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Relativistic magnetic reconnection is one of the most fundamental mechanisms considered responsible for the acceleration of relativistic particles in astrophysical jets and magnetospheres of compact objects. Understanding the properties of the dissipation of magnetic fields and the formation of non-ideal electric fields is of paramount importance to quantify the efficiency of reconnection at energizing charged particles. Recent results from particle-in-cell (PIC) simulations suggest that the fundamental properties of how magnetic fields dissipate in a current sheet might be captured by an "effective resistivity" formulation, which would locally enhance the amount of magnetic energy dissipated and favor the onset of fast reconnection. Our goal is to assess this ansatz quantitatively by comparing fluid models of magnetic reconnection with a non-constant magnetic diffusivity and fully-kinetic models. We perform 2D resistive relativistic magnetohydrodynamic (ResRMHD) simulations of magnetic reconnection combined to PIC simulations using the same initial conditions (namely a Harris current sheet). We explore the impact of crucial parameters such as the plasma magnetization, its mass density, the grid resolution, and the characteristic plasma skin depth. Our ResRMHD models with effective resistivity can quantitatively reproduce the dynamics of fully-kinetic models of relativistic magnetic reconnection. In particular, they lead to reconnection rates consistent with PIC simulations, while for constant-resistivity fluid models the reconnection dynamics is generally 10 times slower. Even at modest resolutions the adoption of an effective resistivity can qualitatively capture the properties of kinetic reconnection models and produce reconnection rates compatible with collisionless models, i.e. of the order of $\sim10^{-1}$., Comment: 17 pages, 17 figures; accepted for publication on A&A

Space plasmas are three-dimensional dynamic entities. Except under very special circumstances, their structure in space and their behavior in time are not related in any simple way. Therefore, single spacecraft in situ measurements cannot unambiguously unravel the full space-time structure of the heliospheric plasmas of interest in the inner heliosphere, in the Geospace environment, or the outer heliosphere. This shortcoming leaves numerous central questions incompletely answered. Deficiencies remain in at least two important subjects, Space Weather and fundamental plasma turbulence theory, due to a lack of a more complete understanding of the space-time structure of dynamic plasmas. Only with multispacecraft measurements over suitable spans of spatial separation and temporal duration can these ambiguities be resolved. We note that these characterizations apply to turbulence across a wide range of scales, and also equally well to shocks, flux ropes, magnetic clouds, current sheets, stream interactions, etc. In the following, we will describe the basic requirements for resolving space-time structure in general, using turbulence' as both an example and a principal target or study. Several types of missions are suggested to resolve space-time structure throughout the Heliosphere., Comment: White Paper submitted to: Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. arXiv admin note: substantial text overlap with arXiv:1903.06890

Neutron stars harbour extremely powerful magnetic fields, leading to their shape being deformed. Their magnetic deformation depends both on the geometry - and strength - of their internal magnetic field and on their composition, encoded by the equation of state. However, both the details of the internal magnetic structure and the equation of state of the innermost part of neutron stars are mostly unkown. We performed a study of numerical models of magnetised, static, axisymmetric neutron stars in general relativity and in one of its most promising extensions, scalar-tensor theories. We did so by using several realistic equations of state currently allowed by observational and nuclear physics constraints, considering also those for strange quark stars. We show that it is possible to find simple relations among the magnetic deformation of a neutron star, its Komar mass, and its circumferential radius in the case of purely poloidal and purely toroidal magnetic configurations satisfying the equilibrium criterion in the Bernoulli formalism. These relations are quasi-universal, in the sense that they mostly do not depend on the equation of state. Our results, being formulated in terms of potentially observable quantities, could help to understand the magnetic properties of neutron stars interiors and the detectability of continuous gravitational waves by isolated neutron stars, independently of their equation of state. In the case of scalar-tensor theories, these relations depend also on the scalar charge of the neutron stars, thus potentially providing a new way to set constraints on the theory of gravitation., Comment: 19 pages, 5 figures, submitted as proceeding to the Sixteenth Marcel Grossmann Meeting, this article draws heavily from arXiv:2106.00603

Neutron stars are known to host extremely powerful magnetic fields. Among other effects, one of the consequences of harbouring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves. On the one hand, the details of their internal magnetic fields are mostly unknown. Likewise, their internal structure, encoded by the equation of state, is highly uncertain. Here we present a study of axisymmetric models of isolated magnetised neutron stars, for various realistic equations of state considered viable by observations and nuclear physics constraints. We show that it is possible to find simple relations between the magnetic deformation of a neutron star, its Komar mass and its circumferential radius. Such relations are quasi-universal, meaning that they are mostly independent on the equation of state of the neutron star and only slightly dependent on the magnetic field configuration. Being formulated in terms of potentially observable quantities, as we discuss, our results could help to constrain the magnetic properties of the neutron star interior and to better assess the detectability of continuous gravitational waves by isolated neutron stars, without knowing their equation of state. Our results are derived both in general relativity and in scalar-tensor theories - one of the most promising extensions of general relativity - in this case by considering also the scalar charge. We show that even in this case general relations hold that account for deviations from general relativity, that could potentially be used to set constraints on the gravitational theory., Comment: Accepted for publication in A&A; minor language corrections

