Principal Component Analysis of RR Lyrae light curves

In this paper, we analyze the structure of RRab star light curves using Principal Component Analysis. We find this is a very efficient way to describe many aspects of RRab light curve structure: in many cases, a Principal Component fit with 9 parameters can describe a RRab light curve including bumps whereas a 17 parameter Fourier fit is needed. As a consequence we show statistically why the amplitude is also a good summary of the structure of a RR Lyrae light curve. We also use our analysis to derive an empirical relation relating absolute magnitude to light curve structure. In comparing this formula to those derived from exactly the same dataset but using Fourier parameters, we find that the Principal Component Analysis approach has disticnt advantages. These advantages are, firstly, that the errors on the coefficients in such formulae are smaller, and secondly, that the correlation between Principal Components is significantly smaller than the correlation between Fourier amplitudes. These two factors lead to reduced formal errors, in some cases estimated to be a factor of 2, on the eventual fitted value of the absolute magnitude. This technique will prove very useful in the analysis of data from existing large scale survey projects concerning variable stars.