Magnetohydrodynamics in full general relativity: Formulation and tests

Abstract

A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a BSSN formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a longterm evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.04.25. Dm, 04.40.Nr, 47.75.+f, 95.30.Qd

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

“…In the code of Shibata and Sekiguchi [17], the energy evolution variable is chosen to be √ γ n µ n ν T µν =τ + ρ * , and the evolution equation may be obtained by adding Eq. (39) to Eq.…”

“…where a In the code of Shibata and Sekiguchi [17] the following dynamical gauge conditions are used:…”

“…For example, choosing K = 2.42 × 10 5 g −1 cm 5 s −2 gives the maximum ADM mass (rest mass) of 2.12M ⊙ (2.32M ⊙ ) for spherical neutron stars and 2.42M ⊙ (2.67M ⊙ ) for rigidly rotating neutron stars. In order to consider the effects of a more realistic neutron star equation of state, star C is constructed from a cold hybrid EOS [1,17] defined as follows:…”

“…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].…”

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

“…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).…”