Scalar-tensor theories are among the most promising alternatives to general relativity that have been developed to account for some long standing issues in our understanding of gravity. Some of these theories predict the existence of a non-linear phenomenon, spontaneous scalarisation, which can lead to the appearance of sizeable modifications to general relativity in the presence of compact matter distributions, namely neutron stars. On the one hand, one of the effects of the scalar field is to modify the emission of gravitational waves, both due to variations in the quadrupolar deformation of the star and to the presence of additional modes of emission. On the other hand, neutron stars are known to harbour extremely powerful magnetic fields which can affect their structure and shape, leading in turn to the emission of gravitational waves, this time due to a magnetic quadrupolar deformation. We investigate here how the presence of spontaneous scalarisation can affect the magnetic deformation of neutron stars and their emission of quadrupolar gravitational waves, both of tensor and scalar nature. We will show that it is possible to provide simple parameterisations of the magnetic deformation and gravitational wave power of neutron stars in terms of their baryonic mass, circumferential radius and scalar charge, and that a universal scaling exists independently of the magnetic field geometry and of the parameters of the scalar-tensor theory. Finally, we comment on the observability of the deviations of the gravitational waves strain from general relativity by current and future observatories., Comment: 9 pages, 2 figures, accepted for publication in A&A

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal general relativistic magnetohydrodynamic (GRMHD) regime, the growth of the magnetic field due to the action of the mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process, combined with the differential rotation of the (proto-)star, is able to produce an exponential growth of any initial magnetic seed field up to the values required to explain the observations. By varying the dynamo coefficient we obtain different growth rates. We find a quasi-linear dependence of the growth rates on the intensity of the dynamo. Furthermore, the time interval in which exponential growth occurs and the growth rates also seems to depend on the initial configuration of the magnetic field., Comment: 12 pages, 4 figures, accepted for publication on Universe

Pulsars out of their parent SNR directly interact with the ISM producing so called Bow-Shock Pulsar Wind Nebulae, the relativistic equivalents of the heliosphere/heliotail system. These have been directly observed from Radio to X-ray, and are found also associated to TeV halos, with a large variety of morphologies. They offer a unique environment where the pulsar wind can be studied by modelling its interaction with the surrounding ambient medium, in a fashion that is different/complementary from the canonical Plerions. These systems have also been suggested as the possible origin of the positron excess detected by AMS and PAMELA, in contrast to dark matter. I will present results from 3D Relativistic MHD simulations of such nebulae. On top of these simulations we computed the expected emission signatures, the properties of high energy particle escape, the role of current sheets in channeling cosmic rays, the level of turbulence and magnetic amplification, and how they depend on the wind structure and magnetisation., Comment: 10 pages, 3 figures, Proceedings of ASTRONUM-2019, Accepted in Journal of Physics Conference Series

Among the possible extensions of General Relativity that have been put forward in order to address some long standing issues in our understanding of the Universe, Scalar-Tensor Theories have received a lot of attention for their simplicity. Interestingly, some of these predict a potentially observable non-linear phenomenon, known as \textit{spontaneous scalarisation}, in the presence of highly compact matter distributions, like the case of neutron stars. Neutron stars are ideal laboratories to investigate the properties of matter under extreme conditions, and in particular they are known to harbour the strongest magnetic fields in the Universe. Here, for the first time, we present a detailed study of magnetised neutron stars in Scalar-Tensor Theories. First, we show that the formalism developed for the study of magnetised neutron stars in General Relativity, based on the \textit{eXtended Conformally Flat Condition}, can easily be extended in the presence of a non-minimally coupled scalar field, retaining many of its numerical advantages. We then carry out a study of the parameter space considering the two extreme geometries of purely toroidal and purely poloidal magnetic fields, varying both the strength of the magnetic field and the intensity of scalarisation. We compare our results with magnetised general-relativistic solutions and un-magnetised scalarised solutions, showing how the mutual interplay between magnetic and scalar fields affect the magnetic and the scalarisation properties of neutron stars. In particular, we focus our discussion on magnetic deformability, maximum mass and range of scalarisation., Comment: accepted for publication by A&A; minor language corrections; minor typos correction

