The Formation and Structure of a Strongly Magnetized Corona above a Weakly Magnetized Accretion Disk

Abstract

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 modiÐ-cation to time-explicit numerical algorithms for MHD that enables us to evolve such highly stratiÐed disks for many orbital times. We Ðnd that for an initially toroidal Ðeld or a poloidal Ðelds with a van-ishing mean MHD turbulence driven by the magnetorotational instability (MRI) produces strong ampli-Ðcation of weak Ðelds 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 gener-ated 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 are contin-Z2 uously produced in the corona in response to mass motions deeper in the disk. Only a very weak mass outÑow is produced through the outer boundary at 5 scale heights, although this is probably a reÑection 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 (b D 50) turbulent core below 2 scale heights and a strongly magnetized corona that is stable to the MRI above. The large-scale Ðeld structure in (b [ 10~1) 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 104 K for protostellar disks and 108 K for disks around neutron stars. The functional form of the stress with vertical height is best described as Ñat within but proportional to the density above For ^2H z ^2H z . initially weak uniform vertical Ðelds, we Ðnd the exponential growth of magnetic Ðeld 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 Ñow back toward the midplane and reform a disk. Thereafter the entire disk is magnetically dominated and not well modeled by the local approx-imation. 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.