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Pulsar wind nebulae inside young supernova remnants, and in particular the Crab nebula, are probably the best laboratories for high-energy astrophysics and relativistic plasma physics. They have been modeled numerically for more than a decade through multi-dimensional relativistic MHD simulations, relying on axial symmetry until a few years ago while currently using full three-dimensional simulations employing adaptive meshes. Here, we discuss the most recent findings, especially those obtained by our Arcetri group, focusing on the problem of magnetic field dissipation inside the nebula.

Aims.We present a new numerical code, ECHO, based on a Eulerian conservative high-orderscheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations.

Aims.Elongated jets from young stellar objects typically present a nodular structure, formed by a chain of bright knotsof enhanced emission with individual proper motions. Though it is generally accepted that internal shocks play an important role in the formation and dynamics of such structures, their precise origin and the mechanisms behind the observed proper motions is still a matter of debate. Our goal is to study numerically the origin, dynamics, and emission properties of such knots.

Aims.A complete set of diagnostic tools aimed at producing synthetic synchrotron emissivity, polarization, and spectral index maps from relativistic MHD simulations is presented. As a first application we consider here the case of the emission from Pulsar Wind Nebulae (PWNe).

We present here the first effort to compute synthetic synchrotron polarization maps of Pulsar Wind Nebulae (PWNe). Our goal is to highlight how polarization can be used as an additional diagnostic tool for the flow structure in the inner regions of these nebulae. Recent numerical simulations suggest the presence of flow velocities ~$ 0.5\; c$in the surroundings of the termination shock, where most of the high energy emission comes from. We construct polarization maps taking into account relativistic effects like Doppler boosting and position angle swing. The effect of different bulk velocities is clarified with the help of a toy-model consisting of a uniformly emitting torus. We also present a map based on recent numerical simulations of the entire nebula and compare it with presently available data. The comparison with upcoming high resolution observations could provide new insight into the inner structure of the nebula and put constraints on the geometrical properties of the magnetic field.

Pulsar bow-shock nebulae are a class of pulsar wind nebulae (PWNe) that form when the pulsar wind is confined by the ram pressure of the ambient medium, and are usually associated with old pulsars, that have already emerged from the progenitor Supernova Remnant (SNR). Until a few years ago these nebulae were mainly observed as Hαsources; recently, also non-thermal emission has been detected. This is the signature of accelerated particles gyrating in a magnetic field. In the same way as Hαradiation is a tool for studying the layer of shocked Interstellar Medium (ISM), the non-thermal radiation might be used to infer the properties of the shocked pulsar wind. However theoretical and numerical models have been presented so far only in the hydrodynamical (HD) regime, while in order to properly model the internal flow structure and the emission properties of these nebulae a magnetohydrodynamical (MHD) treatment is required. We present here relativistic MHD (RMHD) axisymmetric simulations of pulsar wind bow-shock nebulae. The structure and fluid dynamics of such objects is investigated for various values of the pulsar wind magnetization. Simulated synchrotron maps are computed and comparison of the emission pattern with observations is discussed.

The propagation and the evolution of Alfvénic pulses in the solar coronal arcades is investigated by means of MHD numerical simulations. Significant transverse oscillations in coronal loops, triggered by nearby flare events, are often measured in EUV lines and are generally interpreted as standing kink modes. However, the damping times of these oscillations are typically very short (from one to a few periods) and the physical mechanism responsible for the decay is still a matter of debate. Moreover, the majority of the observed cases actually appears to be better modeled by propagating, rather than standing, modes. Here we perform 2.5D compressible MHD simulations of impulsively generated Alfvén waves propagating in a potential magnetic arcade (assumed as a simplified 2D loop model), taking into account the stratification of the solar atmosphere with height from the photosphere to the corona. The results show a strong spreading of the initially localized pulses along the loop, due to the variations in the Alfvén velocity with height, and correspondingly an efficient damping of the amplitude of the oscillations. We believe that simple explanations based on the effects of wave propagation in highly inhomogeneous media may apply to the majority of the reported cases, and that variations of the background density and Alfvén speed along the loop should be considered as key ingredients in future models.

We present high resolution spherically symmetric relativistic magnetohydrodynamical simulations of the evolution of a pulsar wind nebula inside the freely expanding ejecta of the supernova progenitor. The evolution is followed starting from a few years after the supernova explosion and up to an age of the remnant of 1500 years. We consider different values of the pulsar wind magnetization parameter and also different braking indices for the spin-down process. We compare the numerical results with those derived through an approximate semi-analytical approach that allows us to trace the time evolution of the positions of both the pulsar wind termination shock and the contact discontinuity between the nebula and the supernova ejecta. We also discuss, whenever a comparison is possible, to what extent our numerical results agree with former self-similar models, and how these models could be adapted to take into account the temporal evolution of the system. The inferred magnetization of the pulsar wind could be an order of magnitude lower than that derived from time independent analytic models.

