Re-examining Super-Nyquist Frequencies of 68 $\delta$ Scuti Stars Utilizing the Kepler Long Cadence Photometry

TL;DR

This paper applies the sliding Lomb-Scargle periodogram to Kepler data of 68 delta Scuti stars, successfully identifying and correcting super-Nyquist frequency artifacts to improve asteroseismic analysis accuracy.

Contribution

It demonstrates the effectiveness of the sLSP method in detecting super-Nyquist frequencies and correcting aliasing in long-cadence Kepler data for delta Scuti stars.

Findings

Identified 6 previously unrecognized super-Nyquist frequencies.

Validated the sLSP method as a reliable tool for frequency artifact correction.

Enhanced the accuracy of stellar pulsation analysis.

Abstract

The high-precision and long-duration photometry provided by the $Kepler$ mission has greatly advanced frequency analyses of a large number of pulsating stars, a fundamental step in asteroseismology. For $\delta$ Scuti stars, analyses are typically confined to frequencies below the Nyquist frequency. However, signals above this limit can be reflected into the sub-Nyquist range, especially in long-cadence data, where they may overlap with genuine pulsation modes and lead to misinterpretation. To address this issue, a recently proposed method -- the sliding Lomb-Scargle periodogram (sLSP) -- can effectively distinguish real frequencies from aliased ones. In this study, we compiled a sample of 68 $\delta$ Scuti stars whose frequency analyses were based on the $Kepler$ photometry. Using the sLSP method, we systematically examined the 1,406 reported frequencies in the literature. As a result, we identified 6 previously unrecognized reflected super-Nyquist frequencies in four stars: KIC 3440495, KIC 5709664, KIC 7368103, and KIC 9204718. We have once again demonstrated the ability of the sLSP method to detect and correct such artifacts. This technique improves the reliability of frequency selection, thereby enhancing the accuracy of asteroseismic interpretation and stellar modeling for the pulsating stars.