We present the first global model of prompt emission from a short gamma-ray burst that consistently describes the evolution of the central black-hole (BH) torus system, the propagation of the jet through multi-component merger ejecta, the transition into free expansion, and the photospheric emission from the relativistic jet. To this end, we perform a special relativistic neutrino-hydrodynamics simulation of a viscous BH-torus system, which is formed about 500ms after the merger and is surrounded by dynamical ejecta as well as neutron star winds, along with a jet that is injected in the vicinity of the central BH. In a post-processing step, we compute the photospheric emission using a relativistic Monte-Carlo radiative transfer code. It is found that the wind from the torus leaves a strong imprint on the jet as well as on the emission causing narrow collimation and rapid time variability. The viewing angle dependence of the emission gives rise to correlations among the spectral peak energy, E_p, isotropic energy, E_iso, and peak luminosity, L_p, which may provide natural explanations for the Amati- and Yonetoku-relations. We also find that the degree of polarization is small for the emission from the jet core (<2%), while it tends to increase with viewing angle outside of the core and can become as high as ~10-40% for energies larger than the peak energy. Finally, the comparison of our model with GRB170817A strongly disfavors the photospheric emission scenario and therefore supports alternative scenarios, such as the cocoon shock breakout.
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