Improving Harmonic Analysis using Multitapering: Precise frequency estimation of stellar oscillations using the harmonic F-test

TL;DR

This paper introduces an enhanced spectral analysis method combining multitaper power spectrum estimation with the harmonic F-test, enabling precise frequency detection and characterization of stellar oscillations in astronomical time-series data.

Contribution

It combines mtNUFFT with the harmonic F-test to improve detection and frequency estimation of strictly periodic signals, advancing harmonic analysis in astronomy.

Findings

Successfully detects stellar oscillation harmonics in Kepler data

Distinguishes between transient and strictly periodic oscillations

Provides a publicly available Python package for implementation

Abstract

In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle periodogram, but also provides a factor of three speed up in some applications. In this paper, we combine mtNUFFT with the harmonic F-test to test the hypothesis that a strictly periodic signal or its harmonic (as opposed to e.g. a quasi-periodic signal) is present at a given frequency. This mtNUFFT/F-test combination shows that multitapering allows detection of periodic signals and precise estimation of their frequencies, thereby improving both power spectrum estimation and harmonic analysis. Using asteroseismic time-series data for the Kepler-91 red giant, we show that the F-test automatically picks up the harmonics of its transiting exoplanet as well as certain dipole ($l=1$) mixed modes. We use this example to highlight that we can distinguish between different types of stellar oscillations, e.g., transient (damped, stochastically-excited) and strictly periodic (undamped, heat-driven). We also illustrate the technique of dividing a time-series into chunks to further examine the transient versus periodic nature of stellar oscillations. The harmonic F-test combined with mtNUFFT is implemented in the public Python package tapify (https://github.com/aaryapatil/tapify), which opens opportunities to perform detailed investigations of periodic signals in time-domain astronomy.