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

We use three-dimensional magnetohydrodynmic (MHD) simulations to study the formation of a corona above an initially weakly magnetized, isothermal accr etion disk. The simulations are local in the plane of the disk but extend u p to 5 vertical scale heights above and below it. We describe a modificatio n to time-explicit numerical algorithms for MHD that enables us to evolve s uch highly stratified disks for many orbital times. We find that for an ini tially toroidal field or a poloidal fields with a vanishing mean MHD turbul ence driven by the magnetorotational instability (MRI) produces strong ampl ification of weak fields within 2 scale heights of the disk midplane in a f ew orbital times. Although the primary saturation mechanism of the MRI is l ocal dissipation, about 25% of the magnetic energy generated by the MRI wit hin 2 scale heights escapes because of buoyancy, producing a strongly magne tized corona above the disk. Most of the buoyantly rising magnetic energy i s 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 bo undary at 5 scale heights, although this is probably a reflection of our us e of the local approximation in the plane of the disk. On long timescales t he average vertical disk structure consists of a weakly magnetized (beta si milar 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 abo ve. The large-scale field structure in both the disk and the coronal region s is predominately toroidal. Equating the volume averaged heating rate to o ptically thin cooling curves, we estimate the temperature in the corona wil l be of order 10(4) K for protostellar disks and 10(8) K for disks around n eutron stars. The functional form of the stress with vertical height is bes t described as flat within +/-2H(z), but proportional to the density above +/-2H(z). For initially weak uniform vertical Gelds, we find the exponentia l growth of magnetic field via axisymmetric vertical modes of the MRI produ ces strongly buoyant sheets of magnetic energy that break the disk apart in to horizontal channels. These channels rise several scale heights verticall y 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 app roximation. 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.