The recent imaging of the M87 black hole at millimeter wavelengths by the Event Horizon Telescope (EHT) collaboration has triggered a renewed interest in numerical models for the accretion of magnetized plasma in the regime of general relativistic magnetohydrodynamics (GRMHD). Here non-ideal simulations, including both the resistive effects and, above all, the mean-field dynamo action due to sub-scale, unresolved turbulence, are applied for the first time to such systems in the fully nonlinear regime. Combined with the differential rotation of the disk, the dynamo process is able to produce an exponential growth of any initial seed magnetic field up to the values required to explain the observations, when the instability tends to saturate even in the absence of artificial quenching effects. Before reaching the final saturation stage we observe a secondary regime of exponential growing, where the magnetic field increases more slowly due to accretion, which is modifying the underlying equilibrium. By varying the dynamo coefficient we obtain different growth rates, though the field seems to saturate at approximately the same level, at least for the limited range of parameters explored here, providing substantial values for the MAD parameter for magnetized accretion. For reasonable values of the central mass density and the commonly employed recipes for synchrotron emission by relativistically hot electrons, our model is able to reproduce naturally the observed flux of Sgr A*, the next target for EHT., Comment: 15 pages, 13 figures

We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces and are evolved using the constrained transport formalism. Direct application of Stokes' theorem to Faraday's and Ampere's laws ensures that the resulting discretization is divergence-free for the magnetic field and charge-conserving for the electric field. Hydrodynamic variables retain, instead, the usual zone-centred representation commonly adopted in finite-volume schemes. Temporal discretization is based on Runge-Kutta implicit-explicit (IMEX) schemes in order to resolve the temporal scale disparity introduced by the stiff source term in Ampere's law. The implicit step is accomplished by means of an improved and more efficient Newton-Broyden multidimensional root-finding algorithm. The explicit step relies on a multidimensional Riemann solver to compute the line-averaged electric and magnetic fields at zone edges and it employs a one-dimensional Riemann solver at zone interfaces to update zone-centred hydrodynamic quantities. For the latter, we introduce a five-wave solver based on the frozen limit of the relaxation system whereby the solution to the Riemann problem can be decomposed into an outer Maxwell solver and an inner hydrodynamic solver. A number of numerical benchmarks demonstrate that our method is superior in stability and robustness to the more popular charge-conserving divergence cleaning approach where both primary electric and magnetic fields are zone-centered. In addition, the employment of a less diffusive Riemann solver noticeably improves the accuracy of the computations., Comment: 25 pages, 14 figures

This paper briefly reviews a number of fundamental measurements that need to be made in order to characterize turbulence in space plasmas such as the solar wind. It has long been known that many of these quantities require simultaneous multipoint measurements to attain a proper characterization that would reveal the fundamental physics of plasma turbulence. The solar wind is an ideal plasma for such an investigation, and it now appears to be technologically feasible to carry out such an investigation, following the pioneering Cluster and MMS missions. Quantities that need to be measured using multipoint measurements include the two-point, two-time second correlation function of velocity, magnetic field and density, and higher order statistical objects such as third and fourth order structure functions. Some details of these requirements are given here, with a eye towards achieving closure on fundamental questions regarding the cascade rate, spectral anisotropy, characteristic coherent structures, intermittency, and dissipation mechanisms that describe plasma turbuelence, as well as its variability with plasma parameters in the solar wind. The motivation for this discussion is the current planning for a proposed Helioswarm mission that would be designed to make these measurements,leading to breakthrough understanding of the physics of space and astrophysical turbulence., Comment: White paper submitted to the PLASMA 2020 Decadal Survey Committee

Neutron stars are among the most fascinating astrophysical sources, being characterized by strong gravity, densities about the nuclear one or even above, and huge magnetic fields. Their observational signatures can be extremely diverse across the electromagnetic spectrum, ranging from the periodic and low-frequency signals of radio pulsars, up to the abrupt high-energy gamma-ray flares of magnetars, where energies of ~10^46 erg are released in a few seconds. Fast-rotating and highly magnetized neutron stars are expected to launch powerful relativistic winds, whose interaction with the supernova remnants gives rise to the non-thermal emission of pulsar wind nebulae, which are known cosmic accelerators of electrons and positrons up to PeV energies. In the extreme cases of proto-magnetars (magnetic fields of ~10^15 G and millisecond periods), a similar mechanism is likely to provide a viable engine for the still mysterious gamma-ray bursts. The key ingredient in all these spectacular manifestations of neutron stars is the presence of strong magnetic fields in their constituent plasma. Here we will present recent updates of a couple of state-of-the-art numerical investigations by the high-energy astrophysics group in Arcetri: a comprehensive modeling of the steady-state axisymmetric structure of rotating magnetized neutron stars in general relativity, and dynamical 3-D MHD simulations of relativistic pulsar winds and their associated nebulae., Comment: EPS 44th Conference on Plasma Physics (June 2017, Belfast), paper accepted for publication on Plasma Physics and Controlled Fusion

