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We study the narrowest spectra expected from gamma-ray bursts. We present ananalytical function for the spectrum that is emitted from the photosphere of aradiation-dominated flow that is under acceleration. This is the narrowestpossible spectrum and it differs from a Planck function. We also presentnumerical spectra from photospheres occurring during the transition into thecoasting phase of the flow. Using these spectral models, we reanalyse Fermiobservations of GRB100507 and GRB101219, which both have been reported to havevery narrow spectra. The bursts can be fitted by the spectral models: ForGRB101219 the spectrum is consistent with the photosphere occurring below orclose to the saturation radius, while for GRB100507 the photosphere positionrelative to the saturation radius can be determined as a function of time. Inthe latter case, we find that the photosphere initially occurs in theacceleration phase and thereafter transitions into the coasting phase. We alsofind that this transition occurs at the same time as the change in observedcooling behaviour: the temperature is close to constant before the break anddecays after. We argue that such a transition can be explained by an increasingmass outflow rate. Both analysed bursts thus give strong evidence that the jetsare (initially) radiation dominated.

Emission from accelerating jets in gamma-ray bursts: Radiation dominated flows with increasing mass outflow rates