Statistical chronometry of Meteorites: II. Initial abundances and homogeneity of short-lived radionuclides

Astrophysical models of planet formation require accurate radiometric dating of meteoritic components by short-lived (Al–Mg, Mn–Cr, Hf–W) and long-lived (Pb–Pb) chronometers, to develop a timeline of such events in the solar nebula as formation of Ca-rich, Al-rich Inclusions (CAIs), chondrules, planetesimals, etc. CAIs formed mostly around a time (“t=0”) when the short-lived radionuclide ²⁶Al (t_1/2=0.72 Myr) was present and presumably homogeneously distributed at a known level we define as (²⁶Al/²⁷Al)_SS≡5.23×10⁻⁵. The time of formation after t=0 of another object can be found by determining its initial (²⁶Al/²⁷Al)₀ ratio and comparing it to (²⁶Al/²⁷Al)_SS. Dating of meteoritic objects using the Mn–Cr or Hf–W systems is hindered because the abundances (⁵³Mn/⁵⁵Mn)_SS and (¹⁸²Hf/¹⁸⁰Hf)_SS at t=0 are not known precisely. To constrain these quantities, we compile literature Al–Mg, Mn–Cr, Hf–W and Pb–Pb data for 14 achondrites and use novel statistical techniques to minimize the discrepancies between their times of formation across these systems. We find that for (⁵³Mn/⁵⁵Mn)_SS=(8.09±0.65)×10⁻⁶, (¹⁸²Hf/¹⁸⁰Hf)_SS=(10.42±0.25)×10⁻⁵, t_SS=4568.36±0.20Myr, and a ⁵³Mn half-life of 3.80±0.23 Myr, these four free parameters make concordant 37 out of 38 formation times recorded by the different systems in 14 achondrites. These parameters also make concordant the ages derived for chondrules from CB/CH achondrites, formed simultaneously in an impact, and are apparently concordant with the I–Xe chronometer as well. Our findings provide very strong support for homogeneity of ²⁶Al, ⁵³Mn, and ¹⁸²Hf in the solar nebula, and our approach offers a framework for more precise chronometry.