Validation of the Gaia Early Data Release 3 parallax zero-point model with asteroseismology

The 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 two. 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, $Z_5$ and $Z_6$. Using a sample of over 2,000 first-ascent red giant branch stars with asteroseismic parallaxes, I perform an independent check of the $Z_5$ model in a Gaia magnitude range of $9 \lesssim G \lesssim 13$ and color range of $1.4\mu \mathrm{m} ^{-1} \lesssim \nu_{\mathrm{eff}} \lesssim 1.5 \mu \mathrm{m} ^{-1}$. This analysis therefore bridges the Gaia team's consistency check of $Z_5$ for $G > 13$, and indications from independent analysis using Cepheids of a $\approx 15 \mu \mathrm{as}$ over-correction for $G < 11$. I find an over-correction sets in at $G \lesssim 10.8$, such that $Z_5$-corrected EDR3 parallaxes are larger than asteroseismic parallaxes by $15 \pm 3 \mu \mathrm{as}$. For $G \gtrsim 10.8$, 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 under-estimation of EDR3 parallax uncertainties in the sample of $22 \pm 6\%$, 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 $\approx 0.1\deg$), where systematic EDR3 parallax uncertainties are at least $\approx 3-4 \mu \mathrm{as}$.