Super-Nyquist asteroseismology with the Kepler Space Telescope

TL;DR

This paper demonstrates that, despite periodic sampling modulation caused by barycentric corrections, super-Nyquist asteroseismology with Kepler data can accurately recover pulsation frequencies, effectively resolving Nyquist ambiguities.

Contribution

It provides an analytical framework and practical methods to distinguish real pulsation frequencies from aliases in Kepler data, enabling super-Nyquist asteroseismology.

Findings

Nyquist aliases are split into identifiable multiplets.

Real pulsation frequencies are recoverable even in super-Nyquist regime.

No Nyquist ambiguities for data spanning over one Kepler orbital period.

Abstract

Barycentric corrections made to the timing of Kepler observations, necessitated by variations in light arrival time at the satellite, break the regular time-sampling of the data -- the time stamps are periodically modulated. A consequence is that Nyquist aliases are split into multiplets that can be identified by their shape. Real pulsation frequencies are distinguishable from these aliases and their frequencies are completely recoverable, even in the super-Nyquist regime, that is, when the sampling interval is longer than half the pulsation period. We provide an analytical derivation of the phenomenon, alongside demonstrations with simulated and real Kepler data for \delta Sct, roAp, and sdBV stars. For Kepler data sets spanning more than one Kepler orbital period (372.5 d), there are no Nyquist ambiguities on the determination of pulsation frequencies, which are the fundamental data of asteroseismology.