Extragalactic Magnetic Fields and Dynamo

Hui Li

with K. Bowers, X. Tang, and S. Colgate

(Los Alamos National Lab)

Extragalactic magnetic fields and Magnetized Universe Project Implications on Dynamo: a) “Kinematic” dynamo in AGN accretion disks b) Magnetic Relaxation (Flux conversion dynamo?): Dynamical magnetic relaxation in force-free plasmas

Helicity and energy transport and dissipation Astrophysical Implications

Radio Galaxies

Estimating Magnetic Energy

Total magnetic energy: ~ 1060 ergs Total volume: ~ 1072 cm3

Typical size: 30 kpc wide, 300 kpc long Electron energy: 10 GeV – 10 TeV (min unknown) Magnetic fields: 0.5 – 5 Gauss Density: ~10-6 cm-3 (thermal), < 10-7 cm-3 (relativi) Total current: I ~ 5 B R ~ 1018 – 1019 A. drift velocity: ~10 m/sec ! to relativistic ~ c

• Radio luminosity, spectral index• Estimating the volume, filling factor (~0.1)• Use equipartition/minimum energy assumption

Estimate the total particle and magnetic field energy in the lobes.

High z sources

GiantsCluster sources

Kronberg, Dufton, Li, Colgate’02

Magnetic Energy of Radio Lobes

Faraday Rotation Measure (Taylor & Perley’93; Colgate & Li’00)

Very high FRM, giving mean B fields ~ 30 G, over size L ~ 50 kpc

implying total magnetic energy 4x1059 ergs,

and coherent flux of

8x1041 G cm2.

Only supermassive black holes can perhaps provide such energy and flux.

Galaxy Cluster: Perseus A in X-ray

300 Kpc

Perseus A: X-ray + Radio

Ubiquity of Supermassive Black Holes(Kormendy et al. 2001)

SMBH = 5h2 x 105 Msun / Mpc3

Rationale: Energy, Energy, and Energy

Black Hole Mass Growth

Magnetic Energy Growth

The Magnetized Universe Project•Energy Transport:

(1) how do jets/helix collimate?

(2) how do radio lobes form?

•Energy Production:

(1) how to form SMBH?

(2) Accretion disk physics?

•Energy Conversion:

Gravitational Magnetic, dynamo

•Energy Dissipation:

(1) how do magnetic

fields dissipate?

(2) how to accelerate

particles?

•Astrophys. implications:

(1) will lobes expand?

(2) how do they impact structure formation?

(3) how to prove the existence of B fields?

Implications on Dynamo Magnetic energy and flux of radio lobes and their impact to the general IGM

really emphasize the need of understanding: (1) “kinematic” dynamo in accretion disk around SMBHs: How to convert

gravitational energy to magnetic energy? * seed field perhaps a non-issue due to large number of rotations * this dynamo seems to saturate at the limit of extracting a significant fraction of the available energy during the SMBH formation

Colgate et al.: star-disk collision model for dynamo and liquid sodium experiment at NM-Tech(2) magnetic relaxation (flux-conversion dynamo): How would these lobes

evolve in the IGM? ---- Similar to Spheromak and RFP? * degree of magnetization of the IGM, impact on galaxy formation? * ultimate fate of the magnetic energy --- extra-galactic cosmic rays? Li et al.: kinetic simulation of collisionless force-free plasmas

AGN Disk Dynamo:Star-Disk Collisions( Colgate et al; Pariev & Colgate’03 )

-phase: disk rotation – toroidal fields-phase (helicity injection): rotation of the rising plumes made by star-disk collisions

Liquid Sodium Experiment (Colgate et al.)

Magnetic Lobe Relaxation

• Particles are continuously accelerated in-situ, implying continuous energy conversion.

• Lobes made in relatively short time (107-108 yrs), in a finite volume, with a finite amount of energy and helicity. Since it is over-pressured compared to its surrounding, it should evolve (by relaxation?).

• Kinetic physics should be included in reconnection in lobes: Kinetic scales: c/pi ~ 1011 cm (n ~10-6 /cc) Sweet-Parker layer width: (L/v)1/2 ~ 109 cm

(filaments: L ~10 kpc, eta ~ 103, v ~ 108 cm/s)

In astrophysical plasmas, the condition is often assumed and it is nearly force-free .

Q: Is this sheet-pinch configuration unstable?Q: If so, how does it convert B2 into plasmas?

1

An idealized Problem

Bx(z) B0 coszBy(z) B0 sinzBz(z) 0

Sheet-Pinch:

BB

Why would it evolve?

