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

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 Gamma=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.