KIC 6102338 light curve

While the Lomb-Scargle periodogram is foundational to astronomy, it has a significant shortcoming: its variance does not decrease as more data are acquired. Statisticians have a 60-year history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. The F-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise-based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We demonstrate multitapering on simultaneous measurements of the interplanetary magnetic field and the solar 10.7-cm radio flux, finding high coherence at frequencies associated with the sun's activity cycle and quasibiennial oscillations. Next we show that the multitaper--F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both rotation frequencies and suggest an antisolar rotation profile. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.

This article uses Q0, Q3, and Q16 PDCSAP data.