Irregular time series in astronomy and the use of the Lomb-Scargle periodogram

TL;DR

This paper evaluates the effectiveness of the Lomb-Scargle periodogram for detecting signals in irregularly sampled astronomical time series, comparing it with simpler methods and discussing the Nyquist frequency in this context.

Contribution

It demonstrates that simpler techniques often yield results comparable to Lomb-Scargle, clarifies the interpretation of Nyquist frequency for irregular sampling, and discusses practical implementation issues.

Findings

Simpler methods often match Lomb-Scargle results in astronomical data analysis.

The meaning of Nyquist frequency is clarified for irregular sampling.

Lomb-Scargle's theoretical advantages may not always translate into practical benefits.

Abstract

Detection of a signal hidden by noise within a time series is an important problem in many astronomical searches, i.e. for light curves containing the contributions of periodic/semi-periodic components due to rotating objects and all other astrophysical time-dependent phenomena. One of the most popular tools for use in such studies is the "periodogram", whose use in an astronomical context is often not trivial. The "optimal" statistical properties of the periodogram are lost in the case of irregular sampling of signals, which is a common situation in astronomical experiments. Parts of these properties are recovered by the "Lomb-Scargle" (LS) technique, but at the price of theoretical difficulties, that can make its use unclear, and of algorithms that require the development of dedicated software if a fast implementation is necessary. Such problems would be irrelevant if the LS periodogram could be used to significantly improve the results obtained by approximated but simpler techniques. In this work we show that in many astronomical applications simpler techniques provide results similar to those obtainable with the LS periodogram. The meaning of the "Nyquist frequency" is also discussed in the case of irregular sampling.