Motivated by recent observational searches of sub-structure in starless molecular cloud cores, we investigate the evolution of density perturbations on scales smaller than the Jeans length embedded in contracting isothermal clouds, adopting the same formalism developed for the expanding Universe and the solar wind. We find that initially small amplitude, Jeans-stable perturbations (propagating as sound waves in the absence of a magnetic field), are amplified adiabatically during the contraction, approximately conserving the wave action density, until they either become nonlinear and steepen into shocks at a time $t_{\rm nl}$, or become gravitationally unstable when the Jeans length decreases below the scale of the perturbations at a time $t_{\rm gr}$. We evaluate analytically the time $t_{\rm nl}$ at which the perturbations enter the non-linear stage using a Burgers' equation approach, and we verify numerically that this time marks the beginning of the phase of rapid dissipation of the kinetic energy of the perturbations. We then show that for typical values of the rms Mach number in molecular cloud cores, $t_{\rm nl}$ is smaller than $t_{\rm gr}$, and therefore density perturbations likely dissipate before becoming gravitational unstable. Solenoidal modes grow at a faster rate than compressible modes, and may eventually promote fragmentation through the formation of vortical structures., Comment: 8 pages, 4 figures

The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of $10^{15-16}$G. How such a strong magnetic field can originate during the formation of a neutron star is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet driven explosion, manifesting as a gamma ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper we analyze the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric neutron star, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescriptions on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications., Comment: 25 pages, 17 figures, 6 tables, accepted for publication in MNRAS

Pulsar Wind Nebulae (PWNe) constitute an ideal astrophysical environment to test our current understanding of relativistic plasma processes. It is well known that magnetic fields play a crucial role in their dynamics and emission properties. At present, one of the main issues concerns the level of magnetic turbulence present in these systems, which in the absence of space resolved X-ray polarization measures cannot be directly constrained. In this work we investigate, for the first time using simulated synchrotron maps, the effect of a small scale fluctuating component of the magnetic field on the emission properties in X-ray. We illustrate how to include the effects of a turbulent component in standard emission models for PWNe, and which consequences are expected in terms of net emissivity and depolarization, showing that the X-ray surface brightness maps can provide already some rough constraints. We then apply our analysis to the Crab and Vela nebulae and, by comparing our model with Chandra and Vela data, we found that the typical energies in the turbulent component of the magnetic field are about 1.5 to 3 times the one in the ordered field., Comment: 9 pages, 8 figures, accepted for publication in MNRAS

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares., Comment: 30 pages, 12 figures

Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfv\'enic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number $P=1$ in the viscous regime., Comment: Accepted for publication in Plasma Physics and Controlled Fusion

We investigate the possible implications of quark deconfinement on the phenomenology of Long Gamma-Ray Bursts focusing, in particular, on the possibility to describe multiple prompt emission phases in the context of the proto-magnetar model. Starting from numerical models of rotating Hadron Stars and Quark Stars in full general relativity we track the electromagnetic spin-down evolution in both the hadronic and quark phase, linking the two families through conservation of baryon number and angular momentum. We give estimates of the timescales and the energetics involved in the spin-down process deriving, in the relevant spin range, the relation between the initial and the final masses and rotational energies, whenever hadron-quark conversion is possible. We show how the results can be used in relevant astrophysical cases such as the double burst GRB 110709B., Comment: 5 pages, 3 figures, 2 tables

Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1., Comment: 14 pages, 9 figures, accepted for publication (MNRAS)

Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a critical threshold on current sheet's thickness, namely a/L~S^(-1/3), beyond which the tearing modes evolve on fast macroscopic Alfvenic timescales, provided the Lunquist number S is high enough, as invariably found in solar and astrophysical plasmas. Therefore, the classical Sweet-Parker scenario, for which the diffusive region scales as a/L~S^(-1/2) and thus can be up to ~100 times thinner than the critical value, is likely to be never realized in nature, as the current sheet itself disrupts in the elongation process. We present here two-dimensional, compressible, resistive MHD simulations, with S ranging from 10^5 to 10^7, that fully confirm the linear analysis. Moreover, we show that a secondary plasmoid instability always occurs when the same critical scaling is reached on the local, smaller scale, leading to a cascading explosive process, reminiscent of the flaring activity., Comment: Proceedings of ASTRONUM 2015, Avignon, France (11 pages, 6 figures)

The phenomenology of the emission of pulsars and magnetars depends dramatically on the structure and properties of their magnetic field. In particular it is believed that the outbursting and flaring activity observed in AXPs and SRGs is strongly related to their internal magnetic field. Recent observations have moreover shown that charges are present in their magnetospheres supporting the idea that their magnetic field is tightly twisted in the vicinity of the star. In principle these objects offer a unique opportunity to investigate physics in a regime beyond what can be obtained in the laboratory. We will discuss the properties of equilibrium models of magnetized neutron stars, and we will show how internal and external currents can be related. These magnetic field configurations will be discussed considering also their stability, relevant for their origin and possibly connected to events like SNe and GRBs. We will also show what kind of deformations they induce in the star, that could lead to emission of gravitational waves. In the case of a twisted magnetosphere we will show how the amount of twist regulates their general topology. A general formalism based on the simultaneous numerical solution of the general relativistic Grad-Shafranov equation and Einstein equations will be presented., Comment: 9 pages, 3 figures, Proceedings of the 10th International Conference on Numerical Modeling of Space Plasma Flows, 8-12 June 2015, Avignon, France

