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 ≳ 20 GeV and that the Lorentz factor of the emitting material has to be very large 10³ ≲ Γ_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 Γ^΄ ≈ 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.