Constraining Low-luminosity Gamma-Ray Bursts as Ultra-high-energy Cosmic Ray Sources Using GRB 060218 as a Proxy

We study the connection between low-luminosity gamma-ray bursts (llGRBs) and ultra-high-energy cosmic rays (UHECRs) using the canonical low-luminosity GRB 060218 as a proxy. We focus on the consequential synchrotron emission from electrons that are coaccelerated in the UHECR acceleration region, comparing this emission to observations. Both the prompt and afterglow phases are considered. For the prompt phase, we assume the coaccelerated electrons are injected with a power-law distribution instantaneously (without additional heating or reacceleration), which results in bright optical-UV emission in tension with observations. For the afterglow phase, we constrain the total kinetic energy of the blast wave by comparing electron thermal synchrotron radiation to available radio data at ∼ 3 days. Considering mildly relativistic outflows with bulk Lorentz factor Γ ⪆ 2 (slower transrelativistic outflows are not treated), we find that the limited available energy does not allow for GRB 060218-like afterglows to be the main origin of UHECRs. This analysis independently constrains the prompt phase as a major UHECR source as well, given that the prompt energy budget is comparable to that of the afterglow kinetic energy. More generally, our study demonstrates that synchrotron emission from thermal electrons is a powerful diagnostic of the physics of mildly relativistic shocks.