A magnetized thin accretion disk: numerical simulations compared with asymptotic expansion

To obtain a simple description of a geometrically thin magnetic accretion disk, we apply the method of asymptotic expansion. For the first time we write a full set of stationary asymptotic approximation equations of a thin magnetic accretion disk. As the obtained equations cannot be solved without knowledge of the solutions at the disk surface, we combine the results from numerical simulations and from analytical equations to find a simple set of functional expressions describing the radial and vertical dependence of physical quantities in the disk. Except very close to the star, the functional form of the disk variables is quite similar in the HD and MHD cases, with the overall scale of density, and the vertical and radial velocity components modified by the stellar magnetic field.