Abstract
Abstract 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 $ \gt 1 \,\mathrm{MeV}$$ \gt 1 \,\mathrm{MeV}$. If the Lorentz factor distribution has multiple peaks, the distribution of the break energy can be consistent with observations.
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