Self-consistent method to extract non-linearities from pulsating stars light curves I. Combination frequencies

TL;DR

This paper introduces a novel method based on the Volterra series to extract and distinguish non-linear combination frequencies from pulsating star light curves, improving mode identification and revealing hidden frequencies.

Contribution

The paper presents a new non-linear fitting approach that accurately extracts combination frequencies, reducing uncertainties and enhancing asteroseismic analysis of pulsating stars.

Findings

Method effectively isolates combination frequencies from power spectra.

Extracted frequencies have uncertainties much smaller than Rayleigh dispersion.

Compatible with classical O-C method for mono-periodic stars.

Abstract

Combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light curve of a given multi-periodic pulsating star, they can compromise the mode identification in an asteroseismic analysis, hence they must be treated as spurious frequencies and conveniently removed. In this paper, a method based on fitting the set of frequencies that best describe a general non-linear model, like the Volterra series, is presented. The method allows to extract these frequencies from the power spectrum, so helping to improve the frequency analysis enabling hidden frequencies to emerge from the initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, usually taken as the present error in a standard frequency analysis. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method opens the possibility to characterise the non-linear behaviour of a given pulsating star by studying in detail the complex generalised transfer functions.