Fourier Analysis of Gapped Time Series: Improved Estimates of Solar and Stellar Oscillation Parameters

TL;DR

This paper introduces a general maximum likelihood method for analyzing gapped time series in helio- and asteroseismology, significantly improving the precision of oscillation parameter estimates, especially for low signal-to-noise solar-like oscillations.

Contribution

It develops a novel Fourier space fitting technique that accounts for data gaps and phase information, enhancing measurement accuracy over traditional methods.

Findings

Improved frequency estimates with up to fivefold precision gain.

Method reduces bias in low signal-to-noise conditions.

Better understanding of data gaps' impact on oscillation measurements.

Abstract

Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on the total length (T), quality, and completeness of the observations. Except in a few simple cases, the effect of gaps in the data on measurement precision is poorly understood, in particular in Fourier space where the convolution of the observable with the observation window introduces correlations between different frequencies. Here we describe and implement a rather general method to retrieve maximum likelihood estimates of the oscillation parameters, taking into account the proper statistics of the observations. Our fitting method applies in complex Fourier space and exploits the phase information. We consider both solar-like stochastic oscillations and long-lived harmonic oscillations, plus random noise. Using numerical simulations, we demonstrate the existence of cases for which our improved fitting method is less biased and has a greater precision than when the frequency correlations are ignored. This is especially true of low signal-to-noise solar-like oscillations. For example, we discuss a case where the precision on the mode frequency estimate is increased by a factor of five, for a duty cycle of 15%. In the case of long-lived sinusoidal oscillations, a proper treatment of the frequency correlations does not provide any significant improvement; nevertheless we confirm that the mode frequency can be measured from gapped data at a much better precision than the 1/T Rayleigh resolution.