A 3D view of the Taurus star-forming region by

Context. Taurus represents an ideal region to study the three-dimensional distribution of the young stellar population and relate it to the associated molecular cloud. Aims. The second Gaia data release (DR2) enables us to investigate the Taurus complex in three dimensions, starting from a previously defined robust membership. The molecular cloud structured in filaments can be traced in emission using the public far-infrared maps from Herschel. Methods. From a compiled catalog of spectroscopically confirmed members, we analyze the 283 sources with reliable parallax and proper motions in the Gaia DR2 archive. We fit the distribution of parallaxes and proper motions with multiple populations described by multivariate Gaussians. We compute the cartesian Galactic coordinates (X,Y,Z) and, for the populations associated with the main cloud, also the galactic space velocity (U,V,W). We discuss the spatial distribution of the populations in relation to the structure of the filamentary molecular cloud traced by Herschel. Results. We discover the presence of six populations which are all well defined in parallax and proper motions, with the only exception being Taurus D. The derived distances range between ~130 and ~160 pc. We do not find a unique relation between stellar population and the associated molecular cloud: while the stellar population seems to be on the cloud surface, both lying at similar distances, this is not the case when the molecular cloud is structured in filaments. Taurus B is probably moving in the direction of Taurus A, while Taurus E appears to be moving towards them. Conclusions. The Taurus region is the result of a complex star formation history which most probably occurred in clumpy and filamentary structures that are evolving independently