Angular, spectral, and time distributions of highest energy protons and associated secondary gamma-rays and neutrinos propagating through extragalactic magnetic and radiation fields
F.A. Aharonian, S.R. Kelner, A.Y. Prosekin

TL;DR
This paper analyzes the angular, spectral, and temporal characteristics of ultra-high-energy protons and their secondary particles as they traverse extragalactic magnetic and radiation fields, using analytical solutions to the Boltzmann transport equation.
Contribution
It introduces an analytical approach to model the propagation of high-energy particles and their secondary emissions through intergalactic environments.
Findings
Characterizes the distribution of protons, gamma-rays, and neutrinos in space and time.
Provides insights into the effects of magnetic and radiation fields on particle propagation.
Offers a framework for interpreting observational data of high-energy cosmic particles.
Abstract
The angular, spectral and temporal features of the highest energy protons and accompanying them secondary neutrinos and synchrotron gamma-rays propagating through the intergalactic magnetic and radiation fields are studied using the analytical solutions of the Boltzmann transport equation obtained in the limit of the small-angle and continuous-energy-loss approximation.
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