We combine observed metallicity, optical and infrared magnitudes with evolutionary and pulsation models to derive average luminosities for 156 single-mode RR Lyrae stars. These luminosities are compared with those obtained from the Gaia EDR3 parallaxes, and found in excellent agreement with the high accuracy subsample (62 stars, with relative parallax errors less than 2%). With the temperature and metallicity scale used, no parallax shift seems to be necessary when alpha-enhanced evolutionary models are employed. Some 10% of the sample shows curious `distance keeping' between the evolutionary and pulsation models. The cause of this behavior is not clear at this moment but can be cured by an excessive increase of the reddening.
Comment: Submitted to A&A Letters. After the 1st (positive) referee report. Size: 0.24Mb