Unveiling UHECRs source locations using Approximate Bayesian Computation

Abstract: UHECRs at the most extreme energies provide strong constraints on their possible sources. We propose to use the reconstructed properties of individual detected UHECRs to map out three-dimensional constraints on the locations of their unknown sources. We focus on the Amaterasu particle detected by Telescope Array and use CRPropa3 to model all relevant propagation effects, including deflections in the Galactic and extra-Galactic magnetic fields. We consider key input quantities such as distance, position, and energy as free parameters. We use Approximate Bayesian Computation (ABC) to derive constraints on the source locations for this event and demonstrate the impact of uncertainties in the reconstructed UHECR properties on these results. We also highlight possible astrophysical sources that are compatible with these regions and requirements. This complementary perspective serves as a foundation for building more physically-motivated source catalogues and statistical analyses in the future.