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Shocks that occur below a gamma-ray burst (GRB) jet photosphere are mediatedby radiation. Such radiation-mediated shocks (RMSs) could be responsible forshaping the prompt GRB emission. Although well studied theoretically, RMSmodels have not yet been fitted to data due to the computational cost ofsimulating RMSs from first principles. Here, we bridge the gap between theoryand observations by developing an approximate method capable of accuratelyreproducing radiation spectra from mildly relativistic (in the shock frame) orslower RMSs, called the Kompaneets RMS approximation (KRA). The approximationis based on the similarities between thermal Comptonization of radiation andthe bulk Comptonization that occurs inside an RMS. We validate the method bycomparing simulated KRA radiation spectra to first-principleradiation-hydrodynamics simulations, finding excellent agreement both insidethe RMS and in the RMS downstream. The KRA is then applied to a shock scenarioinside a GRB jet, allowing for fast and efficient fitting to GRB data. Weillustrate the capabilities of the developed method by performing a fit to anon-thermal spectrum in GRB 150314A. The fit allows us to uncover the physicalproperties of the RMS responsible for the prompt emission, such as the shockspeed and the upstream plasma temperature.

An efficient method for fitting radiation-mediated shocks to gamma-ray burst data: The Kompaneets RMS approximation