Unraveling Parameter Degeneracy in GRB Data Analysis

Abstract

Gamma-ray burst (GRB) afterglow light curves and spectra provide information about the density of the environment, the energy of the explosion, the properties of the particle acceleration process, and the structure of the decelerating jet. Due to the large number of parameters involved, the model can present a certain degree of parameter degeneracy. In this paper, we generated synthetic photometric data points using a standard GRB afterglow model and fit them using the Markov Chain Monte Carlo (MCMC) method. This method has emerged as the preferred approach for analysing and interpreting data in astronomy. We show that, depending on the choice of priors, the parameter degeneracy can go unnoticed by the MCMC method. Furthermore, we apply the MCMC method to analyse the GRB~170817A afterglow. We find that there is a complete degeneracy between the energy of the explosion $E$, the density of the environment $n$, and the microphysical parameters describing the particle acceleration process (e.g. $\epsilon_e$ and $\epsilon_B$), which cannot be determined by the afterglow light curve alone. Our results emphasise the importance of gaining a deep understanding of the degeneracy properties which can be present in GRB afterglows models, as well as the limitations of the MCMC method. In the case of GRB 170817, we get the following values for the physical parameters: $E=8\times 10^{50}-1 \times 10^{53}$ erg, $n=7\times 10^{-5}-9\times10^{-3}$, $\epsilon_e=10^{-3}-0.3$, $\epsilon_B=10^{-10}-0.3$.