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14 xi 2014 Antony Jameson
Knots, Tangles and Magnetoluminescence
Roger BlandfordKIPAC
StanfordWith Yajie Yuan, Jonathan McKinney,
Sasha Tchekhovskoy, Jonathan Zrake, William East
1
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Hardy? Ramanujan?
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Pulsar Wind Nebulae
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• eg Crab Pulsar/Nebula • Spinning Neutron Star
• 34 ms! • Polarized inner knot is shock • γ-ray flares from nebula • Eγ ~ 400 MeV -- only • ~5 PeV electrons • t ~ hrs; Rnebula ~ lt yrs!
3
Buehler et alFermi
Prostrating myself before your majesty, I hereby report that a guest star has appeared… (This) means that there is a person of great wisdom and virtue in the country. Yang Wei-ti 1054 AD
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14 xi 2014 Antony Jameson
Unipolar Induction
Ω
Φ
V ~ Ω Φ ∼ Εmax/e I ~ (V / Z0) Z0~100Ω P ~ V I ~ (V2/Z0)
EMF from spinning magnetized body
Sun – V ~ 100 MV, I~1 GA, P~100PW Crab – V~ 30 PV, I~300TA, P~ 1031 W
4
SpitkovskyPorth
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1 lt hr = 3 masLarmor radius= 60γ9B-7
-1mas
13 vi 2014 Bochum
W
SJ
TP
=10,000mas
• GeV Crab flares appear to be synchrotron radiation by PeV electrons in mG fields• Challenge to classical electrodynamics• Similar problems in other sources
Crab Flares
Maximum energy ~ α-1 me ~ 100 MeV if E ~ B 5Cool in 10o!
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Quasar Jets
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P~0.1
6
3C273
• eg 3C 273 • 109 Mo Spinning Black Hole • γ-rays from relativistic jet • Eγ ~ 15 GeV • t ~ 10hr, Rjet> 30 lt yr
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14 xi 2014 Antony Jameson
Unipolar Induction
Ω
ΦV ~ Ω Φ ∼ Εmax/e I ~ (V / Z0) Z0~100Ω P ~ V I ~ (V2/Z0)
EMF from spinning magnetized body
Sun – V ~ 100 MV, I~1 GA, P~100PW Crab – V~ 30 PV, I~300TA, P~ 1031 W AGN – V ~ 1 ZV, I ~ 10 EA, P~1040W GRB – V ~ 0.1 YV, I~1 ZA, P~1044W
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Spinning Black Hole
3+1D GRMHD simulation McKinney
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Let there be Light
• Faraday • Maxwell • Initial Condition • Definition
€
∂B∂t
= −∇ × E
∂E∂t
=∇ × B − j
∇ ⋅ B = 0∇ ⋅ E = ρ
=>Maxwell Tensor, Poynting Flux€
∇2A = j
8
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Force-Free Condition
• Ignore inertia of matter σ =UM/UP>>Γ2, 1 • Electromagnetic stress acts on electromagnetic energy density
• Fast and intermediate wave characteristics, evolutionary
€
ρE + j × B = 0⇒ E ⋅ B = E ⋅ j = 0
j =(∇⋅ E)E × B + (B⋅ ∇ × B − E ⋅ ∇ × E)B
B2
9
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Force-Free Electrodynamics in Black Hole Spacetime
• F.J=0 !div TEM=0 – Pair production necessary
• Fµν;ν=Jµ
– ξφ,t => Conserved F, G– I(Φ), V(Φ), Ω(Φ)
• Horizon boundary conditions – EM finite for infalling observer
• Energy outflow in non-rotating frame • Energy inflow in rotating frame
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• Relativistic Force-Free treatment – No inertia
• Relativistic MHD – Maxwell + Inertia + Pressure
• Collisionless plasma has anisotropic pressure tensor
• Can connect to Drifting Orbit Representation • P|| ~n2B-1; P+~nB1/2 … changes dynamics, stability, waves…• Space, time, greater than gyro scales
MagnetoHydroDynamics
€
∇⋅ (TEM +TF ) = 0j =σ(E + v × B)
curvature magnetization gradient ExB gravity acceleration
11
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Knots and Tangles • Knots - links
– Reconnection to tie and untie– Acceleration in a small volume– Slow process, lower energy particles – Shocks also accelerate
• Tangles - braids, hitches… – Sudden transition to lower energy state– E > c B?; runaway acceleration – Volumetric process – Magnetic energy->electrons -> γ-rays – Implosion, chain reaction?– Small fraction of average power
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Alexander (1928): t+t-1-1 etc
Cerrutti
Only connect
Alexander the Great slices Gordian Knot(accompanied by electrical storm!)
Reconnection
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Knots and Tangles • Knots - links
– Reconnection to tie and untie– Acceleration in a small volume– Slow process, lower energy particles – Shocks also accelerate
• Tangles - braids, hitches… – Sudden transition to lower energy state– E > c B?; runaway acceleration – Volumetric process – Magnetic energy->electrons -> γ-rays – Implosion, chain reaction?– Small fraction of average power
14 xi 2014 13Antony Jameson
Alexander: t+t-1-1
Cerrutti
Only connect
Spheromak
“Hairy” magnetic rope
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Sonoluminescence
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Rayleigh-Plesset equation
Cavitation -> implosion -> optical (x-ray??) flashes
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Magnetoluminescence • Topology-preserving re-arrangement of magnetic tangle
• Rapid dissipation of electromagnetic energy • Relativistic conditions • Efficient, volumetric particle acceleration of TeV, PeV electrons, positrons
• Prompt synchrotron emission of γ-rays • Current carried by emitting particles • Pressure loss->non-spherical implosion?
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Force-Free Equilibria • B ~ A ~ j -> Helmholtz equation • Spheromak solutions
• n, l, m, s!• Two phases
• Magnetic ropes, confined to nested surfaces• Chaotic field
• Connect structural stability to microphysics?
13 vi 2014 Bochum 16
Yuan
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Permitted Transition?
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Exploring these and other models with RMHD and RFFcodes to understand nonlinear evolution
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Summary • New mechanisms needed to account for most dramatic gamma ray flares
• Associated with spinning, magnetized compact objects
• Dissipation of electromagnetic energy • Steady emission - relativistic reconnection • Flares – untangling flux tubes? • Interesting applied math, computing
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Happy Birthday!
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`
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