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MRI-driven turbulent resistivity

MRI-driven turbulent resistivity. Pierre-Yves Longaretti (LAOG) Geoffroy Lesur (DAMTP). Turbulent resistivity and ejection. Angular momentum. Angular momentum. Standard accretion disk (non-existent or weak ejection): Outwards transport. Requires « anomalous viscosity »

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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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