-off are not trapped, and are free to propagate into the stellar atmosphere. In solar power spectra, this is observed as a regular, repeating peak-like structure. Known as pseudo-modes, few previous studies have identified and analysed their nature in stars other than our Sun. In this work, we aimed to identify the presence of the pseudo-modes in a sample of 91 ${\it Kepler}$ stars, comprised mainly of the LEGACY sample and KOIs. To determine whether any statistically significant signal existed within the pseudo-modes, we utilised the power spectrum of the power spectrum (PSxPS) method. We generated a PSxPS for each star for a range of frequencies over which we expected to observe the pseudo-modes. Bootstrapping was then used to calculate the false alarm probability (FAP) for the peak at maximum PSxPS power. The presence of pseudo-modes was detected in 51 stars, which displayed a statistically significant peak (&amp;lt;5 per cent FAP) in the PSxPS. Over half had a peak at maximum power greater than the &amp;lt;1 per cent FAP level. We further examined the frequency of maximum PSxPS power, finding most stars had a frequency between one and one-half of the large frequency separation. Stars which showed evidence for a secondary significant (&amp;lt;5 per cent FAP) peak in the PSxPS were also recorded, and 19 stars were identified. The detection and characterisation of pseudo-modes may provide new insights into stellar magnetism.