An all-sky proper-motion map of the Sagittarius stream using Gaia DR2

Aims. We aim to measure the proper motion along the Sagittarius stream, which is the missing piece in determining its full 6D phase space coordinates.Methods. We conduct a blind search of over-densities in proper motion from the Gaia second data release in a broad region around the Sagittarius stream by applying wavelet transform techniques.Results. 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 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 color-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 pericenter of the trailing arm and an underestimation of the total proper motion for the leading arm.Conclusions. Our study provides a starting point for determining the variation of the population of stars along the stream, the distance to the stream from the red clump stars, and the solar motion. It also permits much more accurate measurement of the Milky Way potential.