Lz is the longest length scale

--- no relaxation

Lz < Lx, Ly

--- relaxation

Flipping …

Predicting final Bz flux: Bzf = B0 nx (Lz/Lx)Predicting final magnetic Energy: B2(t=0) = By

2 + Bx2

B2 (tf) = By2 + Bz

2

EB = 1 – (Lz/Lx)2

Lx

Lz Lz

Lx

Stability

For a background B0 = (Bx,By,0), consider a perturbed Bz, with modes k=(kx, ky), one gets:Bz = i(k .B0)uz + non-ideal terms

At resonant layer, k .B0 = 0, energy flows into the layer:

for ’ > 0. Dissipation dominates in this layer: resistivity: Furth et al’63 collisionless: Drake & Lee’77, Bobrova et al.’01, Li et al.’03 x

z

MHD

MHD

MHD

kinetic dissipation

kinetic dissipation

0

2

Lz /2

'2ˆ)ˆˆ(

dxzBEdxdty

W

Resonant Layers in 3D

In 2D, two layers: z = /2, 3/2In 3D, large number of modes and layers!

z

yxyx

xy

yx

yx

L

Ln

jjLn

Lnz

zkzk

,,

0

,...,2,1,0

,...2,1,0arctan

0)sin()cos(

0Bk

Layer-Layer Interaction in 3D is expected to play an important role.

q-Profile of Resonant Surfaces

3D

2D

q = By / Bx

z

Short Wavelength Limit

Collisionless Tearing: Linear Growth Rate(Li et al’03, PoP)

Long Wavelength Limit

V4PICA Particle-in-Cell (PIC) Kinetic Code

• First principles simulation of the relativistic Maxwell-Vlasov system in three dimensions

• Does not need an equation-of-state for closure• Particles are advanced using fields interpolated from a

mesh; fields are advanced using sources accumulated from particles

• V4PIC was designed from the ground up for ultra-high performance on modern commodity processors

nrnn

nn

n

nn

nn

c

ssp

ssss

ss

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Bm

pEq

dt

pd

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DJH

t

BE

,

V4PIC -- Under the Hood

cleaning) divergenceMarder

and dampingradiation TCA with

TD-FEMExplicit Mesh -(Yee

,,

Fields Advance

21

21 1 nnnn BEBE

rotation) Borisorder

6th with (Leapfrog

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Particles Advance

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functions) basis

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icRelativist and Fluxes Densities,

Species Fields, EM (Energies,

sDiagnosticEulerian Lagrangian Euleria

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Timestep Update

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V4PIC -- Current Status

• Sustained 7.1M particles advanced per second per processor (0.14 s per particle) in the common case was demonstrated on a Pentium 4 2.5GHz.– Memory subsystem is at theoretical limits.– Floating point subsystem is near theoretical limits (~60-80%).– Substantially faster (well over an order of magnitude in some

cases) than other PIC codes.

• A simple parallelization of V4PIC has been done.– Tens of processors on particle dominated simulations.– Routinely running ~1003 meshes with ~0.5B particles for ~50K

time steps on 16 to 32 processors (ranging from overnight to a couple of days per run).

• V4PIC has been ported to several x86 clusters and LANL’s Q machine and validated against simple test problems, magnetic reconnection and plasma instabilities simulations.

PIC Simulation Parameters

Total Energy Evolution

2D 3DI II III I II III

I: Linear Stage; II: Layer Interaction Stage; III: Saturation Stage

(Nishimura et al’02,03; Li et al’03a; Li et al’03b)

Global Evolution (I): Tearing with Island Growth and Transition to

Stochastic Field lines

(1,0)

(0,1)

(1,-1)

(1,1)

Global Evolution (II-III): Multi-layer Interactions, Transition to

Turbulence, Relaxation, and Re-Orientation

Helicity and Energy Dissipation )(/)2/ 33 JEddtdEBEddtdH x (x

Run 9c4 Run 9c1

9c4

9c1

Total H

H at k =

H (k < )

H (k > )

Run 9c4

)Re(

)( 33

kkk

k

BAH

HkdBAxd

Two Stage: Total H & W conserved

but with significant spectral transfer.

Net H & W dissipation.

Total H

H at k =

Total W

W at k =

Run 9c1

2/Lx 2/Lz 2/di 2/de

Inertial Range ? Dissipation Range

Relaxation with intermittency

t=0-1.6

7.8

9.3511

14

15.6

(Li et al’03)

• Evolution of |J| in pdf.

• Its mean is decreasing with time, i.e., relaxing.

• But with a significant high |J| tail, i.e., localized high |J| filaments where reconnection is occurring.|J|

f(|J|)

ti = 8

Current Filaments

Current Filamentation

Field-Aligned E

||/ BBE

E E EEBE

JPBJ BvE

inertialthermalhallmhd

dt

dc

enba

e

e

Generalized Ohm’s Law:

SummarySystem evolves by constantly choosing more

“relaxed states” within the constraints of the geometry. In so doing, converting the excess magnetic energy to particle heating/acceleration.

3D simulation shows the existence of intermittent regions, with large local shear, current density and magnetic dissipation rates.

Needs more dynamic range to cleanly separate inertial and dissipation ranges, might recover the helicity conservation?

New Experiments

Expanding and relaxing magnetic bubble experiments without external driving.

Background (4)

and …. Radio Galaxies