cosmic magnetic fields: helicity injection by supermassive black holes, galaxies and laboratory...

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

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

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.Black hole mass3.6 million solar

Masses(Genzel et al.)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Our own backyardGalactic Center

Ubiquity of Supermassive Black Holes

(Kormendy et al. 2001)

Cosmic Energy Flow

Gravity

Stars, galaxies, galaxy clusters,

large scale shocks, etc.

IGM

“Feedback”MechanicalChemicalThermal

Non-ThermalMagnetic

collapse

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

High z sources

GiantsCluster sources

(Kronberg, Dufton, Li, Colgate’02)

Magnetic Energy of Radio Lobes

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?

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

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−ψ

ψmax

⎛

⎝ ⎜

⎞

⎠ ⎟

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/

max2

max22

H

W

z

B

>>∝∝

∝

μλμλμλ

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:



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 =1

2ρv2 +

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


are needed to see this picture.Evolution

Time

Toroidal Flux

Poloidal Fluxz=0

Poloidal Fluxz=6

Poloidal Current Iz

log(density)


Poloidal Jz

Stability: with initial perturbations

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)









Jz = 1.5 Jz = -0.5 Combined

KH Stable

Perseus A426

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



Thank you!

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