Skeletal Kinetics Reduction for Astrophysical Reaction Networks

A. G. Nouri, Y. Liu, P. Givi, H. Babaee and D. Livescu
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Abstract

A novel methodology is developed to extract accurate skeletal reaction models for nuclear combustion. Local sensitivities of isotope mass fractions with respect to reaction rates are modeled based on the forced optimally time-dependent (f-OTD) scheme. These sensitivities are then analyzed temporally to generate skeletal models. The methodology is demonstrated by conducting skeletal reduction of constant density and temperature burning of carbon and oxygen relevant to Type Ia supernovae (SNe Ia). The 495-isotopes Torch model is chosen as the detailed reaction network. A map of maximum production of 56Ni in SNe Ia is produced for different temperatures, densities, and proton-to-neutron ratios. The f-OTD simulations and the sensitivity analyses are then performed with initial conditions from this map. A series of skeletal models are derived and their performances are assessed by comparison against currently existing skeletal models. Previous models have been constructed intuitively by assuming the dominance of α-chain reactions. The comparison of the newly generated skeletal models against previous models is based on the predicted energy release and 44Ti and 56Ni abundances by each model. The consequences of ye ≠ 0.5 in the initial composition are also explored where ye is the electron fraction. The simulated results show that 56Ni production decreases by decreasing ye as expected, and that the 43Sc is a key isotope in proton and neutron channels toward 56Ni production. It is shown that an f-OTD skeletal model with 150 isotopes can accurately predict the 56Ni abundance in SNe Ia for ye ≲ 0.5 initial conditions.
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天体物理反应网络的骨骼动力学还原
我们开发了一种新方法来提取核燃烧的精确骨架反应模型。同位素质量分数对反应速率的局部敏感性是基于强制最优时间依赖(f-OTD)方案建模的。然后对这些敏感性进行时间分析,生成骨架模型。通过对与 Ia 型超新星(SNe Ia)相关的碳和氧的恒定密度和温度燃烧进行骨架还原,对该方法进行了演示。选择 495 同位素 Torch 模型作为详细反应网络。根据不同的温度、密度和质子-中子比,绘制了Ia型超新星中56Ni的最大生成图。然后根据该图中的初始条件进行 f-OTD 模拟和敏感性分析。得出了一系列骨架模型,并通过与现有骨架模型的比较评估了它们的性能。以前的模型是通过假设 α 链反应占主导地位而直观构建的。新生成的骨架模型与以前模型的比较是基于每个模型预测的能量释放以及 44Ti 和 56Ni 丰度。还探讨了初始成分中 ye ≠ 0.5 的后果,其中 ye 是电子分数。模拟结果表明,正如所预期的那样,56Ni 的生成量会随着 ye 的减小而减少,而且 43Sc 是质子和中子通向 56Ni 生成的关键同位素。结果表明,在ye ≲ 0.5的初始条件下,包含150个同位素的f-OTD骨架模型可以准确预测SNe Ia中的56Ni丰度。
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