# Origin of Plutonium-244 in the Early Solar System

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## Abstract

**:**

## 1. Introduction

## 2. Nucleosynthesis Calculations

## 3. Galactic Evolution and Origin of the SLRs in the ESS

#### 3.1. One (Regime III) or Few (Regime II) Events and Time Elapsed from Last Event

#### 3.2. Steady-State Equilibrium (Regime I) and Isolation Time

## 4. Summary and Conclusions

- In Section 3.1 (top section of Table 3), we considered Regimes II and III for ${}^{244}$Pu, corresponding to $\delta >68$ Myr and Regime III for ${}^{129}$I and ${}^{247}$Cm. More than half of the WINNET models that were already shown to reproduce the three ratios that involve ${}^{129}$I and ${}^{247}$Cm in Paper I, also provide a self-consistent solution for ${}^{244}$Pu. These models all correspond to the NS–NS merger disk cases dominated by moderately neutron-rich ejecta.
- In Section 3.2 (bottom section of Table 3), we considered Regime I for ${}^{244}$Pu, i.e., $\delta <68$ Myr, where this SLR reaches a steady-state value in the ISM. It is also possible to find a significant number of r-process models (mostly corresponding to the Jmhf nuclear input) that provide solutions for the ESS ${}^{244}$Pu abundance compatible to those of the SLR isotopes produced also by the s process: ${}^{107}$Pd and ${}^{182}$Hf (and the current ESS upper limit of ${}^{135}$Cs). However, no solutions exist in Regime I for ${}^{244}$Pu if the ESS value of ${}^{244}$Pu was twice as high as the value used here or if the Milky Way model was represented by ${K}_{\mathrm{max}}$.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ESS | early Solar System |

GCE | galactic chemical evolution |

ISM | interstellar medium |

NSM | neutron star merger |

r process | $rapid$ neutron-capture process |

s process | $slow$ neutron-capture process |

SLR | short-lived radioactive |

## Notes

1 | The mean-life ${\tau}_{ratio}$ of the ${}^{129}$I/${}^{247}$Cm ratio given in the table was obtained by Monte Carlo sampling of the uncertainties on the mean lives of the two isotopes, ${\tau}_{129}$ and ${\tau}_{247}$, which are 5% and 6%, respectively, at 2$\sigma $ (for comparison, the uncertainty for ${}^{244}$Pu is 2%) within the usual formula: ${\tau}_{129}\times {\tau}_{247}/({\tau}_{129}-{\tau}_{247})$. Using the recommended values, ${\tau}_{ratio}$ would be equal to 2449 Myr, however, sampling of the uncertainties produces a lower value most of the time because the uncertainties make ${\tau}_{129}$ and ${\tau}_{247}$ move away from each other, and therefore their difference, at denominator in the formula above, increases. In general, it would be extremely useful if the half lives of ${}^{129}$I and ${}^{247}$Cm could be measured with higher precision than currently available. A more detailed statistical analysis should also be carried out considering that the peak value reported in the table is probably not the best statistical choice due to the exponential behaviour of the decay. In fact, although $\tau \sim 270$ Myr is the most common value, when $\tau \gtrsim 1000$ Myr abundances do not vary much anymore within the time scales, roughly $<$200 Myr are of interest for the ESS (discussed in Section 3). Therefore, a more statistically significant value may be higher than the peak value reported in the table, probably around 900 Myr. For the other ratios, the values of the mean lives at numerator and denominator in the equation above are so different that ${\tau}_{\mathrm{ratio}}$ is always within 2% of the $\tau $ of the short-lived isotope. A statistical analysis of the uncertainties would not affect those values, although we will analyse statistically the impact of the uncertainties on all the mean lives when we derive timescales in Section 3. |

2 | https://zenodo.org/record/4446099#.YgKVxWAo-mk (accessed on 15 June 2022). |

3 | https://zenodo.org/record/4456126#.YgKV0GAo-mk (accessed on 15 June 2022). |

4 | This is calculated using the residual method, where the r-process abundance is the total solar abundance of ${}^{129}$Xe minus the predicted s-process abundance. This method cannot be applied to ${}^{247}$Cm and ${}^{244}$Pu as these isotopes do not have one daughter stable nucleus produced exclusively by their decay. |

5 | When we also consider the difference due to fact that while ${}^{127}$I is stable, ${}^{235}$U will also decay. For time intervals of the order of 100–200 Myr, this corresponds to a small effect on the ${}^{247}$Cm/${}^{235}$U ratio of roughly 10–20%. |

6 | Since $\gamma \simeq <\delta >$ (see detailed discussion in [30]) for our purposes here $\gamma $ will be considered equivalent to $\delta $. |

