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Light curve analysis of Variable stars using Fourier coefficients and Principal Component Analysis

We present an efficient and robust method of light curve analysis of variable stars. While several studies have successfully employed Fourier decomposition technique for the structural analysis of a variety of light curves, a few studies have performed a principal component analysis (PCA) by using Fourier components as inputs to reduce the dimensionality further. In this paper, we employ the PCA technique to a large database of RR Lyrae and Cepheid light curves directly and compare the results with those obtained by the Fourier decomposition technique. We show that the first few principal components (PCs) allow us to extract most of the information when the input matrix is an array of magnitudes at different epochs rather than the Fourier coefficients. The first few PCs are thus enough to reconstruct the original light curves, reducing the data dimensionality by a factor of 2 to 3 compared to the Fourier coefficients. The analysis enables us to separate out the modes of RR Lyrae stars and to look for previously known and suspected resonances of Cepheid variables. We also demonstrate that the PCA technique can be used to classify variables into different classes in an automated, unsupervised way, a feature that has immense potential for large databases of the future.