Title: Revisiting the Proper Motions of M31 and M33 Using Massive Supergiant Stars with Gaia DR3 Show Chinese title

Title: 使用Gaia DR3的大质量超巨星重新研究M31和M33的自行运动

Abstract: 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 5-parameter (5p) and 6-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 (GBP - GRP > 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 sigma. We ultimately report the most robust Gaia-based PMs using high-quality 5p sources. For M31, we obtain ({\mu}_{\alpha}*, {\mu}_{\delta})_M31 = (45.9 +/- 8.1, -20.5 +/- 6.6) {\mu}as/yr, consistent with, but more precise than, the HST result. For M33, we find ({\mu}_{\alpha}*, {\mu}_{\delta})_M33 = (45.3 +/- 9.7, 26.3 +/- 7.3) {\mu}as/yr, agreeing with VLBA measurement within 1.5 sigma. These results support a first infall scenario for M33. Show Chinese abstract

Abstract: M31和M33的自行（PMs）对于理解本星系群的动力学演化至关重要。 然而，Gaia蓝色样本和红色样本之间的测量差异，关于横向速度是否显著，引入了重大歧义。 在本工作中，我们使用Gaia数据发布3中的大量超巨星重新测量M31和M33的整体自行。 通过颜色-颜色图选择干净的盘面示踪物，并通过运动学和天体测量切割去除前景污染。 我们将M31的蓝色样本和红色样本之间的差异归因于Gaia的5参数（5p）和6参数（6p）天体测量解之间的系统性差异。 6p解应用于缺乏准确颜色信息的源，依赖于伪颜色近似，导致精度较低和不确定性较大。 6p解的两个关键限制是：1）非常红的源（GBP - GRP > 2.6）的天体测量精度下降；2）显著的自行零点偏移。 在我们的样本中，红色源主要由6p解主导，而蓝色源包括相当一部分的5p源；这种不匹配导致了观察到的差异。 通过排除极端红色源，并使用背景类星体分别校准5p和6p源的自行零点，我们减少了差异，使蓝色和红色测量结果在1个标准差内达成一致。 最终，我们报告了使用高质量5p源的最可靠Gaia基于的自行。 对于M31，我们得到（{\mu }_{\alpha }*,{\mu }_{\delta })_M31 = (45.9 +/- 8.1, -20.5 +/- 6.6){\mu }as/yr，与HST结果一致，但更精确。 对于M33，我们发现（{\mu }_{\alpha }*,{\mu }_{\delta })_M33 = (45.3 +/- 9.7, 26.3 +/- 7.3){\mu }as/yr，与VLBA测量结果在1.5 sigma范围内一致。 这些结果支持M33的首次吸积情景。