Resolution Dependence of Magnetorotational Turbulence in the Isothermal Stratified Shearing Box

Magnetohydrodynamic turbulence driven by the magnetorotational instability can provide diffusive transport of angular momentum in astrophysical disks, and a widely studied computational model for this process is the ideal, stratified, isothermal shearing box. Here we report results of a convergence study of such boxes up to a resolution of N = 256 zones per scale height, performed on blue waters at NCSA with ramses-gpu. We find that the time and vertically integrated dimensionless shear stress $\overline{\alpha }\sim N^{-1/3}$, i.e., the shear stress is resolution dependent. We also find that the magnetic field correlation length decreases with resolution, $\lambda \sim N^{-1/2}$. This variation is strongest at the disk midplane. We show that our measurements of $\overline{\alpha }$ are consistent with earlier studies, and we discuss possible reasons for the lack of convergence.