Distance estimates for AGB stars from parallax measurements

Context. 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. Aims. This paper aims to assess the reliability of the distances derived with Gaia DR3 parallaxes for AGB stars, and provide a new distance catalogue for a sample of similar to 200 nearby AGB stars. Methods. 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 then calculated the distances of a total of similar to 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 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. Results. We find that the errors on the Gaia DR3 parallaxes given in the Gaia DR3 catalogue are underestimated by a factor of 5.44 for the brightest sources (G < 8 mag). Fainter sources (8 <= 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. After correcting the DR3 parallaxes, we find that the derived distances are associated with significant, asymmetrical errors for more than 40% of the sources in our sample. We obtain a PL relation of the form Mbol = (- 3.31 +/- 0.24) [log P - 2.5]+(-4.317 +/- 0.060) for the oxygen-rich Mira variables in the Milky Way. A new distance catalogue based on these results is provided for the sources in the DEATHSTAR sample. Conclusions. The corrected Gaia DR3 parallaxes can be used to estimate distances for AGB stars using the AGB prior, but we confirm that one needs to be careful when the uncertainties on parallax measurements are larger than 20%, which can result in model-dependent distances and source-dependent offsets. We find 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