Parallaxes and Proper Motions of Long Period Variable Stars Determined from VLBI and Gaia DR3

Annual parallaxes of Galactic long period variable stars (LPVs) are essential for determining their distances and intrinsic properties, but their measurement remains challenging because of their large stellar sizes, circumstellar matter, and time-variable surface brightness asymmetry. In this study, we compare astrometric measurements obtained from very long baseline interferometry (VLBI) and Gaia Data Release 3 (DR3) for 43 Galactic LPVs. The parallaxes from the two methods are generally consistent within uncertainties for about half of the sample, although Gaia DR3 parallaxes tend to be slightly smaller than the VLBI values. This is consistent with previously reported systematic offsets. The behavior of parallax uncertainties differs between the two techniques: VLBI parallax errors increase with increasing parallax, whereas Gaia DR3 errors remain nearly constant. Consequently, VLBI measurements are more effective for LPVs with parallaxes smaller than approximately 2 mas, corresponding to distances beyond 500 pc. Proper motions are also compared, showing general agreement with a 2-sigma dispersion of approximately 13 km s−1, consistent with typical AGB outflow velocities. These results demonstrate the complementarity between VLBI and Gaia astrometry. We also find that the dispersion of parallax residuals becomes slightly larger for sources with pulsation periods around one year, suggesting a coupling of timescales between the stellar pulsation and the annual parallax.