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Radially inhomogeneous gamma‐ray burst (GRB) jets release variable photospheric emission and can have internal shocks occurring above the photosphere. We generically formulate a photospheric emission model of GRBs including Compton up‐scattered photospheric (UP) emission off the electrons (and positrons) in the internal shocks, and find that the photospheric emission may correspond to the traditional (band) component at ≲1 MeV and the UP emission to the high‐energy emission observed by  Fermi /LAT for some GRBs at ≳10 MeV. The two components can be separate from each other in the spectrum in some cases or can mimic a smooth broad‐band spectrum in other cases. We apply our formulation to the well‐studied long and short LAT GRBs, GRB 080916C, GRB 090902B and GRB 090510, and typically find reasonable parameters for fitting the time‐binned spectra, although fine‐tuning of several parameters is required. The observed delays of the high‐energy emission with respect to the MeV emission which are large compared to the variability times are unlikely to be due to simple kinematic effects of a non‐evolving jet. These delays may instead be attributed to the temporal evolution of the physical parameters of the jet, and thus the delay time‐scales could provide a potential tool for investigating the structures of GRB jets themselves and their progenitors. The difference of the delay time‐scales of long and short GRBs inferred from the  Fermi  data might be due to the differences in the progenitors of long and short GRBs. Some other properties and consequences of this model are discussed, including temporal correlations among the prompt optical, the soft X‐ray and the distinct high‐energy component as well as the band component.

Photosphere–internal shock model of gamma‐ray bursts: case studies of Fermi /LAT bursts