Fig. 4. Probability density functions for isolation time before the early Solar System.

The ISM ratio for each isotope was computed using equation (2) with K = 2.3. The width of the ²⁰⁵Pb distribution originates in roughly equal parts from the stochastic uncertainty in the ISM ratio and the uncertainty in the meteoritic value (the standard early Solar System (ESS) value from ref. ⁹ in cyan versus the carbonaceous chondrites (CC) ESS value from ref. ¹⁰ in blue). The meteoritic values for ¹⁰⁷Pd/¹⁰⁸Pd and ¹⁸²Hf/¹⁸⁰Hf are better constrained (1σ ≃ 2–3%) than that of ²⁰⁵Pb/²⁰⁴Pb (20–33%), so only the stochastic uncertainty is notable. (The ¹³⁵Cs/¹³³Cs ratio is discussed in Methods only, as ¹³⁵Cs has a substantially (approximately 10–20 times) shorter half-life than the three isotopes shown here and needs to be treated differently).