κ and w parameter. Left panel: map of the κ parameter based on Eq. (18), where the jet spine is excluded (σ <  5). The map shows that the κ parameter is small in the jet sheath and large in the disk. Middle panel: map of the w parameter when ϵ = 0, showing large values in the sheath compared to the disk. Right panel: same as middle panel but now for ϵ = 0.015, the sheath has slightly larger values compared to the ϵ = 0 case.