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

Abstract

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.

Differentially-rotating neutron star models with a parametrized rotation profile

“…For a typical neutron star, we expect a timescale of 10 1 −10 2 yr. In the presence of magnetic fields, the magnetic braking (Spruit 1999) or the magnetorotational instability (MRI) (Balbus & Hawley 1991) may drastically accelerate the redistribution of angular momentum to the order of 1s (Duez et al 2006).…”

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).…”

Three-dimensional evolution of differentially rotating magnetized neutron stars

“…Motivated by this expectation, several groups have implemented the magnetohydrodynamics (MHD) code in the framework of numerical relativity [23][24][25][26][27][28]. These numerical codes developed have been applied to collapse of magnetized hypermassive neutron stars (HMNS) [29][30][31], magnetized neutron starblack hole binary merger [32,33], evolution of magnetized neutron stars [34][35][36], and magnetorotational collapse of massive stellar cores [24,37].…”