RR Lyrae stars as standard candles in the Gaia Data Release 2 Era

We present results from the analysis of 401 RR Lyrae stars (RRLs) belonging to the field of the Milky Way (MW). For a fraction of them multiband (V, K_s, W1) photometry, metal abundances, extinction values, and pulsation periods are available in the literature and accurate trigonometric parallaxes measured by the Gaia mission alongside Gaia G-band time-series photometry have become available with the Gaia Data Release 2 (DR2) on 2018 April 25. Using a Bayesian fitting approach, we derive new near-, mid-infrared period-absolute magnitude-metallicity (PMZ) relations and new absolute magnitude-metallicity relations in the visual (M_V-[Fe/H]) and G bands (M_G-[Fe/H]), based on the Gaia DR2 parallaxes. We find the dependence of luminosity on metallicity to be higher than usually found in the literature, irrespective of the passband considered. Running the adopted Bayesian model on a simulated data set we show that the high-metallicity dependence is not caused by the method, but likely arises from the actual distribution of the data and the presence of a zero-point offset in the Gaia parallaxes. We infer a zero-point offset of -0.057 mas, with the Gaia DR2 parallaxes being systematically smaller. We find the RR Lyrae absolute magnitude in the V, G, K_s, and W1 bands at metallicity of [Fe/H] = -1.5 dex and period of P = 0.5238 d, based on Gaia DR2 parallaxes to be M_V = 0.66 ± 0.06 mag, M_G = 0.63 ± 0.08 mag, M_{K_s}=-0.37± 0.11 mag, and M_W1 = -0.41 ± 0.11 mag, respectively.