Non-Thermal emission from the photospheres of Gamma-Ray Burst outflows. I: High frequency tails

We study the spectrum of high frequency radiation emerging from mildly dissipative photospheres of long-duration gamma-ray burst outflows. Building on the results of recent numerical investigations, we assume that electrons are heated impulsively to mildly relativistic energies by either shocks or magnetic dissipation at Thomson optical depths of several and subsequently cool by inverse Compton, scattering off the thermal photons of the photosphere. We show that even in the absence of magnetic f...