Distance estimates for AGB stars from parallax measurements

Estimating the distances to asymptotic giant branch (AGB) stars using optical measurements of their parallaxes is not straightforward because of the large uncertainties introduced by their dusty envelopes, their large angular sizes, and their surface brightness variability. We compared the parallaxes from Gaia DR3 with parallaxes measured with maser observations with very long baseline interferometry (VLBI) to determine a statistical correction factor for the DR3 parallaxes using a sub-sample of 33 maser-emitting oxygen-rich nearby AGB stars. We found that the nominal errors on the Gaia DR3 parallaxes are underestimated by a factor of 5.44 for the brightest sources ($G<8$ mag). Fainter sources ($8\leq G<12$) require a lower parallax error inflation factor of 2.74. We obtain a Gaia DR3 parallax zero-point offset of -0.077 mas for bright AGB stars. The offset becomes more negative for fainter AGB stars. We calculated the distances of about 200 AGB stars in the DEATHSTAR project using a Bayesian statistical approach on the corrected DR3 parallaxes and a prior based on the previously determined Galactic distribution of AGB stars. We found that the derived Gaia distances are associated with significant, asymmetrical errors for more than 40% of the sources in our sample. We performed radiative transfer modelling of the stellar and dust emission to determine the luminosity of the sources in the VLBI sub-sample based on the distances derived from maser parallaxes, and derived a new bolometric period-luminosity relation for Galactic oxygen-rich Mira variables. A new distance catalogue based on these results is provided for the sources in the DEATHSTAR sample. We found that a RUWE (re-normalised unit weight error) below 1.4 does not guarantee reliable distance estimates and we advise against the use of only the RUWE to measure the quality of Gaia DR3 astrometric data for individual AGB stars.