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-OrganizationCollaborators:

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

Optical X-ray “sound ripples”

radio galaxy

Fabian et al.

Perseus Cluster

Perseus A

Black Hole Accretion Disk

Hydra A

(Taylor & Perley’93; Colgate & Li’00)

70 kpc

EnergyandFlux

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Masses(Genzel et al.)

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Our own backyardGalactic Center

Ubiquity of Supermassive Black Holes

(Kormendy et al. 2001)

Cosmic Energy FlowGravity

Stars, galaxies, galaxy clusters,

large scale shocks, etc.

IGM

“Feedback”MechanicalChemicalThermal

Non-ThermalMagnetic

collapse

Cosmic Energy FlowGravity

Stars, galaxies, galaxy clusters,

large scale shocks, etc.

IGM

“Feedback”MechanicalChemicalThermal

Non-ThermalMagnetic

collapse

Black Holes

RadiationKinetic WindsMagnetic fields

108 Msun 1062 ergs

High z sources

GiantsCluster sources

(Kronberg, Dufton, Li, Colgate’02)

Magnetic Energy of Radio Lobes

Modeling Jets/Lobes

1014

(solar system)

SCALES1019

(10pc)1022-23

(10 kpc)1024

(300 kpc)1025 cm(~3 Mpc)

Black holeDisk aroundblack hole

Host galaxyRadio lobes

Mix with IGM?

Kinetically Dominated vs. Magnetically Dominated

e.g., Norman et al., Clark et al. in 80’sJones & Ryu et al., Ferrari et al. in 90’s

Many, many, others

Kinetic Energy Dominated Regime: v2 >> B2

Problem Set-up

radius

R-3/2

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− ψψmax

⎛ ⎝ ⎜

⎞ ⎠ ⎟2 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

(Li et al. 2001)

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.

Squeezing Flux Tubes(Parker)

Twist Re-distribution --- Collimation

Added twists are concentrated around the axis resulting in collimation.

Radius

q = rBz/B

B

Bz

Br

“RFP in the sky?”

)( / :ratioFlux / :Helicity

/ :Energy

1/max

2

max22

H

W

z

B

>>∝∝

∝

μλμλ

μλ

φ

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)

€

∫

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

€

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:

“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 = 12

ρv2 +Pg

γ −1+ B2

2∂B∂t

=∇× v× B( ) + ˙ B inj ,

S. Li & H. Li (2003, 2006)

“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

log(density)

Nakamura, Li & Li (2006)

Poloidal Jz

Hydro-shock

Tangentialdiscontinuity

Slow-wave

“flux core: & Iz”(“helix/jet”)

toroidal B from Iz (“lobes”)

confinement(B2

/8 ~ pgas)

Jz @ t = 10

Lobes: Pressure Confinement and Nearly Force-Free

€

−∂p∂r

− ∂∂r

Bφ2 + Bz

2

2

⎛

⎝ ⎜

⎞

⎠ ⎟−

Bφ2

r− ρ ∂Φ

∂r≈ 0

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Time

Toroidal Flux

Poloidal Fluxz=0

Poloidal Fluxz=6

Poloidal Current Iz

log(density)

Nakamura, Li & Li (2006)

Poloidal Jz

Stability: with initial perturbations

Nakamura, Li & Li (2006)

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Kink Unstable (m=1 mode)

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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

KH Stable

Perseus A426

M87

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.

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.

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

IndividualGalaxy

GalaxyClusters

Super-Galactic Filaments

The MagnetizedUniverse (?)

Kronberg et al’03

Farady Rotation Measure

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Thank you!