We study the impact of three stochastic parametrizations in the ocean component of a coupled model, on forecast reliability over seasonal timescales. The relative impacts of these schemes upon the ocean mean state and ensemble spread are analyzed. The oceanic variability induced by the atmospheric forcing of the coupled system is, in most regions, the major source of ensemble spread. The largest impact on spread and bias came from the Stochastically Perturbed Parametrization Tendency (SPPT) scheme - which has proven particularly effective in the atmosphere. The key regions affected are eddy-active regions, namely the western boundary currents and the Southern Ocean. However, unlike its impact in the atmosphere, SPPT in the ocean did not result in a significant decrease in forecast error. Whilst there are good grounds for implementing stochastic schemes in ocean models, our results suggest that they will have to be more sophisticated. Some suggestions for next-generation stochastic schemes are made., Comment: 24 pages, 3 figures

We present a quantitative study of vorticity formation in peripheral ultrarelativistic heavy ion collisions at sqrt(s)NN = 200 GeV by using the ECHO-QGP numerical code, implementing relativistic dissipative hydrodynamics in the causal Israel-Stewart framework in 3+1 dimensions with an initial Bjorken flow profile. We consider and discuss different definitions of vorticity which are relevant in relativistic hydrodynamics. After demonstrating the excellent capabilities of our code, which proves to be able to reproduce Gubser flow up to 8 fm/c, we show that, with the initial conditions needed to reproduce the measured directed flow in peripheral collisions corresponding to an average impact parameter b=11.6 fm and with the Bjorken flow profile for a viscous Quark Gluon Plasma with \eta/s=0.1 fixed, a vorticity of the order of some 10^{-2} c/fm can develop at freezeout. The ensuing polarization of Lambda baryons does not exceed 1.4% at midrapidity. We show that the amount of developed directed flow is sensitive to both the initial angular momentum of the plasma and its viscosity., Comment: 13 pages, 22 figures. Minor changes, final version to appear in EPJC

Magnetic fields play a critical role in the phenomenology of neutron stars. There is virtually no observable aspect which is not governed by them. Despite this, only recently efforts have been done to model magnetic fields in the correct general relativistic regime, characteristic of these compact objects. In this work we present, for the first time a comprehensive and detailed parameter study, in general relativity, of the role that the current distribution, and the related magnetic field structure, have in determining the precise structure of neutron stars. In particular, we show how the presence of localized currents can modify the field strength at the stellar surface, and we look for general trends, both in terms of energetic properties, and magnetic field configurations. Here we verify that, among other things, for a large class of different current distributions the resulting magnetic configurations are always dominated by the poloidal component of the current., Comment: 14 pages, 13 figures, accepted for publication in MNRAS

Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars are extreme manifestations of the most magnetized neutron stars: magnetars. The phenomenology of their emission and spectral properties strongly support the idea that the magnetospheres of these astrophysical objects are tightly twisted in the vicinity of the star. Previous studies on equilibrium configurations have so far focused on either the internal or the external magnetic field configuration, without considering a real coupling between the two fields. Here we investigate numerical equilibrium models of magnetized neutron stars endowed with a confined twisted magnetosphere, solving the general relativistic Grad-Shafranov equation both in the interior and in the exterior of the compact object. A comprehensive study of the parameters space is provided to investigate the effects of different current distributions on the overall magnetic field structure., Comment: 15 pages, 14 figures. Accepted for publication in MNRAS

The long-term evolution of large-amplitude Alfven waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind., Comment: 20 pages, 9 figures, accepted for publication in Joural of Plasma Physics

Extremely magnetized neutron stars with magnetic fields as strong as $\sim 10^{15-16}$ G, or magnetars, have received considerable attention in the last decade due to their identification as a plausible source for Soft Gamma Repeaters and Anomalous X-ray Pulsars. Moreover, this class of compact objects has been proposed as a possible engine capable of powering both Long and Short Gamma-Ray Bursts, if the rotation period in their formation stage is short enough (~1 ms). Such strong fields are expected to induce substantial deformations of the star and thus to produce the emission of gravitational waves. Here we investigate, by means of numerical modeling, axisymmetric static equilibria of polytropic and strongly magnetized stars in full general relativity, within the ideal magneto-hydrodynamic regime. The eXtended Conformally Flat Condition (XCFC) for the metric is assumed, allowing us to employ the techniques introduced for the X-ECHO code [Bucciantini & Del Zanna, 2011, Astron. Astrophys. 528, A101], proven to be accurate, efficient, and stable. The updated XNS code for magnetized neutron star equilibria is made publicly available for the community (see www.arcetri.astro.it/science/ahead/XNS). Several sequences of models are here retrieved, from the purely toroidal (resolving a controversy in the literature) or poloidal cases, to the so-called twisted torus mixed configurations, expected to be dynamically stable, which are solved for the first time in the non-perturbative regime., Comment: 24 pages, 22 figures, 5 tables

