An all-sky proper motion map of the Sagittarius stream using Gaia DR2
We aim to measure the proper motion along the Sagittarius stream that is the missing piece to determine its full 6D phase space coordinates. We conduct a blind search of over-densities in proper motion from Gaia DR2 in a broad region around the Sagittarius stream by applying wavelet transform techniques. We find that for most of the sky patches, the highest intensity peaks delineate the path of the Sagittarius stream. The 1500 peaks identified depict a continuous sequence spanning almost $2\pi$ in the sky, only obscured when the stream crosses the Galactic disk. Altogether, around $100\,000$ stars potentially belong to the stream as indicated by a coarse inspection of the colour-magnitude diagrams. From these stars, we determine the proper motion along the Sagittarius stream, making it the proper motion sequence with the largest span and continuity ever measured for a stream. A first comparison with existing N-body models of the stream reveals some discrepancies, especially near the pericentre of the trailing arm and an overestimation of the total proper motion for the leading arm. Our study can be the starting point for determining the variation of the population of stars along the stream, the distance to the stream with red clump stars, and the solar motion. It will also allow a much better measurement of the Milky Way potential.