Abstract

Context. The recent early third data release (EDR3) from the Gaia mission has produced parallaxes for 1.468 x 10(9) sources with better quality than those reported in the previous data release. Nevertheless, there are calibration issues with the data that require corrections to the published values and uncertainties. Aims. We want to properly characterize the behavior of the random and systematic uncertainties of the Gaia EDR3 parallaxes in order to maximize the precision of the derived distances without compromising their accuracy. We also aim to provide a step-by-step procedure for the calculation of distances to stars and stellar clusters when using these parallaxes. Methods. We reanalyzed some of the data presented in the calibration papers for quasar and Large Magellanic Cloud (LMC) parallaxes and combine these results with measurements for six bright globular clusters. We calculated the angular covariance of EDR3 parallaxes at small separations (up to a few degrees) based on the LMC results and combined it with the results for larger angles using quasars to obtain an approximate analytical formula for the angular covariance over the whole sky. The results for the six globular clusters were used to validate the parallax bias correction as a function of magnitude, color, and ecliptic latitude and to determine the multiplicative constant k used to convert internal uncertainties to external ones. Results. The angular covariance at zero separation is estimated to be 106 mu as(2), yielding a minimum (systematic) uncertainty for EDR3 parallaxes of 10.3 mu as for individual stars or compact stellar clusters. This value can be slightly reduced for globular clusters that span greater than or similar to 30 ' after considering the behavior of the angular covariance of the parallaxes for small separations. A recent parallax bias correction is found to work quite well, except perhaps for the brighter magnitudes, where improvements may be possible. The value of k is found to be 1.1-1.7 and to depend on G. We find that stars with moderately large values of the renormalized unit weight error can still provide useful parallaxes, albeit with larger values of k. We give accurate and precise Gaia EDR3 distances to the six globular clusters, and for the specific case of 47 Tuc we are able to beat the angular covariance limit through the use of the background Small Magellanic Cloud as a reference and derive a high-precision distance of 4.53 +/- 0.06 kpc. Finally, a recipe for the derivation of distances to stars and stellar clusters using Gaia EDR3 parallaxes is given.