We present the first kinematic study of an $\alpha\Omega$-dynamo in the General Relativistic Magneto-HydroDynamics (GRMHD) regime, applied to thick disks orbiting around Kerr black holes and using a fully covariant mean field dynamo closure for the Ohm law. We show that the $\alpha\Omega$-dynamo mechanism leads to a continuous exponential growth of the magnetic field within the disk and to the formation of dynamo waves drifting away or toward the equatorial plane. Since the evolution of the magnetic field occurs qualitatively in the same fashion as in the Sun, we present also butterfly diagrams that characterize our models and show the establishment of an additional timescale, which depends on the microscopic properties of the turbulent motions, possibly providing an alternative explanation to periodicities observed in many high-energy astrophysical sources where accretion onto a rotating black hole is believed to operate., Comment: 5 pages, 4 figures. Accepted for publication in MNRAS

We present the first astrophysical application of the ECHO code in its recent version supplemented by a generalized Ohm law, namely a kinematic study of dynamo effects in thick accretion disks. High-order \emph{implicit-explicit} Runge-Kutta time-stepping routines are implemented and validated within $3+1$ \emph{General Relativistic MagnetoHydroDynamics} (GRMHD). The scheme is applied to a differentially rotating torus orbiting a Kerr black hole, where the mean-field dynamo process leads to strong amplification of seed magnetic fields. We show that the interplay between the toroidal and poloidal components occurs qualitatively in the same fashion as in the Sun, butterfly diagrams are reproduced, and a typical time-scale for the field evolution is found, depending on the dynamo and resistivity numbers, which could explain periodicities as observed in several accreting systems., Comment: 6 pages, Proceedings of ASTRONUM 2013, Biarritz. To appear as ASP Conference Series

High-energy phenomena in astrophysics involve quite generally a combination of relativistic motions and strong gravity. The simultaneous solution of Einstein equations and General Relativistic MHD equations is thus necessary to model with accuracy such phenomena. The so-called Conformally Flat Condition (CFC) allows a simplified treatment of Einstein equations, that can be particularly efficient in those contexts where gravitational wave emission is negligible, like core-collapse, or the formation/evolution of neutron stars. We have developed a set of codes to model axisymmetric MHD flows, in General Relativity, where the solution of Einstein equations is achieved with a semi-spectral scheme. Here, we will show how this framework is particularly well suited to investigate neutron star equilibrium models in the presence of strong magnetic fields and we will present the XNS code, that has been recently developed and here updated to treat poloidal and mixed configurations., Comment: 6 pages, 2 figures, Proceedings of the 8th International Conference on Numerical Modeling of Space Plasma Flows, 1-5 July 2013, Biarritz, France

Magnetic fields play a crucial role in many astrophysical scenarios and, in particular, are of paramount importance in the emission mechanism and evolution of Neutron Stars (NSs). To understand the role of the magnetic field in compact objects it is important to obtain, as a first step, accurate equilibrium models for magnetized NSs. Using the conformally flat approximation we solve the Einstein's equations together with the GRMHD equations in the case of a static axisymmetryc NS taking into account different types of magnetic configuration. This allows us to investigate the effect of the magnetic field on global properties of NSs such as their deformation., Comment: 4 pages, 6 figures, Proceedings of the 4th International Conference High Energy Phenomena in Relativistic Outflows "HEPRO IV", 23-26 July 2013, Heidelberg, Germany. To be publised in International Journal of Modern Physics: Conference Series

We present ECHO-QGP, a numerical code for $(3+1)$-dimensional relativistic viscous hydrodynamics designed for the modeling of the space-time evolution of the matter created in high energy nuclear collisions. The code has been built on top of the \emph{Eulerian Conservative High-Order} astrophysical code for general relativistic magneto-hydrodynamics [\emph{Del Zanna et al., Astron. Astrophys. 473, 11, 2007}] and here it has been upgraded to handle the physics of the Quark-Gluon Plasma. ECHO-QGP features second-order treatment of causal relativistic viscosity effects in both Minkowskian or Bjorken coordinates; partial or complete chemical equilibrium of hadronic species before kinetic freeze-out; initial conditions based on the optical Glauber model, including a Monte-Carlo routine for event-by-event fluctuating initial conditions; a freeze-out procedure based on the Cooper-Frye prescription. The code is extensively validated against several test problems and results always appear accurate, as guaranteed by the combination of the conservative (shock-capturing) approach and the high-order methods employed. ECHO-QGP can be extended to include evolution of the electromagnetic fields coupled to the plasma., Comment: 25 pages, two column, Final version: accepted for publication in European Physical Journal C

