On the basis of an extended set of non-linear convective RR Lyrae pulsation models we derive the first theoretical light curves in the Gaia bands G, G_BP_, and G_RP_ and the corresponding intensity-weighted mean magnitudes and pulsation amplitudes. The effects of chemical composition on the derived Bailey diagrams in the Gaia filters are discussed for both Fundamental and first overtone mode pulsators. The inferred mean magnitudes and colours are used to derive the first theoretical Period-Wesenheit relations for RR Lyrae in the Gaia filters. The application of the theoretical Period-Wesenheit relations for both the Fundamental and first overtone mode to Galactic RR Lyrae in the Gaia Data Release 2 data base and complementary information on individual metal abundances allows us to derive theoretical estimates of their individual parallaxes. These results are compared with the astrometric solutions to conclude that a very small offset, consistent with zero, is required in order to reconcile the predicted distances with Gaia results.

Cone search capability for table J/MNRAS/500/5009/tablea1 (RR Lyrae stars used for the comparison with the models with metallicity from high resolution spectroscopy)