Context. The details of the effect of the bar and spiral arms on the disc dynamics of the Milky Way are still unknown. The stellar velocity distribution in the solar neighbourhood displays kinematic substructures, which are possibly signatures of these processes and of previous accretion events. With the Gaia mission, more details of these signatures, such as ridges in the V_ϕ − R plane and thin arches in the V_ϕ − V_R plane, have been revealed. The positions of these kinematic substructures, or moving groups, can be thought of as continuous manifolds in the 6D phase space, and the ridges and arches as specific projections of these manifolds.
Aims: Our aim is to detect and characterize the moving groups along the Milky Way disc, sampling the galactocentric radial and azimuthal velocities of the manifolds through the three dimensions of the disc: radial, azimuthal, and vertical. Method. We developed and applied a novel methodology to perform a blind search for substructure in the Gaia EDR3 6D data, which consists in the execution of the wavelet transform in independent small volumes of the Milky Way disc, and the grouping of these local solutions into global structures with a method based on the breadth-first search algorithm from graph theory. We applied the same methodology to simulations of barred galaxies to validate the method and for comparison with the data.
Results: We reveal the skeleton of the velocity distribution, uncovering projections that were not possible before. We sample nine main moving groups along a large region of the disc in configuration space, covering up to 6 kpc, 60 deg, and 2 kpc in the radial, azimuthal, and vertical directions, respectively, extending significantly the range of previous analyses. In the radial direction we find that the groups deviate from the lines of constant angular momentum that one would naively expect from an epicyclic approximation analysis of the first-order effects of resonances. We reveal that the spatial evolution of the moving groups is complex and that the configuration of moving groups in the solar neighbourhood is not maintained along the disc. We also find that the azimuthal velocity of the moving groups that are mostly detected in the inner parts of the disc (Arcturus, Bobylev, and Hercules) is non-axisymmetric. For Hercules we measure an azimuthal gradient of −0.50 km s⁻¹ deg⁻¹ at R = 8 kpc. We detect a vertical asymmetry in the azimuthal velocity for the Coma Berenices moving group, which is not expected for structures originating from a resonance of the bar, supporting the previous hypothesis of the incomplete vertical phase mixing of the group. In our simulations we extract substructures corresponding to the outer Lindblad resonance and the 1:1 resonances and observe the same deviation from constant angular momentum lines and the non-axisymmetry of the azimuthal velocities of the moving groups in the inner part of the disc.
Conclusions: This data-driven characterization is a starting point for a holistic understanding of the moving groups. It also allows for a quantitative comparison with models, providing a key tool to comprehend the dynamics of the Milky Way.