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Models of Turbulent Angular Momentum Transport Beyond the  Parameterization

Models of Turbulent Angular Momentum Transport Beyond the  Parameterization. Martin Pessah Institute for Advanced Study. C.K. Chan - ITC, Harvard D. Psaltis - University. of Arizona. Workshop on Saturation and Transport Properties of MRI-Driven Turbulence - IAS- June 16, 2008.

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Models of Turbulent Angular Momentum Transport Beyond the  Parameterization

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  1. Models of Turbulent Angular Momentum Transport Beyond the  Parameterization Martin Pessah Institute for Advanced Study C.K. Chan - ITC, Harvard D. Psaltis - University. of Arizona Workshop on Saturation and Transport Properties of MRI-Driven Turbulence - IAS- June 16, 2008

  2. Timescales and Lengthscales in Accretion Disks Hubble Time 1Gyr BH Growth Disk Spectrum Mean Field Models Inside Horizon BLR Viscous BH Variability Saturation 1yr Orbital Numerical Simulations 1sec 0.1AU 1AU 1000AU 107Mo

  3. Standard Accretion Disk Model Shakura & Sunyaev (‘70s) Angular momentum transport: Turbulence and magnetic fields This prescription dictates the structure of the accretion disk Angular momentum transport in turbulent media

  4. Standard Disk MRI Disk MRI

  5. The need to go beyond -viscosity Issues… *Dynamics:is not constant *Causality:Information propagates across sonic points (Stress reacts instantly to changes in the flow) *Stability criterion:Standard model works always (Stresses only for MRI-unstable disks) *”Viscosity”:MRI does not behave like Newtonian viscosity

  6. Long-Term Evolution of MRI large scales small scales MRI drives MHD turbulence at a well defined scale which depends only on the magnetic field and the shear

  7. MRI Accretion Disks in Fourier Space Mode interactions “Stress Power” Parasitic Instabilities k Parker MRI Dissipation small scales large scales (Talk by C.K. Chan later today)

  8. The Closure Problem in MHD Turbulence We can derive an equation for angular momentum conservation which involves 2nd order correlations… We can derive equations for 2nd order correlations… … but they involve 3rd order correlations… We can derive equations for 3nd order correlations… Need for a CLOSURE model beyond alpha!! (Closure models with no mean fields; papers by Kato et al 90’s; Ogilvie 2003)

  9. Stress Modeling with No Mean Fields Kato & Yoshizawa, 1995 Pressure-strain tensor, tends to isotropize the turbulence

  10. Stress Modeling with No Mean Fields Ogilvie 2003 C1, C5 energy dissip. C2 return to isotropy in decaying turbulence C3, C4 energy transfer

  11. A Model for Turbulent MRI-driven Stresses New correlation drives the growth of Reynolds & Maxwell stresses

  12. W in the Turbulent State -Wr W tensor dynamically important! -Maxwell Reynolds

  13. Calibration of MRI Saturation with Simulations Pessah, Chan, & Psaltis, 2006a =0.3 The parameter  controls the ratio between Reynolds & Maxwell stresses The model produces initial exponential growth and leads to stresses with ratios in agreement with the saturated regime

  14. Calibration of MRI Saturation with Simulations Pessah, Chan, & Psaltis, 2006b =11.3 Hawley et al ‘95 The parameter  controls the level at which the magnetic energy saturates A physically motivated model for angular momentum transport Keplerian disks that incorporates the MRI

  15. A Local Model for Angular Momentum Transport in Turbulent Magnetized Disks Shakura & Sunyaev, 1973 Pessah, Chan, & Psaltis, 2008 Shakura & Sunyaev, 1973 Pessah, Chan, & Psaltis, 2006b Pessah, Chan, & Psaltis, 2008 Shakura & Sunyaev, 1973 Pessah, Chan, & Psaltis, 2006b Pessah, Chan, & Psaltis, 2008 Pessah, Chan, & Psaltis, 2006b Simulations by Hawley et al. 1995 Pessah, Chan, & Psaltis, 2006b A model for MRI-driven angular momentum transport in agreement with numerical simulations Simulations by Hawley et al. 1995

  16. Scaling in MRI Simulations Pessah, Chan, & Psaltis, 2007; Sano et al. 2004 Deeper understanding of scalings? Non-zero Bz (few % Beq) Magnetic pressure must be important in setting H Spectral hardening (Blaes et al. 2006) (Talk by S. Fromang later today)

  17. Viscous, Resistive MRI Pm>>1 Pm>>1 Pm<<1 Pm<<1 Pessah & Chan, 2008 (Various limits studied by Sano et al., Lesaffre &Balbus, Lesur & Longaretti, … )

  18. Viscous, Resistive MRI: Stresses & Energy Pm>>1 Pm<<1 Pm>>1 Pm<<1 * Lowest ratio magnetic-to-kinetic: Ideal MHD * Linear MRI effective at low/high Pm as long as Re large * Need higher Re to drive MHD turbulence at low Pm (Lesur & Longaretti, 2007; Fromang et al., 2007)

  19. Viscous, Resistive MRI Modes Pm=1

  20. Viscous, Resistive MRI Modes Ideal MHD kh Parasitic Instabilities sensitive to viscosity and resistivity (Goodman & Xu, 1994)

  21. Viscous, Resistive MRI Modes Pessah & Chan, 2008 Pm>>1 Pm<<1

  22. Viscous, Resistive Parasitic Instabilities 1ow Pm high Pm PRELIMINARY (with J. Goodman, in prep.) Parasitic Instabilities seem to be weaker at high Pm Hint for difficulties to drive MRI at low Pm? Can the destruction of primary MRI modes by parasitic instabilities explain (Re, Pm) dependencies?

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