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Cosmic Magnetic Fields: Helicity Injection bySupermassive Black Holes, Galaxies and
Laboratory Experiments
Hui Li 李暉Los Alamos National Laboratory
and a member of Center for Magnetic Self-Organization
Collaborators:
M. Nakamura, S. Li, S. Colgate, J. Finn, K. Fowler
Overview of astrophysical observations of cosmic magnetic fields Global Electro-Magnetic model for astrophysical jets Synergy between astrophysics and laboratory plasma physics
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Optical X-ray “sound ripples”
radio galaxy
Fabian et al.
Perseus Cluster
Perseus A
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Black Hole Accretion Disk
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Hydra A
(Taylor & Perley’93; Colgate & Li’00)
70 kpc
EnergyandFlux
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QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.Black hole mass3.6 million solar
Masses(Genzel et al.)
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Our own backyardGalactic Center
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Ubiquity of Supermassive Black Holes
(Kormendy et al. 2001)
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Cosmic Energy Flow
Gravity
Stars, galaxies, galaxy clusters,
large scale shocks, etc.
IGM
“Feedback”MechanicalChemicalThermal
Non-ThermalMagnetic
collapse
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Cosmic Energy Flow
Gravity
Stars, galaxies, galaxy clusters,
large scale shocks, etc.
IGM
“Feedback”MechanicalChemicalThermal
Non-ThermalMagnetic
collapse
Black Holes
RadiationKinetic WindsMagnetic fields
108 Msun 1062 ergs
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High z sources
GiantsCluster sources
(Kronberg, Dufton, Li, Colgate’02)
Magnetic Energy of Radio Lobes
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Modeling Jets/Lobes
1014
(solar system)
SCALES
1019 (10pc)
1022-23
(10 kpc)1024
(300 kpc)1025 cm(~3 Mpc)
Black holeDisk aroundblack hole
Host galaxy
Radio lobesMix with IGM?
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Kinetically Dominated vs. Magnetically Dominated
e.g., Norman et al., Clark et al. in 80’s
Jones & Ryu et al., Ferrari et al. in 90’s
Many, many, others
Kinetic Energy Dominated Regime:
v2 >> B2
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Problem Set-up
radius
R-3/2
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Static Limit(vinj << vexpan)
Steps:a. Arcade on disk, (r,z);b. Specify twist profile, ();c. Bounded by pressure, p();d. Find sequences of equilibrium, with increasing toroidal flux,
energy, and helicity; Black Hole
Accretion Disk
€
J × B = ∇p
Δ*ψ + d(H 2 /2) /dψ + 4πr2 dP /dψ = 0
p(ψ) = pc 1−ψ
ψmax
⎛
⎝ ⎜
⎞
⎠ ⎟
2 ⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
(Li et al. 2001)
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Helix Expansion (Li et al. 2001)
• Force-free fields expand 600 away from the axis;
• Radial expansion of outer fields are prevented by the plasma pressure.
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Squeezing Flux Tubes(Parker)
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Twist Re-distribution --- Collimation
Added twists are concentrated around the axis resulting in collimation.
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Radius
q = rBz/B
B
Bz
Br
“RFP in the sky?”
)( / :ratioFlux
/ :Helicity
/ :Energy
1/
max2
max22
H
W
z
B
>>∝∝
∝
μλμλμλ
φ
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disk
Viewing it as a magnetic system…..Key Model Ingredients
Poloidal flux: (r,z) Electric field and voltage:
(-vBz) dl = V(r,z) Injection duration: tinj
Poloidal current: unspecified Iz(r,z) Mag. energy injection rate: dEmag/dt = Iz V - Ploss
Losses: radiation, pdV, heating, kinetic flows, CRs, etc. Expansion: Iz(r,t), (r,t), and Ploss(r,t).
BH
Li et al. (2006)
€
∫
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Laboratory Plasma Experiments (Bellan et al.)
