📝 SummarXiv

Abstract

Photonuclear interactions between ultra-high-energy cosmic ray (UHECR) nuclei and surrounding photon fields are key to understanding the connection between the compositions observed at Earth and those emitted from the sources. These interactions can completely disintegrate a nucleus of iron over trajectory lengths of a few and up to hundreds of megaparsecs, depending on the energy of the UHECR. The stochastic nature of these interactions means that it is not possible to describe them deterministically for a single cosmic ray, and an exact formulation of the probability distributions is not yet available. Current approaches describe these interactions using either Monte Carlo simulations or solving ordinary differential equations that neglect stochasticity. Because of the limitations of these approaches, only partial capture of the process is achieved. This paper presents an analytic probabilistic description of UHECR interactions and the resulting nuclear cascades, establishing their connection to Markov jump processes. The fundamental properties of these cascades are presented, as is the computation of the usual quantities of interest, such as the horizon, spectrum, and composition. The benefits of this description are outlined using astrophysical examples related to extragalactic propagation and UHECR sources.