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Gamma-ray burst spectra and spectral correlations from sub-photospheric Comptonization

One of the most important unresolved issues in gamma-ray burst physics is the origin of the prompt gamma-ray spectrum. Its general non-thermal character and the softness in the X-ray band remain unexplained. We tackle these issues by performing Monte Carlo simulations of radiation-matter interactions in a scattering dominated photon-lepton plasma. The plasma -- initially in equilibrium -- is driven to non-equilibrium conditions by a sudden energy injection in the lepton population, mimicking the effect of a shock wave or the dissipation of magnetic energy. Equilibrium restoration occurs due to energy exchange between the photons and leptons. While the initial and final equilibrium spectra are thermal, the transitional photon spectra are characterized by non-thermal features such as power-law tails, high energy bumps, and multiple components. Such non-thermal features are observed at infinity if the dissipation occurs at small to moderate optical depths, and the spectrum is released before thermalization is complete. We model the synthetic spectra with a Band function and show that the resulting spectral parameters are similar to observations for a frequency range of 2-3 orders of magnitude around the peak. In addition, our model predicts correlations between the low-frequency photon index and the peak frequency as well as between the low- and high-frequency indices. We explore baryon and pair dominated fireballs and reach the conclusion that baryonic fireballs are a better model for explaining the observed features of gamma-ray burst spectra.