Shocks that occur below a gamma-ray burst (GRB) jet photosphere are mediated by radiation. Such radiation-mediated shocks (RMSs) could be responsible for shaping the prompt GRB emission. Although well studied theoretically, RMS models have not yet been fitted to data owing to the computational cost of simulating RMSs from first principles. Here we bridge the gap between theory and observations by developing an approximate method capable of accurately reproducing radiation spectra from mildly relativistic (in the shock frame) or slower RMSs, called the Kompaneets RMS approximation (KRA). The approximation is based on the similarities between thermal Comptonization of radiation and the bulk Comptonization that occurs inside an RMS. We validate the method by comparing simulated KRA radiation spectra to first-principle radiation hydrodynamics simulations, finding excellent agreement both inside the RMS and in the RMS downstream. The KRA is then applied to a shock scenario inside a GRB jet, allowing for fast and efficient fitting to GRB data. We illustrate the capabilities of the developed method by performing a fit to a nonthermal spectrum in GRB 150314A. The fit allows us to uncover the physical properties of the RMS responsible for the prompt emission, such as the shock speed and the upstream plasma temperature.

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.

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 co-accelerated in the UHECR acceleration region, comparing this emission to observations. Both the prompt and afterglow phases are considered. For the prompt phase, we find that bright optical-UV emission is inevitable if the co-accelerated electrons are instantaneously injected into a power-law distribution. To enable acceleration of UHECRs while accommodating the optical-UV emission, it is necessary to keep the electrons from fast cooling (e.g., via reheating). Yet, the energetics of such models are independently constrained from our analysis of the afterglow. For the afterglow phase, we consider mildly relativistic outflows with bulk Lorentz factor Γ 2. Using thermal synchrotron radiation, we show that the initial kinetic energy of the afterglow blast wave of GRB 060218 was 10 times lower than the minimum energy required to satisfy the observed flux of UHECRs. Indeed, a blast wave with sufficient energy and where electrons carry 10-20% of the energy as suggested by particle-in-cell simulations, would typically overshoot the available radio data at ∼ 3 days by more than an order of magnitude. If GRB 060218 is representative of the llGRB population as a whole, then our results show that their relativistic afterglows are unlikely to be the dominant sources of UHECRs. It also implies that for the prompt phase to be the main origin of UHECRs, a majority of the energy would need to escape as cosmic rays, neutrinos, or radiation before the onset of the afterglow, independent of the prompt emission mechanism. More generally, our study demonstrates that synchrotron emission from thermal electrons is a powerful diagnostic of the physics of mildly relativistic shocks.