When the Crab Nebula goes wild

When the Crab Nebula goes wild
(Simulation of 3D pair plasma reconnection)
Benoît Cerutti
Princeton University
Collaborators: G.R. Werner (CU), D.A. Uzdensky (CU), M.C. Begelman(CU-JILA)
« From Black Holes to Cosmic Rays : when plasmas go wild », Oct 14-18, 2013, Les Houches, France.
The Crab Nebula is flaring all the time (!?)
April 2011
Sept. 2007 (Agile)
Sep. 2010
Feb. 2009
March 2013
July 2012
[http://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/]
B. Cerutti
The ultra-short time variability put strong constraints
on the acceleration region
[Buehler et al., 2012]
April 11, 9 days
Flux ×30
(1) Size : ctflare~1016 cm, ~1% radiates 30 times the whole Nebula flux
(2) If tflare= tsync =► B ~ few mG >> 200 μG, and PeV pairs
(3) PeV pairs => tgyration~ tflare , pairs accelerated within ~1 Cyclotron orbit
Inconsistent with diffuse shock acceleration
The acceleration is turned ON during the gamma-ray flare
B. Cerutti
Spectral variability at high energies
April 2011
Pairs e±
375 MeV!
Synchrotron
Flare
Inverse
Compton
[Weisskopf et al. 2013]
(1) No obvious counter-parts (radio, IR, opt., X, TeV)
(2) Spectrum ~mono-energetic, inconsistent with shock-acceleration
(3) Synchrotron photons > 100 MeV
B. Cerutti
The production of synchrotron emission >160 MeV
challenges classical models of acceleration
Radiation reaction force:
Frad= 2/3re2γ2B2
e
+
Accelerating force:
γ
Facc= eE
Particle’s trajectory
Radiation reaction limit: Facc= Frad =► γrad
Synchrotron photon energy: εmax = 3/2 γ2rad ħ ωc = 160×(E/B) MeV
Under ideal MHD conditions: E<B (ideal MHD) =► εmax < 160 MeV
[e.g. Guilbert et al., 1983 ; de Jager et al., 1996 ; Uzdensky et al., 2011]
A way out ?
1. Doppler beaming: εmax= D×160 MeV, D ≈ 3-4. Unlikely in the Crab (v < 0.5 c)
2. By-product decay ultra-energetic particles, Unlikely.
3. Non-ideal MHD process =► Reconnection! Inside the layer E > B!
B. Cerutti
Particle acceleration above the radiation reaction limit
could occur at reconnection sites [Kirk 2004]
Ultra-relativistic, collisionless pair plasma reconnection
y
E
+B0
E
+B0
-B0
-B0
2δ
x
y
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Reconnection
Layer
E>B
Non ideal
MHD!
x
Zeltron: A new radiative PIC code
General properties: (see also http://benoit.cerutti.free.fr/zeltron.html)
3D, parallel (OpenMPI), relativistic, electromagnetic PIC code.
• Developed from scratch
• Includes the radiation reaction force
●
Zeltron solves the Abraham-Lorentz-Dirac equation: [e.g. Jackson, 1975]
Radiation reaction
4-force
Lorentz 4-force
: 4-velocity
: External electromagnetic field-strength tensor
: Relativistic interval
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Numerical setup: Harris equilibrium
Ultrarelativistic reconnection, with radiation reaction force!
Reconnecting field : B0 =5 mG
Guide field : Bz=α B0
Initial plasma temperature :
kT=108 mec2
Grid : 14403
Particles : 5x1010
# Processors : 105
Magnetization : σ=16
Periodic boundary conditions
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System size: L = 7×1015 cm or 2.7 light-days
The layer is unstable to kink and tearing modes
VS
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2D yz-plane
2D xy-plane
kz
kx
Oblique modes
Time evolution of the plasma density with no guide field
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Particle spectra
2D yz-plane
2D xy-plane
Kink only
Tearing only
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Tearing modes =►Fast reconnection
Kink modes =►Heating
The guide field strabilizes the layer
Kink
Tearing
[Zenitani & Hoshino 2008]
[Cerutti et al., in preparation, 2013b]
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Time evolution of the plasma density with no guide field
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A typical high-energy particle orbit with γ > γrad, 2D simu
END
2δ
START
“Speiser orbit”
Orbit shrinks
E>B
Phase 1. Drifting towards the layer
Phase 2. Linear acceleration, weak rad.
losses, where E>B (non-ideal MHD)
Phase 3. Ejection, fast cooling and emission
of >160 MeV synchrotron
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Energy-resolved radiation’ angular distribution
+y
-z
-x
+x
+z
-y
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-z
Energy-resolved radiation’ angular distribution
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Energy-resolved radiation’ angular distribution
Direction upstream
field lines
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HE particles and radiation anisotropy
Particles
Synchrotron (optically thin)
>160 MeV!
[Cerutti et al., in prep., 2013b, see also Cerutti et al. 2013a]
Strong energy-dependent anisotropy of the energetic particle.
=► beaming of the high-energy radiation !
B. Cerutti
Observed correlation Flux/Energy
Flux
Flux
Apr. 11
εcut
εcut [MeV]
Flux = K εcut+3.42±0.86
[Buehler et al., 2012]
B. Cerutti
Expected correlation Flux/Energy
MODEL (2D runs)
Flux
OBSERVATIONS
εcut [MeV]
Flux = K εcut+3.42±0.86
[Buehler et al., 2012]
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Flux = K εcut+3.8±0.6
[Cerutti et al., 2013a]
Expected lightcurves, including the light propag. time
MODEL
Observer
Symmetric shape Δt<< Lx/c
Ultra-short time
variability < 6 hours due
to particle bunching and
anisotropy
OBSERVATIONS
Symmetric shape Δt<< Lx/c
B. Cerutti
[Cerutti et al., 2013a]
Apr. 11 flare
Observed ultra-short
time variability < 8 hours
[Buehler et al., 2012]
Super-fast time variability
High-energy particles only
[Cerutti et al., 2012a]
Application to blazar flares ? High σ jet ?
PKS 2155-304
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[Aharonian et al. 2007]
Where could magnetic reconnection operate
in the Crab?
Pulsar wind
Current sheet (striped wind), pulsed ?
[Coroniti 1990]
Polar region
- High magnetic field (Z-pinch)
- Kink unstable [Begelman 1998]
(See also Lyubarsky 2012)
Flares: Analog of Sawtooth crashes
in tokamaks? [Uzdensky + 2011]
© Kirk et al. 2009
Termination shock
Dissipation of the striped wind
[Lyubarsky 2003]
© Sironi & Spitkovsky 2011b
B. Cerutti
© Mignone+2013
© NASA-CXC-SAO F.Seward et al.
Towards a high-σ nebula and solution to the σ-problem !
●
●
●
●
●
Relativistic reconnection operates in a
high-sigma nebula, σ~>1
Flares = First observational evidence of
magnetic dissipation ?
First 3D RMHD global simulations favor
σ>~1, (contrary to 2D-axisymmetric
simulations) [Porth+2013a,b]
Inefficient diffuse shock acceleration if
magnetized plasma
Is it all about reconnection ?
We may have to revise our models in GRBs,
AGN jets, magnetars, …, all inspired on our
understand of the Crab Nebula
B. Cerutti
[Porth+2013a,b]