Marginally fast cooling synchrotron models for prompt GRBs

Previous studies have considered synchrotron as the emission mechanism for prompt gammaray 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 amajority of the electrons in the emitting region are contributing to the observed peak, we find that the energy per electron has to be E ≳ 20 GeV and that the Lorentz factor of the emitting material has to be very large 10³ ≲ λ _em ≲ 10⁴, 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 λ' ≈10, relative to the bulk frame of the jet and that the jet must be highly magnetized upstream of the emission region, σ_up ≳ 30. The emission radius is also strongly constrained in this model to R ≳ 10¹⁶ 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.