The peak energy of dissipative gamma-ray burst photospheres

The radiation released at the transparency radius of an ultrarelativistic flow can account for the observed properties of gamma-ray bursts (GRBs) provided that sufficient energy is dissipated in the sub-photospheric region. Here, I investigate how the peak energy of the Ef(E) spectrum and its overall shape depend on the properties of the jet for various dissipative photospheres. I find that continuous energy release which results in electron heating over a wide range of distances may be the key to explain the GRB emission. In this picture, the peak of the spectrum forms at a Thomson optical depth of several tens. The peak depends mainly on the bulk Lorentz factor G of the flow and can, therefore, be used to determine it. The G is predicted to range from similar to 10 to 1000 from X-ray flashes to the brightest observed GRBs in agreement with recent observational inferences. The Amati relation can be understood if the brightest bursts are the least baryon loaded ones. Implications from this interpretation of the GRB emission for the central engine are discussed.