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Accretion-ejection and magnetic star-disk interaction: a numerical perspective

Accretion-ejection and magnetic star-disk interaction: a numerical perspective. Claudio Zanni Laboratoire d’Astrophysique de Grenoble. 5 th JETSET School January 8 th – 12 th 2008 Galway - Ireland. Outline. Observational evidences supporting these scenarios:

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Accretion-ejection and magnetic star-disk interaction: a numerical perspective

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  1. Accretion-ejection and magnetic star-disk interaction: a numerical perspective Claudio Zanni Laboratoire d’Astrophysique de Grenoble 5th JETSET School January 8th – 12th 2008 Galway - Ireland

  2. Outline • Observational evidences supporting these scenarios: • - accretion-ejection (disk-winds) (45 min) • - magnetically controlled accretion (45 min) • What analytical models can do? • - pros: exact solutions, analysis of the parameter space • - cons: stationarity, self-similarity • What numerical simulations can do? • - pros: time-dependent, no self-similarity, 3D • - cons: can you trust them?

  3. Ejection: jets from YSO • They are directly observed ! • - dynamics (speed, rotation) • - thermodynamics (temperature, • chemistry) • … but not close enough to the • central source to give direct • informations on their origin

  4. Proposed scenarios Extended disk wind X-wind Stellar wind • Succesful models require large-scale magnetic fields with • plasma flowing along the magnetic surfaces: • -extended disk wind: Bz distributed on a large radial extension • -X-wind: Bz exists only in a tiny region around the magnetopause • -stellar wind: opened magnetic field anchored on the star

  5. Why extended disk winds are important ? Ferreira, Dougados, Cabrit (2006) For a given footpoint r0 relation between toroidal and poloidal speed: • Extended disc winds, X-winds, and stellar winds occupy distinct regions in the plane Only extended disk winds give results consistent with observations

  6. Ejection: how it works?The magneto-centrifugal mechanism • At Alfven surface matter inertia • bends the lines and field gets • wound up • Toroidal magnetic field controls • collimation (magnetic “hoop • stress”) and pushes the outflow • Magnetic field lines frozen in a disk • rotating at Keplerian rate k • “Bead on the wire” accelerated with • constant k if fieldline is open •  > 60o • Angular momentum extraction •  accretion

  7. Framework: MHD • Conservation of: • Mass • Momentum • Energy • Induction equation: with • Solenoidality of the field:

  8. Assumptions: • - stationarity • - axisymmetry • - self-similarity (Radially self-similar solution) Analytical solutions (1) • Invariants: • Specific angular momentum • (lever arm) • Mass loading • Field angular velocity • Entropy • Energy (Bernoulli equation)

  9. Analytical solutions (2) • An entire class of radially self-similar • MHD solutions can be constructed • (Vlahakis et al. 1998, see Rammos’ poster) • Examples (Contopoulos & Lovelace 1994): Bz/ r -1.2 Bz/ r -0.98 Bz/ r -1.1 • Blandford & Payne (1982) • - Trans-Alfvenic solution • - Bz/ r -5/4

  10. Numerical solutions • Why time-dependent simulations? • - Test the analytical models • - Go beyond self-similarity • - time-dependent  variability • - 3D models – stability • - combine different components (stellar wind)

  11. Ejection: initial conditions Keplerian rotation + injection boundary Initial analytical solution (one ore more superposed) + boundary conditions (Gracia et al. 2006, Matsakos et al. 2008, and see Stute’s poster) B) A) Boundary conditions (rotation/injection) + non-rotating magnetized corona (Ouyed & Pudritz 1997)

  12. Ejection: boundary conditions • Injection boundary: number of incoming characteristics = number of fixed • variables. Other variables must be free to evolve. • Outer boundaries: even if the flow is • super-fastmagnetosonic, pay attention • at the direction of the Mach cones • (  below or beyond the separatrix) Example: “outflow” condition on B at rout Artificial collimating effect Ustyugova et al. (1999)

  13. Testing stationary models (1) • Axisymmetric MHD invariants • are almost constant Ustyugova et al. (1999) Ustyugova et al. (1999) • Acceleration mechanism IS • magneto-centrifugal: dominant • forces are centrifugal (C) and • Lorentz (M)

  14. Testing stationary models (2) • MHD invariants Matsakos et al. (2008) Matsakos et al. (2008) • Wave-structure and • characteristic surfaces of • analytical solutions are • recovered

  15. Non-stationarity / variability • When the outflow is too • mass-loaded, the flow • “lags behind” the • Keplerian rotation and falls • towards the center • (Anderson et al. 2004) 1) • “Overdetermined” • boundary conditions • force the propagation of • MHD shocks along the jet • (Ouyed & Pudritz 1997b) 2)

