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

A model is developed for the confinement and collimation of a baryon-poor outflow by its surrounding medium. Both confinement by kinetic pressure of a static corona and confinement by the ram pressure of a supersonic wind emanating from a disk surrounding the inner source are considered. Solutions are presented for the structure of the shocked layers of a deflected baryon-poor jet (BPJ) and exterior wind. The dependence of the opening angle of the BPJ on the parameters of the confining medium are carefully examined. It is found that the BPJ shock may either converge to the symmetry axis or diverge away from it, depending on the opening angle of the BPJ injection cone. In the latter case, the inner flow exhibits a nonuniform structure, consisting of an ultrarelativistic core containing the unshocked BPJ enveloped by the slower, shocked BPJ layer. The implications of our results to the prompt GRB emission are briefly discussed.