The photospheric radiation model for the prompt emission of Gamma-ray Bursts: Interpreting four observed correlations

We show that the experiential $E_{\rm p}-L$, $\Gamma-L$, $E_{\rm p}-\Gamma$ and ${\rm \bar{\eta}_\gamma}-E_{\rm p}$ correlations (where $L$ is the time-averaged luminosity of the prompt emission, $E_{\rm p}$ is the spectral peak energy, $\Gamma$ is the bulk Lorentz factor and $\bar{\eta}_\gamma$ is the emission efficiency of Gamma-ray bursts) are well consistent with the relations between the resembling parameters predicted in the photospheric radiation model of the prompt emission of Gamma-ray bursts. The time-resolved thermal radiation of GRB 090902B does follow the $E_{\rm p}-L$ and $\Gamma-L$ correlations. A reliable interpretation of the four correlations in alternative models is still lacking. These facts may point towards a photospheric origin of prompt emission of some Gamma-ray Bursts.