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Gaia Early Data Release 3 (Gaia EDR3) gives trigonometric parallaxes fornearly 1.5 billion sources. Inspection of the EDR3 data for sources identifiedas quasars reveals that their parallaxes are biased, that is systematicallyoffset from the expected distribution around zero, by a few tens ofmicroarcsec. We attempt to map the main dependencies of the parallax bias inEDR3. In principle this could provide a recipe for correcting the EDR3parallaxes. For faint sources the quasars provide the most direct way toestimate parallax bias. In order to extend this to brighter sources and abroader range of colours, we use differential methods based on physical pairs(binaries) and sources in the Large Magellanic Cloud. The functional forms ofthe dependencies are explored by mapping the systematic differences betweenEDR3 and DR2 parallaxes. The parallax bias is found to depend in a non-trivialway on (at least) the magnitude, colour, and ecliptic latitude of the source.Different dependencies apply to the five- and six-parameter solutions in EDR3.While it is not possible to derive a definitive recipe for the parallaxcorrection, we give tentative expressions to be used at the researcher'sdiscretion and point out some possible paths towards future improvements.

Gaia Early Data Release 3: Parallax bias versus magnitude, colour, and position