MHD JET MHD JET ACCELERATION AMR ACCELERATION AMR

SIMULATIONSSIMULATIONS Claudio Zanni, Attilio Ferrari, Silvano Massaglia

Università di Torino

in collaboration withGianluigi Bodo, Paola Rossi

Osservatorio Astronomico di TorinoTimur Linde, Robert Rosner

University of Chicago

AGN & YSOAGN & 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 The jet/disk paradigmparadigm

• CompositionComposition: ion/electron and/or electron/positron plasma and/or Poynting flux

• Driving force 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 mass flow rate and jet velocity connected with disk velocity connected with disk accretion rateaccretion rate and other physical parameters ?

Ingredients of modelsIngredients 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

starBH

disk

wind

magnetic lines

Theoretical Theoretical issues issues • Highly nonlinear problem• Analytic stationary solutions• Numerical experiments• Physics to test

Role of ordered Role of ordered magnetic fieldsmagnetic fields (and currents)

MechanismsMechanisms– 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 windsMHD 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

0)/1( BvE c

zBz

B

zz

P

Bv

4

1

8

1 2

zv

2/1000 /)(),(),()(',),( rGMfgfrr vr

• 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)

poloidal velocity

toroidal velocity

NONLINEAR NONLINEAR MODELLINGMODELLING

• Evolution towards a stationary solution

• Dynamical timescales

– YSO days

– AGN days

• Stability

• Role of dissipation – “thermally loaded” jets (Casse & Ferreira 2000)

k

t

2

0

2/1

2/30

0/

AU1.0/8.10

sunMM

rt

sunSchw M

M

r

rt

8

2/3

00 1010

3

Use of an adaptive mesh code to simulate longer spatial and temporal scales – FLASHFLASH (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 APPROACHNUMERICAL 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

""0.1

"mid"5.0

high""1

nessdisk thick1.0

/exp

212

2

2

0

4

low

rH

HzcH

t

pE

pEt

E

pt

t

Alfven

BBuuBB

BBuu

BBguBBuuBB

gBBIBB

uuu

u

INITIAL CONDITIONSINITIAL CONDITIONSOutflow

Ref

lect

ive

Ref

lect

ive

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):

33.32

2

z

diskplasma B

p

3/51

1

01.011

5.0

20

20

1

12

5.0

00

diskdisk

k

sdisk

k

p

v

c

rR

r

rvv “Keplerian” disk ε

~ 1

41

20

21

1

101

4.01

atm

k

saatm

p

v

ca

Low resistivity

EVOLUTION OF THE EVOLUTION OF THE SYSTEMSYSTEM

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

ACCELERATIONACCELERATION

Lorentz force changes sign at the disk upper boundary

Both Jr and –Jθ change 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

ANGULAR MOMENTUM ANGULAR MOMENTUM TRANSPORTTRANSPORT

Toroidal Lorentz forces transfer angular momentum from the disk to the outflow

Jr and Jz changes sign at the disk surface

Outflow centrifugally accelerated

COLLIMATIONCOLLIMATION

Lorentz forces collimate the ouflow

Magnetic pressure pushes outwards

Magnetic “hoop stress” collimates

High resistivityMid resistivityLow resistivity

ASYMPTOTIC VELOCITIESASYMPTOTIC VELOCITIES

Fast

Alfvèn

Super-Alfvenic and super-fast-magnetosonic flow

Asymptotic speed Keplerian speed

ENERGY FLUXESENERGY FLUXES

Asymptotically kinetic flux ~ Poynting flux

Poynting flux: • on the disk scale the - vθBθBz component dominates (extraction of angular momentum)• on the jet scale the Bθ

2vz component dominates (advection)

rrrzr BvBBvvBB 22flux Poynting

zvv2

2

1flux kinetic

Mass outflow / inflow Mass outflow / inflow rate ratiorate ratio

High resistivityMid resistivityLow resistivity

SUMMARIZING …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