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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