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tokens: constituting a plasma. Importantly, the observed β = 1 and the obtained Γ = 4/3 indicate that the longitudinal current, though in general not obliged to conserve along the magnetic tube, appears as an exact integral of motion at the scales under consideration, Since ρ ∝ r −2 − β = r −3 , we have for a hot flow h ∝ ρ Γ − 1 = ρ 1/3 ∝ r −1 ; therefore, by equation ( 2 ) the equality ( 49 ) holds, whatever the nature of the force balance in the jet. Energy conservation ( 10 ) then leads us to the above conclusion. This is direct evidence of a stable longitudinal current structure in the jet. It is interesting to consider what happens at 8 marcsec. Mertens et al. ( 2016 ), taking into account the results of Lyubarsky ( 2009 ), discuss that the jet may there enter a non-equilibrium regime or rather exhibit an early saturation of Poynting-flux conversion. Meanwhile, an alternative explanation may be a change of the jet thermodynamics. The relativistic gas is not characterized by a single polytropic index, and the general expression for its enthalpy is h = K 3 (1/Θ)/ K 2 (1/Θ), where K ν ( z ) is the Macdonald function of order ν and Θ = p /ρ is the temperature (Synge 1957 ). Useful simpler analytic approximations of the exact expression are presented in Mathews ( 1971 ), Meliani et al. ( 2004 ), Chattopadhyay Ryu ( 2009 ). In the two opposite limiting cases it corresponds to a polytrope with index Γ = 4/3 when Θ ≫ 1 and with index Γ = 5/3 when Θ ≪ 1. From equations ( 2 ) and ( 3 ) we have which allows us to formally estimate the polytropic index, respectively, for the case of a dominating longitudinal magnetic, transverse electromagnetic, and centrifugal pressure: Since Γ TEM = Γ CH 4/3, a hot flow with a dominating transverse electromagnetic or centrifugal pressure is not realized over 8 marcsec. The two other indices correspond to a cold flow: Γ LM is close to but yet slightly larger than the maximum possible 5/3, while, surprisingly, Γ CC almost coincides with 5/3 ≈ 1.67. Therefore, a transition from γ ∝ z 0.58 to γ ∝ z 0.16 at z ∼ 8 marcsec may be explained by the plasma cooling and transition from a hot flow with p ∝ ρ 4/3 to a cold flow with p ∝ ρ 5/3 . Over 8 marcsec we likely have a cold flow whose pressure is determined mainly by centrifugal forces, possibly with some contribution from the pressure of longitudinal magnetic field, while transverse electromagnetic fields give forces that almost compensate each other and result in a modest net effect. Determination of Γ from the jet acceleration and collimation profiles has power in revealing plasma composition, which is important for conclusions about exact mechanisms of jet launching. The transition directly from 4/3 to 5/3 as cooling occurs may be a sign of a pure electron–positron plasma component: electrons and positrons have the same mass and behave as the mentioned single-component perfect Synge gas. In the case of an electron–proton plasma, however, the transition from 4/3 to 5/3