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“Gun” Parameter
€
λ =I pol
Ψpol
r0
Gcm2) I ~ 1019-20 Amperes r0 ~ 1015 cm (disk)
λ ~ 0.1-10
Gcm2) I ~ 105 Amperes r0 ~ 10 cm (gun)
λ ~ 0.1-1
Supermassive Black Hole: Caltech’s Experiment:
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Ipol
r
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€
magnetic field injection :
Ψinj = r2 exp(−r2 − k2z2 )
Bφ inj = αΨinj / r,
∂B
∂t= Binj(r, z)• γ(t)
Li et al. (2006)
compresses the inner fluxes along the equatorial plane. “squeezes” the flux vertically out. expands the outer fluxes outwards. no azimuthal rotation.
Consequences:
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“Ideal” MHD Simulations
€
∂∂t
+∇ • ρv( ) = ˙ ρ inj
∂(ρv)
∂t+∇ • ρvv+ Pg +
B2
2− BB
⎡
⎣ ⎢
⎤
⎦ ⎥= −ρ∇Φ
∂E
∂t+∇ • E + Pg +
B2
2
⎛
⎝ ⎜
⎞
⎠ ⎟v− v• B( )B
⎡
⎣ ⎢
⎤
⎦ ⎥= −ρv• ∇Φ + ˙ E inj
E =1
2ρv2 +
Pg
γ −1+
B2
2
∂B
∂t=∇× v× B( ) + ˙ B inj ,
S. Li & H. Li (2003, 2006)
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“Ideal” 3D MHD Simulations
Spherical isothermal background in density
and pressure
T=8 keV, c = 3x10-3 cm-3,
rc=150 kpc;
Injection: 3x107 yrs, 3x1059 ergs
320x320x320 simulation
(700 kpc)3
Mass injection: ~ 5 Msun/yr within central 35
kpc
€
=0
1+(r / rc )2[ ]
β
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log(density)
Nakamura, Li & Li (2006)
Poloidal Jz
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Hydro-shock
Tangentialdiscontinuity
Slow-wave
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“flux core: & Iz”(“helix/jet”)
toroidal B from Iz (“lobes”)
confinement(B2
/8 ~ pgas)
Jz @ t = 10
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Lobes: Pressure Confinement and Nearly Force-Free
€
−∂p
∂r−
∂
∂r
Bφ2 + Bz
2
2
⎛
⎝ ⎜
⎞
⎠ ⎟−
Bφ2
r− ρ
∂Φ
∂r≈ 0
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QuickTime™ and aTIFF (LZW) decompressor
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Time
Toroidal Flux
Poloidal Fluxz=0
Poloidal Fluxz=6
Poloidal Current Iz
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log(density)
Nakamura, Li & Li (2006)
Poloidal Jz
Stability: with initial perturbations
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Nakamura, Li & Li (2006)
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Kink Unstable (m=1 mode)
€
VA = 8 − 9, Lkink = 2 − 4, τ A−1 = 2.0 − 4.5
→ Im(ω) =d f (m,k)
2
dt≈ O τ A
−1( ) Nakamura & Li (2006)
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Jz = 1.5 Jz = -0.5 Combined
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KH Stable
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Perseus A426
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M87
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Summary on Jet/Lobe Modeling
Lobes are magnetically dominated and are confined by the surrounding pressure.
Lobes form via background density/pressure changes, accompanied by flux conversion.
Helix is kink-unstable, though the overall structure is not completely destroyed.
Lobes are far from relaxation.
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Why Plasma Astrophysics?Common physical processes:
dynamo (magnetic field generation) and flux-conversion dynamo ideal and resistive MHD stabilities magnetic reconnection flow generation angular momentum transport particle acceleration
Common numerical tools: ideal and resistive MHD codes PIC gyrokinetic, hybrid, etc.
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Laboratory Magnetized Plasma Astrophysics
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You et al. 2005Hsu & Bellan’03
Laboratory Plasma Experiments for Understanding the Formation and Collimation of Jets
Lebedev et al. 2005
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IndividualGalaxy
GalaxyClusters
Super-Galactic Filaments
The MagnetizedUniverse (?)
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Kronberg et al’03
Farady Rotation Measure
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Thank you!