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

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

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

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

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 jet star BH disk wind magnetic lines Theoretical issues Highly nonlinear problem Analytic stationary solutions Numerical experiments Physics to test Role of ordered magnetic fields Role of ordered magnetic fields (and currents)

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… )

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

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 ~ v φ,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) poloidal velocity toroidal velocity

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

FLASH  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 NUMERICAL APPROACH

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

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

Low resistivity EVOLUTION OF THE SYSTEM

Mid resistivity

High resistivity

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

ACCELERATION   Lorentz force changes sign at the disk upper boundary  Both J r and –J θ change sign at the disk surface  Magnetic pressure associated with B r seems to be dominant   Disk is supported by thermal pressure against gravity and magnetic pinch  Lorentz force accelerates the outflow

ANGULAR MOMENTUM TRANSPORT   Toroidal Lorentz forces transfer angular momentum from the disk to the outflow  J r and J z changes sign at the disk surface  Outflow centrifugally accelerated

COLLIMATION   Lorentz forces collimate the ouflow  Magnetic pressure pushes outwards  Magnetic “hoop stress” collimates

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

ENERGY FLUXES   Asymptotically kinetic flux ~ Poynting flux  Poynting flux: on the disk scale the - v θ B θ B z component dominates (extraction of angular momentum) on the jet scale the B θ 2 v z component dominates (advection)

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

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