Theoretical implications of thermal emission from gamma-ray bursts

Recent analysis show evidence for a thermal emission component that accompanies the non-thermal emission during the prompt phase of GRBs. We show that this component is naturally explained by considering emission from the photosphere. The photosphere of a relativistically expanding plasma wind strongly depends on the angle to the line of sight, θ. As a result, thermal emission can be seen after tens of seconds. Using probability density function P(r, θ) to describe photon escape at radius r and angle θ, we show that the thermal flux is expected to decay at late times as F _BB̃ t^-2 , and the observed temperature decays as T ̃ t^-a, with a ̃ 1/2 - 2/3. We discuss the relation between thermal emission and high energy, non-thermal spectra observed by FERMI. We show how thermal emission can be used to directly measure the Lorentz factor of the flow and the initial radius of the jet.