  16. 3D simulations • Some technical issues: • How to put a circle inside a • square: smoothly reduce the • rotation to zero between r0 and rmax • Ensure r v = 0 and r B = 0 in • the injection boundary Ouyed, Clarke & Pudritz (2003)

  17. 3D simulations – stability (1) • “Corescrew” or wobbling solutions are • found which are not destroyed by the • non-axisymmetric (m=1) modes • A self-regulatory mechanism is found • which maintains the flow sub-Alfvenic • and therefore more stable (Ray 1981, • Hardee & Rosen 1999) Ouyed, Clarke & Pudritz (2003)

  18. 3D simulations – stability (2) • Asymmetric outflow stabilized by • a (light) fast- moving outflow • near the axis with a poloidally • dominated magnetic field. Anderson et al. (2006)

  19. … what about accretion? • Additional elements must be taken into account … • - Accretion (mass conservation) • - Disk vertical equilibrium (mass loading) • - Field diffusion

  20. … what about accretion? • Mass conservation: : ejection efficiency • Disk vertical equilibrium: Only thermal pressure can uplift matter at the disk surface • Magnetic field diffusion: Diffusion must counteract advection of the footpoints of the fieldlines

  21. Analytical self-similar solutions Radially self-similar solution now depends on the disk parameters: magnetization disk thickness Ferreira (1997) magnetic diffusion • Important results: • - jet parameter space strongly reduced • - field must be around equipartition (» 1) and m» 1 (or strongly anisotropic)

  22. What simulations can do? Zanni et al. (2007) Casse & Keppens (2004) … And give a look to Tzeferacos’ poster

  23. Initial-boundary conditions Self-similar Keplerian disk in equilibrium with gravity, pressure gradients and Lorentz forces. Disk parameters: Resolution: FLASH – AMR / 7 levels of refinement / 512x1536 eq. resolution

  24. Resistivity parameter m = 1 Smooth, trans-Alfvenic, trans-fastmagnetosonic outflow is accelerated

  25. … as seen in 3D

  26. Mass loading - acceleration P G M • Lorentz toroidal force changes • sign at the disk surface • Magnetic field extracts angolar • momentum from the disk and • transfer to the outflow • Thermal pressure gradients supports • the disk against gravity and magnetic • pinch • Pressure provides the mass loading • and then Lorentz forces accelerate • the outflow

  27. Current circuits - collimation Lorentz force (JxB) perpendicular to electric current circuits (rB = const) Outflow collimated only towards the axis. Outer part still uncollimated Zanni et al. (2007) Ferreira (1997)

  28. Axisymmetric MHD invariants r0 = 2 r0 = 8 r0 = 4 r0 = 4 r0 = 2 r0 = 8 Flow perpendicular to the fieldlines in the disk and parallel in the jet (resistive – ideal MHD transition) Weber & Davis (1967) Inner fieldlines more stationary Radial dependency of  and k

  29. Resistivity parameter m = 0.1 Footpoints of the fieldline advected towards the central object Differential rotation along the fieldlines triggers a “magnetic tower”

  30. … as seen in 3D

  31. Parameter study - diagnostics Increasing m Increasing m • Ejection efficiencies consistent • with observations (Cabrit 2002) • Terminal speeds around 1-2 times • the escape velocity ! Simulated spatial scale too small to check rotation ! But » 9 in the outer fieldlines of the outflow (see Ferreira et al. 2006)

  32. Is everything ok? Despite having the same disk parameters (» 0.6, m» 1, » 0.1), analytical and numerical solutions have different jet parameters Numerical: - k » 0.1 - 0.3 -» 4 - 9 -» 0.09 Analytical: - k » 2£ 10-2 -» 35 -» 0.01 Analytical solution less mass loaded and faster ( )

  33. A physical reason Zanni et al. (2007) Casse & Keppens (2004) • No analytical trans-Alfvenic solutions found when the electric current • enters the surface of the disk (mass loading too high) • Inner boundary forces the current to enter at the surface of the disk in • its inner radii. The mass outflow is strongly enhanced in this region

  34. A numerical reason Casse & Ferreira (2000) • Density jump at the disk surface • under-resolved in current • simulations • Numerical solutions closer to • “warm” analytical models. • Dissipation at the disk surface • With a resolution 4 times lower it is • possible to find stationary solutions • even with m» 0.1 • Radial numerical diffusion of Bz

  35. Perspectives • Parameter space analysis • - Magnetization (see Tzeferacos’ poster) • - Transition between jet emitting and non-emitting • disks (standard accretion disk) • - The missing link between the small and the large scale • - Interaction with an inner component (Meliani et al. 2006) • Go to 3D …

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