Hidden structures in the UHE sky: unveiling potential sources via spectral signatures

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.