Empirical relations for cluster RR Lyrae

The most significant contribution to the absolute magnitude M_V_ comes from the period P and from the first Fourier amplitude A_1_, but there are statistically significant contributions also from additional higher order components, most importantly from A_3_ and in a lesser degree from the Fourier phase phi_51_.

When different colors are combined in reddening-free quantities, we obtain basically period-luminosity-color relations. From the standard deviations of the various regressions, an upper limit can be obtained on the overall inhomogeneity of the reddening in the individual clusters. This yields {sigma}_E(B-V)_<0.012mag, which also implies an average minimum observational error of {sigma}_V_>0.018mag.