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.
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 sy
nchrotron 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.
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.
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 Einsteins 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.
