[Paper Review] Validation of the Gaia Early Data Release 3 parallax zero-point model with asteroseismology

Joel Zinn|arXiv (Cornell University)|Jan 18, 2021

Stellar, planetary, and galactic studies114 references69 citations

TL;DR

This study validates the Gaia EDR3 parallax zero-point model (Z5) using asteroseismic parallaxes of 2,000 first-ascent red giant branch stars in the Kepler field. It finds that Z5 over-corrects parallaxes by 15±3 µas for G ≲10.8, while agreement holds at G ≳10.8 after a color-dependent adjustment, and confirms a 22±6% underestimation of EDR3 parallax uncertainties.

ABSTRACT

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 $1.4\mu \mathrm{m} ^{-1} \lesssim u_{\mathrm{eff}} \lesssim 1.5 \mu \mathrm{m} ^{-1}$. 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 $\approx 3-4 \mu \mathrm{as}$.

Motivation & Objective

• To independently test the Gaia EDR3 Z5 parallax zero-point correction model in the magnitude and color range 9 ≲ G ≲13 and 1.4µm⁻¹ ≲ νeff ≲1.5µm⁻¹.
• To assess the accuracy of EDR3 parallaxes and their reported uncertainties using asteroseismic parallaxes as a reference.
• To investigate spatially correlated systematic uncertainties in EDR3 parallaxes at small angular scales.
• To bridge the gap between Gaia team’s validation at G > 13 and independent Cepheid-based studies at G < 11.

Proposed method

• Uses asteroseismic parallaxes derived from νmax and Δν measurements of 2,000 first-ascent red giant branch stars from APOKASC-2 and SYD pipelines.
• Compares Z5-corrected Gaia EDR3 parallaxes to asteroseismic parallaxes as a function of G magnitude and effective temperature (νeff).
• Performs Markov Chain Monte Carlo (MCMC) analysis on a model of the parallax residual as a function of magnitude and color to infer systematic offsets.
• Extends the Gaia team’s spatial covariance model to brighter magnitudes (G < 13) and smaller angular scales (down to ≈0.1°) using a parametric covariance function.
• Quantifies the significance of χ²/dof and Bayesian Information Criterion (BIC) to compare model fits and assess statistical preference.
• Validated results using multiple asteroseismic datasets (APOKASC-2, SYD, and independent studies) to test robustness.

Experimental results

Research questions

• RQ1 Does the Gaia EDR3 Z5 parallax zero-point model produce accurate parallaxes for stars with G ≲13 and 1.4µm⁻¹ ≲ νeff ≲1.5µm⁻¹?
• RQ2 Is there evidence of over-correction in the Z5 model at bright magnitudes (G < 10.8)?
• RQ3 Are the formal uncertainties in Gaia EDR3 parallaxes systematically underestimated?
• RQ4 What is the level of spatially correlated systematic uncertainty in Gaia EDR3 parallaxes at small angular scales (≈0.1°)?
• RQ5 How does the performance of the Z5 model compare to independent estimates from Cepheids and other stellar populations?

Key findings

• The Z5-corrected EDR3 parallaxes are over-corrected by 15±3 µas for stars with G ≲10.8, indicating a systematic over-correction in the model at bright magnitudes.
• For G ≳10.8, EDR3 and asteroseismic parallaxes agree within a constant offset consistent with expected spatial variations after a linear color-dependent adjustment.
• The formal uncertainties in EDR3 parallaxes are on average underestimated by 22±6%, consistent with Gaia team estimates and independent wide binary studies.
• Systematic EDR3 parallax uncertainties at small angular scales (down to ≈0.1°) are at least 3–4 µas, indicating significant spatial correlation.
• The spatial covariance model for EDR3 parallaxes is extended to brighter magnitudes (G < 13), revealing non-negligible systematic uncertainties at sub-degree scales.
• The study provides independent validation of the Z5 model in a previously untested region of parameter space, filling a critical gap between high- and low-magnitude validation studies.