Recent Very Long Baseline Interferometry observations of the relativistic jet in the M87 radio galaxy at 43 GHz show gradual relativistic acceleration of the plasma and suggest a linear dependence of Lorentz factor on jet radius at scales up to 8 marcsec (0.65 pc) from the core (2.5 marcsec in projection). General analysis of integrals of motion being unaltered along the jet and reflecting fundamental conservation laws shows that the above dependence implies a polytropic equation of state with index 4/3. The inferred value of the polytropic index appears independent of the exact nature of forces sustaining the transverse balance of the jet and indicates exact conservation of the longitudinal electric current and hence the existence of a stable internal electromagnetic structure at the scales under consideration. At this index the flow is hot and corresponds to relativistic thermodynamic motion of particles. Considerable weakening of the acceleration efficiency after 8 marcsec with the jet form being unchanged can be related to the plasma cooling, when the polytropic index becomes 5/3. Such a sharp change in the index without intermediate delay at 1.44 during cooling favours the existence of an electron-positron plasma and requires at least partial participation of the Blandford-Znajek mechanism in the launching of the M87 jet.
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