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

The merger of two magnetized compact objects, such as neutron stars, forms a compact object which may launch a relativistic and collimated jet. Numerical simulations of the process show that a dense and highly magnetized medium surrounds the system. This study presents a semi-analytical model that models the effects that a static magnetized medium with a tangled field produces in relativistic, collimated, and non-magnetized 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 may be affected by high magnetic fields ($\gtrsim 10^{15}$~G) and mixing. The evolution of the system may vary up to $\sim10\%$ (compared to the non-magnetized case). Low-mixing may produce a slower-broader jet with a broader and more energetic cocoon would be produced. On the other hand, high-mixing could 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. Although the magnetic field and mixing have a limited effect, our semi-analytic model captures the general trend consistent with numerical results. For high magnetization, the results were found to be more consistent with the low mixing case in our semi-analytic model.