Relativistic reconnection at the origin of the Crab gamma-ray flares Benoît Cerutti Center for Integrated Plasma Studies University of Colorado, Boulder, USA Collaborators: Gregory Werner (CIPS), Dmitri Uzdensky (CIPS), Mitch Begelman (JILA) Variable Galactic Gamma-ray Sources, April 16-18, 2013, Barcelona.
Agile and Fermi discovered gamma-ray flares in the Crab Nebula [http://fermi.gsfc.nasa.gov/ssc/data/access/lat/msl_lc/] April 2011 March 2013 Oct. 2007 Sep. 2010 Feb. 2009 July 2012 [Tavani et al., Science, 2011] ; [Fermi-LAT, Science, 2011]
The ultra-short time variability put strong constraints on the acceleration region [Buehler et al., 2012] April 11, 9 days Flux 30 Flare few days = emitting region size ctflare~1016 cm << Nebula (~0.1 pc) (Shortest variability timescale ~ hours) If tacc= tsync = B ~ few mg >> 200 μg, and PeV pairs!
Spectral variability at high energies April 2011 375 MeV! Synchrotron Flare Inverse Compton [Weisskopf et al. 2013] Synchrotron photons > 100 MeV No obvious counter-parts (radio, IR, opt., X, TeV) April 2011 spectrum very hard, inconsistent with shock-acceleration
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!
Particle acceleration above the radiation reaction limit could occur at reconnection sites +B0 2δ Current layer Observer E0 Synchrotron Photons -B0 Ultra-relativistic, collisionless pair plasma reconnection The reconnecting magnetic field vanishes inside the current layer: y +B0 -B0 2δ Current layer E0>B0 x Non ideal MHD!
Zeltron: A new radiative PIC code General properties: 3D, parallel (OpenMPI), relativistic, electromagnetic PIC code. Developed from scratch by 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
Numerical setup: Harris equilibrium Ultrarelativistic reconnection, with radiation reaction force! Numerical parameters: Layer thickness: 2δ +B0=5mG - 100 particles per cell - 1440² grid cells - 9000 time steps - 8 cells per δ - Periodic boundary cond. -B0 Physical parameters: - B0 = 5mG = γrad 109 - Thermal drifting particles, kt=4 107 mc² +B0 - Non-thermal background particles: dn/dγ = Kγ-2, 4 107 < γ < 4 108 System size: L = 7 1015 cm or 2.7 light-days
Overall time evolution of reconnection 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 [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Time evolution of the particle energy distribution tω1 = 0 tω1 = 220 γrad [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Time evolution of the particle energy distribution tω1 = 0 tω1 = 220 γrad tω1 = 440 [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Time evolution of the particle energy distribution tω1 = 0 tω1 = 220 γrad tω1 = 440 tω1 = 660 [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Energetic particles are bunched into the layers and magnetic islands 8 γ > 5x10 [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Evidence for relativistic Speiser orbits Sample of 150 particle orbits Speiser orbits! Particles beam E>B, non-ideal MHD! y/ρ1 Particles well magnetized ideal MHD z/ρ1
A typical high-energy particle orbit with γ > γrad 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
Evidence for >160 MeV synchrotron photons! Total synchrotron flux (optically thin) Isotropic >160 MeV! [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Energy-resolved radiation angular distribution +y -z -x +z -y +x -z
Energy-resolved radiation angular distribution
Energy-resolved radiation angular distribution
Energy-resolved radiation angular distribution
Energy-resolved radiation angular distribution Strong energy-dependent anisotropy of the energetic particle. = beaming of the high-energy radiation!
Evidence for >160 MeV synchrotron photons! Total synchrotron flux (optically thin) is n A c i p o ot r Observer! Isotropic >160 MeV! [Cerutti et al., submitted, 2013, arxiv:1302.6247] Apparent high-energy flux INCREASED! = «KINETIC BEAMING» [Cerutti et al., 2012b]
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 MODEL Observer Symmetric shape Δt<< Lx/c Ultra-short time variability < 6 hours due to particle bunching and anisotropy OBSERVATIONS [Cerutti et al., submitted, 2013, arxiv:1302.6247] Symmetric shape Δt<< Lx/c Apr. 11 flare Observed ultra-short time variability < 8 hours [Buehler et al., 2012]
Expected correlation Flux/Energy MODEL Flux OBSERVATIONS εcut [MeV] Flux = K εcut+3.42±0.86 [Buehler et al., 2012] Flux = K εcut+3.8±0.6 [Cerutti et al., submitted, 2013, arxiv:1302.6247]
Where could magnetic reconnection operate in the Crab? Pulsar wind Current sheet (striped wind) [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 Porth et al. 2012 NASA-CXC-SAO F.Seward et al.
The discovery of these flares has a considerable impact in high-energy astrophysics! Smoking gun of rapid magnetic dissipation in the Nebula Solution to the long-standing «σ-problem»? DISSIPATION RECONNECTION (?) Poynting Fluxdominated plasma Particle kineticenergy-dominated plasma The model of the Crab Nebula is a prototype for ALL the other high-energy astrophysical sources: AGN jets, lobes, gamma-ray bursts, magnetars,