A semi-analytical model for the propagation of a structured jet in a magnetized medium

This study presents a semi-analytical model that models the effects that a static magnetized medium with a tangled field produces in relativistic collimated jets. The model is a first approximation that addresses the magnetic field present in the medium and is based on pressure equilibrium principles between the jet, cocoon, and external medium. A fraction of the ambient medium field is allowed to be entrained in the cocoon. We find that the jet and cocoon properties are affected at high magnetic fields and that they are sensitive to the mixing in the cocoon. For low-mixing a slower-broader jet with a broader and more energetic cocoon would be produced. On the other hand, high-mixing would produce a faster-narrower jet with a narrow and less-energetic cocoon. Two-dimensional hydrodynamical simulations are used to validate the model and to constrain the mixing parameter. We found good qualitative agreement between the model and the simulations. For high magnetization, the results were found to be consistent with the low mixing case of our semi-analytical model.