宇宙线膝的种群视角：超新星最大刚度方差的作用
A Population View of the Cosmic-Ray Knee: The Role of Variance in Supernova Maximum Rigidities
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中文总结 AI 辅助
本研究提出宇宙线膝可由超新星遗迹最大能量的源间差异产生，通过对数正态分布模型拟合质子谱发现PeV成分来自均匀遗迹子集，无需普适最大刚度假设。
中文摘要 AI 辅助
银河系宇宙线膝的宽阔形态对所有超新星遗迹都具有近乎普适的尖锐最大刚度的源模型提出了挑战。我们探究了膝是否可以作为一种种群效应出现，即由银河系超新星遗迹最大能量的源间差异产生。我们推导了具有单个尖锐截断且$E_{\max}$呈分布的源的种群平均谱，表明其由底层传播幂律谱乘以截断分布的存活概率给出。对数正态分布的$E_{\max}$自然产生平滑、连续弯曲的膝，而幂律尾则产生近似恒定的膝后谱陡化。随后我们通过最大能量随爆炸能量和环境密度的标度关系，将对数正态分布的宽度与超新星遗迹物理联系起来，发现预期的方差主要由爆炸能量的弥散驱动。用双成分对数正态截断模型拟合测得的质子谱，我们发现PeV成分要求$σ_{\log_{10}E_{\max}}\simeq 0.24$。该宽度远小于银河系全部遗迹种群预期的方差，表明PeV成分必定来自一个更受限、相对更均匀的遗迹子集。我们的结果表明，膝可以被理解为具有产生PeV粒子能力的异质超新星遗迹种群的逐渐耗尽，无需普适的最大刚度。
英文摘要
The broad shape of the Galactic cosmic-ray knee challenges source models in which all supernova remnants share a nearly universal, sharp maximum rigidity. We investigate whether the knee can instead arise as a population effect, produced by source-to-source variations in the maximum energy of Galactic supernova remnants. We derive the population-averaged spectrum for sources with sharp individual cutoffs and distributed $E_{\max}$, showing that it is given by an underlying propagated power law multiplied by the survival probability of the cutoff distribution. A lognormal distribution of $E_{\max}$ naturally produces a smooth, continuously curving knee, while a power-law tail gives an approximately constant post-knee steepening. We then connect the lognormal width to supernova-remnant physics through maximum-energy scalings with explosion energy and ambient density, finding that the expected variance is mainly driven by the spread in explosion energies. Fitting the measured proton spectrum with a two-component lognormal-cutoff model, we find that the PeV component requires $σ_{\log_{10}E_{\max}}\simeq 0.24$. This width is substantially smaller than the variance expected for the full Galactic remnant population, indicating that the PeV component must originate from a more restricted and comparatively homogeneous subset of remnants. Our results show that the knee can be understood as the gradual exhaustion of a heterogeneous population of PeV-capable supernova remnants, without requiring a universal maximum rigidity.
