Inconsistencies in the application of harmonic analysis to pulsating stars

TL;DR

This paper reveals that certain pulsating stars have non-analytic light curves, challenging the assumption that all physical processes can be modeled as smooth, continuous functions, and questions the validity of Fourier analysis in these cases.

Contribution

It provides the first counterexample showing that some stellar light curves are non-analytic, undermining the use of Fourier analysis for these pulsating stars.

Findings

Light curves of some AF pulsating stars are non-analytic.

Fourier expansion is not guaranteed for these stars.

Periodograms may not reliably estimate frequency content in these cases.

Abstract

Using ultra-precise data from space instrumentation we found that the underlying functions of stellar light curves from some AF pul- sating stars are non-analytic, and consequently their Fourier expansion is not guaranteed. This result demonstrates that periodograms do not provide a mathematically consistent estimator of the frequency content for this kind of variable stars. More importantly, this constitutes the first counterexample against the current paradigm which considers that any physical process is described by a contin- uous (band-limited) function that is infinitely differentiable.