Identification and characterization of 15265 super-Nyquist frequencies in 1309 δ Scuti stars from Kepler photometry

The frequency of pressure (p) mode in $\delta$~Scuti stars can exceed the Nyquist limit of $\mathit{\text{Kepler}}$ long-cadence photometry. {These ‘super-Nyquist frequencies’ (SNFs) are observed as ‘reflected’ peaks at lower frequencies, i.e., they are Nyquist aliases that pose} a threat to asteroseismic diagnostics. Their impact on $\delta$~Scuti p modes has yet to be comprehensively explored. We performed a systematic survey to search for SNFs in 1,838 $\mathit{\text{Kepler}}$ $\delta$~Scuti stars through a novel technique based on sliding Lomb-Scargle periodogram, identifying 15,265 confirmed SNFs in 1,309 stars, from a total of 259,883 frequencies. We observe that the total number of detected frequencies per star remains featureless across the $\delta$~Scuti instability strip; however, young stars pulsate in higher frequencies and so have significantly more SNFs on average. Both the number and the rate of SNFs diminishes accordingly as $\delta$~Scuti stars become more evolved, which is consistent with both observation and stellar models. Furthermore, our method detects a greater fraction of modes as SNFs at higher frequencies, rising from approximately 1% at 20 $\mu$Hz to 23% at the Nyquist limit. The rate of underdetection is highest amongst low-amplitude modes. The SNF modulation patterns can be well distinguished from phase modulations induced by binarity or nonlinear mode interactions. We provide a frequency catalog for future asteroseismic studies of $\delta$~Scuti stars, wherein we identify each peak as being real or an alias, enabling further investigations into regular patterns of pulsation modes, linear combination frequencies, and theoretical modeling.