Super Nyquist Analysis of Combined Quarters of Kepler Light Curves: KIC 8264492

Generally, Nyquist frequency ( \({\text{f}}_{\text{Ny}}\) ) is the upper limit of probing the pulsation frequencies of Long Cadence (LC) data of Kepler targets. Infrequent, the fundamental frequency of some targets appeared above the Nyquist frequency limit which can be detected only through super Nyquist frequency analysis. The Nyquist aliases occur and are split into multiplets due to the barycentric time corrections of the Kepler observations. The main focus of this study is the investigation of the Nyquist aliases to distinguish the real fundamental frequency from aliases and to identify the alias patterns by their multiplet structures. The four quarters of the LC data of KIC 8264492, a binary system with Delta ( \(\updelta \) ) Scuti component, were analyzed in this study. To combine the four quarters of data, the inter and intra quarter offsets were corrected by median aligned approach and then normalized. The super Nyquist analysis was applied extending the analysis up to eight times \({\text{f}}_{\text{Ny}}\) using Period04 software. In the combined light curve, the alias multiplet were resolved and identified that the mulitplets are separated approximately by the Kepler spacecraft orbital frequency (~ \({0.0027\text{ d}}^{-1}\) ). The presence of the number of alias multiplet of KIC 8264492 can be denoted by the theoretical relationship \(2\text{n}+1\) , where \(\text{n}\) denotes the alias order. This super Nyquist analysis confirmed that the real fundamental frequency of KIC 8264492 is \(31.292208\pm 0.000016 {\text{ d}}^{-1}\) which is above the Nyquist frequency \({24.469\text{ d}}^{-1}\) of the Kepler LC data. Furthermore, the mirrored aliases produced a triplet, quintuplet, septuplet and nonuplet structures when \(\text{n}=\text{1,2},3,\) and \(4,\) respectively. The observational results of KIC 8264492 concluded the importance of super Nyquist analysis to distinguish real fundamental frequency from Nyquist aliases. Furthermore, this study noted that combined dataset of at least four quarters of Kepler data is essential to accurately investigate the Nyquist alias.