Improving Power Spectral Estimation using Multitapering: Precise asteroseismic modelling of stars, exoplanets, and beyond.
Asteroseismic time-series data have imprints of stellar oscillation modes, whose detection and characterization through time-series analysis allows us to probe stellar interiors physics. Such analyses usually occur in the Fourier domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the power spectrum underlying unevenly sampled time-series data. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. In addition, it is designed to detect strictly periodic signals but is suboptimal for non-sinusoidal periodic or quasi-periodic signals. Here, we develop a multitaper spectral estimation method that tackles the inconsistency and bias problems of the LS periodogram. We combine this multitaper method with the Non-Uniform Fast Fourier Transform (mtNUFFT) to more precisely estimate the frequencies of asteroseismic signals that are non-sinusoidal periodic (e.g., exoplanet transits) or quasi-periodic (e.g., pressure modes). We illustrate this using a simulated and the Kepler-91 red giant light curve. Particularly, we detect the Kepler-91b exoplanet and precisely estimate its period, 6.246 +/- 0.002 days, in the frequency domain using the multitaper F-test alone. We also integrate mtNUFFT into the PBjam package to obtain a Kepler-91 age estimate of 3.96 +/- 0.48 Gyr. This improvement in age estimation relative to the APOKASC-2 (uncorrected) estimate of 4.27 +/- 0.75 Gyr illustrates that mtNUFFT has promising implications for Galactic archaeology, in addition to stellar interiors and exoplanet studies. Our method generally applies to time-domain astronomy and is implemented in the public Python package tapify, available online at https://github.com/aaryapatil/tapify.