Metallicity-light curve relation for RR Lyrae in Kepler field based on the PTF public released data

The Palomar Transient Factory (PTF) is a synoptic survey, mainly using the 48-inch telescope located at the Palomar Observatory, for detecting transients in the Universe. The accumulated time-series photometric data can also be used in other studies beside transients, such as asteroids and variable stars studies. In this work, we used the PTF public released data to derive the metallicity-light curve relation for RR Lyrae located in the Kepler Survey Field, at which spectroscopic measurements of their metallicity are also available from literature. We only concentrated on the fundamental mode RR Lyrae (the ab-type) that do not exhibit Blazhko effect. Based on a subset of good fitted light curves with Fourier decomposition technique, the metallicity-light curve relation in R_PTF-band is found to be [Fe/H] = -3.261 - 8.274P + 1.219φ₃₁.