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MRI-driven turbulent resistivity

Investigating the role of turbulent resistivity and ejection processes in magnetorotational instability-driven accretion disks. Exploring differences in properties between jet-emitting disks (JEDs) and standard accretion disks (SADs). Utilizing 3D MHD simulations to study resistive transport and correlation between current and electromotive force. Analyzing resistive transport in various configurations and addressing open issues in the field.

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MRI-driven turbulent resistivity

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

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

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

  4. Points of contention opening Br+ << Bz Br+~Bz tn ~ th  Pm ~ or > R/H  Pm ~ 1 for JEDs ejection pressure • LPP 94a: advection of flux by the disk conflicts with ejection requirement: • Relevance of initial conditions (Br~Bz on td due to collapse) ? • LPP94b, Cao & Spruit 02: ejection instability: • Quenched by magnetic pressure (Königl 04) ? 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 MRI Transport properties

  6. « shearing box » Image Simulationbox Image 3D simulations:Methodology Alternatively: B = B0 ez + ΔB0 eφor B = B0 eφ + ΔB0 eφ αη = function of dimensionless parameters : β, ε(and Re, Rm…) MRI Transport properties

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

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

  9. Linear analysisProblem 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 MRI Transport properties

  10. Linear analysisResistive transport channel mode Nice, but… Correlation preserved but wrong magnitude Wrong sign ! ε = 0.3, channel mode ε = 0.3, kx =1 mode Only the channel mode has some qualitative bearing on the problem Why is < u x B >φso large ? Unexpected unless direct backreaction on the MRI driving process Wrong behavior MRI Transport properties

  11. Linear transport : how ? < U x B >φ = < UzBr – UrBz > ~ Correlation between fundamental channel mode and its deviations Uz1Br0 ε = 0.3, channel mode Bz1Ur0 MRI Transport properties

  12. Linear transport : why ?Origin of Ur0Bz1 correlation MRI Transport properties

  13. Summary • Efficient resistive transport: • Large turbulent diffusion :  ~ a few 10-2 to 0.1 • Smaller than viscous diffusion (unless mean Bφ ) • Radial diffusion of B ~ 3 to 4 times radial diffusion of Bz • 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 (Pm ) ? MRI Transport properties 1/8 8

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