超高能宇宙线（UHECR）到达方向分布的高熵有利于轻成分
The high entropy of the UHECR arrival direction distribution favors a light composition
AI总结：
本研究通过提出一种半解析描述方法、引入与银河磁场无关的各向异性熵度量，分析Auger数据后发现，UHECR到达方向分布的高熵支持轻成分（质子）模型，在96%置信水平下排除重核模型。
AI中文摘要：
我们利用一种新颖的半解析描述方法，对能量大于2×10^19 eV的原子核（A>4）的传播能量损失进行分析，以此推断超高能宇宙线（UHECR）的成分、其源的密度与分布所受的约束，该方法生成UHECR到达图的速度比详细传播模拟更快，且能揭示传播能量损失的影响。我们发现，物质分布的大尺度结构（LSS）导致的UHECR到达方向各向异性，对于重核成分而言比质子更大，尽管重核受磁场偏转更大，但由于其传播距离更短且刚度对观测能量的依赖性更弱。对于重核，由于不确定的银河磁场（GMF）造成的大偏转，识别LSS各向异性信号受到阻碍。我们引入了一种新的各向异性度量——到达方向分布的“熵”，该度量在很大程度上独立于GMF的构型，且在重核与轻成分模型间具有很强的区分能力。通过分析公开的能量大于3.2×10^19 eV的Auger数据，我们发现其与大角尺度LSS的相关性较弱，且需要低源密度s0≤10^-4 Mpc^-3才能通过“宇宙方差”掩盖LSS信号（s0=10^-2 Mpc^-3在99%置信水平（CL）下被排除）。对于s0≥10^-5 Mpc^-3的情况，该分布的高熵与质子模型一致，而在96% CL下与重核模型不一致。降低绝对能量校准的不确定性可能使质子模型能够检测到LSS相关性（仅增加曝光量不足以实现，因为宇宙方差占主导）。
英文摘要：
We analyze the constraints on the composition of ultra-high-energy cosmic rays (UHECRs), and on the density and distribution of their sources, that may be inferred from their arrival-direction distribution, using a novel semi-analytical description of the propagation energy loss of atomic nuclei ($A>4$) with energy $>2\times10^{19}~\text{eV}$, that allows generating UHECR arrival maps faster than by using detailed propagation simulations and yields insights to the impact of propagation energy loss. We show that the anisotropy of the UHECR arrival direction distribution due to the large-scale structure (LSS) of matter distribution is larger for heavy nuclei composition compared to protons, despite their larger deflections by magnetic fields, due to their shorter propagation distance and weaker dependence of rigidity on observed energy. Identifying the LSS anisotropy signal is hampered for heavy nuclei due to their large deflections by the uncertain Galactic magnetic field (GMF). We introduce a new measure of anisotropy, an "entropy" of the arrival-direction distribution, that is largely independent of the GMF configuration and has strong discriminating power between heavy- and light-composition models. Analyzing the public $>3.2\times10^{19}$~eV Auger data, we show that the correlation with the LSS on large angular scales is weak and requires a low source density, $s_0\le10^{-4}{\rm Mpc}^{-3}$, to allow masking the LSS signature by "cosmic-variance" ($s_0=10^{-2}{\rm Mpc}^{-3}$ is ruled out at $>99\%$ confidence level (CL)). The high entropy of the distribution is consistent with proton models and inconsistent with heavy nuclei models at $>96\%$ CL for $s_0\ge10^{-5}{\rm Mpc}^{-3}$. Reducing the absolute energy calibration uncertainty may allow detection of the LSS correlation for proton models (increased exposure alone will not suffice due to the dominance of cosmic variance).
