Extragalactic Magnetic Fields and Dynamo • 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 Hui Li with K. Bowers, X. Tang, and S. Colgate (Los Alamos National Lab)
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 (gmin unknown) • Magnetic fields: 0.5 – 5 m Gauss • Density: ~10-6 cm-3 (thermal), < 10-7 cm-3 (relativi) • Total current: I ~ 5 B R ~ 1018 – 1019 A. • drift velocity: ~10 mm/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.
Magnetic Energy of Radio Lobes Kronberg, Dufton, Li, Colgate’02 Giants Cluster sources High z sources
Faraday Rotation Measure(Taylor & Perley’93; Colgate & Li’00) Very high FRM, giving mean B fields ~ 30 mG, 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.
Ubiquity of Supermassive Black Holes(Kormendy et al. 2001) rSMBH = 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 • Astrophys. implications: • (1) will lobes expand? • (2) how do they impact structure formation? • (3) how to prove the existence of B fields? • Energy Dissipation: • (1) how do magnetic • fields dissipate? • (2) how to accelerate • particles?
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 ) W-phase: disk rotation – toroidal fields a-phase (helicity injection): rotation of the rising plumes made by star-disk collisions
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/wpi ~ 1011 cm (n ~10-6 /cc) Sweet-Parker layer width: (Lh/v)1/2 ~ 109 cm (filaments: L ~10 kpc, eta ~ 103, v ~ 108 cm/s)
An idealized Problem Sheet-Pinch: 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?
Why would it evolve? Lz < Lx, Ly --- relaxation Lz is the longest length scale --- no relaxation
Lx Flipping … Lz Lz Lx • Predicting final Bz flux: Bzf = B0 nx (Lz/Lx) • Predicting final magnetic Energy: B2(t=0) = By2 + Bx2 B2 (tf) = By2 + Bz2 DEB = 1 – (Lz/Lx)2
Stability z • For a background B0 = (Bx,By,0), • consider a perturbed Bz, with modes k=(kx, ky), one gets: • gBz = i(k .B0)uz + non-ideal terms • At resonant layer, k .B0 = 0, energy flows into the layer: • for D’ > 0. Dissipation dominates in this layer: • resistivity: Furth et al’63 • collisionless: Drake & Lee’77, Bobrova et al.’01, Li et al.’03 2p MHD kinetic dissipation MHD Lz /2 kinetic dissipation 0 MHD x
Resonant Layers in 3D • In 2D, two layers: az = p/2, 3p/2 • In 3D, large number of modes and layers! Layer-Layer Interaction in 3D is expected to play an important role.
q-Profile of Resonant Surfaces q = By / Bx 2D z 3D
Collisionless Tearing: Linear Growth Rate(Li et al’03, PoP) Short Wavelength Limit 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
V4PIC -- Under the Hood Lagrangian Eulerian
V4PIC -- Current Status • Sustained 7.1M particles advanced per second per processor (0.14 ms 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.
Total Energy Evolution (Nishimura et al’02,03; Li et al’03a; Li et al’03b) I: Linear Stage; II: Layer Interaction Stage; III: Saturation Stage 2D 3D I II III I II III
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 Run 9c4 Run 9c1
Run 9c4 Total H H at k = a H (k < a) • Two Stage: • Total H & W conserved but with significant spectral transfer. • Net H & W dissipation. H (k > a)
Run 9c1 Total H Total W H at k = a W at k = a
Inertial Range ? Dissipation Range 2p/Lx 2p/Lz 2p/di 2p/de
Relaxation with intermittency (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. t=0-1.6 15.6 7.8 f(|J|) 14 11 9.35 |J|
CurrentFilaments tWi = 8
Field-Aligned E Generalized Ohm’s Law:
Summary • System 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.