Studies of gamma-ray bursts (GRBs) and their multiwavelength afterglows have led to insights in electron acceleration and emission properties from relativistic, high-energy astrophysical sources. Broad-band modelling 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 broad-band 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, ϵe; the fraction of electrons that gets accelerated into a power-law distribution of energies, ζe; and the minimum Lorentz factor of the accelerated electrons, γm. 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 ϵe and ζe to within about one order of magnitude, 0.01 ≲ ϵe ≲ 0.2 and 0.1 ≲ ζe ≲ 1. Such stringent constraints are inaccessible for ζe from broad-band studies due to model degeneracies.
Bibliographical noteFunding Information:
The authors would like to thank the anonymous referee for their useful comments that strengthened the manuscript. RAD would like to thank Michael Moss for assistance with PYTHON programming and feedback on this paper; and Sarah Chastain for assistance with with data collection. RAD would also like to thank the George Washington University Undergraduate Research Award and the Physics Department Frances E. Walker Fellowship for financial support to carry out the research presented in this paper. PB was supported by a grant (no. 2020747) from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.
© 2022 The Author(s).
- acceleration of particles
- gamma-ray burst: general
- radiation mechanisms: non-thermal
- relativistic processes
- shock waves