Vertical Structure of Magnetohydrodynamic Turbulence in Accretion Disks

Abstract

The vertical structure of magnetohydrodynamic turbulence in accretion disks with density stratification is considered by applying one-point closure modeling of the turbulence. The transport equations of turbulent kinetic energy (K), turbulent magnetic energy (KW ), and density variance (KD) are solved simultaneously under the assumptions of isothermal disks and no global magnetic field. Moreover, the turbulence in the disk is assumed to be homogeneous in the horizontal plane. The imposed boundary conditions are: (i) both the turbulent energy K and the density variance KD do not escape from the disk through the surface; (ii) on the other hand, the escape of turbulent magnetic energy KW is considered phenomenologically. The results show that both K and KW /ρM (magnetic energy per unit mass) increase with height due to turbulent diffusion. It follows that the so-called α-value generally increases from the equator of disks toward the surface, though it decreases, due to the escape of magnetic fields, in a region rather close to the surface. The results further show that the magnetic energy is larger than the turbulent kinetic energy over a wide range of the disk height, implying that the main contributor to angular-momentum transport and viscous heating in the disks is the magnetic fields.