AI 中文总结
本研究通过扩展半解析框架建立超新星遗迹质子时变演化模型，再现观测到的谱参数年龄趋势，结合源谱弥散计算得到的银河质子能谱与观测吻合，支持超新星遗迹是膝区以下银河宇宙线质子主要来源的假设。
AI 中文摘要
近期的γ射线观测表明，超新星遗迹（SNR）的质子能谱可由折断幂律很好地描述，其中谱折断能$E_{\rm br}$和低能谱指数$\u03b1$均随SNR年龄呈现系统演化。这些演化趋势的物理起源及其对银河宇宙线（CR）总体的意义仍知之甚少。本研究通过扩展Zhang & Fang的半解析框架，建立了SNR中质子的时变演化模型，其中最大加速能量和注入谱指数均随遗迹的动力学演化而变化。计算得到的质子能谱再现了观测推断出的$E_{\rm br}$和$\u03b1$的年龄依赖趋势。我们将辐射阶段起始时的质子能谱作为银河CR传播的源谱，并纳入SNR之间源谱指数的固有弥散。随后在扩散模型中计算得到累积银河质子能谱，传播后的能谱在宽能段上与观测到的CR质子流吻合良好，尤其在几十GeV以上的能段。我们的结果提供了一个自洽框架，将单个SNR中质子加速的时变演化与地球观测到的银河CR质子能谱联系起来，进一步支持了长期以来的假设：SNR是膝区以下银河CR质子的主要来源。
英文摘要
Recent $γ$-ray observations indicate that the proton spectra of supernova remnants (SNRs) are well described by broken power laws, with both the spectral break energy, $E_{\mathrm{br}}$, and the low-energy spectral index, $α$, exhibiting systematic evolution with SNR age. The physical origin of these evolutionary trends and their implications for the Galactic cosmic-ray (CR) population remain poorly understood. In this work, we develop the temporal evolution model for protons in SNRs by extending the semi-analytical framework of Zhang \& Fang, in which both the maximum acceleration energy and the injection spectral index evolve with the dynamical evolution of the remnant. The calculated proton spectra reproduce the age-dependent trends of both $E_{\mathrm{br}}$ and $α$ inferred from observations. We adopt the proton spectrum at the onset of the radiative phase as the source spectrum for Galactic CR propagation and incorporate the intrinsic dispersion of source spectral indices among SNRs. The resulting cumulative Galactic proton spectrum is then calculated within a diffusion model. The propagated spectrum agrees well with the observed CR proton flux over a broad energy range, particularly above several tens of GeV. Our results provide a self-consistent framework linking the time-dependent evolution of proton acceleration in individual SNRs to the Galactic CR proton spectrum observed at Earth, and further support the long-standing hypothesis that SNRs are the dominant sources of Galactic CR protons below the knee.
Comments16 pages, 4 figures
