Hydrodynamic Collimation of Relativistic Outflows: Semianalytic Solutions and Application to Gamma-Ray Bursts

摘要

A model is developed for the confinement and collimation of a baryon pooroutflow by its surrounding medium. Both, confinement by kinetic pressure of astatic corona, and confinement by the ram pressure of a supersonic windemanating from a disk surrounding the inner source are considered. Solutionsare presented for the structure of the shocked layers of a deflected baryonpoor jet (BPJ) and exterior wind. The dependence of the opening angle of theBPJ on the parameters of the confining medium are carefully examined. It isfound that the BPJ shock may either converge to the symmetry axis or divergeaway from it, depending on the opening angle of the BPJ injection cone. In thelatter case the inner flow exhibits a non-uniform structure, consisting of anultra-relativistic core containing the unshocked BPJ enveloped by the slower,shocked BPJ layer. The implications of our results to the prompt GRB emissionare briefly discussed.