Contents List of Figures

278 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
6.3 Fundamental Parameters for Jets
Already in early simulations, it turned out that one of the fundamental parameters
for jet propagation is the density contrast η = ρB/ρ0, where ρB denotes the beam
density and ρ0 the external density of the surrounding medium. For relativistic
beams propagating with a Lorentz bulk factor ΓB, the density contrast is given by
η = ρBhBΓ 2 B
ρ0
, (678)
with hB as the specific enthalpy of the beam plasma (= 1 for cold plasma) and ΓB
as the Lorentz factor of the beam propagation. For Quasar jets we typically find
ΓB 5 − 10 from superluminal motion on the parsec–scale. The third parameter
which determines the morphology of a jet is the internal Mach number M = VB/cS
5−10 for the beam plasma. The Mach number is not an independent quantity, since
the beam is steadily heated up by means of internal shocks. In addition, the ratio
Figure 130: Fundamental plane for hydro jets.
between external pressure and internal pressure is also important for the initial
launch of the jet. Overpressured jets will initially expand and then recollimate.
The density contrast determines the hot spot advance speed over momentum
balance at the working surface
vHS = vB
√
ηɛ
1 + √ , (679)
ηɛ