  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.
