Turbulent mixing of r-process elements in the Milky Way

We study turbulent gas diffusion affects on r-process abundances in Milky Way stars, by a combination of an analytical approach and a Monte Carlo simulation. Higher r-process event rates and faster diffusion, lead to more efficient mixing corresponding to a reduced scatter of r-process abundances and causing r-process enriched stars to start appearing at lower metallicities. We use three independent observations to constrain the model parameters: (i) the scatter of radioactively stable r-process element abundances, (ii) the largest r-process enrichment values observed in any solar neighborhood stars, and (iii) the isotope abundance ratios of different radioactive r-process elements (²⁴⁴Pu/²³⁸U and ²⁴⁷Cm/²³⁸U) at the early Solar system as compared to their formation. Our results indicate that the Galactic r-process rate and the diffusion coefficient are respectively r < 4 × 10⁻⁵ yr⁻¹, D > 0.1 kpc² Gyr⁻¹ (r < 4 × 10⁻⁶ yr−⁻¹, D > 0.5 kpc² Gyr⁻¹ for collapsars or similarly prolific r-process sources) with allowed values satisfying an approximate anticorrelation such that D ≈ r^(−2/3), implying that the time between two r-process events that enrich the same location in the Galaxy, is τ_(mix) ≈ 100−200 Myr. This suggests that a fraction of ∼0.8 (∼0.5) of the observed ²⁴⁷Cm (²⁴⁴Pu) abundance is dominated by one r-process event in the early Solar system. Radioactively stable element abundances are dominated by contributions from ∼10 different events in the early Solar system. For metal poor stars (with [Fe/H] ≲ −2), their r-process abundances are dominated by either a single or several events, depending on the star formation history.