High efficiency photospheric emission entailed by formation of a collimation shock in gamma-ray bursts

The primary dissipation mechanism in jets of gamma-ray bursts (GRBs), and the high efficiency of the prompt emission are long-standing issues. One possibility is strong collimation of a weakly magnetized relativistic jet by the surrounding medium, which can considerably enhance the efficiency of the photospheric emission. We derive a simple analytic criterion for the radiative efficiency of a collimated jet showing that it depends most strongly on the baryon loading. We confirm this analytic result by 3D numerical simulations, and further find that mixing of jet and cocoon material at the collimation throat leads to a substantial stratification of the outflow as well as sporadic loading, even if the injected jet is uniform and continuous. One consequence of this mixing is a strong angular dependence of the radiative efficiency. Another is large differences in the Lorentz factor of different fluid elements that lead to formation of internal shocks. Our analysis indicates that in both long and short GRBs a prominent photospheric component cannot be avoided when observed within an angle of a few degrees to the axis, unless the asymptotic Lorentz factor is limited by baryon loading at the jet base to _∞ < 100 (with a weak dependence on outflow power). Photon generation by newly created pairs behind the collimation shock regulates the observed temperature at ∼ 50 θ₀⁻¹ keV, where θ₀ is the initial jet opening angle, in remarkable agreement with the observed peak energies of prompt emission spectra. Further consequences for the properties of the prompt emission are discussed at the end.