# Relativistic polytrope from the collimation and acceleration profiles of the M87 jet at subparsec scales and thermodynamic evidence for the Blandford-Znajek mechanism

## TL;DR

This study analyzes VLBI observations of the M87 jet to infer a relativistic polytropic equation of state, providing thermodynamic evidence supporting the Blandford-Znajek mechanism for jet launching.

## Contribution

It links jet acceleration profiles to a relativistic polytropic model and suggests the Blandford-Znajek mechanism's role in jet formation based on thermodynamic and electromagnetic evidence.

## Key findings

- Jet Lorentz factor linearly depends on radius up to 0.65 pc.
- Polytropic index of 4/3 indicates relativistic thermodynamics.
- Change to index 5/3 suggests plasma cooling and electron-positron plasma presence.

## Abstract

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.