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 multi-band ( V , K _ { \mathrm { s } } , W 1 ) 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 second data release ( 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 dataset 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 W 1 bands at metallicity of [ Fe/H ] = -1.5 dex and period of P = 0.5238 days , based on Gaia DR2 parallaxes to be M _ { V } = 0.66 \pm 0.06 mag , M _ { G } = 0.63 \pm 0.08 mag , M _ { K _ { s } } = -0.37 \pm 0.11 mag and M _ { W 1 } = -0.41 \pm 0.11 mag , respectively .