Bayesian calibration of the 40K decay scheme with implications for 40K-based geochronology

Abstract

The K/Ar and ⁴⁰Ar/³⁹Ar geochronometers are based on the naturally occurring radionuclide ⁴⁰K. Their precision and accuracy are limited by uncertainties on the ⁴⁰K decay constants and, in the case of the ⁴⁰Ar/³⁹Ar geochronometer, the isotopic composition of neutron fluence monitors. To address these limitations, we introduce a Bayesian calibration of the ⁴⁰K decay scheme. We formulate robust priors for all model parameters including partial ⁴⁰K decay constants, ²³⁸U and ²³⁵U decay constants, and age offset parameters to account for phenomena that can perturb apparent U-Pb and ⁴⁰Ar/³⁹Ar ages. We then harness a set of complementary ⁴⁰Ar/³⁹Ar, ²³⁸U/²⁰⁶Pb, and ²³⁵U/²⁰⁷Pb data from well- characterized geological samples with ages from 1.919 ka to 2000 Ma to derive Bayesian estimates of the ⁴⁰K decay constants. Posterior values for the partial ⁴⁰K decay constants are ${\lambda }_{{\beta }^{-}}$= (4.9252 $\pm$ 0.0054) $\times$ 10⁻¹⁰ yr⁻¹, ${\lambda }_{{\beta }^{+}}$ = (5.6658 $\pm$ 0.1543) $\times$ 10⁻¹⁵ yr⁻¹, ${\lambda }_{{\mathrm{EC}}^{\ast }}$ = (5.7404 $\pm$ 0.0053) $\times$ 10⁻¹¹ yr⁻¹, and ${\lambda }_{{\mathrm{EC}}_0}$= (4.9060 $\pm$ 0.2942) $\times$ 10⁻¹³ yr⁻¹ (uncertainties reported at the 68 % (1$\sigma$) credible interval). These combine to a total ⁴⁰K decay constant ${\lambda }_{\mathrm{tot}}$= (5.5042 $\pm$ 0.0054) $\times$ 10⁻¹⁰ yr⁻¹. Model estimates of the ²³⁸U and ²³⁵U decay constants are statistically indistinguishable from those reported by Jaffey et al. (1971). Posterior values of the ⁴⁰K decay constants and the ⁴⁰Ar*/⁴⁰K isotopic composition of Fish Canyon sanidine (FCs) define a K/Ar FCs age of 28.183 $\pm$ 0.017 Ma (1$\sigma$). Significantly, Bayesian calibrated ⁴⁰Ar/³⁹Ar ages align with astronomically tuned ages throughout the Cenozoic and with ²³⁸U/²⁰⁶Pb and ²³⁵U/²⁰⁷Pb ages in the Mesozoic, Paleozoic, and Proterozoic, as well as having comparable precision to the ²³⁸U/²⁰⁶Pb method. Thus, Bayesian calibration of the ⁴⁰K decay scheme and the K/Ar age of FCs reconciles the ⁴⁰Ar/³⁹Ar, U-Pb, and astronomical chronometers.