Infrared period-luminosity relations of Galactic Miras based on multi-epoch photometry and the Gaia parallax uncertainty

Miras and other long-period variable (LPV) stars on the AGB follow period-luminosity (PL) relations. These relations have been difficult to study for Galactic LPVs because their distances were poorly known in the past. We aim to establish the PL relations of solar-neighbourhood Miras for several near-IR photometric bands. To this end, we used multi-epoch photometry from the DIRBE and unTimely/WISE catalogues, Gaia parallax distances, and contemporary pulsation periods obtained from optical observations of a well-selected sample of solar-neighbourhood Miras. We show that clearly defined PL relations in the nine investigated near-IR bands emerge from our data, and we report the slopes and zero-point magnitudes. We find that Galactic Miras are fainter in the near-IR than their Large Magellanic Cloud siblings. We derive average period-temperature, period-bolometric-luminosity, and period-radius relations from fits to synthetic SEDs constructed from the PL relations. By applying AGB evolutionary models, the scatter of stars around the PL sequences can also be used to test whether the parallax uncertainties quoted in the Gaia catalogue are realistic. Furthermore, we performed such tests based on a comparison with parallaxes obtained with the VLBI and with a sample of LPVs in the globular cluster 47 Tuc. We conclude that, for Galactic Miras with a fractional parallax uncertainty of<0.1 in the Gaia catalogue, the parallax uncertainty is underestimated by factors between 1.0 and 1.7, and most likely by $\sim1.3$. For more uncertain parallaxes, we find evidence that the distances (parallaxes) are generally overestimated (underestimated). Nevertheless, we find strong evidence that the large error-inflation factors reported for AGB stars in the literature are unrealistic. Our results lend confidence to the parallax measurements of these highly extended, variable stars.