Acceleration of ultra-high energy cosmic rays in the early afterglows of gamma-ray bursts: concurrence of jet's dynamics and wave-particle interactions

TL;DR

This paper presents a time-dependent model demonstrating that gamma-ray burst early afterglows can accelerate protons and nuclei to ultra-high energies, aligning with observed cosmic-ray spectra and compositions.

Contribution

It introduces a novel dynamic model combining jet physics and wave-particle interactions to explain UHECR acceleration in GRB afterglows.

Findings

Protons can reach 10^19 eV during early afterglow.

Ultra-high energy nuclei can survive photodisintegration in external shocks.

Spectral slope consistent with observed UHECR composition.

Abstract

The origin of ultra-high energy cosmic rays $($UHECRs$)$ remains a mystery. It has been suggested that UHECRs can be produced by the stochastic acceleration in relativistic jets of gamma-ray bursts $($GRBs$)$ at the early afterglow phase. Here, we develop a time-dependent model for proton energization by cascading compressible waves in GRB jets considering the concurrent effect of the jet's dynamics and the mutual interactions between turbulent waves and particles. Considering fast mode of magnetosonic wave as the dominant particle scatterer and assuming interstellar medium $($ISM$)$ for the circumburst environment, our numerical results suggest that protons can be accelerated up to $\textrm{10}^{\textrm{19}}\,$eV during the early afterglow. An estimation shows ultra-high energy nuclei can easily survive photodisintegration in the external shocks in most cases, thus allowing the acceleration of $\textrm{10}^{\textrm{20}}\,$eV cosmic-ray nuclei in the proposed frame. The spectral slope can be as hard as $\textrm{d}\textit{N}/\textrm{d}\textit{E} \propto \textit{E}^\textrm{0}$, which is consistent with the requirement for the interpretation of intermediate-mass composition of UHECR as measured by the Pierre Auger Observatory.