7 | This lower limit is defined such that $\tau /\delta <0.3$ for ${}^{129}$I and ${}^{247}$Cm, but it is close to the 57.5 Myr value defined by $\tau /\delta >2$ for ${}^{244}$Pu. |

8 | Note that the evaluation of the ESS ratio of ${}^{129}$I/${}^{247}$Cm depends on the time from the last event itself, given that its ${\tau}_{\mathrm{ratio}}$ is variable due to the uncertainties in ${\tau}_{129}$ and ${\tau}_{247}$, as discussed in Section 1. The ESS values reported in Table 1 and used here were calculated assuming a time from last event in the range 100–200 Myr and composing all the uncertainties, as discussed in detail in the supplementary material of Paper I. A more precise analysis would instead use the range of times from the last event for each model solution to derive the range of corresponding ESS ${}^{129}$I/${}^{247}$Cm ratios, and find if the model matches such a specific range. However, given that, as noted above, most solutions provide times in the 100–200 Myr range, this more accurate treatment would not change our results. |

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**Figure 1.**Ratios of the ${}^{129}$I/${}^{247}$Cm isotopic ratio from all the WINNET (circles) and PRISM (triangles) models, with color as indicated in the box on the right side. The detailed label description can be found in Table 2 and in Paper I. Note that the scale is logarithmic.

**Figure 3.**Examples of solutions obtained using the WINNET set of yields and ${K}_{\mathrm{best}}$ for the time elapsed from the last r-process event to the formation of the first solids in the ESS that are consistent for all the isotopic ratios of Table 1, except for the right top and middle panels, which correspond to ${}^{129}$I/${}^{247}$Cm ratios just outside the required range. The colored dashed lines show the time elapsed as function of the free parameter $\delta $ derived from each ratio (labels in the top left corner). The dashed blue vertical line represent the $\delta $ value 345 Myr for which ${\tau}_{244}/\delta =0.3$, which marks the border between Regimes II and III. Uncertainty bands are a composition of the error distributions around the $\tau $ and the ESS ratio for each isotope. They are calculated using a Monte-Carlo sampling of such error distributions (using the 1$\sigma $ values and normal distributions, as required). The plotted uncertainty bands are the 2$\sigma $ uncertainty of the Monte-Carlo runs. (Note that these areas are smaller than those shown in Figure S2 of Paper I because there all the different values of K where included in the bands).

**Table 1.**Properties of the three ratios that involve SLR nuclei of r-process origin that were present in the ESS: the mean lives of the isotopes at numerator, at denominator, and of their ratio (${\tau}_{\mathrm{num}}$, ${\tau}_{\mathrm{den}}$, and ${\tau}_{\mathrm{ratio}}={\tau}_{\mathrm{num}}\times {\tau}_{\mathrm{den}}/({\tau}_{\mathrm{num}}-{\tau}_{\mathrm{den}})$, respectively, all in Myr), and the ESS values (at 2$\sigma $, from [1]). We also show, in the last column, the three values of the K factor that affect each of the ratios when predicted by the GCE model. This factor accounts for the star formation history and efficiency, the star-to-gas mass ratio, and the galactic outflows (Section 3). The uncertainties on these quantities result in a minimum (${K}_{\mathrm{min}}$), a best-fit (${K}_{\mathrm{best}}$), and a maximum (${K}_{\mathrm{max}}$) value of each ratio.

Ratio | ${\mathit{\tau}}_{\mathbf{num}}$ | ${\mathit{\tau}}_{\mathbf{den}}$ | ${\mathit{\tau}}_{\mathbf{ratio}}$ | ESS Ratio | ${\mathit{K}}_{\mathbf{min}}$, ${\mathit{K}}_{\mathbf{best}}$, ${\mathit{K}}_{\mathbf{max}}$ |
---|---|---|---|---|---|

${}^{129}$I/${}^{127}$I | 22.6 | stable | 22.6 | ($1.28\pm 0.03)\times {10}^{-4}$ | 1.6, 2.3, 5.7 |

${}^{244}$Pu/${}^{238}$U | 115 | 6447 | 117 | ($7\pm 2)\times {10}^{-3}$ | 1.5, 1.9, 4.1 |

${}^{247}$Cm/${}^{235}$U | 22.5 | 1016 | 23.0 | ($5.6\pm 0.3)\times {10}^{-5}$ | 1.1, 1.2, 1.8 ${}^{b}$ |

${}^{129}$I/${}^{247}$Cm | 22.6 | 22.5 | 270 ${}^{a}$ (100–3000) | $438\pm 184$ | 1, 1, 1 |

^{a}Values taken from the asymmetric ${\tau}_{\mathrm{ratio}}$ distribution shown in Figure S4 of Paper I. The first value is roughly the peak of the distribution, and the values in parenthesis represent most of its total range.

