Instability of Magnetohydrostatic Stellar Interiors from Magnetic Buoyancy. I.

We show that magnetic buoyancy gives rise to a normal-mode instability in fluids in magnetobydrostatic balance whose diffusivity of heat is large compared with viscosity and magnetic diffusivity, such as in stellar interiors. In an unbounded compressible fluid acted upon by external gravity containing a straight horizontal magnetic field; the instability occurs if the magnetic field decreases with height. The unstable modes are narrow cross-section loops of magnetic field and matter whose finite wavenumber k along the magnetic field lies in the range 0 < k2 < - (g/S2) a/az ln B, where B(z) is the basic magnetic field, g is gravity, and S is the isothermal sound speed. Thus, in a star with a toroidal magnetic field, the analysis for which we are giving in a later paper, this would be a nonaxisymmetric instability. A detailed analysis is made of the special case in which the Alfven and sound speeds are independent of height and which thus elucidates the role of magnetic buoyancy. Sufficiently large rotation perpendicular to gravity is shown to be stabilizing in this case. The instability simultaneously releases potential and magnetic energy, through downward transport of mass and upward transport of magnetic flux, respectively. The instability gives a mechanism by which magnetic flux may be expelled from stellar interiors.