Self-gravitating body with an internal magnetic field. I. New analytical equilibria

We construct exact analytical solutions of the equations describing the equilibrium of a self-gravitating magnetized fluid body, possibly rigidly rotating, by superposing two solutions of finite energy defined in the whole space, one describing a non-magnetized gravitating equilibrium (ST1) and the other describing a magnetized non-gravitating equilibrium (ST2). A large number of ST1s can be found in the literature and directly used for our constructions, and we thus concentrate on ST2s, which are difficult to obtain. We derive some of their general properties and exhibit two explicit classes of axisymmetric "elementary" such equilibria. The first one is extracted from the stellar models proposed by Prendergast and by Kutvitskii & Solov'ev, respectively. The second one is constructed by using Palumbo's theory of isodynamic equilibria, for which the magnetic pressure is constant on each flux surface. Both types of ST2s have their magnetic field confined within a bounded region, respectively, of spherical and toroidal shapes. A much more general ST2 can be obtained by juxtaposing n+q elementary ST2s, with n of the first type and q of the second type, in such a way that the magnetic regions do not pairwise overlap. The specific equilibria we obtain by superposition thus have no external field extending to infinity, and may be three dimensional (3D), which invalidates a recent nonexistence conjecture. Moreover, they may be arranged to contain force-free regions. Our superposition method can be considered as a 3D generalization of the axisymmetric splitting method previously developed by Kutvitskii & Solov'ev.