Marginally fast cooling synchrotron models for prompt GRBs

Previous studies have considered synchrotron as the emission mechanism for prompt gamma-ray bursts (GRBs). These works have shown that the electrons must cool on a time-scale comparable to the dynamic time at the source in order to satisfy spectral constraints while maintaining high radiative efficiency. We focus on conditions where synchrotron cooling is balanced by a continuous source of heating, and in which these constraints are naturally satisfied. Assuming that a majority of the electrons in the emitting region are contributing to the observed peak, we find that the energy per electron has to be E greater than or similar to 20 GeV and that the Lorentz factor of the emitting material has to be very large 10(3) less than or similar to Gamma(em) less than or similar to 10(4), well in excess of the bulk Lorentz factor of the jet inferred from GRB afterglows. A number of independent constraints then indicate that the emitters must be moving relativistically, with Gamma' approximate to 10, relative to the bulk frame of the jet and that the jet must be highly magnetized upstream of the emission region, sigma(up) greater than or similar to 30. The emission radius is also strongly constrained in this model to R greater than or similar to 10(16) cm. These values are consistent with magnetic jet models where the dissipation is driven by magnetic reconnection that takes place far away from the base of the jet.