Inferred jet velocities close to the speed of light suggest that jets are formed within a few gravitational radii of the event horizon of the black hole. Moreover, very-long-baseline interferometric (VLBI) radio observations reveal that jets are already collimated at subparsec scales. Current theoretical models assume that accretion disks are the source of the bipolar outflows which are further collimated and accelerated via MHD processes (see, e.g., [16]). There is a large number of parameters which are potentially important for jet powering: the black hole mass and spin, the accretion rate and the type of accretion disk, the properties of the magnetic field and of the environment.
At parsec scales the jets, observed via their synchrotron and inverse Compton emission at radio frequencies with VLBI imaging, appear to be highly collimated with a bright spot (the core) at one end of the jet and a series of components which separate from the core, sometimes at superluminal speeds. In the standard model [17], these speeds are interpreted as a consequence of relativistic bulk motions in jets propagating at small angles to the line of sight with Lorentz factors up to 20 or more. Moving components in these jets, usually preceded by outbursts in emission at radio wavelengths, are interpreted in terms of traveling shock waves.
Finally, the morphology and dynamics of jets at kiloparsec scales are dominated by the interaction of the jet with the surrounding extragalactic medium, the jet power being responsible for dichotomic morphologies (the so called Fanaroff-Riley I and II classes [56], FR I and FR II, respectively). Current models [14, 91] interpret FR I morphologies as the result of a smooth deceleration from relativistic to non-relativistic, transonic speeds on kpc scales due to a slower shear layer. For the most powerful radio galaxies (FR II) and quasars on the other hand, the observation of flux asymmetries between jet and counter-jet indicates that in these sources relativistic motion extends up to kpc scales, although with smaller values of the overall bulk speeds [21].
Although MHD and general relativistic effects seem to be
crucial for a successful launch of the jet (for a review see,
e.g., [23]), purely hydrodynamic, special relativistic simulations are
adequate to study the morphology and dynamics of relativistic
jets at distances sufficiently far from the central compact
object (i.e., at parsec scales and beyond). The development of
relativistic hydrodynamic codes based on HRSC techniques (see
Sections
3
and
4) has triggered the numerical simulation of relativistic jets at
parsec and kiloparsec scales.
At kiloparsec scales, the implications of relativistic flow
speeds and / or relativistic internal energies for the morphology
and dynamics of jets have been the subject of a number of papers
in recent years [112,
46,
110
,
111
,
86]. Beams with large internal energies show little internal
structure and relatively smooth cocoons allowing the terminal
shock (the hot spot in the radio maps) to remain well defined
during the evolution. Their morphologies resemble those observed
in naked quasar jets like 3C273 [37]. Fig.
12
shows several snapshots of the time evolution of a light,
relativistic jet with large internal energy. The dependence of
the beam's internal structure on the flow speed suggests that
relativistic effects may be relevant for the understanding of the
difference between slower, knotty BL Lac jets and faster,
smoother quasar jets [60].
Highly supersonic models, in which kinematic relativistic
effects due to high beam Lorentz factors dominate, have extended
over-pressured cocoons. These over-pressured cocoons can help to
confine the jets during the early stages of their
evolution [110] and even cause their deflection when propagating through
non-homogeneous environments [148]. The cocoon overpressure causes the formation of a series of
oblique shocks within the beam in which the synchrotron emission
is enhanced. In long term simulations (see Fig.
13), the evolution is dominated by a strong deceleration phase
during which large lobes of jet material (like the ones observed
in many FR IIs, e.g., Cyg A [25]) start to inflate around the jet's head. These simulations
reproduce some properties observed in powerful extragalactic
radio jets (lobe inflation, hot spot advance speeds and
pressures, deceleration of the beam flow along the jet) and can
help to constrain the values of basic parameters (such as the
particle density and the flow speed) in the jets of real
sources.
The development of multidimensional relativistic hydrodynamic
codes has allowed, for the first time, the simulation of parsec
scale jets and superluminal radio components [68,
85
,
117]. The presence of emitting flows at almost the speed of light
enhances the importance of relativistic effects in the appearance
of these sources (relativistic Doppler boosting, light
aberration, time delays). Hence, one should use models which
combine hydrodynamics and synchrotron radiation transfer when
comparing with observations. In these models, moving radio
components are obtained from perturbations in steady relativistic
jets. Where pressure mismatches exist between the jet and the
surrounding atmosphere reconfinement shocks are produced. The
energy density enhancement produced downstream from these shocks
can give rise to stationary radio knots as observed in many VLBI
sources. Superluminal components are produced by triggering small
perturbations in these steady jets which propagate at almost the
jet flow speed. One example of this is shown in Fig.
14
(see also [68]), where a superluminal component (apparent speed
times the speed of light) is produced from a small variation of
the beam flow Lorentz factor at the jet inlet. The dynamic
interaction between the induced traveling shocks and the
underlying steady jet can account for the complex behavior
observed in many sources [67].
The first magnetohydrodynamic simulations of relativistic jets
have been already undertaken in 2D [82,
81
] and 3D [128
,
129
] to study the implications of ambient magnetic fields in the
morphology and bending properties of relativistic jets. However,
despite the impact of these results in specific problems like,
e.g., the understanding of the misalignment of jets between pc
and kpc scales, these 3D simulations have not addressed the
effects on the jet structure and dynamics of the third spatial
degree of freedom. This has been the aim of the work undertaken
by Aloy et al. [2].
Finally, Koide et al. [83] have developed a general relativistic MHD code and applied it
to the problem of jet formation from black hole accretion disks.
Jets are formed with a two-layered shell structure consisting of
a fast gas pressure driven jet (Lorentz factor
) in the inner part and a slow magnetically driven outflow in
the outer part, both of which are being collimated by the global
poloidal magnetic field penetrating the disk.
![]() |
Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller http://www.livingreviews.org/lrr-1999-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |