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Poynting flux dominated jets challenged by their photospheric emission

One of the key open question in the study of jets in general, and jets in gamma-ray bursts (GRBs) in particular, is the magnetization of the outflow. Here we consider the photospheric emission of Poynting flux dominated outflows, when the dynamics is mediated by magnetic reconnection. We show that thermal three-particle processes, responsible for the thermalization of the plasma, become inefficient at a radius $r_{\rm sup} \sim 10^{9.5}$~cm, far below the photosphere, at $\sim 10^{11.5}$~cm. Conservation of the total photon number above $r_{\rm sup}$ combined with Compton scattering below the photosphere enforces kinetic equilibrium between electrons and photons. This, in turn, leads to an increase in the observed photon temperature, which reaches $\gtrsim 8$~MeV (observed energy) when decoupling the plasma at the photosphere. This result is weakly dependent on the free model parameters. We show that in this case, the expected thermal luminosity is a few \% of the total luminosity, and could therefore be detected. The predicted peak energy is more than an order of magnitude higher than the observed peak energy of most GRBs, which puts strong constraints on the magnetization of these outflows.