3+1 Magnetodynamics

The Magnetodynamics, or Force-Free Degenerate Electrodynamics, is recognized as a very useful approximation in studies of magnetospheres of relativistic stars. In this paper we discuss various forms of Magnetodynamic equations which can be used to study magnetospheres of black holes. In particular, we focus on the 3+1 equations which allow for curved and dynamic spacetime.Comment: The revised version. Expanded by including the derivation of the force-free 4-curren

The remarkable AGN jets

The jets from active galactic nuclei exhibit stability which seems to be far superior compared to that of terrestrial and laboratory jets. They manage to propagate over distances up to a billion of initial jet radii. Yet this may not be an indication of some exotic physics but mainly a reflection of the specific environment these jets propagate through. The key property of this environment is a rapid decline of density and pressure along the jet, which promotes its rapid expansion. Such an expansion can suppress global instabilities, which require communication across the jet, and hence ensure its survival over huge distances. At kpc scales, some AGN jets do show signs of strong instabilities and even turn into plumes. This could be a result of the flattening of the external pressure distribution in their host galaxies or inside the radio lobes. In this regard, we discuss the possible connection between the stability issue and the Fanaroff-Riley classification of extragalactic radio sources. The observations of AGN jets on sub-kpc scale do not seem to support their supposed lack of causal connectivity. When interpreted using simple kinematic models, they reveal a rather perplexing picture with more questions than answers on the jets dynamics.Comment: Invited talk at the AU Symposium No. 324 "New Frontiers in Black Hole Astrophysics", Ljubljana, Slovenia, 201

Rarefaction acceleration of ultrarelativistic magnetized jets in gamma-ray burst sources

When a magnetically-dominated super-fast magnetosonic GRB jet leaves the progenitor star the external pressure support may drop and the jet may enter the regime of ballistic expansion during which its magnetic acceleration becomes highly ineffective. However, recent numerical simulations suggested that the transition to this regime is accompanied by a sudden "burst" of acceleration. We confirm this finding and attribute the acceleration to the sideways expansion of the jet - the magnetic energy is converted into the kinetic one in the strong magnetosonic rarefaction wave, which is launched when the jet loses its external support. This type of acceleration, the rarefaction acceleration, is specific to relativistic jets because their energy budget can still be dominated by magnetic energy even in highly super-fast magnetosonic regime. Just like the collimation acceleration of externally confined magnetized jets, it is connected with the geometry of magnetic flux sufaces. In both cases, in the acceleration zone the poloidal field lines diverge faster than in the monopolar configuration. On the other hand, whereas the collimation acceleration keeps the product of jet opening angle and Lorentz factor somewhat below unity, the rarefaction acceleration allows to make it significantly larger, in agreement with the standard model of jet breaks in afterglow light curves.Comment: Submitted to MNRA

On the inadmissibility of non-evolutionary shocks

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry

Transformation of the Poynting flux into the kinetic energy in relativistic jets

The acceleration of relativistic jets from the Poynting to the matter dominated stage is considered. The are generally two collimation regimes, which we call equilibrium and non-equilibrium, correspondingly. In the first regime, the jet is efficiently accelerated till the equipartition between the kinetic and electro-magnetic energy. We show that after the equilibrium jet ceases to be Poynting dominated, the ratio of the electro-magnetic to the kinetic energy decreases only logarithmically so that such jets become truly matter dominated only at extremely large distances. Non-equilibrium jets remain generally Poynting dominated till the logarithmically large distances. In the only case when a non-equilibrium jet is accelerated till the equipartition level, we found that the flow is not continued to the infinity but is focused towards the axis at a finite distance from the origin.Comment: Submitted to MNRAS Minor changes in the Conclusion

Observations of the Blandford-Znajek and the MHD Penrose processes in computer simulations of black hole magnetospheres

In this paper we report the results of axisymmetric relativistic MHD simulations for the problem of Kerr black hole immersed into a rarefied plasma with ''uniform'' magnetic field. The long term solution shows properties which are significantly different from those of the initial transient phase studied recently by Koide(2003). The topology of magnetic field lines within the ergosphere is similar to that of the split-monopole model with a strong current sheet in the equatorial plane. Closer inspection reveals a system of isolated magnetic islands inside the sheet and ongoing magnetic reconnection. No regions of negative hydrodynamic ''energy at infinity'' are seen inside the ergosphere and the so-called MHD Penrose process does not operate. Yet, the rotational energy of the black hole continues to be extracted via purely electromagnetic mechanism of Blandford and Znajek(1977). However, this is not followed by development of strong relativistic outflows from the black hole. Combined with results of other recent simulations this signals a potential problem for the standard MHD model of relativistic astrophysical jets should they still be observed at distances as small as few tens of gravitational radii from the central black hole.Comment: Submitted to MNRA

Impulsive acceleration of strongly magnetized relativistic flows

The definitive version can be found at: http://onlinelibrary.wiley.com/ Copyright Royal Astronomical SocietyThe strong variability of magnetic central engines of active galactic nuclei (AGNs) and gamma-ray bursts (GRBs) may result in highly intermittent strongly magnetized relativistic outflows. We find a new magnetic acceleration mechanism for such impulsive flows that can be much more effective than the acceleration of steady-state flows. This impulsive acceleration results in kinetic-energy-dominated flows that are conducive to efficient dissipation at internal magnetohydrodynamic shocks on astrophysically relevant distances from the central source. For a spherical flow, a discrete shell ejected from the source over a time t0 with Lorentz factor Γ∼ 1 and initial magnetization σ0=B20/4πρ0c2≫ 1 quickly reaches a typical Lorentz factor Γ∼σ1/30 and magnetization σ∼σ2/30 at the distance R0≈ct0. At this point, the magnetized shell of width Δ∼R0 in the laboratory frame loses causal contact with the source and continues to accelerate by spreading significantly in its own rest frame. The expansion is driven by the magnetic pressure gradient and leads to relativistic relative velocities between the front and back of the shell. While the expansion is roughly symmetric in the centre of the momentum frame, in the laboratory frame, most of the energy and momentum remains in a region (or shell) of width Δ∼R0 at the head of the flow. This acceleration proceeds as Γ∼ (σ0R/R0)1/3 and σ∼σ2/30 (R/R0)-1/3 until reaching a coasting radius Rc∼R0σ20, where the kinetic energy becomes dominant: Γ∼σ0 and σ∼ 1 at Rc. The shell then starts coasting and spreading (radially), its width growing as Δ∼R0(R/Rc), causing its magnetization to drop as σ∼Rc/R at R > Rc. Given the typical variability time-scales of AGNs and GRBs, the magnetic acceleration in these sources is a combination of the quasi-steady-state collimation acceleration close to the source and the impulsive (conical or locally quasi-spherical) acceleration farther out. The interaction with the external medium, which can significantly affect the dynamics, is briefly addressed in the discussion.Peer reviewe