Detecting Local Deflection Patterns of Ultra-high Energy Cosmic Rays using the Principal Axes of the Directional Energy Distribution

From deflections in galactic and extragalactic magnetic fields energy dependent structures in the arrival directions of ultra-high energy cosmic rays (UHECR) are expected. We propose to characterize these structures by the strength of collimation of energy along the principal axes in selected regions in the sky. While the strength of collimation are indicators of anisotropy in the arrival distribution of UHECR, the orientation of the principal system holds information about the direction of the deflections of UHECR. We discuss the method and present expected limits on the strength of deflection and density of sources using simulated scenarios of UHECR proton propagation.