The first interstellar objects, 1I/'Oumuamua, 2I/Borisov, and 3I/ATLAS, were discovered over the past decade. We follow the trajectories of known interstellar objects in the gravitational potential of the Milky Way galaxy to constrain their possible origin. We performed Monte Carlo orbital integrations using an ensemble of 10, 000 trajectories per object to propagate measurement uncertainties in both object velocities and solar motion parameters through a Milky Way potential. We then used a Bayesian statistical framework that combines the resulting distributions of maximum vertical excursion (z_ max) with age--velocity--dispersion relations and star-formation-rate priors to infer plausible stellar ages. Our Monte Carlo analysis yields median z_ max values of 0. 016 ± 0. 002 kpc for 1I/'Oumuamua, 0. 121 ± 0. 010 kpc for 2I/Borisov, and 0. 481 +0. 023 _ -0. 017 kpc for 3I/ATLAS. The Bayesian age inference indicates that 1I/'Oumuamua originated from a young stellar system (3. 2 Gyr, 68% credible interval (CI): 0. 5--8. 8 Gyr), 2I/Borisov from an intermediate-age population (5. 0 Gyr, 68% CI: 1. 8--9. 7 Gyr), and 3I/ATLAS from an old thick-disk source (8. 7 Gyr, 68% CI: 5. 2--10. 3 Gyr). Taken together, these estimates are consistent with smaller vertical excursions tracing younger parent populations under our stated kinematic assumptions.
Kakharov et al. (Wed,) studied this question.