Magnetic Braking and Viscous Damping of Differential Rotation in Cylindrical Stars

Differential rotation in stars generates toroidal magnetic fields whenever an initial seed poloidal field is present. The resulting magnetic stresses, along with viscosity, drive the star toward uniform rotation. This magnetic braking has important dynamical consequences in many astrophysical contexts. For example, merging binary neutron stars can form "hypermassive" remnants supported against collapse by differential rotation. The removal of this support by magnetic braking induces radial fluid motion, which can lead to delayed collapse of the remnant to a black hole. We explore the effects of magnetic braking and viscosity on the structure of a differentially rotating, compressible star, generalizing our earlier calculations for incompressible configurations. The star is idealized as a differentially rotating, infinite cylinder supported initially by a polytropic equation of state. The gas is assumed to be infinitely conducting and our calculations are performed in Newtonian gravitation. Although highly idealized, our model allows for the incorporation of magnetic fields, viscosity, compressibility, and shocks with minimal computational resources in a (1 + 1)-dimensional Lagrangian MHD code. Our evolution calculations show that magnetic braking can lead to significant structural changes in a star, including quasi-static contraction of the core and ejection of matter in the outermost regions to form a wind or an ambient disk. These calculations serve as a prelude and a guide to more realistic MHD simulations in full 3 + 1 general relativity.