Turbulent resistivity evaluation in magnetorotational instability generated turbulence

Abstract

Context. MRI turbulence is a leading mechanism for the generation of an efficient turbulent transport of angular momentum in an accretion disk through a turbulent viscosity effect. It is believed that the same process could also transport large-scale magnetic fields in disks, reshaping the magnetic structures in these objects. This process, known as turbulent resistivity, has been suggested and used in several accretion-ejection models and simulations to produce jets. Still, the efficiency of MRI-driven turbulence to transport largescale magnetic fields is largely unknown. Aims. We present new analytical and numerical results aiming at quantifying the turbulent resistivity produced by MRI-driven turbulence in accretion disks. Methods. We investigate this problem both analytically and numerically. We introduce a linear calculation of the MRI in the presence of a spatially inhomogeneous mean magnetic field. We show that, in this configuration, MRI modes lead to an efficient magnetic field transport, on the order of the angular momentum transport. We next use fully non linear simulations of MRI turbulence to compute the turbulent resistivity in several magnetic configurations. Results. We find that the turbulent resistivity is on the order of the turbulent viscosity in all our simulations, although somewhat lower. The variations in the turbulent resistivity are correlated with the variation in the turbulent viscosity as a function of the imposed mean field. Finally, the turbulent resistivity tensor is found to be highly anisotropic with a diffusion coefficient 3 times greater in the radial direction than in the vertical direction. Conclusions. These results support the possibility of driving jets from turbulent disks; the resulting jets may not be steady.

Jet launching and field advection in quasi-Keplerian discs

“…Lubow et al (1994) showed that a SAD would get rid off its magnetic field unless the turbulent viscosity is much larger than the diffusivity (precisely, P m ∼ r/h). This is kind of problematic as our current view of turbulence would suggest instead P m ∼ o(1) Lesur & Longaretti (2009). However, they did not take into account the disc vertical equilibrium and, as pointed out by Rothstein & Lovelace (2008), advection could still be occurring.…”

“…Whether or not 3D MHD turbulence in accretion discs can indeed be described by a local prescription is an open question. However, recent work on 3D MRI in shearing box has shown that a fully turbulent medium displays both a viscosity and a magnetic diffusivity, such that the effective magnetic Prandtl number lies between 2 and 5 (Lesur & Longaretti 2009). Moreover, the functional dependency of the transport coefficients on the magnetic field is the same as the one we used (ν v ∝ ν m ∝ V A h).…”

Is the disc thermal state controlling the Blandford & Znajek/Blandford & Payne jet dichotomy?

“…Therefore, strongly inclined fields would be possible only for a magnetic Prandtl number P m = ⌫ v /⌫ m ⇠ r/h [32]. However, our current understanding of (and conventional wisdom on) MHD turbulence favors P m around unity [33,34]. Thus, according to this simple argument, any large scale B z field would just di↵use outwardly in a thin accretion disc.…”

Magnetospheric outflows in young stellar objects

“…In order to compress all the open flux in a small region around corotation ("flux-trapping", in the X-wind jargon), the X-wind magnetic configuration requires a magnetic Prandtl number, given by the ratio between the disk (turbulent) viscosity and magnetic diffusivity, of order r/h 1. Our current knowledge about MRI-driven turbulence in accretion disks seems to favor magnetic Prandtl number values around unity [38]. Over such a small radial extent, the accretion disk does not contain enough mechanical energy to fuel an outflow with the typical characteristics of an X-wind, but it can launch a less massive/powerful outflow only.…”