Shear and Pressure Collimation of Relativistic Jets Inside a Stellar Envelope

A relativistic jet launched at a stellar centre must cross the envelope, and the crossing reshapes it. Cocoon pressure collimates the jet while shear at the jet boundary entrains material and drains energy. This paper computes the collimated opening angle and beaming correction across jet powers and derives the corresponding true energy for a fixed isotropic-equivalent energy. Using the calculation described in the Methods, the headline results are: theta_1e50_deg = 5.16, fbeam_1e50 = 247, Etrue_for_Eiso1e53_erg = 404858299595141676134343661119430388789241307987968. For a jet power of 10^50 erg per second the collimated half-opening angle is about five degrees and the beaming factor is of order one hundred, reducing a 10^53 erg isotropic-equivalent event to a true energy near 10^51 erg. The corrected energies cluster near the canonical supernova energy scale, supporting the view that beaming, rather than an extraordinary central engine, explains most of the apparent energy spread. This study is simulated and computed from stated assumptions; it is not a measurement. All headline numbers in this abstract appear in the deposited results file and are reproduced by running the deposited code without modification.