Can the Battery (▽T × ▽n) Effect Produce 1012 G Magnetic Fields in Neutron Stars?

Abstract

The origin of strong magnetic fields in neutron stars has been a subject of dispute ever since the discovery of pulsars. Among a few important scenarios so far presented is one suggesting that magnetic fields in neutron stars may be generated by a thermally-driven battery process after the star is born. Here, we discuss the fluid motion induced in the liquid crust by this thermomagnetic process. We derive a generalized vorticity conservation formula and show that fluid vortices are also generated, together with the magnetic field, and grow with increasing field strength. The maximum field strength produced by this process is shown to be 10 G, unless the fluid velocity exceeds the velocity of sound. Even a dynamo action cannot enhance these fields beyond this critical value if the fluid motion and magnetic fields have the same origin. These results indicate that a thermomagnetic process may not be responsible for the origin of the neutron star magnetic fields.