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper-Frye formula to particles with spin 1/2 and allows to predict their polarization in relativistic heavy ion collisions at the freeze-out., Comment: 15 pages. Final version to appear in Annals of Physics

The powerful high-energy phenomena typically encountered in astrophysics invariably involve physical engines, like neutron stars and black hole accretion disks, characterized by a combination of highly magnetized plasmas, strong gravitational fields, and relativistic motions. In recent years numerical schemes for General Relativistic MHD (GRMHD) have been developed to model the multidimensional dynamics of such systems, including the possibility of an evolving spacetime. Such schemes have been also extended beyond the ideal limit including the effects of resistivity, in an attempt to model dissipative physical processes acting on small scales (sub-grid effects) over the global dynamics. Along the same lines, magnetic fields could be amplified by the presence of turbulent dynamo processes, as often invoked to explain the high values of magnetization required in accretion disks and neutron stars. Here we present, for the first time, a further extension to include the possibility of a mean-field dynamo action within the framework of numerical 3+1 (resistive) GRMHD. A fully covariant dynamo closure is proposed, in analogy with the classical theory, assuming a simple alpha-effect in the comoving frame. Its implementation into a finite-difference scheme for GRMHD in dynamical spacetimes [the X-ECHO code: (Bucciantini and Del Zanna 2011)] is described, and a set of numerical test is presented and compared with analytical solutions wherever possible., Comment: 16 pages, 11 figures, accepted for publication in MNRAS

We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as for the evolution of magnetized neutron stars or for 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 is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. 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 solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build 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., Comment: 18 pages, 9 figures, accepted for publication in A&A

The main goal of our present work is to provide, for the first time, a simple computational tool that can be used to compute the brightness, the spectral index, the polarization, the time variability and the spectrum of the non-thermal light (both synchrotron and inverse Compton, IC) associated with the plasma dynamics resulting from given relativistic magnetohydrodynamics (RMHD) simulations. The proposed method is quite general, and can be applied to any scheme for RMHD and to all non-thermal emitting sources, e.g. pulsar wind nebulae (PWNe), and in particular to the Crab Nebula (CN) as in the present proceeding. Here only the linear optical and X-ray polarization that characterizes the PWNe synchrotron emission is analyzed in order to infer information on the inner bulk flow structure, to provide a direct investigation of the magnetic field configuration, in particular the presence and the strength of a poloidal component, and to understand the origin of some emitting features, such as the knot, whose origins are still uncertain. The inverse Compton radiation is examined to disentangle the different contributions to radiation from the magnetic field and the particle energy distribution function, and to search for a possible hadronic component in the emitting PWN, and thus for the presence of ions in the wind. If hadronic radiation was found in a PWN, young supernova remnants would provide a natural birth-place of the cosmic-rays (CRs) up to the so-called knee in the CR spectrum., Comment: 6 pages, 2 figures, workshop: Polarimetry days in Rome: Crab status, theory and prospects, October 16-17 2008, Rome, Italy

We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spindown of a newly formed millisecond, B ~ 10^{15} G, magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum, and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spindown powers (~ 10^{51}-10^{52} ergs/s), the magnetar wind is super-fast at almost all latitudes, while for lower spindown powers (~ 10^{50} erg/s), the wind is sub-fast but still super-Alfvenic. In all cases, the rates at which the neutron star loses mass, angular momentum, and energy are very similar to the corresponding free wind values (<~ 30% differences), in spite of the causal contact between the neutron star and the stellar envelope. In addition, in all cases that we consider, the magnetar drives a collimated (~5-10 deg.) relativistic jet out along the rotation axis of the star. Nearly all of the spindown power of the neutron star escapes via this polar jet, rather than being transferred to the more spherical SN explosion. The properties of this relativistic jet and its expected late-time evolution in the magnetar model are broadly consistent with observations of long duration gamma-ray bursts (GRBs) and their associated broad-lined Type Ic SN., Comment: 15 pages, 7 figures, submitted to MNRAS

We study the evolution of an accelerating hyperrelativistic shock under the presence of upstream inhomogeneities wrinkling the discontinuity surface. The investigation is conducted by means of numerical simulations using the PLUTO code for astrophysical fluid dynamics. The reliability and robustness of the code are demonstrated against well known results coming from the linear perturbation theory. We then follow the nonlinear evolution of two classes of perturbing upstream atmospheres and conclude that no lasting wrinkle can be preserved indefinitely by the flow. Finally we derive analytically a description of the geometrical effects of a turbulent upstream ambient on the discontinuity surface., Comment: 54 Pages, 24 Figures. Accepted for Publication in the Astrophysical Journal

