Principal-component analysis of RR Lyrae light curves

In this paper, we analyse the structure of RRab starlight curves using principal-component analysis. We find this to be a very efficient way of describing many aspects of RRab light-curve structure: in many cases, a principal-component fit with nine parameters can describe a RRab light curve including bumps, whereas a 17-parameter Fourier fit is needed. Consequently, we show statistically why the amplitude is also a good summary of the structure of these RR Lyrae light curves. We also use our analysis to derive an empirical relation relating absolute magnitude to light-curve structure. In comparing this formula with those derived from exactly the same data set but using Fourier parameters, we find that the principal-component analysis approach has distinct advantages. These advantages are, firstly, that the errors on the coefficients multiplying the fitted parameters in such formulae are much smaller, and secondly, that the correlation between the 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 and new large-scale survey projects concerning variable stars.