Impact of the collision model on the multi-messenger emission from Gamma-Ray Burst internal shocks

We discuss the production of multiple astrophysical messengers (neutrinos, cosmic rays, gamma-rays) in the Gamma-Ray Burst (GRB) internal shock scenario, focusing on the impact of the collision dynamics between two shells on the fireball evolution. In addition to the inelastic case, in which plasma shells merge when they collide, we study the Ultra Efficient Shock scenario, in which a fraction of the internal energy is re-converted into kinetic energy and, consequently, the two shells survive and remain in the system. We find that in all cases a quasi-diffuse neutrino flux from GRBs at the level of $10^{-11}$ to $10^{-10} \, \mathrm{GeV \, cm^{-2} \, s^{-1} \, sr^{-1}}$ (per flavor) is expected for protons and a baryonic loading of ten, which is potentially within the reach of IceCube-Gen2. The highest impact of the collision model for multi-messenger production is observed for the Ultra Efficient Shock scenario, that promises high conversion efficiencies from kinetic to radiated energy. However, the assumption that the plasma shells separate after a collision and survive as separate shells within the fireball is found to be justified too rarely in a multi-collision model that uses hydrodynamical simulations with the PLUTO code for individual shell collisions.