The Sagittarius stream in Gaia eDR3 and the origin of the bifurcations

The Sagittarius dwarf spheroidal (Sgr) is a dissolving galaxy being tidally disrupted by the Milky Way (MW). Its stellar stream still poses serious modelling challenges, which hinders our ability to use it effectively as a probe of the MW gravitational potential. Our goal is to construct the best possible sample of stars with which we can advance our understanding of the Sgr-MW interaction, focusing on the characterisation of the bifurcations. We improve on previous methods based on the use of the wavelet transform to systematically search for the kinematic signature of the Sgr stream in the Gaia data. We refine our selection via the use of a clustering algorithm on the statistical properties of the colour-magnitude diagrams. Our final sample contains > 700k candidate stars, 3x larger than previous samples. We have been able to detect the bifurcation of the stream in both the northern and southern hemispheres, requiring four branches to fully describe this system. We present the detailed proper motion distribution of the trailing arm as a function of Lambda showing the presence of a sharp edge (on the side of the small proper motions) beyond which there are no Sgr stars. We also characterise the correlation between kinematics and distance. The chemical analysis of our sample shows a significant difference between the faint and bright branches. We provide analytical descriptions for the proper motion trends as well as for the sky distribution of the four branches of the stream. We interpret the bifurcations as the misaligned overlap of the material stripped at the antepenultimate pericentre (faint branches) with the stars ejected at the penultimate pericentre (bright branch). The source of this misalignment is still unknown but we argue that models with some internal rotation in the progenitor, at least during the time of stripping of the stars in the faint branches, are worth exploring.