We show how the level of turbulence in accretion disks can be derived from a self-consistency requirement that the associated e †ective viscosity should match the instantaneous accretion rate. This method is applicable when turbulence has a direct energy cascade. Only limited information on the origin and properties of the turbulence, such as its injection scale and anisotropy, is needed. The method is illustrated by considering the case of turbulence originating from the magnetic shearing instability. The corresponding e †ective kinematic viscosity coefficient is shown to scale as the 1/3 power of surface mass density at a given radius in optically thick disks, and to be describable by a Shakura-Sunyaev law with a B 0.04. Mass Ñow in disks fed at a localized hot spot is calculated for accretion regimes driven by such turbulence, as well as passive magnetic Ðeld di †usion and dragging. An important result of this analysis is that thin disks supported by turbulence driven by the magnetic shearing instability, and more generally any turbulence with injection scale of order of the disk thickness, are very low magnetic Reynolds number systems. Turbulent viscosity-driven solutions with negligible Ðeld dragging and no emission of cold winds or jets are natural consequences of such regimes. Disks of accreting objects that are magnetized enough to be shielded by a magnetopause, however, may not operate in their innermost regions in the magnetic shearing instability regime. The possibility therefore remains to be explored of centrifugally driven winds emanating from such regions.

Abstract.We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo equations and a free-decay mode expansion using the thin-disk approximation. Contrary to expectations, a vertical velocity can enhance dynamo action, provided the velocity is not too strong. In the nonlinear regime this can lead to super-exponential growth of the magnetic field.

We consider accreting systems in which the central object interacts, via the agency of its magnetic field, with the disc that surrounds it. The disc is turbulent and, so, has a finite effective conductivity. The field sweeps across the face of the disc, thereby forming a current that is directed radially within the disc. In turn, this disc current creates a toroidal field, where the interaction between the disc current and the toroidal field produces a Lorentz force that compresses the disc. We investigate this compression, which creates a magnetic scaleheight of the disc that can be much smaller than the conventional scaleheight. We derive an analytic expression for the magnetic scaleheight and apply it to fully ionized discs.

The interaction between a stellar magnetic field and a turbulent accretion disc creates a twist of the magnetic field which leads to an inflation of this magnetic field. This work shows that this inflation occurs for a large range of twists, and is significant even for twists of order 1.

Magnetized objects surrounded by a turbulent and keplerian accretion disk are considered. In such systems, magnetic field lines are embedded into the disk. The magnetic field of the central object is assumed to be dipolar in the absence of the accretion disk. In the presence of a turbulent accretion disk, it is shown that the interaction with the disk stretches magnetic field lines along the disk and that most of the non-magnetospheric magnetic flux is expelled outside the disk.