Magnetic helicity in astrophysics

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Abstract
Magnetic helicity, which is conserved in ideal MHD, measures the linkage of magnetic lines of force. After a brief review, I consider the helicity of a stellar magnetic field and show that a modified definition of helicity, called relative helicity, enables one to compute the relative amount of linkage of two field configurations above the photosphere even though the subphotospheric field is unobservable. I also show how the relative helicity changes as the result of motions of photospheric material. Then I consider the dissipation of helicity and show that in certain situations it is dissipated much more slowly than magnetic energy. Finally, I propose a variational principle for static problems, and show that in the presence of finite pressure, helicity conservation yields the usual equation of magnetostatic equilibrium. Woltjer’s conclusion that the result is a force‐free field is a result of his neglect of pressure.

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