Relativistic reconnection at the origin of the Crab gamma-ray flares

Benoît Cerutti

Center for Integrated Plasma StudiesUniversity of Colorado, Boulder, USA

Collaborators: Gregory Werner (CIPS), Dmitri Uzdensky (CIPS), Mitch Begelman (JILA)

Variable Galactic Gamma-ray Sources, April 16-18, 2013, Barcelona.

[http://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/]

B. Cerutti

April 2011

Sep. 2010

March 2013

Feb. 2009 July 2012

Agile and Fermi discovered gamma-ray flares in the Crab Nebula

Oct. 2007

[Tavani et al., Science, 2011] ; [Fermi-LAT, Science, 2011]

The ultra-short time variability put strong constraints on the acceleration region

B. Cerutti

[Buehler et al., 2012]

April 11, 9 days Flux ×30

Flare few days =► emitting region size ctflare

~1016 cm > 200 μG, and PeV pairs !

Spectral variability at high energies

Synchrotron photons > 100 MeV No obvious counter-parts (radio, IR, opt., X, TeV) April 2011 spectrum very hard, inconsistent with shock-acceleration

B. Cerutti

[Weisskopf et al. 2013]

Synchrotron

Inverse Compton

375 MeV!April 2011

Flare

The production of synchrotron emission >160 MeV challenges classical models of acceleration

Under ideal MHD conditions: E B!

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e+

Particle acceleration above the radiation reaction limit could occur at reconnection sites

The reconnecting magnetic field vanishes inside the current layer:

+B0

-B0

x

y

2δE0>B0

Non ideal MHD!

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2δ

+B0

-B0

E0Synchrotron

Photons

ObserverCurrent layer

Current layer

Ultra-relativistic, collisionless pair plasma reconnection

Zeltron: A new radiative PIC codeGeneral properties:

• 3D, parallel (OpenMPI), relativistic, electromagnetic PIC code.• Developed from scratch by B. Cerutti• Includes the radiation reaction force

Zeltron solves the Abraham-Lorentz-Dirac equation: [e.g. Jackson, 1975]

Lorentz 4-force

Radiation reaction 4-force

: 4-velocity: External electromagnetic field-strength tensor: Relativistic interval

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Numerical setup: Harris equilibrium

Layer thickness: 2δ

-B0

+B0

+B0=5mG

Ultrarelativistic reconnection, with radiation reaction force!

System size: L = 7×1015 cm or 2.7 light-days

Numerical parameters:

- 100 particles per cell- 1440² grid cells- 9000 time steps- 8 cells per δ- Periodic boundary cond.

Physical parameters:

- B0 = 5mG =► γ

rad ≈ 109

- Thermal drifting particles, kT=4×107 mc²

- Non-thermal background particles:

dN/dγ = Kγ-2,4×107 < γ < 4×108

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Overall time evolution of reconnection

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Particles are accelerated at X-points along the ±z-direction, and deflected along the ±x-directions by the magnetic tension.

Time evolution of the particle energy distribution

tω1 = 0 γrad

B. Cerutti[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Time evolution of the particle energy distribution

tω1 = 0 tω

1 = 220

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γrad

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Time evolution of the particle energy distribution

tω1 = 440

tω1 = 0 tω

1 = 220

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γrad

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Time evolution of the particle energy distribution

tω1 = 440

tω1 = 660

tω1 = 0 tω

1 = 220

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γrad

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Energetic particles are bunched into the layers and magnetic islands

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γ > 5x108

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Evidence for relativistic Speiser orbitsSample of 150 particle orbits

Particles well magnetized

≈ ideal MHD

Particles’ beamE>B, non-ideal

MHD!

Speiser orbits!y/

ρ 1

z/ρ1B. Cerutti

A typical high-energy particle orbit with γ > γrad

START

END

2δ

“Speiser orbit”Orbit shrinks

E>B

Phase 1. Drifting towards the layerPhase 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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Evidence for >160 MeV synchrotron photons!

>160 MeV!

Isotropic

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Total synchrotron flux (optically thin)

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

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Energy-resolved radiation’ angular distribution

+z +x-x-z -z

+y

-y

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Energy-resolved radiation’ angular distribution

Energy-resolved radiation’ angular distribution

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Energy-resolved radiation’ angular distribution

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Energy-resolved radiation’ angular distribution

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Strong energy-dependent anisotropy of the energetic particle.

=► beaming of the high-energy radiation !

Evidence for >160 MeV synchrotron photons!

>160 MeV!

Isotropic

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Total synchrotron flux (optically thin)

Anisotro

pic !

Apparent high-energy flux INCREASED! =► « KINETIC BEAMING »[Cerutti et al., 2012b]

Observer

[Cerutti et al., submitted, 2013, arXiv:1302.6247]

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Time variation of the >100 MeV flux

The beam of high-energy radiation sweeps across the line of sight intermittently =► bright symmetric flares.

Expected lightcurves, including the light propag. time

Ultra-short time variability < 6 hours due to particle bunching and

anisotropy

Apr. 11 flare

[Buehler et al., 2012]

Observed ultra-short time variability < 8 hours

Observer

MODEL

OBSERVATIONS

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Symmetric shape Δt

Expected correlation Flux/Energy

Flux = K εcut

+3.8±0.6

εcut

[MeV]

Flux

Flux = K εcut

+3.42±0.86

[Buehler et al., 2012]

OBSERVATIONS MODEL

B. Cerutti[Cerutti et al., submitted, 2013, arXiv:1302.6247]

Where could magnetic reconnection operate in the Crab?

© NASA-CXC-SAO F.Seward et al.

Pulsar windCurrent sheet (striped wind)

[Coroniti 1990]

© Kirk et al. 2009

Termination shockDissipation of the striped wind

[Lyubarsky 2003]

© Sironi & Spitkovsky 2011b

Polar region- High magnetic field (Z-pinch)- Kink unstable [Begelman 1998]

(See also Lyubarsky 2012)Flares: Analog of Sawtooth crashes

in tokamaks? [Uzdensky + 2011]

© Porth et al. 2012B. Cerutti

The discovery of these flares has a considerable impact in high-energy astrophysics!

Poynting Flux-dominated plasma

RECONNECTION (?)

Particle kinetic- energy-dominated

plasma

DISSIPATION

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• Smoking gun of rapid magnetic dissipation in the NebulaSolution to the long-standing « σ-problem »?

• The model of the Crab Nebula is a prototype for ALL the other high-energy astrophysical sources: AGN jets, lobes, gamma-ray bursts, magnetars, …

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