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Estimating the distances to asymptotic giant branch (AGB) stars using opticalmeasurements of their parallaxes is not straightforward because of the largeuncertainties introduced by their dusty envelopes, their large angular sizes,and their surface brightness variability. We compared the parallaxes from GaiaDR3 with parallaxes measured with maser observations with very long baselineinterferometry (VLBI) to determine a statistical correction factor for the DR3parallaxes using a sub-sample of 33 maser-emitting oxygen-rich nearby AGBstars. We found that the nominal errors on the Gaia DR3 parallaxes areunderestimated 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 factorof 2.74. We obtain a Gaia DR3 parallax zero-point offset of -0.077 mas forbright AGB stars. The offset becomes more negative for fainter AGB stars. Wecalculated the distances of about 200 AGB stars in the DEATHSTAR project usinga Bayesian statistical approach on the corrected DR3 parallaxes and a priorbased on the previously determined Galactic distribution of AGB stars. We foundthat the derived Gaia distances are associated with significant, asymmetricalerrors for more than 40% of the sources in our sample. We performed radiativetransfer modelling of the stellar and dust emission to determine the luminosityof the sources in the VLBI sub-sample based on the distances derived from maserparallaxes, and derived a new bolometric period-luminosity relation forGalactic oxygen-rich Mira variables. A new distance catalogue based on theseresults is provided for the sources in the DEATHSTAR sample. We found that aRUWE (re-normalised unit weight error) below 1.4 does not guarantee reliabledistance estimates and we advise against the use of only the RUWE to measurethe quality of Gaia DR3 astrometric data for individual AGB stars.

Distance estimates for AGB stars from parallax measurements