Jose M. Ibanez

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.

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.

A numerical study of relativistic Bondi-Hoyle accretion onto a moving black hole: axisymmetric computations in a Schwarzschild background

A fully relativistic numerical study of nonspherical Bondi-Hoyle accretion onto a Schwarzschild black hole is presented. The simulations are performed in axisymmetry with a high-resolution shock-capturing numerical scheme that makes use of a linearized Riemann solver as a key ingredient to handle shock waves. A broad family of initial flow parameters is considered. The main differences among the accretion patterns of the different models is discussed. A detailed comparative study with a previous relativistic simulation is performed. The results of this study reveal a qualitative agreement in the morphology and dynamics of the flow. However, there are important discrepancies concerning quantitative results as the mass accretion rates. All models evolved numerically in this paper relax to a final steady state accretion pattern, and, as the simulations are performed in axisymmetry, no evidence of any kind of instabilities (e.g., flip-flop) is present.

Non-axisymmetric relativistic Bondi—Hoyle accretion on to a Schwarzschild black hole

We present the results of an exhaustive numerical study of fully relativistic non-axisymmetric Bondi–Hoyle accretion on to a moving Schwarzschild black hole. We have solved the equations of general relativistic hydrodynamics with a high-resolution shock-capturing numerical scheme based on a linearized Riemann solver. The numerical code was previously used to study axisymmetric flow configurations past a Schwarzschild black hole. We have analysed and discussed the flow morphology for a sample of asymptotically high Mach number models. The results of this work reveal that initially asymptotic uniform flows always accrete on to the hole in a stationary way, which closely resembles the previous axisymmetric patterns. This is in contrast with some Newtonian numerical studies where violent flip-flop instabilities were found. As discussed in the text, the reason can be found in the initial conditions used in the relativistic regime, as they cannot exactly duplicate the previous Newtonian setups where the instability appeared. The dependence of the final solution on the inner boundary condition as well as on the grid resolution has also been studied. Finally, we have computed the accretion rates of mass and linear and angular momentum.

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.

A "horizon-adapted" approach to the study of relativistic accretion flows onto rotating black holes

We present a new geometrical approach to the study of accretion flows onto rotating black holes. Instead of Boyer-Lindquist coordinates, the standard choice in all existing numerical simulations in the literature, we employ the simplest example of a horizon-adapted coordinate system, the Kerr-Schild coordinates. This choice eliminates unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle accretion onto extreme Kerr black holes, performed here for the first time, demonstrate the key advantages of this procedure. We argue that it offers the best approach to the numerical study of the observationally increasingly, more accessible, relativistic inner region around black holes.

Gravitational Waves from the Collapse and Bounce of a Stellar Core in Tensor-Scalar Gravity

Tensor-scalar theory of gravity allows the generation of gravitational waves from astrophysical sources, like supernovae, even in the spherical case. That motivated us to study the collapse of a degenerate stellar core, within tensor-scalar gravity, leading to the formation of a neutron star through a bounce and the formation of a shock. This paper discusses the effects of the scalar field on the evolution of the system, as well as the appearance of strong nonperturbative effects of this scalar field (the so-called spontaneous scalarization). As a main result, we describe the resulting gravitational monopolar radiation (form and amplitude) and discuss the possibility of its detection by the gravitational detectors currently under construction, taking into account the existing constraints on the scalar field. From the numerical point of view, it is worthy to point out that we have developed a combined code that uses pseudo-spectral methods for the evolution of the scalar field and High-Resolution Shock-Capturing schemes, as well as for the evolution of the hydrodynamical system. Although this code has been used to integrate the field equations of that theory of gravity, in the spherically symmetric case, a by-product of the present work is to gain experience for an ulterior extension to multidimensional problems in Numerical Relativity of such numerical strategy.