Revisiting the proper motions of M31 and M33 using massive supergiant stars with Gaia DR3

The proper motions (PMs) of M31 and M33 are key to understanding the Local Group’s dynamical evolution. However, measurement discrepancies between Gaia blue and red samples, regarding whether the transverse velocity is remarkable, introduce significant ambiguity. In this work, we remeasure the systemic PMs of M31 and M33 using massive supergiant stars from Gaia Data Release 3. Clean disk tracers are selected via color–color diagrams, with foreground contaminants removed through kinematic and astrometric cuts. We identify the discrepancy in M31’s blue and red samples as arising from systematic differences between Gaia ’s five-parameter (5p) and six-parameter (6p) astrometric solutions. The 6p solution, applied to sources lacking accurate color information, relies on a pseudo-color approximation, leading to lower precision and larger uncertainties. Two key limitations of the 6p solution are: (1) degraded astrometric accuracy for very red sources ( G BP − G RP > 2.6); (2) significant PM zero-point offsets. In our sample, red sources are dominated by the 6p solution, while blue sources include a substantial fraction of 5p sources; this mismatch drives the observed discrepancy. By excluding extreme red sources and calibrating PM zero-points separately for 5p and 6p sources using background quasars, we reduce the discrepancy, bringing blue and red measurements into agreement within 1 σ . We ultimately report the most robust Gaia -based PMs using high-quality 5p sources. For M31, we obtain ( μ α ∗ , μ δ ) M31 = (45.9±8.1, − 20.5±6.6)μas yr −1 , consistent with, but more precise than, the HST result. For M33, we find that ( μ α ∗ , μ δ ) M33 = (45.3±9.7, 26.3±7.3) μ as yr −1 , which agrees with the VLBA measurement within 1.5 σ . These results support a first infall scenario for M33.