Using Io's Sulfur Isotope Cycle to Understand the History of Tidal Heating

Stable isotope fractionation of sulfur offers a window into Io's tidal heating history, which is difficult to constrain because Io's dynamic atmosphere and high resurfacing rates leave it with a young surface. We constructed a numerical model to describe the fluxes in Io's sulfur cycle using literature constraints on rates and isotopic fractionations of relevant processes. Combining our numerical model with measurements of the ³⁴S/³²S ratio in Io's atmosphere, we constrain the rates for the processes that move sulfur between reservoirs and model the evolution of sulfur isotopes over time. Gravitational stratification of SO₂ in the upper atmosphere, leading to a decrease in ³⁴S/³²S with increasing altitude, is the main cause of sulfur isotopic fractionation associated with loss to space. Efficient recycling of the atmospheric escape residue into the interior is required to explain the ³⁴S/³²S enrichment magnitude measured in the modern atmosphere. We hypothesize this recycling occurs by SO₂ surface frost burial and SO₂ reaction with crustal rocks, which founder into the mantle and/or mix with mantle-derived magmas as they ascend. Therefore, we predict that magmatic SO₂ plumes vented from the mantle to the atmosphere will have lower ³⁴S/³²S than the ambient atmosphere, yet are still significantly enriched compared to solar-system average sulfur. Observations of atmospheric variations in ³⁴S/³²S with time and/or location could reveal the average mantle melting rate and hence whether the current tidal heating rate is anomalous compared to Io's long-term average. Our modeling suggests that tides have heated Io for >1.6 Gyr if Io today is representative of past Io.