^{b}Values corrected relative to those reported in Paper I.

**Table 2.**The correspondence of the astrophysical site and nuclear input labels are used here to indicate the WINNET models and those used in Paper I, where a full description of each site and nuclear model and relevant references can also be found. The total mass ejected by each site is also indicated.

Site Label | Site Label (Paper I) | Mass Ejected (M${}_{\odot}$) | Nuclear Label | Nuclear Label (Paper I) |
---|---|---|---|---|

R1010 | NS-NS merger dyn. ejecta (R) | $7.64\times {10}^{-3}$ | Dhf | DZ10 |

R1450 | NS-BH merger dyn. ejecta (R) | $2.38\times {10}^{-2}$ | Jhf | FRDM |

Bs125 | NS-NS merger dyn. ejecta (B) | $5.50\times {10}^{-4}$ | Jmhf | FRDM(D3C*) |

FMdef | NS-NS merger disk ejecta 1 | $1.70\times {10}^{-3}$ | 1 | Panov |

FMs6 | NS-NS merger disk ejecta 2 | $1.27\times {10}^{-3}$ | 2 | K & T |

FMv0.10 | NS-NS merger disk ejecta 3 | $4.06\times {10}^{-3}$ | 4 | ABLA07 |

Wmhd | MR SN | $6.72\times {10}^{-3}$ |

**Table 3.**Summary of the different regimes combinations for the different SLRs, their corresponding $\delta $ values in Myr (${\delta}_{r}$ and ${\delta}_{s}$, for the r- and s-process events, respectively), r-process model solutions, and elapsed time (${t}_{\mathrm{e},r}$ and ${t}_{\mathrm{e},s}$, for the last r- and s-process event, respectively) or isolation time (${t}_{\mathrm{i}}$) in Myr. Notes: ${}^{a}$ For all the four ratios in Table 1: 6 = FMdef(3xDhf,3xJhf) + FMs6Jmhf4, all valid for each of the three values of K. We did not check the PRISM models for these regimes. ${}^{b}$ Of which 23 have Jmhf nuclear input. ${}^{c}$ The two NS–NS merger models with the three nuclear inputs: SLY4, TF_Mkt, and UNEDF0.

Regime | $\mathit{\delta}$ (Myr) | Solutions | Times (Myr) |
---|---|---|---|

III for ${}^{129}$I, ${}^{247}$Cm, and ${}^{244}$Pu | ${\delta}_{r}$ > 345 | 7 WINNET ${}^{a}$ | ${t}_{\mathrm{e},r}$ ≃ 100–200 |

III for ${}^{129}$I and ${}^{247}$Cm and II for ${}^{244}$Pu | 68 < ${\delta}_{r}$ < 345 | ||

II for ${}^{129}$I and ${}^{247}$Cm and I for ${}^{244}$Pu, ${}^{107}$Pd, and ${}^{182}$Hf | 11 < ${\delta}_{r}$ < 68, ${\delta}_{s}$ < 5 | 32 WINNET ${}^{b}$, 6 PRISM ${}^{c}$, 0 for ${K}_{\mathrm{max}}$ | ${t}_{\mathrm{e},r}$ ≃ 80–130, ${t}_{\mathrm{i}}$ ≃ 9–16 |

OR III for ${}^{107}$Pd and ${}^{182}$Hf | 11 < ${\delta}_{r}$ < 68, ${\delta}_{s}$ > 30 | 20 more than above | ${t}_{\mathrm{e},s}$ ≃ 25, ${t}_{\mathrm{i}}$ > 0 |

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**MDPI and ACS Style**

Lugaro, M.; Yagüe López, A.; Soós, B.; Côté, B.; Pető, M.; Vassh, N.; Wehmeyer, B.; Pignatari, M. Origin of Plutonium-244 in the Early Solar System. *Universe* **2022**, *8*, 343.
https://doi.org/10.3390/universe8070343

**AMA Style**

Lugaro M, Yagüe López A, Soós B, Côté B, Pető M, Vassh N, Wehmeyer B, Pignatari M. Origin of Plutonium-244 in the Early Solar System. *Universe*. 2022; 8(7):343.
https://doi.org/10.3390/universe8070343

**Chicago/Turabian Style**

Lugaro, Maria, Andrés Yagüe López, Benjámin Soós, Benoit Côté, Mária Pető, Nicole Vassh, Benjamin Wehmeyer, and Marco Pignatari. 2022. "Origin of Plutonium-244 in the Early Solar System" *Universe* 8, no. 7: 343.
https://doi.org/10.3390/universe8070343