Detecting multiple periodicities in observational data with the multifrequency periodogram - II. Frequency Decomposer, a parallelized time-series analysis algorithm

TL;DR

This paper introduces FREDEC, a parallelized GPU algorithm for decomposing noisy time series into sinusoidal components, capable of identifying multiple periodicities, including aliases and noise, with applications to exoplanet data.

Contribution

The paper presents a novel GPU-accelerated algorithm for multifrequency analysis of time series, enabling efficient detection of multiple periodic signals including potential new exoplanets.

Findings

Successfully identified known exoplanets in radial-velocity data.

Detected a new 9.8-day variation in 55 Cnc data suggesting a possible sixth planet.

Demonstrated significant performance improvements using GPU parallelization.

Abstract

This is a parallelized algorithm performing a decomposition of a noisy time series into a number of sinusoidal components. The algorithm analyses all suspicious periodicities that can be revealed, including the ones that look like an alias or noise at a glance, but later may prove to be a real variation. After selection of the initial candidates, the algorithm performs a complete pass through all their possible combinations and computes the rigorous multifrequency statistical significance for each such frequency tuple. The largest combinations that still survived this thresholding procedure represent the outcome of the analysis. The parallel computing on a graphics processing unit (GPU) is implemented through CUDA and brings a significant performance increase. It is still possible to run FREDEC solely on CPU in the traditional single-threaded mode, when no suitable GPU device is available. To verify the practical applicability of our algorithm, we apply it to an artificial time series as well as to some real-life exoplanetary radial-velocity data. We demonstrate that FREDEC can successfully reveal several known exoplanets. Moreover, it detected a new $9.8$-day variation in the Lick data for the five-planet system of 55 Cnc. It might indicate the existence of a small sixth planet in the 3:2 commensurability with the planet 55 Cnc b, although this detection is model-dependent and still needs a detailed verification.