Draft version October 3, 2022 Typeset using L A T E X twocolumn style in AASTeX63 Improving Power Spectral Estimation using Multitapering: Precise asteroseismic modeling of stars, exoplanets, and beyond Aarya A. Patil, 1, 2 Gwendolyn M. Eadie, 1, 3 Joshua S. Speagle (沈佳士), 3, 1, 2, 4 and David J. Thomson 5, ∗ 1 David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St George Street, Toronto ON M5S 3H4, Canada 2 Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S 3H4, Canada 3 Department of Statistical Sciences, University of Toronto, 9th Floor, Ontario Power Building, 700 University Ave, Toronto, ON M5G 1Z5, Canada 4 Data Sciences Institute, University of Toronto, 17th Floor, Ontario Power Building, 700 University Ave, Toronto, ON M5G 1Z5, Canada 5 Department of Math & Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada ABSTRACT Asteroseismic time-series data have imprints of stellar oscillation modes, whose detection and char- acterization 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 unsuitable for non-sinusoidal periodic or quasi-periodic signals. Here, we develop a multitaper spectral estimation method that tack- les 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. Par- ticularly, 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 36% improvement in age preci- sion relative to the 4.27 ± 0.75 Gyr APOKASC-2 (uncorrected) estimate illustrates that mtNUFFT has promising implications for Galactic archaeology, in addition to stellar interiors and exoplanet studies. Our frequency analysis method generally applies to time-domain astronomy and is implemented in the public Python package tapify, available at https://github.com/aaryapatil/tapify. 1. INTRODUCTION Modern advances in the theory of stellar structure and evolution are driven by high-precision photometric ob- servations of stars over time using space-based telescopes such as the MOST (Walker et al. 2003), CoRoT (Baglin et al. 2009; Auvergne et al. 2009), Kepler (Borucki et al. 2010; Koch et al. 2010) (and K2), BRITE (Weiss et al. 2014), TESS (Ricker et al. 2014), and the upcoming PLATO mission (Rauer et al. 2014) (e.g., Buzasi et al. 2000; Michel et al. 2008; Miglio et al. 2009; Aerts et al. 2010; De Ridder et al. 2009; Degroote et al. 2010; Chap- lin et al. 2011; Li et al. 2020). Analyses of these obser- Corresponding author: Aarya A. Patil patil@astro.utoronto.ca ∗ FRSC & Emeritus Professor vations in the Fourier domain exhibit the frequencies at which stars oscillate. By studying these frequencies, as- teroseismology provides a unique pathway to investigate the deep interiors of stars and the physical mechanisms that drive oscillations. To obtain Fourier domain representations of stellar oscillations, one estimates the power spectrum from the light curve, or time-series, data. The features in the power spectrum across frequencies are associated with different physical phenomena, and these features in turn depend on the type of pulsating star (refer to the pulsa- tion HR diagram in Aerts et al. 2010, chapter 2). In the case of solar-like oscillators, we can observe the following spectral features (Garc´ ıa & Ballot 2019): 1. rotational modulation peaks and harmonics, 2. transitory exoplanet peaks and harmonics, arXiv:2209.15027v1 [astro-ph.IM] 29 Sep 2022