| Abstract
| - Context. The young local associations (YLAs) constitute an excellent sample for the study of a variety of astrophysical topics, especially the star formation process in low-density environments. Data from the Gaia mission allows us to undertake studies of the YLAs with unprecedented accuracy. Aims. We determine the dynamical age and place of birth of a set of associations in a uniform and dynamically consistent manner. There are nine YLAs in our sample ϵ Chamaeleontis, TW Hydrae, β Pictoris, Octans, Tucana-Horologium, Columba, Carina, Argus, and AB Doradus. Methods. We designed a method for deriving the dynamical age of the YLAs based on the orbital integration. The method involves a strategy to account for the effect of observational errors. We tested the method using mock YLAs. Finally, we applied it to our set of nine YLAs with astrometry from the first Gaia data release and complementary on-ground radial velocities from the literature. Results. Our orbital analysis yields a first estimate of the dynamical age of 33 −0+9 Myr, 1313 −0+7 Myr, and 55 −0+23 Myr for ϵ Chamaeleontis, β Pictoris, and Tucana-Horologium, respectively. For four other associations (Octans, Columba, Carina, and Argus), we provide a lower limit for the dynamical age. Our rigorous error treatment indicates that TW Hydrae and AB Doradus deserve further study. Conclusions. The dynamical ages that we obtain are compatible spectroscopic and isochrone fitting ages obtained elsewhere. From the orbital analysis, we suggest a scenario for these YLAs where there were two episodes of star formation: one ~40 Myr ago in the first quadrant that gave birth to ϵ Chamaeleontis, TW Hydrae, and β Pictoris, and another 5−15 Myr ago close to the Sun that formed Tucana-Horologium, Columba, and Carina. Future Gaia data will provide the necessary accuracy to improve the present results, especially for the controversial age determinations, and additional evidence for the proposed scenario once a complete census of YLAs and better membership can be obtained.
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