Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion, the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. derived a general simplified (semi-)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model.We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g. collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian.We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at http://www.astro.tau.ac.il/~ore/propagation.html.