We present a numerical investigation of the development of Rayleigh-Taylor instability at the interface between an expanding Pulsar Wind Nebula and its surrounding Supernova Remnant. These systems have long been thought to be naturally subject to this kind of instability, given their expansion behavior and the density jump at the contact discontinuity. High resolution images of the Crab Nebula at optical frequencies show the presence of a complex network of line-emitting filaments protruding inside the synchrotron nebula. These structures are interpreted as the observational evidence that Rayleigh-Taylor instability is in fact at work. The development of this instability in the regime appropriate to describe Supernova Remnant-Pulsar Wind Nebula systems is non-trivial. The conditions at the interface are likely close to the stability threshold, and the inclusion of the nebular magnetic field, which might play an important role in stabilizing the system, is essential to the modeling. If Rayleigh-Taylor features can grow efficiently a mixing layer in the outer portion of the nebula might form where most of the supernova material is confined. When a magnetic field close to equipartition is included we find that the interface is stable, and that even a weaker magnetic field affects substantially the growth and shape of the fingers.

The structure and the evolution of Pulsar Wind Nebulae (PWNe) are studied by means of two-dimensional axisymmetric relativistic magnetohydrodynamic (RMHD) simulations. After the first imaging of the Crab Nebula with Chandra, a growing number of objects has been found to show in the X-rays spatial features such as rings and jets, that clearly cannot be accounted for within the standard framework of one-dimensional semi-analytical models. The most promising explanation suggested so far is based on the combined effects of the latitude dependence of the pulsar wind energy flux, shaping the wind termination shock and naturally providing a higher equatorial emission, and of the wind magnetization, likely responsible for the jet collimation by hoop stresses downstream of the shock. This scenario is investigated here by following the evolution of a PWN interacting with the confining Supernova Remnant (SNR), from the free expansion to the beginning of the reverberation phase. Our results confirm the oblate shape of the wind termination shock and the formation of a polar jet with supersonic velocities ($v\approx 0.5 {-} 0.7 c$) for high enough values of the equatorial wind magnetization parameter ($\sigma\ga0.01$).

Pulsars, formed during supernova explosions, are known to be sources of relativistic magnetized winds whose interaction with the expanding supernova remnants (SNRs) gives rise to a pulsar wind nebula (PWN). We present spherically symmetric relativistic magnetohydrodynamics (RMHD) simulations of the interaction of a pulsar wind with the surrounding SNR, both in particle and magnetically dominated regimes. As shown by previous simulations, the evolution can be divided into three phases: free expansion, a transient phase characterized by the compression and reverberation of the reverse shock, and a final Sedov expansion. The evolution of the contact discontinuity between the PWN and the SNR (and consequently of the SNR itself) is almost independent of the magnetization of the nebula as long as the total (magnetic plus particle) energy is the same. However, a different behaviour of the PWN internal structure is observable during the compression-reverberation phase, depending on the degree of magnetization. The simulations were performed using the third order conservative scheme by Del Zanna et al. (2003).

A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and efficient centralscheme described in Paper I (Del Zanna & Bucciantini [CITE]) for relativistic hydrodynamics is here extended to the magnetic case by following the strategies prescribed for classical MHD by Londrillo & Del Zanna ([CITE]). The scheme completely avoids spectral decomposition into characteristic waves, which is computationally expensive and subject to many degenerate cases in the magnetic case, while it makes use of a two-speed Riemann solver that just requires the knowledge of the two local fast magnetosonic velocities. Moreover, the onset of spurious magnetic monopoles, which is a typical problem for multi-dimensional MHD upwind codes, is prevented by properly taking into account the solenoidal constraint and the specific antisymmetric nature of the induction equation. Finally, the extension to generalized orthogonal curvilinear coordinate systems is included, thus the scheme is ready to incorporate general relativistic (GRMHD) effects.

Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive variables and to the consequent complexity of the Jacobian matrices (needed for the spectral decomposition in most of the approximate Riemann solvers of common use). Here an efficient and easy-to-implement three-dimensional (3-D) shock-capturing scheme for ideal RHD is presented. Based on the algorithms developed by P. Londrillo & L. Del Zanna (2000, ApJ, 530, 508) for the non-relativistic magnetohydrodynamic (MHD) case, and having in mind its relativistic MHD extension (to appear in a forthcoming paper), the scheme uses high order (third) Convex Essentially Non-Oscillatory (CENO) finite difference interpolation routines and central-type averaged Riemann solvers, which do not make use of time-consuming characteristic decomposition. The scheme is very efficient and robust, and it gives results comparable to those obtained with more sophisticated algorithms, even in ultrarelativistic multidimensional test problems.

