1. June 08MRI Transport properties1 MRI-driven turbulent resistivity Pierre-Yves Longaretti (LAOG) Geoffroy Lesur (DAMTP)

2. June 08 MRI Transport properties 2 Turbulent resistivity and ejection Standard accretion disk (non-existent or weak ejection):  Outwards transport. Requires « anomalous viscosity » Jet-emitting disk (strong ejection, requires β~1 and Pm T ~1):  Vertical transport. Requires « anomalous resistivity » : Ambipolar diffusion in YSOs (Königl and coworkers) Turbulence Angular momentum

3. June 08 MRI Transport properties 3 Jet emitting disks (JED) vs standard accretion disks (SAD) At given accretion rate, in JEDs w.r.t. SADs:  Smaller surface densities  Higher accretion velocities Much slower protoplanet migration Dead zone moving outwards Surface density vs radius (fixed accretion rate) (Combet & Ferreira 08)

4. June 08 MRI Transport properties 4 Points of contention LPP 94a: advection of flux by the disk conflicts with ejection requirement:  Relevance of initial conditions (B r ~B z on t d due to collapse) ? LPP94b, Cao & Spruit 02: ejection instability:  Quenched by magnetic pressure (Königl 04) ? B r + << B z B r + ~B z t   t   P m ~ or > R/H  P m ~ 1 for JEDs ejection opening pressure

5. June 08 MRI Transport properties 5 What do we want to know ? Turbulent resistivity = correlation between the emf and J :  Is it present ?  If so, why and what is the resulting « η »? Weapons:  3D MHD shearing box simulations : r:φ:z=2:4:1 128x128x64 Re=1600 Pm=1  Linear analysis of axisymmetric modes

6. June 08 MRI Transport properties 6 3D simulations: Methodology « shearing box » Image Simulation box α η = function of dimensionless parameters : β, ε (and Re, Rm…) Alternatively: B = B 0 e z + ΔB 0 e φ or B = B 0 e φ + ΔB 0 e φ

7. June 08 MRI Transport properties 7 3D simulations: Current and emf correlation Remarkable linear correlation Unexpected off-diagonal turbulent resistivity component at least in one configuration B, ΔB along z B along z ΔB along φ

8. June 08 MRI Transport properties 8 3D simulations: Anisotropy (diag. component) and correlations Collapse of β and ε dependence ? ? Anisotropy ~ 2 to 4 Varying efficiency of transport with vertical or azimuth. mean field

9. June 08 MRI Transport properties 9 Linear analysis Problem formulation Interest  recurrence of channel mode in 3D simulations Axisymmetric modes, incompressible motions  reduced to second order equation for the poloidal velocity stream function Analytic solution through an expansion in ε = ΔB/B (B, ΔB // z) ε = 0.3 channel mode

10. June 08 MRI Transport properties 10 Linear analysis Resistive transport ε = 0.3, channel mode Wrong sign ! Only the channel mode has some qualitative bearing on the problem Why is φ so large ? Unexpected unless direct backreaction on the MRI driving process Wrong behavior ε = 0.3, k x =1 mode Correlation preserved but wrong magnitude channel mode Nice, but…

11. June 08 MRI Transport properties 11 Linear transport : how ? φ = ~ Correlation between fundamental channel mode and its deviations ε = 0.3, channel mode Uz1Br0Uz1Br0 Bz1Ur0Bz1Ur0

12. June 08 MRI Transport properties 12 Linear transport : why ? Origin of U r 0 B z 1 correlation

13. June 08 MRI Transport properties 13 Summary Efficient resistive transport:  Large turbulent diffusion :   ~ a few 10 -2 to 0.1  Smaller than viscous diffusion (unless mean B φ )  Radial diffusion of B  ~ 3 to 4 times radial diffusion of B z Implications for jet-emitting disks:  Anisotropy in the right direction but   about an order of magnitude too small Open issues :  What of more realistic configurations (vertical stratification) ?  Role of physical dissipation (P m ) ? 1/88