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arXiv 2007.06087astro-ph.HEastro-ph.SR
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核心坍缩超新星的爆炸能量I：解析的球对称解

Explosion Energies for Core-collapse Supernovae I: Analytic, Spherically Symmetric Solutions

Mariam Gogilashvili, Jeremiah W. Murphy, Quintin Mabanta

备注：
Figure 10 most clearly illustrates the main conclusions
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摘要：

最近对核心坍缩超新星的多维模拟正在产生成功的爆炸和爆炸能量预测。在一般情况下，爆炸能量的演变是单调的，相对平滑，这表明一个可能的解析解。我们推导出解析解的增益区的扩展下，以下假设：球对称，一区壳，并由中微子和$α$粒子复合供电。我们考虑两个假设：爆炸能量由中微子和$α$复合提供动力，II）爆炸能量仅由中微子提供动力。在这些假设下，我们推导出基本的无量纲参数和解析标度。对于只有中微子的假设（II），渐近爆炸能量标度为$E_{\infty} \approx 1.5 M_g v_0^2 η^{2/3}$，其中$M_g$是增益质量，$v_0$是激波处的自由落体速度，$η$是加热时间标度和动力学时间标度的比值。包括中微子和复合（假设I），渐近爆炸能量是$E_{\infty} \approx M_g v_0^2 (1.5η^{2/3} + βf(ρ_0))$，其中$β$是无量纲复合参数。我们使用贝叶斯推断，以适应这些分析模型的模拟。这两种假设都符合对倾向于球形爆炸的最低祖先质量的模拟。拟合不倾向于假设I或II;然而，先前的研究表明$α$重组是重要的。正如预期的那样，这两种假设都不适合表现出非球面爆炸的更高质量的模拟。总之，这种爆炸能量理论与低原始质量的球形爆炸是一致的;与更高原始质量的模拟不一致表明，它们的理论必须包括非球形动力学。

英文摘要：

Recent multi-dimensional simulations of core-collapse supernovae are producing successful explosions and explosion-energy predictions. In general, the explosion-energy evolution is monotonic and relatively smooth, suggesting a possible analytic solution. We derive analytic solutions for the expansion of the gain region under the following assumptions: spherical symmetry, one-zone shell, and powered by neutrinos and $α$ particle recombination. We consider two hypotheses: I) explosion energy is powered by neutrinos and $α$ recombination, II) explosion energy is powered by neutrinos alone. Under these assumptions, we derive the fundamental dimensionless parameters and analytic scalings. For the neutrino-only hypothesis (II), the asymptotic explosion energy scales as $E_{\infty} \approx 1.5 M_g v_0^2 η^{2/3}$, where $M_g$ is the gain mass, $v_0$ is the free-fall velocity at the shock, and $η$ is a ratio of the heating and dynamical time scales. Including both neutrinos and recombination (hypothesis I), the asymptotic explosion energy is $E_{\infty} \approx M_g v_0^2 (1.5η^{2/3} + βf(ρ_0))$, where $β$ is the dimensionless recombination parameter. We use Bayesian inference to fit these analytic models to simulations. Both hypotheses fit the simulations of the lowest progenitor masses that tend to explode spherically. The fits do not prefer hypothesis I or II; however, prior investigations suggest that $α$ recombination is important. As expected, neither hypothesis fits the higher-mass simulations that exhibit aspherical explosions. In summary, this explosion-energy theory is consistent with the spherical explosions of low progenitor masses; the inconsistency with higher progenitor-mass simulations suggests that a theory for them must include aspherical dynamics.

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