Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Duez, Matthew D.; Liu, Yuk Tung; Shapiro, Stuart L.; Stephens, B. C.

doi:10.1103/physrevd.72.024028

Cited by 193 publications

(383 citation statements)

References 97 publications

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“…where the density variable is ρ * = α √ γρ 0 u 0 , the momentum-density variable isS i = α √ γT 0 i , the energydensity variable as adopted by Duez et al [16] …”

Section: B Evolution Of the Electromagnetic Fieldsmentioning

confidence: 99%

“…In the code of Duez et al [16], additional constraint damping terms are included in the BSSN evolution system, as described in [32,33] (see Eqs. (45) and (46) of [32], Eqs.…”

Section: A Evolution Of the Gravitational Fieldsmentioning

confidence: 99%

“…In particular, the evolution of magnetized HMNSs can only be determined by solving the coupled EinsteinMaxwell-MHD equations self-consistently in full general relativity. Recently, Duez et al [16] and Shibata and Sekiguchi [17] independently developed codes designed to do such calculations for the first time (see also [18]). The first simulations of magnetized hypermassive neutron star collapse (assuming both axial and equatorial symmetry) were reported in [19], and the implications of these results for short GRBs were presented in [20].…”

Section: Introductionmentioning

confidence: 99%

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Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

et al. 2006

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We study the effects of magnetic fields on the evolution of differentially rotating neutron stars, which can be formed in stellar core collapse or binary neutron star coalescence. Magnetic braking and the magnetorotational instability (MRI) both act on differentially rotating stars to redistribute angular momentum. Simulations of these stars are carried out in axisymmetry using our recently developed codes which integrate the coupled Einstein-Maxwell-MHD equations. We consider stars with two different equations of state (EOS), a gamma-law EOS with Γ = 2, and a more realistic hybrid EOS, and we evolve them adiabatically. Our simulations show that the fate of the star depends on its mass and spin. For initial data, we consider three categories of differentially rotating, equilibrium configurations, which we label normal, hypermassive and ultraspinning. Normal configurations have rest masses below the maximum achievable with uniform rotation, and angular momentum below the maximum for uniform rotation at the same rest mass. Hypermassive stars have rest masses exceeding the mass limit for uniform rotation. Ultraspinning stars are not hypermassive, but have angular momentum exceeding the maximum for uniform rotation at the same rest mass. We show that a normal star will evolve to a uniformly rotating equilibrium configuration. An ultraspinning star evolves to an equilibrium state consisting of a nearly uniformly rotating central core, surrounded by a differentially rotating torus with constant angular velocity along magnetic field lines, so that differential rotation ceases to wind the magnetic field. In addition, the final state is stable against the MRI, although it has differential rotation. For a hypermassive neutron star, the MHD-driven angular momentum transport leads to catastrophic collapse of the core. The resulting rotating black hole is surrounded by a hot, massive, magnetized torus undergoing quasistationary accretion, and a magnetic field collimated along the spin axis-a promising candidate for the central engine of a short gamma-ray burst.

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“…where the density variable is ρ * = α √ γρ 0 u 0 , the momentum-density variable isS i = α √ γT 0 i , the energydensity variable as adopted by Duez et al [16] …”

Section: B Evolution Of the Electromagnetic Fieldsmentioning

confidence: 99%

“…In the code of Duez et al [16], additional constraint damping terms are included in the BSSN evolution system, as described in [32,33] (see Eqs. (45) and (46) of [32], Eqs.…”

Section: A Evolution Of the Gravitational Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

et al. 2006

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“…However, as for the solenoidal condition for the magnetic field, non-evolutionary constraints must be preserved in the numerical evolution, and computational methods for modern codes are divided into two main classes: 1) free-evolution schemes, mainly based on hyperbolic equations alone, where this problem is alleviated by appropriate reformulations of the equations (BSSN: Shibata & Nakamura 1995;Baumgarte & Shapiro 1999), eventually with the addition of propagating modes and damping terms (Z4: Bona et al 2003;Bernuzzi & Hilditch 2010); 2) fully constrained schemes, where the constraints are enforced at each timestep through the solution of elliptic equations (Bonazzola et al 2004), a more robust but computationally demanding option, since elliptic solvers are notoriously difficult to parallelize. Most of the state-of-the-art 3D codes for GRMHD in dynamical spacetimes are based on freeevolution schemes in Cartesian coordinates (Duez et al 2005;Shibata & Sekiguchi 2005;Anderson et al 2006;Giacomazzo & Rezzolla 2007;Montero et al 2008;Farris et al 2008), and have been used for gravitational collapse in the presence of magnetized plasmas Shibata et al 2006a,b;Stephens et al 2007Stephens et al , 2008, evolution of NSs (Duez et al 2006b;Liebling et al 2010), binary NS mergers (Anderson et al 2008;Liu et al 2008;Giacomazzo et al 2009Giacomazzo et al , 2011, and accreting tori around Kerr BHs (Montero et al 2010).…”

Section: Introductionmentioning

confidence: 99%

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

Bucciantini

Zanna

2011

A&A

109

136

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We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This aims at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as in the evolution of magnetized neutron stars or in 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 extends the Eulerian conservative high-order (ECHO) scheme (Del Zanna et al. 2007, A&A, 473, 11) for GRMHD, here coupled to a novel solver of the Einstein equations in the extended conformally flat condition (XCFC). We solve the equations in the 3 + 1 formalism, assuming axisymmetry and adopting spherical coordinates for the conformal background metric. 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 are solved, for each harmonic, by inverting band diagonal matrices. As a side product, we built 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.

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“…We have also adopted the Harten-Lax-van-LeerEinfeld approximate Riemann solver [36,37]. We also refer to [26,38] for similar treatments and more detailed discussion.…”

Section: Numerical Implementationmentioning

confidence: 99%

Numerical relativity in spherical polar coordinates: Off-center simulations

Baumgarte¹,

Montero

Müller

2015

Phys. Rev. D

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We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system. 04.25.dg, 95.30.Lz, 97.60.Lf

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Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Cited by 193 publications

References 97 publications

Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

Numerical relativity in spherical polar coordinates: Off-center simulations

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