The nonlinear evolution of monochromatic large-amplitude circularly polarized Alfvén waves subject to the decay instability is studied via numerical simulations in one, two, and three spatial dimensions. The asymptotic value of the cross helicity depends strongly on the plasma beta: in the low beta case multiple decays are observed, with about half of the energy being transferred to waves propagating in the opposite direction at lower wave numbers, for each saturation step. Correspondingly, the other half of the total transverse energy (kinetic and magnetic) goes into energy carried by the daughter compressive waves and to the associated shock heating. In higher beta conditions we find instead that the cross helicity decreases monotonically with time towards zero, implying an asymptotic balance between inward and outward Alfvénic modes, a feature similar to the observed decrease with distance in the solar wind. Although the instability mainly takes place along the propagation direction, in the two and three-dimensional case a turbulent cascade occurs also transverse to the field. The asymptotic state of density fluctuations appears to be rather isotropic, whereas a slight preferential cascade in the transverse direction is seen in magnetic field spectra. Finally, parametric decay is shown to occur also in a non-periodic domain with open boundaries, when the mother wave is continuously injected from one side. In two and three dimensions a strong transverse filamentation is found at long times, reminiscent of density ray-like features observed in the extended solar corona and pressure-balanced structures found in solar wind data.

Aims. We develop a set of diagnostic tools for synchrotron-emitting sources, presented in a previous paper, to include a computation of inverse-Compton radiation from the same relativistic particles that give rise to the synchrotron emission. For the first time, we then study the gamma-ray emission properties of Pulsar Wind Nebulae, in the context of the axisymmetric jet-torus scenario.Methods. We evolve the relativistic MHD equations and the maximum energy of the emitting particles, including adiabatic and synchrotron losses along streamlines. The particle energy distribution function is split into two components: one corresponds to radio-emitting electrons, which are interpreted to be a relic population that is born at the outburst of the supernova, and the other is associated with a wind population that is continuously accelerated at the termination shock and emits up to the gamma-ray band. The inverse Compton emissivity is calculated using the general Klein-Nishina differential cross-section and three different photon targets for the relativistic particles are considered: the nebular synchrotron photons, photons associated with the far-infrared thermal excess, and the cosmic microwave background.Results. When the method is applied to the simulations that match the optical and X-ray morphology of the Crab Nebula, the overall synchrotron spectrum can only be fitted assuming an excess of injected particles and a steeper power law (E-2.7) with respect to previous models. The resulting TeV emission has then the correct shape but is in excess of the data. This is related to the magnetic-field structure in the nebula, derived using simulations: in particular, the field is strongly compressed close to the termination shock, but with a lower than expected volume average. The jet-torus structure is also found to be visible clearly in high-resolution gamma-ray synthetic maps. We present a preliminary exploration of time variability in X- and gamma-rays. We find variations with timescales of about 2 years in both bands. The variability observed originates in the strongly time-dependent MHD motions inside the nebula.

We present here a series of numerical simulations of the development of Kelvin-Helmholtz instability in a?relativistically hot plasma. The physical parameters in the unperturbed state are chosen to be representative of local conditions encountered in Pulsar Wind Nebulae (PWNe), with a?main magnetic field perpendicular to a?mildly relativistic shear layers. By using a?numerical code for Relativistic MHD, we investigate the effect of an?additional magnetic field component aligned with the shear velocity, and we follow the evolution of the instability to the saturation and turbulent regimes. Based on the resulting flow structure, we then compute synchrotron maps in order to evaluate the signature of Kelvin-Helmholtz instability on the emission and we investigate how the time scale and the amplitude of the synchrotron modulations depend on shear velocity and magnetic field. Finally we compare our results to the observed variable features in the Crab?Nebula. We show that the Kelvin-Helmholtz instability cannot account for the wisps variability, but it might be responsible for the time dependent filamentary structure observed in the main torus.

Coronal plumes are believed to be essentially magnetic features: they are rooted in magnetic flux concentrations at the photosphere and are observed to extend nearly radially above coronal holes out to at least 15 solar radii, probably tracing the open field lines. The formation of plumes itself seems to be due to the presence of reconnecting magnetic field lines and this is probably the cause of the observed extremely low values of the Ne/Mg abundance ratio. In the inner corona, where the magnetic force is dominant, steady MHD models of coronal plumes deal essentially with quasi-potential magnetic fields but further out, where the gas pressure starts to be important, total pressure balance across the boundary of these dense structures must be considered. In this paper, the expansion of plumes into the fast polar wind is studied by using a thin flux tube model with two interacting components, plume and interplume. Preliminary results are compared with both remote sensing and solar wind in situ observations and the possible connection between coronal plumes with pressure-balance structures (PBS) and microstreams is discussed.

We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This aims at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as in the evolution of magnetized neutron stars or in the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code extends the Eulerian conservative high-order (ECHO) scheme (Del Zanna et al. 2007, A&A, 473, 11) for GRMHD, here coupled to a novel solver of the Einstein equations in the extended conformally flat condition (XCFC). We solve the equations in the 3 + 1 formalism, assuming axisymmetry and adopting spherical coordinates for the conformal background metric. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and are solved, for each harmonic, by inverting band diagonal matrices. As a side product, we built and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.

Aims.We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes.