The formation and structure of a strongly magnetized corona above a weakly magnetized accretion disk

We use three-dimensional magnetohydrodynmic (MHD) simulations to study the formation of a corona above an initially weakly magnetized, isothermal accretion disk. The simulations are local in the plane of the disk but extend up to 5 vertical scale heights above and below it. We describe a modification to time-explicit numerical algorithms for MHD that enables us to evolve such highly stratified disks for many orbital times. We find that for an initially toroidal field or a poloidal fields with a vanishing mean MHD turbulence driven by the magnetorotational instability (MRI) produces strong amplification of weak fields within 2 scale heights of the disk midplane in a few orbital times. Although the primary saturation mechanism of the MRI is local dissipation, about 25% of the magnetic energy generated by the MRI within 2 scale heights escapes because of buoyancy, producing a strongly magnetized corona above the disk. Most of the buoyantly rising magnetic energy is dissipated between 3 and 5 scale heights, suggesting that the corona will also be hot. Strong shocks with Mach numbers greater than or similar to 2 are continuously produced in the corona in response to mass motions deeper in the disk. Only a very weak mass outflow is produced through the outer boundary at 5 scale heights, although this is probably a reflection of our use of the local approximation in the plane of the disk. On long timescales the average vertical disk structure consists of a weakly magnetized (beta similar to 50) turbulent core below 2 scale heights and a strongly magnetized (beta less than or similar to 10(-1)) corona that is stable to the MRI above. The large-scale field structure in both the disk and the coronal regions is predominately toroidal. Equating the volume averaged heating rate to optically thin cooling curves, we estimate the temperature in the corona will be of order 10(4) K for protostellar disks and 10(8) K for disks around neutron stars. The functional form of the stress with vertical height is best described as flat within +/-2H(z), but proportional to the density above +/-2H(z). For initially weak uniform vertical Gelds, we find the exponential growth of magnetic field via axisymmetric vertical modes of the MRI produces strongly buoyant sheets of magnetic energy that break the disk apart into horizontal channels. These channels rise several scale heights vertically before the onset of the Parker instability distorts the sheets and allows matter to flow back toward the midplane and reform a disk. Thereafter the entire disk is magnetically dominated and not well modeled by the local approximation. We suggest that this evolution may be relevant to the dynamical processes that disrupt the inner regions of a disk when it interacts with a strongly magnetized central object.