Light curve analysis of variable stars using Fourier decomposition and principal component analysis

¹ Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India e-mail: sdeb@physics.du.ac.in,hpsingh@physics.du.ac.in
² CRAL-Observatoire de Lyon, CNRS UMR 142, 69561 Saint-Genis Laval, France

Received: 8 July 2009
Accepted: 1 September 2009

Abstract

Context. Ongoing and future surveys of variable stars will require new techniques to analyse their light curves as well as to tag objects according to their variability class in an automated way.

Aims. We show the use of principal component analysis (PCA) and Fourier decomposition (FD) method as tools for variable star light curve analysis and compare their relative performance in studying the changes in the light curve structures of pulsating Cepheids and in the classification of variable stars.

Methods. We have calculated the Fourier parameters of 17 606 light curves of a variety of variables, e.g., RR Lyraes, Cepheids, Mira Variables and extrinsic variables for our analysis. We have also performed PCA on the same database of light curves. The inputs to the PCA are the 100 values of the magnitudes for each of these 17 606 light curves in the database interpolated between phase 0 to 1. Unlike some previous studies, Fourier coefficients are not used as input to the PCA.

Results. We show that in general, the first few principal components (PCs) are enough to reconstruct the original light curves compared to the FD method where 2 to 3 times more parameters are required to satisfactorily reconstruct the light curves. The computation of the required number of Fourier parameters on average needs 20 times more CPU time than the computation of the required number of PCs. Therefore, PCA does have some advantages over the FD method in analysing the variable stars in a larger database. However, in some cases, particularly in finding the resonances in fundamental mode (FU) Cepheids, the PCA results show no distinct advantages over the FD method. We also demonstrate that the PCA technique can be used to classify variables into different variability classes in an automated, unsupervised way, a feature that has immense potential for larger databases in the future.