A dipole anisotropy in ultra–high-energy cosmic ray (UHECR) arrival directions, of extragalactic origin, is now firmly established at energies E > 8 EeV. Furthermore, the UHECR angular power spectrum shows no power at smaller angular scales than the dipole, apart from hints of possible individual hot or warm spots for energy thresholds ≳40 EeV. Here we exploit the magnitude of the dipole and the limits on smaller-scale anisotropies to place constraints on two quantities: the extragalactic magnetic field (EGMF) and the number density of UHECR sources or the volumetric event rate if UHECR sources are transient. We also vary the bias between the extragalactic matter and the UHECR source densities, reflecting whether UHECR sources are preferentially found in over- or underdense regions, and find that little or no bias is favored. We follow Ding et al. (2021) in using the CosmicFlows-2 density distribution of the local universe as our baseline distribution of UHECR sources, but we improve and extend that work by employing an accurate and self-consistent treatment of interactions and energy losses during propagation. Deflections in the Galactic magnetic field are treated using either the full JF12 magnetic field model, with both random and coherent components, or just the coherent part, to bracket the impact of the GMF on the dipole anisotropy. This large-scale structure model gives good agreement with both the direction and magnitude of the measured dipole anisotropy and forms the basis for simulations of discrete sources and the inclusion of EGMF effects.

中文翻译：

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方向各向异性对 UHECR 源和河外磁场的约束

起源于河外的超高能宇宙射线（UHECR）到达方向的偶极子各向异性现已在能量上牢固确立乙> 8 EV。此外，除了能量阈值 ≳40 EeV 可能存在的个别热点或暖点的暗示之外，UHECR 角功率谱在比偶极子更小的角尺度上没有显示任何功率。在这里，我们利用偶极子的大小和小尺度各向异性的限制来对两个量进行约束：河外磁场 (EGMF) 和 UHECR 源的数密度或体积事件率（如果 UHECR 源是瞬态的）。我们还改变了偏见河外物质和 UHECR 源密度之间的关系，反映 UHECR 源是否优先在密度过高或过低的区域中发现，并发现很少或没有偏差受到青睐。我们关注丁等人。 （2021）使用本地宇宙的 CosmicFlows-2 密度分布作为 UHECR 源的基线分布，但我们通过对传播过程中的相互作用和能量损失采用准确且自洽的处理来改进和扩展这项工作。银河磁场的偏转可以使用完整的 JF12 磁场模型（具有随机分量和相干分量）或仅使用相干部分来处理，以限制 GMF 对偶极子各向异性的影响。这种大规模结构模型与测量的偶极子各向异性的方向和大小非常一致，并构成了模拟离散源和包含 EGMF 效应的基础。