We argue that if ultrahigh-energy ($E\gtrsim {10}^{10}\text{GeV}$) cosmic rays are heavy nuclei (as indicated by existing data), then the pointing of cosmic rays to their nearest extragalactic sources is expected for ${10}^{10.6}\lesssim E/\text{GeV}\lesssim {10}^{11}$. This is because for a nucleus of charge Ze and baryon number A, the bending of the cosmic ray decreases as $Z/E$ with rising energy, so that pointing to nearby sources becomes possible in this particular energy range. In addition, the maximum energy of acceleration capability of the sources grows linearly in Z, while the energy loss per distance traveled decreases with increasing A. Each of these two points tend to favor heavy nuclei at the highest energies. The traditional bi-dimensional analyses, which simultaneously reproduce Auger data on the spectrum and nuclear composition, may not be capable of incorporating the relative importance of all these phenomena. In this paper we propose a multi-dimensional reconstruction of the individual emission spectra (in E, direction, and cross-correlation with nearby putative sources) to study the hypothesis that primaries are heavy nuclei subject to GZK photo-disintegration, and to determine the nature of the extragalactic sources. More specifically, we propose to combine information on nuclear composition and arrival direction to associate a potential clustering of events with a 3-dimensional position in the sky. Actually, both the source distance and maximum emission energy can be obtained through a multi-parameter likelihood analysis to accommodate the observed nuclear composition of each individual event in the cluster. We show that one can track the level of GZK interactions on an statistical basis by comparing the maximum energy at the source of each cluster. We also show that nucleus-emitting-sources exhibit a cepa stratis structure on Earth which could be pealed off by future space-missions, such as POEMMA. Finally, we demonstrate that metal-rich starburst galaxies are highly-plausible candidate sources, and we use them as an explicit example of our proposed multi-dimensional analysis.

我们认为，如果超高能（$Ë\gtrsim {10}^{10}\text{GeV}$）宇宙射线是重核（如现有数据所示），则预期宇宙射线指向其最近的银河外源 ${10}^{10.6}\lesssim Ë/\text{GeV}\lesssim {10}^{11}$。这是因为对于电荷Ze和重子数A的原子核，宇宙射线的弯曲随着$ž/Ë$随着能量的增加，在这个特定的能量范围内指向附近的源成为可能。另外，源的加速能力的最大能量在Z中线性增长，而每行进距离的能量损失随A的增加而减小。这两个点中的每一个都倾向于在最高能量下偏重核。传统的二维分析同时复制频谱和核成分的俄歇数据，可能无法纳入所有这些现象的相对重要性。在本文中，我们提出了单个发射光谱的多维重构（在E中，方向以及与附近推定来源的互相关性），以研究原代是受GZK光分解作用的重核的假说，并确定河外来源的性质。更具体地说，我们建议结合有关核成分和到达方向的信息，以将事件的潜在聚类与天空中的3维位置相关联。实际上，可以通过多参数似然分析来获得源距离和最大发射能量，以适应​​集群中每个事件的观察到的核成分。我们显示，通过比较每个群集源处的最大能量，可以在统计基础上跟踪GZK相互作用的水平。我们还表明，核发射源表现出cepa层状地球上的结构可能会被未来的太空任务（例如POEMMA）消除。最后，我们证明了富含金属的爆炸形星系是高度可信的候选源，并且我们将它们用作我们提出的多维分析的明确示例。