A comparative study of four significance measures for periodicity detection in astronomical surveys

TL;DR

This paper compares four statistical methods for detecting periodic signals in large astronomical datasets, focusing on false alarm probability estimation, computational efficiency, and robustness across different observational cadences.

Contribution

It evaluates and contrasts the effectiveness of the F^M, Baluev, GEV, and direct threshold estimation methods for large-scale periodicity detection in Gaia data.

Findings

GEV and Baluev methods perform well for large-scale processing

GEV provides the best scientific accuracy with moderate pre-processing

Baluev offers a computationally inexpensive alternative with some biases

Abstract

We study the problem of periodicity detection in massive data sets of photometric or radial velocity time series, as presented by ESA's Gaia mission. Periodicity detection hinges on the estimation of the false alarm probability (FAP) of the extremum of the periodogram of the time series. We consider the problem of its estimation with two main issues in mind. First, for a given number of observations and signal-to-noise ratio, the rate of correct periodicity detections should be constant for all realized cadences of observations regardless of the observational time patterns, in order to avoid sky biases that are difficult to assess. Second, the computational loads should be kept feasible even for millions of time series. Using the Gaia case, we compare the $F^M$ method (Paltani 2004, Schwarzenberg-Czerny 2012), the Baluev method (Baluev 2008) and the GEV method (S\"uveges 2014), as well as a method for the direct estimation of a threshold. Three methods involve some unknown parameters, which are obtained by fitting a regression-type predictive model using easily obtainable covariates derived from observational time series. We conclude that the GEV and the Baluev methods both provide good solutions to the issues posed by a large-scale processing. The first of these yields the best scientific quality at the price of some moderately costly pre-processing. When this pre-processing is impossible for some reason (e.g. the computational costs are prohibitive or good regression models cannot be constructed), the Baluev method provides a computationally inexpensive alternative with slight biases in regions where time samplings exhibit strong aliases.