Numerical simulations of the interaction of accretion disks with young star magnetospheres

Aims. We present the results of the numerical simulations of the interaction between a magnetized star and an imperfectly conducting accretion disk. The star is rotating with constant angular velocity. The differentially rotating Keplerian disk is treated as a boundary condition. We are interested in the magnetic field topology dependence on the electrical conductivity of the disk. Methods. To analyze the "star-disk" interaction we numerically investigate the MHD equations using Godunov-type high resolution numerical methods. Results. It was found that in our model the "star-disk" interaction occurs with a quasi-periodic reconnection of the magnetic field coronal loops and plasmoid ejections. In the case of the perfect disk conductivity, the evolution of the coronal magnetic field leads to the periodic outflow of angular momentum from the disk. In the case of an imperfectly conducting disk, the configuration of the magnetic field is formed such that the disk angular momentum carried by the magnetic field is balanced by angular momentum carried by matter. It should be noted that we used the ideal MHD equation to obtain the solutions. The reconnection process in the disk corona depends on the numerical diffusivity that exists in our numerical code. Our simulations treat reconnection as occurring in current sheets. The thickness of the current sheet is broadened by numerical resistivity. Nevertheless, we suppose that the reconnection and plasmoid ejection takes place as well for real magnetic diffusivity. To verify the method and results we also used several more detailed grids to estimate the numerical diffusivity of the scheme. It is turned out that the setup model presented in the paper quite reasonable satisfies the goal of this paper, i.e., to investigate the regime of interaction between the magnetized star and the disk.