Jose Ma Marti

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e., Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic MHD equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic MHD in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick disks accreting onto a black hole and subject to the magnetorotational instability.

The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

We have generalized the exact solution of the Riemann problem in special relativistic hydrodynamics (Marti & Muller 1994) for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multi-dimensional relativistic hydrodynamic codes (of Godunov type) is discussed.

A new spherically symmetric general relativistic hydrodynamical code

In this paper we present a full general relativistic one-dimensional hydro-code which incorporates a modern high-resolution shock-capturing algorithm, with an approximate Riemann solver, for the correct modelling of formation and propagation of strong shocks. The efficiency of this code in treating strong shocks is demonstrated by some numerical experiments. The interest of this technique in several astrophysical scenarios is discussed.

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Lucas Serrano, Arturo, Arturo.Lucas@uv.es ; Font Roda, Jose Antonio, .Antonio.Font@uv.es ; Ibanez Cabanell, Jose Maria, Jose.M.Ibanez@uv.es ; Marti Puig, Jose Maria, jose-maria.marti@uv.esWe assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straight- forwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

Subparsec Polarimetric Radio Observations of 3C 120: A Close-up Look at Superluminal Motion

We present two-epoch polarimetric images of the radio galaxy 3C 120 obtained with the Very Long Baseline Array at 22 and 43 GHz. Because of the proximity of 3C 120 (z = 0.033), the 43 GHz observations allow us to observe superluminal motions with the highest resolution achieved to date, 0.07 h-1 pc. Up to ten different superluminal components, with velocities between 2.3 and 5.4 h-1c, can be observed in this active source, with approximately monthly ejections of new components. Polarization is observed in several components and at both frequencies, with peaks in the linearly polarized flux not always coincident with the peaks in total intensity. The orientation of the magnetic field is observed to vary with respect to the jet flow direction as a function of frequency, epoch, and position along the jet. These observations are in agreement with previous numerical simulations of superluminal sources (Gomez et al. 1997). The classical association of lower frequency components with single shocks does not appear to be valid, and multiple components may be the result of a single disturbance in the jet flow. This is a consequence of the interaction of the shocked plasma with the external medium and the underlying jet, as well as hydrodynamical processes inside the shocked region, neglected in previous analytical shock studies owing to the nonlinearity of the jet fluid dynamics.

The exact solution of the Riemann problem in relativistic magnetohydrodynamics with tangential magnetic fields

We have extended the procedure to find the exact solution of the Riemann problem in relativistic hydrodynamics to a particular case of relativistic magnetohydrodynamics in which the magnetic field of the initial states is tangential to the discontinuity and orthogonal to the flow velocity. The wave pattern produced after the break up of the initial discontinuity is analogous to the non-magnetic case and we show that the problem can be understood as a purely relativistic hydrodynamical problem with a modified equation of state. The new degree of freedom introduced by the non-zero component of the magnetic field results in interesting effects consisting in the change of the wave patterns for given initial thermodynamical states, in a similar way to the effects arising from the introduction of tangential velocities. Secondly, when the magnetic field dominates the thermodynamical pressure and energy, the wave speeds approach the speed of light, leading to fast shocks and fast and arbitrarily thin rarefaction waves. Our approach is the first non-trivial exact solution of a Riemann problem in relativistic magnetohydrodynamics and it can also be of great interest to test numerical codes against known analytical or exact solutions.

THE INTERNAL STRUCTURE OF OVERPRESSURED, MAGNETIZED, RELATIVISTIC JETS

This work presents the first characterization of the internal structure of overpressured steady superfast magnetosonic relativistic jets in connection with their dominant type of energy. To this aim, relativistic magnetohydrodynamic simulations of different jet models threaded by a helical magnetic field have been analyzed covering a wide region in the magnetosonic Mach number - specific internal energy plane. The merit of this plane is that models dominated by different types of energy (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux dominated jets) occupy well separated regions. The analyzed models also cover a wide range of magnetizations. Models dominated by the internal energy (i.e., hot models, or Poynting-flux dominated jets with magnetizations larger than but close to 1) have a rich internal structure characterized by a series of recollimation shocks and present the largest variations in the flow Lorentz factor (and internal energy density). Conversely, in kinetically dominated models there is not much internal nor magnetic energy to be converted into kinetic one and the jets are featureless, with small variations in the flow Lorentz factor. The presence of a significant toroidal magnetic field threading the jet produces large gradients in the transversal profile of the internal energy density. Poynting-flux dominated models with high magnetization (>10) are prone to be unstable against magnetic pinch modes, which sets limits to the expected magnetization in parsec-scale AGN jets {and/or constrains their magnetic field configuration}.

Field theoretical model for nuclear and neutron matter. IV: radial oscillations of warm cores in neutron stars

The relativistic equations for the radial oscillations of warm cores in neutron stars have been solved and the eigenfrequencies of the fundamental modes have been obtained for a large sample of configurations in relativistic thermal equilibrium. The equation of state used was derived in the frame of a field theoretical model for the analysis of relativistic nuclear and neutron matter at nonzero temperatures. The Lagrangian describing the microdynamics has been introduced by coupling the nucleons to sigma, pi, omega, and rho meson fields in a renormalizable way. Moreover, the results of this paper allow the so-called static stability criterion to be reviewed and a central temperature-central density diagram to be built which displays a well-defined region of stability and admits an evolutive interpretation. 29 references.

2D hydrodynamic simulations of relativistic jets from collapsars

Using a collapsar progenitor model of MacFadyen & Woosley we have simulated the propagation of an axisymmetric relativistic jet through a collapsing rotating massive star. The jet forms as a consequence of an assumed constant or variable energy deposition in the range 1050 erg s−1 to 1051 erg s−1 within a 30° cone around the rotation axis. The jet flow is strongly beamed (≲ few degrees), spatially inhomogeneous, and time dependent. The jet reaches the surface of the stellar progenitor (R*=2.98×1010 cm) intact with a maximum Lorentz factor Γmax=33. After break-out the jet accelerates into the circumstellar medium, whose density is assumed to decrease exponentially and then being constant. Outside the star the flow also expands laterally (v∼c), but the beam remains very well collimated. At a distance of 2.54×R*, where we had to stop the simulation, the Lorentz factor has increased to 44.