Magnetic Field Diffusion in Self‐consistently Turbulent Accretion Disks

Abstract

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.

Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All

“…This last term can be smaller than unity, but not small enough to prevent the conclusion that, typically, Re m 3 1 at the surface of the disk, and diffusion of the magnetic field can be neglected. This is in contrast with the main body of the disk, where Re m % H /r (if we assume that the magnetic field is not strong enough to affect the accretion speed) and diffusion of the magnetic field therefore dominates over advection (Lubow et al 1994;Lovelace et al 1994;Heyvaerts et al 1996).…”

The absence of jets in cataclysmic variable stars

“…See recent reviews by Königl & Pudritz (2000), Shu et al (2000) and Ferreira (2002). It should, however, be pointed out that the origin of the large scale magnetic fields and the manner that open field lines of sufficiently strong magnitude persist (in the centrifugal wind models), or the manner by which a stellar field interacts with the disk, allowing inflow and at the same time driving an outflow (in the X-wind models) are still open key issues of the theory (e.g., Heyvaerts et al 1996). In addition, it seems that thermal pressure is needed in some of these models (e.g., Ferreira & Casse 2004).…”

The effects of vertical outflows on disk dynamos

“…Advection appears unlikely as turbulence leads to enhanced viscosity and magnetic diffusivity, so that the two are of the same order (Prandtl number of order unity; Pouquet et al 1976). Thus, turbulent magnetic diffusivity can compensate the dragging of the field by viscously induced accretion flow (van Ballegooijen 1989;Lubow et al 1994;Heyvaerts et al 1996). Dynamo action is a plausible mechanism for producing magnetic fields in accretion disks (Pudritz 1981;Stepinski & Levy 1988).…”