Constraints on Electron Acceleration in Gamma-Ray Bursts Afterglows from Radio Peaks

Studies of gamma-ray bursts (GRBs) and their multi-wavelength afterglows have led to insights in electron acceleration and emission properties from relativistic, high-energy astrophysical sources. Broadband modeling across the electromagnetic spectrum has been the primary means of investigating the physics behind these sources, although independent diagnostic tools have been developed to inform and corroborate assumptions made in particle acceleration simulations and broadband studies. We present a methodology to constrain three physical parameters related to electron acceleration in GRB blast waves: the fraction of shock energy in electrons, $\epsilon_e$; the fraction of electrons that gets accelerated into a power-law distribution of energies, $\xi_e$; and the minimum Lorentz factor of the accelerated electrons, $\gamma_m$. These parameters are constrained by observations of the peaks in radio afterglow light curves and spectral energy distributions. From a sample of 49 radio afterglows, we are able to find narrow distributions for these parameters, hinting at possible universality of the blast wave microphysics, although observational bias could play a role in this. Using radio peaks and considerations related to the prompt gamma-ray emission efficiency, we constrain the allowed parameter ranges for both $\epsilon_e$ and $\xi_e$ to within about one order of magnitude, $0.01\lesssim\epsilon_e\lesssim0.2$ and $0.1\lesssim\xi_e\lesssim1$. Such stringent constraints are inaccessible for $\xi_e$ from broadband studies due to model degeneracies.