Galactic Trajectories of Interstellar Objects 1I/'Oumuamua, 2I/Borisov, and 3I/Atlas

Abstract

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 perform Monte Carlo orbital integrations using 10,000 trajectory ensembles per object to properly account for measurement uncertainties in both object velocities and Solar motion parameters. We implement a Bayesian statistical framework that combines a Rayleigh-like likelihood function with star formation rate priors to infer stellar ages from the maximum vertical excursions ($z_{\text{max}}$) of orbital trajectories. The likelihood function incorporates age-dependent velocity dispersions reflecting the thin-thick disk transition and dynamical heating over galactic history. Our Monte Carlo analysis yields median $z_{\text{max}}$ values of 0.016 $\pm$ 0.002 kpc for 1I/`Oumuamua, 0.121 $\pm$ 0.010 kpc for 2I/Borisov, and 0.480 $\pm$ 0.020 kpc for 3I/ATLAS. The Bayesian age inference indicates that 1I/`Oumuamua originated from a young stellar system (1.0 Gyr, 68\% CI: 0.1-4.1 Gyr), 2I/Borisov from an intermediate-age population (3.8 Gyr, 68\% CI: 1.8-5.9 Gyr), and 3I/ATLAS from an old thick-disk source (9.6 Gyr, 68\% CI: 7.8-10.3 Gyr). These results demonstrate clear age discrimination where smaller vertical excursions correspond to younger stellar origins.