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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

We present high resolution spherically symmetric relativistic magnetohydrodynamical simulations of the evolution of a pulsar wind nebula inside the free 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., Comment: 11 pages, 7 figures, Accepted for publication on A&A

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the 'Constrained Transport' (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures div(B)=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here 'Upwind Constrained Transport' (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second order Roe-type positive scheme by Liu and Lax (J. Comp. Fluid Dynam. 5, 133, 1996), and both the second and third order versions of a central-type MHD scheme presented by Londrillo and Del Zanna (Astrophys. J. 530, 508, 2000), where the basic UCT strategies have been first outlined.

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 in 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=2E The simulations were performed using the third order conservative scheme by Del Zanna et al. (2003)., Comment: 11 pages, Latex, 22 Encapsulated PostScript figures, accepted f or publication on A&A

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 central scheme described in Paper I (Del Zanna and Bucciantini, Astron. Astrophys., 390, 1177--1186, 2002) for relativistic hydrodynamics is here extended to the magnetic case by following the strategies prescribed for classical MHD by Londrillo and Del Zanna (Astrophys. J., 530, 508--524, 2000). The scheme avoids completely spectral decomposition into characteristic waves, computationally expensive and subject to many degenerate cases in the magnetic case, while it makes use of a two-speed Riemann solver that just require 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., Comment: 18 pages, Latex, 8 Encapsulated PostScript figures, accepted for publication in A&A

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 and L. Del Zanna ({\em Astrophys. J.} 530, 508-524, 2000) 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., Comment: 11 pages, Latex, 9 Encapsulated PostScript figures, accepted for publication in A&A

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint $\divb=0$ for the magnetic field vector $\bb$, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the $\bb$ field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate $\divb=0$ relation for any numerical $\bb$ field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the $\bb$ vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented., Comment: 34 pages, including 14 figures