Relativistic tearing and drift-kink instabilities in two-fluid simulations

The stability of current sheets in collisionless relativistic pair plasma was studied via two-dimensional two-fluid relativistic magnetohydrodynamic simulations with vanishing internal friction between fluids. In particular, we investigated the linear growth of the tearing and drift-kink modes in the current sheets both with and without the guide field and obtained the growth rates which are very similar to what has been found in the corresponding particle in cell (PIC) simulations. This suggests that the two-fluid simulations can be useful in studying the large-scale dynamics of astrophysical relativistic plasmas in problems involving magnetic reconnection

Dynamics of carving runs in alpine skiing. I. The basic centrifugal pendulum

We studied perfect carving turns of alpine skiing using the simple model of an inverted pendulum which is subject to the gravity force and the force mimicking the centrifugal force emerging in the turns. Depending on the turn speed the model describes two different regimes. In the subcritical regime, there exist three equilibrium positions of the pendulum where the total torque applied to the pendulum vanishes—the marginally stable vertical position and two unstable tilted positions on both sides of the vertical. The tilted equilibria correspond to the ski turns executed in perfect balance. The vertical equilibrium corresponds to gliding down the fall line without turns. In the supercritical regime, the tilted equilibria disappear. In addition to the equilibria, the model allows fall-rise solutions, where the pendulum (skier) rises from the ground on one side and hits the ground on the other side, and solutions describing oscillations about the vertical equilibrium. These oscillations correspond to the so-called dynamic skiing where the skier never settles to a balanced position in the turn. Analysis of the available data on World Cup races shows that elite racers ski mostly in the supercritical regime

Mechanics of side-slipping in alpine skiing. Braking and skidded traversing

A recently proposed simple approximate theory of snow machining is applied to modelling of several basic manoeuvres of alpine skiing: fall-line side-slipping, traversing, and hockey stop. The results agree with the skiing practice and explain the abnormally high friction reported in previous field studies. They also prepare foundation for future rigorous testing of the theory, which will determine its accuracy and limits of applicability

Three-dimensional magnetohydrodynamic simulations of the Crab Nebula

In this paper, we give a detailed account of the first three-dimensional (3D) relativistic magnetohydrodynamic simulations of pulsar wind nebulae, with parameters most suitable for the Crab nebula. In contrast to the previous 2D simulations, we also consider pulsar winds with much stronger magnetization, up to σ ≃ few. The 3D models preserve the separation of the post-termination shock flow into the equatorial and polar components, but the polar jets are disrupted by the kink mode of the current driven instability and 'dissolve' into the main body of the nebula after propagation of several shock radii. With the exception of the region near the termination shock, the 3D models do not exhibit the strong z-pinch configuration characteristic of the 1D and 2D models. Contrary to the expectations based on 1D analytical and semi-analytical models, the 3D solutions with highly magnetized pulsar winds still produce termination shocks with radii comparable to those deduced from the observations. The reason for this is not only the randomization of magnetic field observed in the 3D solutions, but also the magnetic dissipation inside the nebula. Assuming that the particle acceleration occurs only at the termination shock, we produced synthetic maps of the Crab nebula synchrotron emission. These maps retain most of the features revealed in the previous 2D simulations, including thin wisps and the inner knot. The polarization and variability of the inner knot is in a particularly good agreement with the observations of the Crab nebula and the overall polarization of the inner nebula is also reproduced quite well. However, the polar jet is not as bright as observed, suggesting that an additional particle acceleration, presumably related to the magnetic dissipation, has to be invoked

Rayleigh–Taylor instability in two-component relativistic jets

Relativistic jets associated with active galactic nuclei and gamma-ray bursts propagate over huge distances without significant loss of momentum. At the same time they are bright emitters, which is indicative of strong energy dissipation. This points towards a mechanism of internal dissipation which does not result in a global disruption of the flow. One possibility is internal shocks and another one is turbulence driven by local instabilities. Such instabilities can be triggered when a freely expanding jet is reconfined by either the cocoon or external gas pressure. In this paper, we study the dynamics of two-component spine-sheath hydrodynamic jets coming into pressure equilibrium with external gas using 2D computer simulations. We find that the jet oscillations lead to a rapid onset of Rayleigh–Taylor-type instabilities, which results in additional internal dissipation and mixing of the jet components. Although slightly different in details, this outcome holds both for the heavy-spine-light-sheath and light-spine-heavy-sheath configurations. The results may provide an explanation to the spatial flaring observed in some AGN jets on kpc-scales

Mechanics of side-slipping in alpine skiing: theory of machining snow and ice

Side-slipping (or skidding) is a feature of several manoeuvres in alpine skiing, including a few types of skiing turns. On hard snow, side-slipping involves removal of a thin top layer of snow, that makes it similar to machining of materials in manufacturing. In this paper, we briefly review the theory of machining and then propose an approximate model that can be used to describe side-slipping in skiing. We test this model against published results of laboratory experiments in machining of ice and snow and find agreement

Electrically-charged black holes and the Blandford-Znajek mechanism

Recently, it was claimed by King & Pringle that accretion of electric charge by a black hole rotating in an aligned external magnetic field results in a “dead” vacuum magnetosphere, where the electric field is totally screened, no vacuum breakdown is possible, and the Blandford-Znajek mechanism cannot operate. Here we study in details the properties of the Wald solution for electrically charged black holes discussed in their paper. Our results show that the claim is erroneous as in the solution with the critical charge q0 = 2aB0 there exists a drop of electrostatic potential along all magnetic field lines except the one coinciding with the symmetry axis. It is also found that while uncharged rotating black holes expel external vacuum magnetic field from their event horizon (the Meissner effect), electric charging of black holes pulls the magnetic field lines back on it, resembling what has been observed in some previous force-free, RMHD and PIC simulations of black hole magnetospheres. This suggests that accretion of electric charge may indeed be a feature of the black hole electrodynamics. However, our analysis shows that the value q0 of the BH charge given by Wald is likely to be only an upper limit, and that the actual value depends of the details of the magnetospheric physics

Stationary relativistic jets

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with vz≈cvz≈c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ctz=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialised code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres and elucidated the nature of radial oscillations of steady-state jets

Observations of 'wisps' in magnetohydrodynamic simulations of the Crab Nebula

In this paper, we describe results of new high-resolution axisymmetric relativistic magnetohydrodynamic (MHD) simulations of pulsar wind nebulae. The simulations reveal strong breakdown of the equatorial symmetry and highly variable structure of the pulsar wind-termination shock. The synthetic synchrotron maps, constructed using a new more accurate approach, show striking similarity with the well-known images of the Crab Nebula obtained by Chandra and the Hubble Space Telescope. In addition to the jet–torus structure, these maps reproduce the Crab's famous moving wisps whose speed and rate of production agree with the observations. The variability is then analysed using various statistical methods, including the method of structure function and wavelet transform. The results point towards the quasi-periodic behaviour with the periods of 1.5–3 years and MHD turbulence on scales below 1 year. The full account of this study will be presented in a follow-up paper