The Limited Contribution of Low- and High-Luminosity Gamma-Ray Bursts to Ultra-High Energy Cosmic Rays

TL;DR

This study evaluates gamma-ray bursts as sources of ultra-high energy cosmic rays, concluding that most GRBs are unlikely to accelerate protons or iron to the highest observed energies, with some conditions allowing for potential acceleration.

Contribution

It provides new constraints on the maximum proton and iron energies achievable in GRB models, challenging their role as primary UHECR sources.

Findings

High-luminosity GRBs cannot accelerate protons to 10^{20} eV.

Low-luminosity GRBs can accelerate protons to below 10^{19} eV.

Iron in low-luminosity GRBs could reach 10^{20} eV under certain conditions.

Abstract

The acceleration site for ultra-high energy cosmic rays (UHECR) is still an open question despite extended research. In this paper, we reconsider the prompt phase of gamma-ray bursts (GRBs) as a possible candidate for this acceleration and constrain the maximum proton energy in optically thin synchrotron and photospheric models, using properties of the prompt photon spectra. We find that neither of the models favour acceleration of protons to $10^{20}$ eV in high-luminosity bursts. We repeat the calculations for low-luminosity GRBs (llGRBs) considering both protons and completely stripped iron and find that the highest obtainable energies are $< 10^{19}$ eV and $< 10^{20}$ eV for protons and iron respectively, regardless of the model. We conclude therefore that for our fiducial parameters, GRBs, including low-luminosity bursts, contribute little to none to the UHECR observed. We further constrain the conditions necessary for an association between UHECR and llGRBs and find that iron can be accelerated to $10^{20}$ eV in photospheric models, given very efficiency acceleration and/or a small fractional energy given to a small fraction of accelerated electrons. This will necessarily result in high prompt optical fluxes, and the detection of such a signal could therefore be an indication of successful UHECR acceleration at the source.