Stochastic Chemical Evolution of Radioactive Isotopes with a Monte Carlo Approach

Coté, Benoit and Yagüe López, Andrés and Világos, Blanka and Lugaro, Maria (2019) Stochastic Chemical Evolution of Radioactive Isotopes with a Monte Carlo Approach. ASTROPHYSICAL JOURNAL, 887 (2). ISSN 1538-4357

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Abstract

Short-lived radionuclides (SLRs) with mean lives τ of a few to hundreds of Myr provide unique opportunities to probe recent nucleosynthesi events in the interstellar medium and the physical conditions in whic the Sun formed. Here we quantify the uncertainty in the predicte evolution of SLRs within a parcel of interstellar gas given th stochastic nature of stellar enrichment events. We assume that a enrichment progenitor is formed at every time interval γ. For eac progenitor, we randomly sample the delay time between its formation an its enrichment event, based on several delay-time distribution (DTD functions that cover a wide range of astrophysical sites. For each se of τ, γ, and DTD functions, we follow the abundances of SLRs for 15 Gy and repeat this process thousands of times to derive their probabilit distributions. For τ/γ ≳ 2, the distributions depend on the DT function, and we provide tabulated values and analytical expressions t quantify the spread. The relative abundance uncertainty reaches maximum of ∼60% for τ/γ = 1. For τ/γ ≲ 1, we provide the probability fo the SLR abundance to carry the signature of only one enrichment event which is greater than 50% when τ/γ ≲ 0.3. For 0.3 ≲ τ/γ ≲ 2, a smal number of events contributed to the SLR abundance. This case needs to b investigated with a separate statistical method. We find that a isolation time for the birth of the Sun of roughly 9─13 Myr i consistent with the observed abundances of 60Fe 107Pd, and 182Hf in the early solar system whe assuming τ/γ ∼ 3 for these isotopes

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