On the use of Principal Component Analysis in analysing Cepheid light curves

We show how Principal Component Analysis can be used to analyse the structure of Cepheid light curves. This method is more efficient than Fourier analysis at bringing out changes in light curve shape as a function of period. Using this technique, we study the shape of fundamental and first overtone mode Cepheid light curves in the Galaxy, LMC and SMC over a wide period range. For fundamentals, we find evidence for structural changes at $\log P \approx 1.55, 2.1$. It is suggested that the feature at $\log P \approx 2.1$ is associated with a resonance in the Cepheid normal mode spectrum. For overtones, we recover the Z shape in the $R_{21}$ period plane and reproduce the metallicity dependence of this Z shape.