Determination of Cepheid parameters by light‐curve template fitting

We describe techniques to characterize the light curves of regular variable stars by applying principal component analysis (PCA) to a training set of high‐quality data, and to fit the resulting light‐curve templates to sparse and noisy photometry to obtain parameters such as periods, mean magnitudes etc. The PCA approach allows us to efficiently represent the multiband light‐curve shapes (LCSs) of each variable, and hence quantitatively describe the average behaviour of the sample as a smoothly varying function of period, and also the range of variation around this average. In this paper we focus particularly on the utility of such methods for analysing Hubble Space Telescope ( HST ) Cepheid photometry, and present simulations which illustrate the advantages of our PCA template‐fitting approach. These are: accurate parameter determination, including LCS information; simultaneous fitting to multiple passbands; quantitative error analysis; objective rejection of variables with non‐Cepheid‐like light curves or those with potential period aliases. We also use PCA to confirm that Cepheid LCSs are systematically different (at the same period) between the Milky Way and the Large and Small Magellanic Clouds, and consider whether LCS might therefore be used to estimate the mean metallicities of Cepheid samples, thus allowing metallicity corrections to be applied to derived distance estimates.