Contents List of Figures

6.5 Relativistic Jet Propagation 289
Figure 137: The kpc–scale jet of M 87 is embedded into a much more extended faint
radio halo (VLA image at 327 MHz). Such extended radio halos are now found in
many clusters of galaxies.
The state vector is defined by
and the flux vector F i as
U = (D, S 1 , S 2 , S 3 , τ) T
(701)
F i = (Dv i , S 1 v i + P δ 1i , S 2 v i + P δ 2i , S 3 v i + P δ 3i , S i − Dv i ) T . (702)
The five conserved quantities D, S 1 , S 2 , S 3 and τ are the rest–mass density, the three
components of the momentum density, and the energy density (measured relative to
the rest mass energy density), respectively. They are all measured in the laboratory
frame, and are related to quantities in the local rest frame of the fluid (primitive
variables) through
D = ρΓb (703)