Determination of fundamental asteroseismic parameters using the Hilbert transform

TL;DR

This paper introduces a robust method combining Fourier and Hilbert transforms to accurately determine fundamental asteroseismic parameters, such as large and small frequency separations, even in low signal-to-noise data.

Contribution

The paper presents a novel approach using the analytic signal and envelope spectral analysis to extract seismic parameters from noisy stellar oscillation data.

Findings

Large frequency separation can be extracted from poor SNR data.

Method reveals regularities in stellar oscillation periodograms.

Applicable to both solar and stellar data.

Abstract

Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because they give information about e.g. the evolutionary state and the mass of a star. Aims. We want to develop a robust method to determine the large and small frequency separations for time series with low signal-tonoise ratio. For this purpose, we analyse a time series of the Sun from the GOLF instrument aboard SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite by employing a combination of Fourier and Hilbert transform. Methods. We use the analytic signal of filtered stellar oscillation time series to compute the signal envelope. Spectral analysis of the signal envelope then reveals frequency differences of dominant modes in the periodogram of the stellar time series. Results. With the described method the large frequency separation $\Delta\nu$ can be extracted from the envelope spectrum even for data of poor signal-to-noise ratio. A modification of the method allows for an overview of the regularities in the periodogram of the time series.