Differential rotation in neutron stars: Magnetic braking and viscous damping

Differentially rotating stars can support significantly more mass in equili brium than nonrotating or uniformly rotating stars, according to general re lativity. The remnant of a binary neutron star merger may give rise to such a "hypermassive" object. While such a star may be dynamically stable again st gravitational collapse and bar formation, the radial stabilization due t o differential rotation is likely to be temporary. Magnetic braking and vis cosity combine to drive the star to uniform rotation, even if the seed magn etic field and the viscosity are small. This process inevitably leads to de layed collapse, which will be accompanied by a delayed gravitational wave b urst and, possibly, a gamma-ray burst. We provide a simple, Newtonian MHD c alculation of the braking of differential rotation by magnetic fields and v iscosity. The star is idealized as a differentially rotating, infinite cyli nder consisting of a homogeneous, incompressible conducting gas. We solve a nalytically the simplest case in which the gas has no viscosity and the sta r resides in an exterior vacuum. We treat numerically cases in which the ga s has internal viscosity and the star is embedded in an exterior, low-densi ty, conducting medium. Our evolution calculations are presented to stimulat e more; realistic MHD simulations in full 3 + 1 general relativity. They se rve to identify some of the key physical and numerical parameters, scaling behavior, and competing timescales that characterize this important process .