Crab flares - explosive Reconnection Events in the Nebula Maxim Lyutikov (Purdue) in collaboration with Sergey Komissarov (Leeds) Lorenzo Sironi (Columbia) Oliver Porth (Frankfurt) - ApJ 2017; - JPP, 2017abc 1
Part I: The Crab wind and Nebula 2
Few times per year Random Flux increase by 40 100 MeV - 1GeV Crab flares lasts for a day (<< dynamical time) The synchrotron limit eec = ebc = 4e4 9m 2 c 3 B2 2 ~! s ~ 2 eb m e c = m e~c 3 e 2 200 MeV Nearly monoenergetic! Tavani + 2011 9 10 400 MeV flare Fermi CGRO COMPTEL CGRO EGRET HESS MAGIC CANGAROO VERITAS HEGRA ] E 2.F [erg cm 2 s 1 10 10 10 11 CELESTE 12 10 1 10 2 10 3 10 10 Energy [MeV] 4 5 10 6 10 7 10 8 10 Diffusive Shock acceleration is excluded 3
Flares from Crab Inner Knot? L w / sin 2 y axis incoming sound wave phase velocity of corrugation v ph post-shock flow x axis y shock surface upstream velocity Komissarov & Lyutikov 2011 Lyutikov +, 2012 4
Crab Inner knot Scales ~ 0.5 (light day) Rudy +, 2015 5
In the knot sigma is small! =0 =1 = 10 Lyutikov + 2016 + + + σ max σ striped wind zone 0 π 4 θ π 2 Bogovalov 1999 6
Inner knot: surface of relativistic shock Location: The knot is on the same side of the pulsar as the Crab jet, along the symmetry axis, on the opposite side as the brighter section of the Crab torus. Size: The knot size is comparable to its separation from the pulsar. Only models with σ < 1 agree Elongation: The knot is elongated in the direction perpendicular to the symmetry axis. Only models with σ < 1 agree Brightness peak: The observations indicate that the brightness peak is shifted in the direction away from the pulsar. Polarization: The knot polarization degree is high, and the electric vector is aligned with the symmetry axis. Luminosity: Taking into account Doppler beaming, the observed radiative efficiency of the inner knot is fairly low << 1%. Variability: The knot flux is anticorrelated with its separation from the pulsar. Not a sight of gamma-ray flares. 7
Wind properties Knot: Thermal (!) spectrum, w =3 10 4 Porth +, 2017 8
Pulsar winds: coming together of theory, simulations and observations 1.0 1017 s Bogovalov 1999 Komissarov+ 2003 Porth+ 2014 Sironi +, 2011 Lyutikov+, 2016 Yuan + 2016 5 0.8 0.6 0.4 High sigma regions, flares Just thermalization, Beff ~ large Reconnection mediated termination shock 4 3 2 0.2 0.0 Highly magnetized wind Striped equatorial zone Reconnection mediated acceleration at Mach belt, Beff ~ 0, like sigma=0 0.0 0.5 1.0 1.5 2.0 10 17 1 0 9
Conclusion 1 We made an important progress in understanding pulsar winds Equatorial sigma << 1 flow - shock acceleration in a narrow equatorial wedge Only thermalization at intermediate latitudes High sigma >> 1 polar flow - location of flares Origin of radio/optical particles Nano-flares in the bulk? Fermi-II in the bulk? 10
Part II: What about flares? - Explosive reconnection and particle acceleration in relativistic plasmas
Crab flares: very demanding conditions on acceleration Acceleration by E ~ B (energy gain & loss on one gyro radius) on macroscopic scales >> skin depth acceleration size ~ thousands skins acceleration size ~0.1-1 of the system size (in Crab) Few particles are accelerated to radiation-reaction limit - gamma ~ 10 9 for Crab flares (NOT all particles are accelerated) Slow accumulation of magnetic energy, spontaneously triggered dissipation (relativistic bulk motion) Explosive Reconnection in relativistic plasmas 12
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Dissipation in relativistic force-free plasma: resistive tearing mode Resistive force-free j k = E k / Lyutikov 2003 Komissarov +, 2006 Formation of magnetic islands, just like in non-relativistic case Growth like in non-relat.: p A Fast, but not fast enough! Collisionless - fast on skin, slow on macroscopic scales Reconnection driven by large scale uncompensated magnetic stresses 14
Large scale simulations Toroidally-dominated B-fields are unstable to large-scale kinks Formation of current-tubes Porth +, 2014 Parallel currents attract. Can flux merger be the source of Crab flares? 15
6 4 2D force-free state with constant B = { sin( y), sin( x), cos( x) + cos( y)}b 0 Color- out of the plane B-field Arrows - in plane Is it stable? (A type of the ABC flow) 2 0-2 X-point -4-6 -6-4 -2 0 2 4 6 Detailed investigation of stability using analytical, relativistic fluidtype and PIC simulations (Lyutikov, + 2016) 16
Collapse of stressed magnetic X-point in force-free plasma Dynamics force-free: infinitely magnetized plasma: currents & charges ensure EB =0, no particle inertia = B2 4 c 2 1 analytics a 2 B = ahtl 10 8 6 4 2 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time explosive dynamics on Alfven time slow initial evolution Starting with smooth conditions Finite time singularity 2 y L B?, yb0 c, xb 0 x La 2 B?,B 0 E = c, x 2 2 + y 2 a 4 cl 2 a 2 a @ t 2 4 2 ln a = A Driven by large-scale stresses 4 (a la Syrovatsky), A = c2 L 2 B 2? B 2 0 @ t ln a 17
Can produce power-laws E ~ B PIC simulations by Sironi 18
Acceleration in X-point collapse: charge starvation Highly efficient acceleration by E ~ B Driven by large scale magnetic stresses - wide-open X- point (not like in tearing mode - flat X-point) Acceleration starts abruptly, when reaching charge starvation. During collapse current density grows J z c 4 B? L a(t)2 But J< 2 n e c - not enough particles to carry the current curlb = 4 c J + @ te/c E-field grows Condition for charge starvation: demanding for Crab) a(t) > r L 1 1/4 (not too 19
Collapse of an ABC system of magnetic islands p=2.2 sigma=85 Two stages: - Fast acceleration, not much B- field dissipated (X-point collapse) - Slower acceleration, dissipation (island merger)
Current attraction: two stages: ``Free-fall and ``slow-resistive v L>Lcrit - plasmoid instability of current sheet E.B Initial attraction due to large-scale stresses Quasi-steady (repulsion by the current sheet) - slow resistive reconnection Two stages of particle acceleration: fast-impulsive and slow-resistive. 21
Clausen-Brown, Lyutikov 2012 Flare statistics: isotropic flares probability of flare flux average flare flux is dominated by bright rare flares. Flares can be on top of persistent emission, OR all emission are flares small ones average out Time binned Monte Carlo Power-law from shot noise! 22
max Where in Crab and AGNs? 0 max 1/ 1/ oblique shock, inner knot Porth+ 2014 AGN Komissarov & Lyutikov, 2011 Dissipation zone @ r < 1pc (approximately where ) B 0 B 0 p 23
Conclusion 2 Reconnection in magnetically-dominated plasma can proceed explosively efficient particle acceleration the explosive stage - X-point collapse - produces (seems to) a separate accelerated component is an important, perhaps dominant for some phenomena, mechanism of particle acceleration in high energy astrophysical sources. 24