What is the Numerically Converged Amplitude of Magnetohydrodynamics Turbulence in Stratified Shearing Boxes?

We study the properties of the turbulence driven by the magnetorotational instability in a stratified shearing box with outflow boundary conditions and an equation of state determined by self-consistent dissipation and radiation losses. A series of simulations with increasing resolution are performed within a fixed computational box. We achieve numerical convergence with respect to radial and azimuthal resolution. As vertical resolution is improved, the ratio of stress to pressure increases slowly, but the absolute levels of both the stress and the pressure increase noticeably. These results are in contrast with those of previous work on unstratified shearing boxes, in which improved resolution caused a diminution in the magnetic field strength. We argue that the persistence of strong magnetic field at higher resolution found in the stratified case is due to buoyancy. In addition, we find that the time-averaged vertical correlation length of the magnetic field near the disk midplane is 3 times larger than that found in previous unstratified simulations, decreasing slowly with improved vertical resolution. We further show that the undulatory Parker instability drives the magnetic field upwelling at several scale heights from the midplane that is characteristic of stratified magnetohydrodynamics-turbulent disks.