Context. The β Pictoris moving group is one of the most well-known young associations in the solar neighbourhood and several members are known to host circumstellar discs, planets, and comets. Measuring its age precisely is essential to the study of several astrophysical processes, such as planet formation and disc evolution, which are strongly age-dependent. Aims. We aim to determine a precise and accurate dynamical traceback age for the β Pictoris moving group. Methods. Our sample combines the extremely precise Gaia DR2 astrometry with ground-based radial velocities measured in an homogeneous manner. We use an updated version of our algorithm to determine dynamical ages. The new approach takes into account a robust estimate of the spatial and kinematic covariance matrices of the association to improve the sample selection process and to perform the traceback analysis. Results. We estimate a dynamical age of 18.5−2.4+2.0 Myr for the β Pictoris moving group. We investigated the spatial substructure of the association at the time of birth and we propose the existence of a core of stars that is more concentrated. We also provide precise radial velocity measurements for 81 members of β Pic, including ten stars with the first determinations of their radial velocities. Conclusions. Our dynamical traceback age is three times more precise than previous traceback age estimates and, more importantly, for the first time it reconciles the traceback age with the most recent estimates of other dynamical, lithium depletion boundaries and isochronal ages. This has been possible thanks to the excellent astrometric and spectroscopic precisions, the homogeneity of our sample, and the detailed analysis of binaries and membership.

Context. The distribution of member stars in the surroundings of an open cluster (OC) can shed light on the process of its formation, evolution, and dissolution. The analysis of structural parameters of OCs as a function of their age and position in the Galaxy constrains theoretical models of cluster evolution. The Gaia catalog is very appropriate for finding members of OCs at large distance from their centers. Aims. We revisit the membership lists of OCs from the solar vicinity, in particular, by extending these membership lists to the peripheral areas through Gaia EDR3. We then take advantage of these new member lists to study the morphological properties and the mass segregation levels of the clusters. Methods. We used the clustering algorithm HDBSCAN on Gaia parallaxes and proper motions to systematically search for members up to 50 pc from the cluster centers. We fit a King’s function on the radial density profile of these clusters and a Gaussian mixture model (GMM) on their two-dimensional member distribution to study their shape. We also evaluated the degree of mass segregation of the clusters and the correlations of these parameters with the age and Galactic position of the clusters. Results. Our method performs well on 389 clusters out of the 467 clusters we selected, including several recently discovered clusters that were poorly studied until now. We report the detection of vast coronae around almost all the clusters and report the detection of 71 OCs with tidal tails. This multiplies the number of these structures that are identified by more than four. The size of the cores is smaller for old clusters than for young ones on average. Moreover, the overall size of the clusters seems to increase slightly with age, but the fraction of stars in the halo seems to decrease. As expected, the mass segregation is more pronounced in the oldest clusters, but no clear trend with age is evident. Conclusions. OCs are more extended than previously expected, regardless of their age. The decrease in the proportion of stars populating the clusters halos highlights the different cluster evaporation processes and the short timescales they need to affect the clusters. Reported parameters such as cluster sizes or mass segregation levels all depend on cluster ages, but cannot be described as single functions of time.