Computation of the Fourier parameters of RR Lyrae stars by template fitting

Aims.Due to the importance of accurate Fourier parameters, we devise a method that is more appropriate for deriving these parameters for low-quality data than the traditional Fourier fitting. Methods.Based on the accurate light curves of 248 fundamental mode RR Lyrae stars, we test the power of a full-fetched implementation of the template method in the computation of the Fourier decomposition. The applicability of the method is also demonstrated on data sets of filter passbands different from those of the template set. Results.We examine in more detail the question of the estimation of Fourier-based iron abundance [Fe/H] and average brightness. We get, for example, for light curves sampled randomly in 30 data points with $\sigma=0.03$ mag observational noise, that optimized direct Fourier fits yield $\sigma({\rm [Fe/H]})=0.33$, whereas the template fits result in $\sigma({\rm [Fe/H]})=0.18$. Tests made on the RR Lyrae database of the Large Magellanic Cloud of the Optical Gravitational Lensing Experiment support the applicability of the method on real photometric time series. These tests also show that the dominant part of error in estimating the average brightness comes from other sources, most probably from crowding effects, even for under-sampled light curves.