Dispersion of the break energy in the GRB internal shock model

In order to investigate the dispersion of the spectral break energy in gamma-ray bursts, we simulate internal shocks, including effects of shell-splitting after shell collisions and the Thomson optical depth due to electron-positron pairs produced by synchrotron photons. We produce pseudo-observational data and estimate the break energy. If the distribution of initial Lorentz factors of shells has only one peak, many pulses with a break energy much lower than the typical observed value should be detected, while the effect of the Thomson optical depth reduces pulses with a break energy of > 1 MeV. If the Lorentz factor distribution has multiple peaks, the distribution of the break energy can be consistent with observations.