Electrons' energy in GRB afterglows implied by radio peaks

Gamma-ray burst (GRB) afterglows have been observed across the electromagnetic spectrum, and physical parameters of GRB jets and their surroundings have been derived using broad-band modelling. While well-sampled light curves across the broad-band spectrum are necessary to constrain all the physical parameters, some can be strongly constrained by the right combination of just a few observables, almost independently of the other unknowns. We present a method involving the peaks of radio light curves to constrain the fraction of shock energy that resides in electrons, is an element of(e). This parameter is an important ingredient for understanding the microphysics of relativistic shocks. Based on a sample of 36 radio afterglows, we find is an element of(e) has a narrow distribution centred around 0.13-0.15. Our method is suggested as a diagnostic tool for determining is an element of(e), and to help constrain the broad-band modelling of GRB afterglows. Some earlier measurements of the spreads in parameter values for is an element of(e), the kinetic energy of the shock and the density of the circumburst medium, based on broad-band modelling across the entire spectrum, are at odds with our analysis of radio peaks. This could be due to different modelling methods and assumptions, and possibly missing ingredients in past and current modelling efforts. Furthermore, we show that observations at greater than or similar to 10 GHz performed 0.3-30 d after the GRB trigger are best suited for pinpointing the synchrotron peak frequency, and, consequently, is an element of(e). At the same time, observations at lower radio frequencies can pin down the synchrotron self-absorption frequency and help constrain the other physical parameters of GRB afterglows.