Dynamical traceback age of the Octans young stellar association

Octans is one of the most distant ($d pc) young stellar associations of the solar neighbourhood, and it has not yet been sufficiently explored. Its age is still poorly constrained in the literature and requires further investigation. We take advantage of the state-of-the-art astrometry delivered by the third data release of the Gaia space mission combined with radial velocity measurements obtained from high-resolution spectroscopy to compute the 3D positions and 3D spatial velocities of the stars and derive the dynamical traceback age of the association. We created a clean sample of cluster members by removing potential outliers from our initial list of candidate members. We then performed an extensive traceback analysis using different subsamples of stars, different metrics to define the size of the association, and different models for the Galactic potential to integrate the stellar orbits in the past. We derive a dynamical age of $34^ $ Myr that is independent from stellar models and represents the most precise age estimate currently available for the Octans association. After correcting the radial velocity of the stars for the effect of gravitational redshift, we obtain a dynamical age of $33^ $ Myr, which is in very good agreement with our first solution. This shows that the effect of gravitational redshift is small for such a distant young stellar association. Our result is also consistent with the less accurate age estimates obtained in previous studies from lithium depletion (30-40 Myr) and isochrones (20-30 Myr). By integrating the stellar orbits in time, we show that the members of Octans and Octans-Near had different locations in the past, which indicates that the two associations are unrelated despite the close proximity in the sky. This is the first reliable and precise dynamical age result for the Octans young stellar association. Our results confirm that it is possible to derive precise dynamical ages via the traceback method for $ Myr old stellar clusters at about $ pc with the same precision level that has been achieved in other studies for young stellar groups within 50 pc of the Sun. This represents one more step towards constructing a self-consistent age scale based on the 3D space motion of the stars in the young stellar clusters of the solar neighbourhood.