Structure of magneto-Keplerian discs: an analytical solution for thin accretion discs threaded by stellar magnetic fields

The structure of Keplerian discs which are threaded by the magnetic field lines of each central star are considered. Under the assumptions of thin discs, stationarity and of axisymmetry, a fairly simple analytical solution is found. In such a disc, the electromagnetic force does not play any important role in the radial force balance, but it is this force that maintains the disc structure in the latitudinal direction. As suggested by Ghosh & Lamb, the angular momentum transfer is controlled by the global structure of the magnetic field. In contrast to their results, however, our solution does not predict the switching of $$B_\phi$$ (the azimuthal component of the magnetic field) as a function of the radial distance in the disc. The difference of the angular momenta coming in at the outer edge and going out of the inner edge of the disc is transmitted from the disc to the star, when the disc is in a direct Keplerian orbit, and vice versa. Similarly to the result in the standard model of viscous discs, about one half of the gravitational energy is released in the magnetized disc through the Joule dissipation. The basic equations that we employ in this paper are those of resistive MHD in which the electrical conductivity is assumed to be constant.