Rotating neutron stars without light cylinders

We find a class of twisted and differentially rotating neutron star magnetospheres that do not have a light cylinder, generate no wind, and thus do not spin-down. The magnetosphere is composed of embedded differentially rotating flux surfaces, with the angular velocity decreasing as omega proportional to 1/r (equivalently, becoming smaller at the foot-points closer to the axis of rotation). For each given North-South self-similar twist profile there is a set of self-similar angular velocity profiles (limited from above) with a 'smooth', dipolar-like magnetic field structure extending to infinity. For spin parameters larger than some critical value, the light cylinder appears, magnetosphere opens up, and the wind is generated.