Explosive X-point reconnection & Crab flares. Maxim Lyutikov (Purdue U.)

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1 Explosive X-point reconnection & Crab flares Maxim Lyutikov (Purdue U.)

2 Spectra of Crab nebula & flares Tavani et al. 20 Beuhler et al., 2011 ] E 2.F [erg cm 2 s Break at ~ 0 MeV Fermi CGRO COMPTEL CGRO EGRET HESS MAGIC CANGAROO VERITAS HEGRA CELESTE Energy [MeV]

3 Spectra of Crab nebula & flares Tavani et al. 20 Beuhler et al., 2011 ] E 2.F [erg cm 2 s Break at ~ 0 MeV flare spectrum break ~ 400 MeV Fermi CGRO COMPTEL CGRO EGRET HESS MAGIC CANGAROO VERITAS HEGRA CELESTE Energy [MeV]

4 Upper limit to synchrotron frequency Accelerating E-field < B-field eec = ηebc = E p = 27 16π η mhc3 e 2 4e4 9m 2 c 3 B2 γ 2 = 236 η MeV. - Same as Fermi acceleration on inverse gyroscale - Typically eta < -2 for stochastic shock acceleration: this excludes stochastic acceleration schemes even for normal PWN emission Need E ~ B & more: - relativistic motion AND/OR - multi-zone E ~ B -> reconnection For sigma ~ 1, va ~ c, E ~ B 3

5 Wind with varying magnetization Porth+2013, Komissarov+ 2013; Lyubarsky 2012 First 3D simulations Magnetic flux is destroyed in reconnection events near the axis The model can keep the morphology of small-sigma models and allow for reconnection in sigma ~ 1 regions 4

6 Size and location of emission region ph 500MeV, τ s 1day γ 5 9,B 3 G γ max e Ė m e c 2 c 11 θ 5, r em 16 cm B wind 3 B NSR 3 NS Ω2 c 2 r r 17 cm Emission occurs at r ~ few 16 cm in a region occupying ~ few degrees (Lyutikov, in prep) 5

7 Not enough B-energy and particles Total energy How many particles needed? E B B2 8π (cτ)3 39 erg not enough N L γτ d γm e c 2 37 Ṅ = λ 6 33 s 1 Pulsar production rate (in about a second) Total number of particles in the emitting volume Ṅ N = 4πr 2 c (cτ)3 λ 33 Almost all need to be accelerated - no way, will run into Alfven current limitation I L γ c I A = γ m ec 3 (Need background plasma to provide the return current) e 6

8 Relativistic bulk motion Relativistic bulk motion with Doppler factor ~ few resolves all the problems: ph δ ph L γ δ 3 L γ τ τ/δ 2 7

9 Bulk Gamma, shock corrugation Γ max 1/χ Γ max Lyutikov et al, 2012 oblique shock, inner knot Long wavelength ~ months Komissarov Komissarov & Lyutikov, & Lyutikov Short intensity variations (No time of flight effects) Γ 8

10 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! Clausen-Brown, Lyutikov

11 Г ~ few increases flux and peak energy, nearly mono-energetic spectrum mild boost - huge increase in flux Flare spectrum: nearly mono-energetic Flares are not seen at lower energies Consistent with observations (Clausen-Brown & Lyutikov 2012)

12 Acceleration by reconnection: efficient, non-stationary v E ~ (vin/c) B - need relativistic inflow to have E ~ B + bulk motion with Gamma ~ few and/or acceleration in B < E, emission on exit E-field created by bulk particles, kinetic motion of high energy particles ~ along neutral line 11

13 Acceleration by reconnection: efficient, non-stationary v E E ~ (vin/c) B - need relativistic inflow to have E ~ B + bulk motion with Gamma ~ few and/or acceleration in B < E, emission on exit E-field created by bulk particles, kinetic motion of high energy particles ~ along neutral line 11

14 Acceleration by reconnection: efficient, non-stationary v E γ 1 Reconnection in sigma >> 1 plasma: inflow & outflow can be relativistic (Lyutikov & Uzdensky 2002, others) E ~ (vin/c) B - need relativistic inflow to have E ~ B + bulk motion with Gamma ~ few and/or acceleration in B < E, emission on exit E-field created by bulk particles, kinetic motion of high energy particles ~ along neutral line 11

15 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing Lyutikov 2003, Komissarov

16 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing Lyutikov 2003, Komissarov

17 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing plasmoids Lyutikov 2003, Komissarov

18 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing X-point collapse: plasmoids Lyutikov 2003, Komissarov

19 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing X-point collapse: plasmoids Lyutikov 2003, Komissarov explosive dynamics on Alfven (light) time Starting with smooth conditions E ~ B0 (field outside), E>B with resistivity Particles drift towards null line 12

20 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing X-point collapse: current sheet formation plasmoids Lyutikov 2003, Komissarov explosive dynamics on Alfven (light) time Starting with smooth conditions E ~ B0 (field outside), E>B with resistivity Particles drift towards null line 12

21 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing X-point collapse: current sheet formation plasmoids Lyutikov 2003, Komissarov at Finite time singularity Time explosive dynamics on Alfven (light) time Starting with smooth conditions E ~ B0 (field outside), E>B with resistivity Particles drift towards null line 12

22 Physical model: collapse of magnetic X-point in force-free plasma (formation of current sheet) Current sheet can be unstable to tearing X-point collapse: current sheet formation plasmoids Lyutikov 2003, Komissarov at Finite time singularity Time explosive dynamics on Alfven (light) time Starting with smooth conditions E ~ B0 (field outside), E>B with resistivity Particles drift towards null line y particle trajectories x 12

23 Volumetric break-down Force-free X-point collapse predicts Ez/B ~ y Simulations do show volumetric break-down B 2 -E 2 Komissarov & Lyutikov, in prep 13

24 Can produce power-laws PIC simulations by Sironi 14

25 The plasma regimes Relativistic skin depth(n γ w n): δ rel r λ λ 4 6 Needed L ~ 1 r, S = L 2 /δ Problem: Need DC-type acceleration on sub-skin depth scales (gamma ~ 4-8 over ~ 0 skins)? In relativistic plasma waves on sub-skin scales will be Landau-damped. 15

26 The plasma regimes Relativistic skin depth(n γ w n): δ rel r λ Ė 4πr 2 γ w nm e c 3 λ 4 6 Needed L ~ 1 r, S = L 2 /δ n = λn GJ Problem: Need DC-type acceleration on sub-skin depth scales (gamma ~ 4-8 over ~ 0 skins)? In relativistic plasma waves on sub-skin scales will be Landau-damped. 15

27 What causes flares? - How to create the X- point? Tearing mode on Alfven (light crossing time along the sheet) 1/3 Γ tearing = v A /L for a δ ~ 1/few (Pucci & Velli 2013) L L Collision of two fast waves Collision of two shear flows Collision of two Alfven CD

28 What causes flares? - How to create the X- point? Tearing mode on Alfven (light crossing time along the sheet) 1/3 Γ tearing = v A /L for a δ ~ 1/few (Pucci & Velli 2013) L L Collision of two fast waves Collision of two shear flows Collision of two Alfven CD

29 Relevance to other sources: AGNs, GRBs BHs in AGNs and GRBs work similar to pulsar: rotating, magnetized central object produces relativistic magnetized wind Paradigm change (?): some (most?) particles are accelerated by magnetic reconnection (and not shocks) 17