Slow Heating Model of Gamma-Ray Burst: Photon Spectrum and Delayed Emission

We propose a new mechanism for the prompt emission of gamma-ray burst. In our model electrons are continuously accelerated in the post shock region via plasma turbulence. Using the Monte Carlo technique, we mimic the second-order Fermi acceleration due to plasma turbulence and obtain photon spectra. Since the acceleration balances with the synchrotron cooling, the observed low-energy spectral index is naturally explained. The resultant spectra can be consistent with observed spectra at least below $\sim 1$ MeV. The model also predicts delayed GeV-TeV emission due to inverse Compton and broad pulse profile of optical emission in some cases. Although nontrivial assumptions are required to reproduce MeV-GeV power-law spectra, the model implies the possibility to explain various kinds of luminosity correlations.