Gaia Data Release 3. Astrometric binary star processing

Context. The Gaia Early Data Release 3 contained the positions, parallaxes, and proper motions of 1.5 billion sources, some of which did not show a good fit to the `single star' model. Binarity is one of the causes of this.
Aims: Four million of these stars were selected and various models were tested to detect binary stars and to derive their parameters.
Methods: We used a preliminary treatment to discard the partially resolved double stars and to correct the transits for perspective acceleration. We then investigated whether the measurements show a good fit to an acceleration model with or without jerk. We tried the orbital model when the fit of any acceleration model was beyond our acceptance criteria. We also tried a Variability-Induced Mover (VIM) model when the star was photometrically variable. A final selection was made in order to keep only solutions that probably correspond to the real nature of the stars.
Results: Following our analysis, 338 215 acceleration solutions, about 165 500 orbital solutions, and 869 VIM solutions were retained. In addition, formulae for calculating the uncertainties of the Campbell orbital elements from orbital solutions expressed in Thiele-Innes elements are given in an appendix.