发表机构
Universidade Estadual de Campinas; Universidade de São Paulo（坎皮纳斯州立大学; 圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于能谱函数$\mu_E$的补充度量，解耦通量归一化与谱形，推广Li-Ma公式，通过最大似然分析识别硬谱区域，增强UHECR源发现潜力。
AI 中文摘要
对超高能宇宙射线（UHECRs）起源的搜寻通常依赖于识别粒子通量中的方向性超出。虽然这种方法已得到充分验证，但它无法探测局域的谱特征，而这些特征若被测量，可为UHECRs的源提供约束。在本工作中，我们提出了一种用于方向性搜寻的补充度量，基于给定到达方向上的能谱函数$\mu_E$。我们证明，$\mu_E$在数学上将天空区域的通量归一化与谱形解耦，为方向依赖的谱提供了独特的探针。为评估该度量的统计显著性，我们推导了Li-Ma显著性公式对能量加权度量的推广。利用探索性蒙特卡洛模型中的最大似然分析，我们表明$\mu_E$可通过识别在标准粒子通量图中不明显的硬谱区域来增强发现潜力，从而为潜在的UHECR源提供补充探针。
英文摘要
The search for the origin of ultrahigh-energy cosmic rays (UHECRs) typically relies on identifying directional excesses in the particle flux. While this approach is well established, it cannot detect localized spectral features, which could provide constraints on the sources of UHECRs if measured. In this work, we propose a complementary metric for directional searches, based on a functional $μ_E$ of the energy spectrum in a given arrival direction. We demonstrate that $μ_E$ mathematically decouples the flux normalization of a sky region from the spectral shape, providing a distinct probe for direction-dependent spectra. To assess the statistical significance of this metric, we derive a generalization of the Li-Ma significance formula for energy-weighted metrics. Using a maximum-likelihood analysis within an exploratory Monte-Carlo model, we show that $μ_E$ can enhance discovery potential by identifying hard-spectrum regions that are not apparent in standard particle-flux maps, thereby providing a complementary probe of potential UHECR sources.
