Characterizing and correcting the proper motion bias of the bright Gaia EDR3 sources

In this paper we characterize magnitude-dependent systematics in the proper motions of the Gaia EDR3 catalog and provide a prescription for their removal. The reference frame of bright stars (G<13) in EDR3 is known to rotate with respect to extragalactic objects, but this rotation has proven difficult to characterize and correct. We employ a sample of binary stars and a sample of open cluster members to characterize this proper motion bias as a magnitude-dependent spin of the reference frame. We show that the bias varies with G magnitude, reaching up to 80 μas/yr for sources in the range G = 11 - 13, several times the formal EDR3 proper motion uncertainties. We also show evidence for an additional dependence on the color of the source, with a magnitude up to 10 μas/yr. However, a color correction proportional to the effective wavenumber is unsatisfactory for very red or very blue stars and we do not recommend its use. We provide a recipe for a magnitude-dependent correction to align the proper motion of the Gaia EDR3 sources brighter than G=13 with the International Celestial Reference Frame.