Bayesian calibration of the 40K decay scheme with implications for 40K-based geochronology
The K/Ar and 40 Ar/ 39 Ar geochronometers are based on the naturally occurring radionuclide 40 K. Their precision and accuracy are limited by uncertainties on the 40 K decay constants and, in the case of the 40 Ar/ 39 Ar geochronometer, the isotopic composition of neutron fluence monitors. To address these limitations, we introduce a Bayesian calibration of the 40 K decay scheme. We formulate robust priors for all model parameters including partial 40 K decay constants, 238 U and 235 U decay constants, and age offset parameters to account for phenomena that can perturb apparent U-Pb and 40 Ar/ 39 Ar ages. We then harness a set of complementary 40 Ar/ 39 Ar, 238 U/ 206 Pb, and 235 U/ 207 Pb data from well- characterized geological samples with ages from 1.919 ka to 2000 Ma to derive Bayesian estimates of the 40 K decay constants. Posterior values for the partial 40 K decay constants are λ β - "> λ β - = (4.9252 ± "> ± 0.0054) × "> × 10 −10 yr −1 , λ β + "> λ β + = (5.6658 ± "> ± 0.1543) × "> × 10 −15 yr −1 , λ EC ∗ "> λ EC0 = (5.7404 ± "> ± 0.0053) × "> × 10 −11 yr −1 , and λ EC 0 "> λ EC0 = (4.9060 ± "> ± 0.2942) × "> × 10 −13 yr −1 (uncertainties reported at the 68 % (1 σ "> σ ) credible interval). These combine to a total 40 K decay constant λ tot "> λ tot = (5.5042 ± "> ± 0.0054) × "> × 10 −10 yr −1 . Model estimates of the 238 U and 235 U decay constants are statistically indistinguishable from those reported by Jaffey et al. (1971) . Posterior values of the 40 K decay constants and the 40 Ar*/ 40 K isotopic composition of Fish Canyon sanidine (FCs) define a K/Ar FCs age of 28.183 ± "> ± 0.017 Ma (1 σ "> σ ). Significantly, Bayesian calibrated 40 Ar/ 39 Ar ages align with astronomically tuned ages throughout the Cenozoic and with 238 U/ 206 Pb and 235 U/ 207 Pb ages in the Mesozoic, Paleozoic, and Proterozoic, as well as having comparable precision to the 238 U/ 206 Pb method. Thus, Bayesian calibration of the 40 K decay scheme and the K/Ar age of FCs reconciles the 40 Ar/ 39 Ar, U-Pb, and astronomical chronometers.