The puzzle of combination frequencies found in heat-driven pulsators

TL;DR

This paper investigates the challenge of distinguishing true physical combination frequencies from chance alignments in the frequency spectra of pulsating stars, emphasizing the importance of statistical analysis and simulations.

Contribution

It demonstrates how to differentiate real from spurious combination frequencies using statistical distributions and artificial data comparisons in high-precision space-based observations.

Findings

Significant difference in low-order combinations between stars with and without real frequencies

High probability of chance combinations in random data sets

Careful interpretation of frequency combinations improves asteroseismological analysis

Abstract

Searching for combinations in the frequency spectra of variable stars is a commonly used method within the asteroseismological community, as harmonics and linear combinations of individual frequencies are expected to appear not only by chance, but also as a characteristic signature linked to different physical phenomena, e.g., nonlinear oscillations, binarity, and rotation. Furthermore it is very important to identify independent frequencies for modelling purposes. We show that using high precision data sets delivered by recent space missions, the distinction between combinations having a real physical meaning and spurious combinations which only appear by chance gets more and more difficult. We demonstrate how careful one should be with the interpretation of such combination frequencies by presenting the statistical distributions derived from artificial data sets. Based on comparisons to observations, we find that, despite the high statistical probability of finding combinations in random data sets (having similar properties to the ones of real stars), there is a significant difference in the number of the lowest order combinations between stars with and starts without real combination frequencies. This way, a search for frequency combinations is very useful when interpreted properly, and when results are compared to simulations.