An analytical formulation of isotope fractionation due to self-shielding

Isotope fractionation due to photochemical self-shielding is believed to be responsible for the enrichment of inner solar system planetary materials in the rare isotopes of carbon, nitrogen, and oxygen relative to the Sun. Self-shielding may also contribute to sulfur isotope mass-independent fractionation in modern atmospheric sulfates, although its role in the early Earth atmosphere has not yet been convincingly established. Here, I present an analytical formulation of isotopic photodissociation rate coefficients that describe self-shielding isotope signatures for 3 and 4-isotope systems broadly representative of O and S isotopes. The analytic equations are derived for idealized molecular spectra, making an analytic formulation tractable. The idealized spectra characterize key features of actual isotopologue spectra, particularly for CO and SO₂, but are applicable to many small molecules and their isotopologues. The analytic expressions are convenient for evaluating the magnitude of isotope effects without having to pursue involved numerical solutions. More importantly, the analytic expressions illustrate the origin of particular isotope signatures, such as the previously unexplained large mass-dependent fractionation associated with photodissociation of optically-thick SO₂. The formulation presented here elucidates the origin of some of these important isotopic fractionation processes.