The ratio η (Equation (B1)) between energy density and free–free energy production. The blue (θ = 0﹩\mathop{.}\limits^{\unicode{x000b0}}﹩5), orange (θ = 1﹩\mathop{.}\limits^{\unicode{x000b0}}﹩6), and green (θ = 3﹩\mathop{.}\limits^{\unicode{x000b0}}﹩1) lines are for the fluid elements along different polar angles. The black dashed line is the threshold for the LTE condition η ≤ 1. Almost all fluid elements of the jet-cocoon system are in the LTE regime except for the layer near the stellar surface (the gas near and outside the stellar surface is unimportant for the subsequent cocoon evolution).