Vertical Structure of Stationary Accretion Disks with a Large-Scale Magnetic Field

Abstract

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. Here, we calculate the vertical profiles of the {\it stationary} accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Also, here we require that the radial accretion speed be zero at the disk's surface and we assume that the ratio of the turbulent viscosity to the turbulent magnetic diffusivity is of order unity. Thus at the disk's surface there are three boundary conditions. As a result, for a fixed dimensionless viscosity $\alpha$-value, we find that there is a definite relation between the ratio $\mathcal{R}$ of the accretion power going into magnetic disk winds to the viscous power dissipation and the midplane plasma-$\beta$, which is the ratio of the plasma to magnetic pressure in the disk. For a specific disk model with $\mathcal{R}$ of order unity we find that the critical value required for a stationary solution is ${\beta }_c\approx 2.4r/(\alpha h)$, where $h$ the disk's half thickness. For weaker magnetic fields, $\beta >{\beta }_c$, we argue that the poloidal field will advect outward while for $\beta <{\beta }_c$ it will advect inward. Alternatively, if the disk wind is negligible ($\mathcal{R}\ll 1$), there are stationary solutions with $\beta \gg {\beta }_c$.

5 pages, 3 figures

References in corpus (8)

• Transport of Large Scale Poloidal Flux in Black Hole Accretion
• Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All
• The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks
• The synchrotron boiler and the spectral states of black hole binaries
• Advection/Diffusion of Large-Scale B-Field in Accretion Disks
• Stability Properties of Magnetic Tower Jets
• Large Scale B-Field in Stationary Accretion Disks
• MRI-driven Accretion onto Magnetized stars: Axisymmetric MHD Simulations

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• Radial Transport of Large-Scale Magnetic Fields in Accretion Disks. I. Steady Solutions and an Upper Limit on the Vertical Field Strength
• Radial Transport of Large-Scale Magnetic Fields in Accretion Disks. II. Relaxation to Steady States
• The high efficiency jets magnetically accelerated from a thin disk in powerful lobe-dominated FRII radio galaxies
• Advection of Matter and B-Fields in Alpha-Discs
• Neutrinos and gravitational waves from magnetized neutrino-dominated accretion discs with magnetic coupling
• State transitions triggered by inverse magnetic field: probably applied in high-mass X-ray binaries?