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., ). 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 , 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 , 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 .
Although MHD and general relativistic effects seem to be crucial for a successful launch of the jet (for a review see, e.g., ), 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 . 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 .
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  and even cause their deflection when propagating through non-homogeneous environments . 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 ) 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 ), 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 .
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. .
Finally, Koide et al.  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
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