In this paper we complete the set of diagnostic tools for synchrotron emitting sources presented by Del Zanna et al. (Astron. Astrophys. 453, 621, 2006) with the computation of inverse Compton radiation from the same relativistic particles. Moreover we investigate, for the first time, the gamma-ray emission properties of Pulsar Wind Nebulae in the light of the axisymmetric jet-torus scenario. The method consists in evolving the relativistic MHD equations and the maximum energy of the emitting particles. The particle energy distribution function is split in two components: the radio one connected to a relic population born at the outburst of the supernova and the other associated to the wind population continuously accelerated at the termination shock and emitting up to the gamma-ray band. We consider the general Klein-Nishina cross section and three different photon targets: the nebular synchrotron photons, far-infrared thermal ones and the cosmic microwave background. The overall synchrotron spectrum is fitted assuming an excess of injected particles and a steeper power law with respect to previous models. The TeV emission has the correct shape but is in excess of the data. This is due to the nebular magnetic field structure as obtained by the simulations. The jet-torus morphology is visible in high-resolution gamma-ray synthetic maps too. We present a preliminary exploration of time variability in the X and gamma-ray bands., Comment: 13 pages, 7 figures, accepted by Astronomy and Astrophysics

Elongated jets from young stellar objects typically present a nodular structure, formed by a chain of bright knots of 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. Axisymmetric simulations are performed with a shock-capturing code for gas dynamics, allowing for molecular, atomic, and ionized hydrogen in non-equilibrium concentrations subject to ionization/recombination processes. Radiative losses in SII lines are computed, and the resulting synthetic emission maps are compared with observations. We show that a pattern of regularly spaced internal oblique shocks, characterized by individual proper motions, is generated by the pressure gradient between the propagating jet and the time variable external cocoon. In the case of under-expanded, light jets the resulting emission knots are found to move downstream with the jet flow, with increasing velocity and decaying brightness toward the leading bow shock. This suggests that the basic properties of the knots observed in stellar jets can be reproduced even without invoking ad hoc pulsating conditions at the jet inlet, though an interplay between the two scenarios is certainly possible., Comment: 11 pages, accepted for publication by A&A

We present a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme 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, different algorithms, and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Various high order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the Upwind Constrained Transport (UCT) procedures, appropriate to preserve the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the matter contribution to the stress tensor. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, including a novel test on the propagation of large amplitude circularly polarized Alfven waves. In particular, we show that reconstruction based on a Monotonicity Preserving filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities., Comment: 20 pages, revised version submitted to A&A

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., Comment: 10 pages, 7 figures, Accepted for publication in A&A

We solve for the time-dependent dynamics of axisymmetric, general relativistic magnetohydrodynamic winds from rotating neutron stars. The mass loss rate is obtained self-consistently as a solution to the MHD equations, subject to a finite thermal pressure at the stellar surface. We consider both monopole and dipole magnetic field geometries and we explore the parameter regime extending from low magnetization (low-sigma_o), almost thermally-driven winds to high magnetization (high-sigma_o), relativistic Poynting-flux dominated outflows. We compute the angular momentum and rotational energy loss rates as a function of sigma_o and compare with analytic expectations from the classical theory of pulsars and magnetized stellar winds. In the case of the monopole, our high-sigma_o calculations asymptotically approach the analytic force-free limit. If we define the spindown rate in terms of the open magnetic flux, we similarly reproduce the spindown rate from recent force-free calculations of the aligned dipole. However, even for sigma_o as high as ~20, we find that the location of the Y-type point (r_Y), which specifies the radius of the last closed field line in the equatorial plane, is not the radius of the light cylinder R_L = c/omega (R = cylindrical radius), as has previously been assumed in most estimates and force-free calculations. Instead, although the Alfven radius at intermediate latitudes quickly approaches R_L as sigma_o exceeds unity, r_Y remains significantly less than R_L. Because r_Y < R_L, our calculated spindown rates thus exceed the classic ``vacuum dipole'' rate. We discussthe implications of our results for models of rotation-powered pulsars and magnetars, both in their observed states and in their hypothesized rapidly rotating initial state., Comment: Accepted for publication in MNRAS. 19 pages, 21 figures

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., Comment: Accepted for publication on A&A, 6 pages, 2 figures

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 \halpha sources; 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 \halpha radiation 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., Comment: 11 pages, 5 figures, Accepted for publication in A&A

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., Comment: 14 pages, 6 figures, accepted for publication in A&A

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~0.5-0.7 c) for high enough values of the equatorial wind magnetization parameter (sigma~0.01)., Comment: Astron. Astrophys., in press. 11 pages, 9 figures