SIMBAD references

Gaia Early Data Release 3 (EDR3) provides trigonometric parallaxes for 1.5 billion stars, with reduced systematics compared to Gaia Data Release 2 and reported precisions better by up to a factor of 2. New to EDR3 is a tentative model for correcting the parallaxes of magnitude-, position-, and color-dependent systematics for five- and six-parameter astrometric solutions, Z₅ and Z₆. Using a sample of over 2000 first-ascent red giant branch stars with asteroseismic parallaxes, I perform an independent check of the Z₅ model in a Gaia magnitude range of 9 <= G <= 13 and color range of 1.4 µm^–1 <= ν_eff <= 1.5 µm^–1. This analysis therefore bridges the Gaia team's consistency check of Z₅ for G > 13 and indications from independent analysis using Cepheids of a ≃15 µas overcorrection for G < 11. I find overcorrection sets in at G <= 10.8, such that Z₅-corrected EDR3 parallaxes are larger than asteroseismic parallaxes by 15 ± 3 µas. For G >= 10.8, EDR3 and asteroseismic parallaxes in the Kepler field agree up to a constant consistent with expected spatial variations in EDR3 parallaxes after a linear, color-dependent adjustment. I also infer an average underestimation of EDR3 parallax uncertainties in the sample of 22% ± 6%, consistent with the Gaia team's estimates at similar magnitudes and independent analysis using wide binaries. Finally, I extend the Gaia team's parallax spatial covariance model to brighter magnitudes (G < 13) and smaller scales (down to ≃0.°1), where systematic EDR3 parallax uncertainties are at least ≃3-4 µas.