Beyond the Local Void: A data-driven search for the origins of the Amaterasu particle

TL;DR

This paper presents a simulation-based Bayesian inference framework to trace the origins of ultra-high-energy cosmic rays, exemplified by the Amaterasu particle, enabling more comprehensive source localization.

Contribution

It introduces a novel integration of 3D propagation modeling with Bayesian inference to better constrain cosmic ray sources from individual high-energy events.

Findings

Broader source candidate regions identified than previous studies.

Quantitative posterior distributions for source parameters.

Framework applicable to future cosmic ray analyses.

Abstract

We introduce a simulation-based inference framework to constrain the origins of individual ultra-high-energy cosmic rays by combining realistic three-dimensional propagation modeling with Bayesian parameter estimation. Our method integrates CRPropa 3 simulations, including all relevant interactions and magnetic deflections in both Galactic and extra-Galactic fields, with Approximate Bayesian Computation to infer posterior distributions over key parameters such as source position, distance, energy, and magnetic field properties. This approach allows joint constraints from the observed energy and arrival direction to be applied simultaneously, naturally incorporating their correlations in addition to relevant modelling uncertainties. We demonstrate our method by applying it to the Amaterasu particle detected by the Telescope Array observatory, the second-highest-energy cosmic ray ever detected. The resulting posterior distributions quantify the regions of space consistent with its reconstructed properties under different energy and composition assumptions, revealing a broader set of nearby source candidates than found in previous analyses. This application highlights the framework's ability to translate individual UHECR observations into directly interpretable source constraints and provides a foundation for future simulation-based analyses of cosmic rays at the highest energies.