The instability of a horizontal magnetic field in an atmosphere stable against convection

The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3R beneath the surface of the Sun, a field of 10² G develops ripples over a scale of 10³ km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10¹⁰ years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001