Full 5D characterisation of the Sagittarius stream with Gaia DR2 RR Lyrae

Context. The Sagittarius (Sgr) stream is one of the best tools that we currently have to estimate the mass and shape of our Galaxy. However, assigning membership and obtaining the phase-space distribution of the stars that form the tails of the stream is quite challenging.Aims. Our goal is to produce a catalogue of the RR Lyrae stars of Sgr and obtain an empiric measurement of the trends along the stream in sky position, distance, and tangential velocity.Methods. We generated two initial samples from the Gaia DR2 RR Lyrae catalogue: one selecting only the stars within 20 degrees of the orbital plane of Sagittarius (Strip), and the other resulting from application of the Pole Count Map (nGC3) algorithm. We then used the model-independent, deterministic method developed in this work to remove most of the contamination by detecting and isolating the stream in distance and proper motions.Results. The output is two empiric catalogues: the Strip sample (higher-completeness, lower-purity) which contains 11 677 stars, and the nGC3 sample (higher-purity, lower-completeness) with 6608 stars. We characterise the changes along the stream in all the available dimensions, namely the five astrometric dimensions plus the metallicity, covering more than 2 pi rad in the sky, and obtain new estimates for the apocentres and the mean [Fe/H] of the RR Lyrae population. Also, we show the first map of the two components of the tangential velocity thanks to the combination of distances and proper motions. Finally, we detect the bifurcation in the leading arm and report no significant difference between the two branches in terms of metallicity, kinematics, or distance.Conclusions. We provide the largest sample of RR Lyrae candidates of Sgr, which can be used as input for a spectroscopic follow-up or as a reference for the new generation of models of the stream through the interpolators in distance and velocity that we constructed.