ALBERT

Description: In a prior paper, we considered the linear stability of magnetized jets that carry no net electric current and do not have current sheets. In this paper, in addition to physically well-motivated magnetic field structures, we also include the effects of jet shear. The jets we study have finite thermal pressure in addition to having realistic magnetic field structures and velocity shear. We find that shear has a strongly stabilizing effect on various modes of jet instability. Increasing shear stabilizes the fundamental pinch modes at long wavelengths and short wavelengths. Increasing shear also stabilizes the first reflection pinch modes at short wavelengths. Increasing shear has only a very modest stabilizing effect on the fundamental kink modes at long wavelengths; however, increasing shear does have a strong stabilizing effect on the fundamental kink modes at short wavelengths. The first reflection kink modes are strongly stabilized by increasing shear at shorter wavelengths. Overall, we find that the combined effect of magnetic field and shear stabilizes jets more than shear alone. In addition to the results from a formal linear stability analysis, we present a novel way of visualizing and understanding jet stability. This gives us a deeper understanding of the enhanced stability of sheared, magnetized jets. We also emphasize the value of our numerical approach in understanding the linear stability of jets with realistic structure.

Description: We model the inner knot of the Crab nebula as a synchrotron emission coming from the non-spherical MHD termination shock of relativistic pulsar wind. The post-shock flow is mildly relativistic; as a result the Doppler beaming has a strong impact on the shock appearance. The model can reproduce the knot location, size, elongation, brightness distribution, luminosity and polarization provided the effective magnetization of the section of the pulsar wind producing the knot is low, ≤ 1. In the striped wind model, this implies that the striped zone is rather wide, with the magnetic inclination angle of the Crab pulsar ≥45°; this agrees with the previous model-dependent estimate based on the gamma-ray emission of the pulsar. We conclude that the tiny knot is indeed a bright spot on the surface of a quasi-stationary magnetic relativistic shock and that this shock is a site of efficient particle acceleration. On the other hand, the deduced low magnetization of the knot plasma implies that this is an unlikely site for the Crab's gamma-ray flares, if they are related to the fast relativistic magnetic reconnection events.

Description: In this paper we consider stability of magnetized jets that carry no net electric current and do not have current sheets. The non-relativistic magnetohydrodynamics equations are linearized around the background velocity and the magnetic field structure of the jet. The resulting linear equations are solved numerically inside the jet. We find that introduction of current-sheet-free magnetic field significantly improves jet stability relative to unmagnetized jets or magnetized jets with current sheets at their surface. This particularly applies to the fundamental pinch and kink modes – they become completely suppressed in a wide range of long wavelengths that are known to become most pernicious to jet stability when the evolution enters the non-linear regime. The reflection modes, both for the pinch and kink instability, also become progressively more stable with increased magnetization.

Description: In stark contrast to their laboratory and terrestrial counterparts, cosmic jets appear to be very stable. They are able to penetrate vast spaces, which exceed by up to a billion times the size of their central engines. We propose that the reason behind this remarkable property is the loss of causal connectivity across these jets, caused by their rapid expansion in response to fast decline of external pressure with the distance from the ‘jet engine’. In atmospheres with power-law pressure distribution, p ext z – , the total loss of causal connectivity occurs, when  〉 2 – the steepness which is expected to be quite common for many astrophysical environments. This conclusion does not seem to depend on the physical nature of jets – it applies both to relativistic and non-relativistic flows, both magnetically dominated and unmagnetized jets. In order to verify it, we have carried out numerical simulations of moderately magnetized and moderately relativistic jets. The results give strong support to our hypothesis and provide with valuable insights. In particular, we find that the z-pinched inner cores of magnetic jets expand slower than their envelopes and become susceptible to instabilities even when the whole jet is stable. This may result in local dissipation and emission without global disintegration of the flow. Cosmic jets may become globally unstable when they enter flat sections of external atmospheres. We propose that the Fanaroff–Riley (FR) morphological division of extragalactic radio sources into two classes is related to this issue. In particular, we argue that the low power FR-I jets become reconfined, causally connected and globally unstable on the scale of galactic X-ray coronas, whereas more powerful FR-II jets reconfine much further out, already on the scale of radio lobes and remain largely intact until they terminate at hotspots. Using this idea, we derived the relationship between the critical jet power and the optical luminosity of the host galaxy, which is in a very good agreement with the observations.

Description: 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  ~= 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.

Description: This paper describes an explicit multidimensional numerical scheme for special relativistic two-fluid magnetohydrodynamics of electron–positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third-order weighted essentially non-oscillatory interpolation. Time integration is carried out using the third-order total variation diminishing method of Runge–Kutta type, thus ensuring overall third-order accuracy on smooth solutions. The magnetic field is kept near divergence-free by means of the method of generalized Lagrange multiplier. The test simulations, which include linear and non-linear continuous plasma waves, shock waves, strong explosions and the tearing instability, show that the scheme is sufficiently robust and confirm its accuracy.

Description: In this paper, we discuss the development of Rayleigh–Taylor (RT) filaments in axisymmetric simulations of pulsar wind nebulae (PWN). High-resolution adaptive mesh refinement magnetohydrodynamic simulations are used to resolve the non-linear evolution of the instability. The typical separation of filaments is mediated by the turbulent flow in the nebula and hierarchical growth of the filaments. The strong magnetic dissipation and field randomization found in recent global three-dimensional simulations of PWN suggest that magnetic tension is not strong enough to suppress the growth of RT filaments, in agreement with the observations of prominent filaments in the Crab nebula. The long-term axisymmetric results presented here confirm this finding.

Description: 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.