MHD JET ACCELERATION AMR SIMULATIONS

1. MHD JET ACCELERATION AMR SIMULATIONS Claudio Zanni, Attilio Ferrari, Silvano Massaglia Università di Torino in collaboration with Gianluigi Bodo, Paola Rossi Osservatorio Astronomico di Torino Timur Linde, Robert Rosner University of Chicago

2. AGN & YSO • Highly collimated • supersonic/relativistic • jets from small regions • Jet-disk connection

3. The jet/disk paradigm AGN Central black hole or star Subsonic/supersonic inflow Supersonic (relativistic) outflow

4. Composition: ion/electron and/or electron/positron plasma and/or Poynting flux • Driving force pushing matter into winds and jets ? • Thermal gas pressure gradient • Radiation pressure • Magnetic pressure • Electrodynamic Lorentz force • How are mass flow rate and jet velocity connected with disk accretion rate and other physical parameters ?

5. jet wind star BH disk magnetic lines Ingredients of models • Central object: star or black hole • Accretion disk • Wind • Jet • Magnetic fields: turbulent in disk, ordered in magnetosphere • Boundary layer disk-star/BH • Theoretical issues • Highly nonlinear problem • Analytic stationary solutions • Numerical experiments • Physics to test Role of ordered magnetic fields (and currents)

6. Mechanisms • Twin-exhaust scheme (Blandford & Rees 1972) • Radiation pressure in accretion funnels (FRT 1985) • Electrodynamic effects in accretion funnels and Poynting flux jets (Lovelace 1976, Blandford 1976) • Magneto-centrifugal acceleration (Blandford & Payne 1982) • Simulations: magnetic sweeping pinch, etc. (Uchida & Shibata 1985) • … and many more (see Hawley, Keppens, Kato, Krasnopolski…)

7. MHD winds • Blandford & Payne (1982) include inertia and assume MHD conditions • Stationary axisymmetric MHD flow • The transfield equation • Self-similar analysis • Solutions scale with spherical radius along a given direction • Magneto-centrifugal acceleration • A wind is launched when the inclination angle of magnetic lines on the disk is < 60° • After launch the flow is dominated by the toroidal magnetic field imposed by rotation • Collimation along the magnetic axis

8. poloidal velocity • Close to disk: • Centrifugal acceleration drive the gas out • Acceleration by magnetic pressure • Force-free type magnetic fields • Far away from disk: • Acceleration by Lorentz force • Asymptotic speed ~ vφ,disk • Field predominantly toroidal • Narrow jets in balance between hoop stress (inward) and magnetic pressure (outward) • Two super-Alfvénic flows: • Poynting flux dominated • Matter dominated • Stability ? • Extension to relativistic flows (Li, Chiueh, Begelman 1992) toroidal velocity

9. NONLINEAR MODELLING • Evolution towards a stationary solution • Dynamical timescales • YSO days • AGN days • Stability • Role of dissipation – “thermally loaded” jets (Casse & Ferreira 2000)

10. NUMERICAL APPROACH • Use of an adaptive mesh code to simulate longer spatial and temporal scales – FLASH (Univ.of Chicago) • Implementation of the required physics and modules: geometry, resistivity, semi-relativistic module • Godunov type numerical scheme: characteristics linear reconstruction, HLLE solver, second order Hancock predictor • 2.5 ( 3) dimensions - viscosity - resistivity

11. In this work: • High resolution • Consistent treatment of disk and jet starting from equilibrium (thick disk, Abramowicz 1980) • No forcing of accretion, starting with an ordered poloidal magnetic field aligned with the rotation axis • Long time scales of integration to reach steady-state configurations • Test physical parameters

13. INITIAL CONDITIONS Outflow Outflow Reflective Disk + Inflow Reflective Hydrostatic + Inflow Reflective • AMR – 6 levels of refinement with 8x8 cells blocks 256 x 768 equivalent resolution • Disk: “Keplerian” disk ε~ 1 • Atmosphere: • Magnetic field (at the disk midplane):

14. EVOLUTION OF THE SYSTEM Low resistivity

15. Mid resistivity

16. High resistivity

17. Extraction of angular momentum by torsional Alfvén waves starts accretion (the system is steady without magnetic field) • Late stages reach a quasi-steady mass and angular momentum ejection • The end results are similar for all resistivity values

18. ACCELERATION • Lorentz force changes sign at the disk upper boundary • Both Jr and –Jθchange sign at the disk surface • Magnetic pressure associated with Br seems to be dominant • Disk is supported by thermal pressure against gravity and magnetic pinch • Lorentz force accelerates the outflow

19. ANGULAR MOMENTUM TRANSPORT • Toroidal Lorentz forces transfer angular momentum from the disk to the outflow • Jr and Jz changes sign at the disk surface • Outflow centrifugally accelerated

20. COLLIMATION • Lorentz forces collimate the ouflow • Magnetic pressure pushes outwards • Magnetic “hoop stress” collimates

21. Fast Alfvèn High resistivity Mid resistivity Low resistivity ASYMPTOTIC VELOCITIES Asymptotic speed  Keplerian speed Super-Alfvenic and super-fast-magnetosonic flow

22. Asymptotically kinetic flux ~ Poynting flux • Poynting flux: • on the disk scale the - vθBθBz component dominates (extraction of angular momentum) • on the jet scale the Bθ2vz component dominates (advection) ENERGY FLUXES

23. Mass outflow / inflow rate ratio High resistivity Mid resistivity Low resistivity

24. SUMMARIZING … • We were able to produce a higly collimated jet starting from a Keplerian disk without forcing accretion and treating the accretion disk consistently • The disk is supported by thermal pressure while gravity and magnetic field pinch it • Accretion and jet acceleration are driven by the magnetic field that also collimates the outflow (magnetic “hoop stress”) • The outflow reaches a steady mass flux (knots ?) • The outflow reaches super-fast magnetosonic speeds and has comparable kinetic and Poynting fluxes • Resistivity slows down the extraction of angular momentum and defines the time of evolution to steady state