Separation between the X-ray to optical positions for the 842 direct matches of LG11-Gaia stars with the eRASS1 catalog. All 2148 possible Gaia-DR2 CTPs found with the reverse match within 15” are shown in gray. The same objects after the application of their P.M. correction are plotted in green. The red histogram represents the Gaia-DR2 CTP that is closest to each eRASS1 source of our sample, the 734 closest CTPs that correspond to the LG11-Gaia stars studied in this work are shown in blue, and the final LG11-Gaia/eRASS1 sample of 673 M dwarfs is shown in black.