Improving Power Spectrum Estimation using Multitapering: Prospects for understanding stars, the Milky Way, and beyond

Metro Toronto Convention Centre 

Stars oscillate in much the same way as musical instruments, but at millions of closely-spaced frequencies. Time-series data of stars have imprints of these oscillations, whose detection and characterization allow us to probe stellar interiors physics. This is usually done by computing the Lomb-Scargle (LS) periodogram, a power spectrum estimator for unevenly sampled time-series. However, the LS periodogram suffers from the statistical problems of (1) inconsistency (or noise) and (2) bias due to high spectral leakage. Here, I develop a multitaper spectral estimation method using the Non-Uniform Fast Fourier Transform (mtNUFFT) that tackles the inconsistency and bias problems of the LS. My method allows precise estimation of frequencies of stellar oscillations and exoplanet transits, thereby providing precise age estimates of stars. For e.g., I obtained a 3.96 +/- 0.48 Gyr age estimate of the Kepler-91 star with 36% better precision than the state-of-the-art. In this talk, I will discuss these results to illustrate that mtNUFFT has promising implications for understanding stars, exoplanets, and galaxies. I will also highlight the Python package I have developed for this work.