Magnetic Reconnection& Particle Accelerationin Solar Flares

Markus AschwandenLockheed Martin Solar and Astrophysics Laboratory

Magnetic Reconnection in Relativistic Wind WorkshopStanford Linear Accelerator Center (SLAC), Menlo Park, April 28-29, 2011

Laboratory: Accelerator known – but target products unknown

Solar Flares: Accelerator unknown – but target emission known

1) Magnetic Topology in Solar Flares2) Localization of Acceleration Region3) Physics of Particle Acceleration 4) Particle Kinematics and Propagation5) Largest flares (SEP and GLE events)6) Self-organized criticality

Contents:

Magnetic Reconnection & Particle Acceleration in solar flares

Refs : (1) Aschwanden M.J. 2002, Space Science Reviews, Vol. 101, p.1-227 “Particle Acceleration and Kinematics in Solar Flares”

(2) Aschwanden M.J. 2004, Springer/Praxis, Berlin, New York “Physics of the Solar Corona. An Introduction” http://www.lmsal.com/~aschwand/eprints/2004_book/

(3) Aschwanden M.J. 2011, Springer/Praxis, Berlin, New York “Self-Organized Criticality in Astrophysics”

Magnetic Topology in Solar Flares

The basic configurations of X-type magentic reconnection topologies in solar flares entail combinations between open and closed field lines :bipolar, tripolar, and quadrupolar cases, in 2D as well as in 3D.

MACROSCOPIC SCALES :

Energy argument forlocation of particleaccelerator in solarflares:

Free magnetic energyis available in areconnection regionwhere the magneticfield lines shrink:

€

dW = Bbefore (s)ds − Bafter (s)ds∫ > 0

Bipolar reconnection (examples from Yohkoh)

Bipolar topologies Tripolar topologies

Bastille-Day flare2000 Jul 14:The footpointsIn two-ribbonflares separateConsequence of magnetic reconnecion to progress in altitude

Aschwanden & Alexander (2001)

Discovery of symmetrc dual coronal hard X-ray sourcesconfirm the X-point geometry with upward/downwardacceleration of hard X-ray producing electrons.

TRACE 1600 A on 2002 Apr 15, 23:07 UT, overlaid with RHESSI10-15 keV contours. The energies of the symmetric coronal sourcesdecrease progressively with distance from X-point, as expected fromthe temperature drop of conductive cooling (Sui & Holman 2003).

6-8 keV10-12 keV6-20 keV

Coronal hard X-ray source is found to initally drop in altitudebefore it rises in the later flare phase. This discovery is still unexplained:

- relaxation of newly-reconnected field line ? - implosion after CME launch ? --> check EUV dimming !

Sui & Holman (2003)

The hard X-ray flux F(t) is correlated with the acceleration d2h/dt2(t) ofthe CME (Temmer et al. 2008). The upward-directed CME accelerationcould push the X-point initially down, while it sucks it in upward directionafter the pressure drops when the CME expands into interplanetary space.

Krucker & Lin (2002)

Does a simple HXR double footpoint source mean a single flare loop? Time profiles indicate multiple loops with different timing

Propagation ofreconnection sites

2002 July 23 flare:

Motions of footpointsare observed to increase in size andto move systematicallyalong the ribbons.

see simulationsof zipper effect byMark Linton

Krucker, Hurford & Lin (2003)

The footpoints of conjugate hard X-ray footpoints are observedto systematically propagate along the flare ribbons (in 2002 Nov 9 flare),rather than apart as predicted in the Kopp-Pneuman modelreconnection propagates along neutral line

Grigis & Benz (2005)

Where are the hard X-ray double ribbons ?

During the 2005 May 13 flare (color=RHESSI, white contour=TRACE 1600 A) extended hard X-ray ribbons are seen,interpreted in terms of a particular sigmoid-to-arcade evolution.

(Chang) Liu et al. (2007)

3D nullpoint spine reconnection

Krucker et al. (2004)

Quadrupolar topologies

Magnetic flux transfer (Melrose)3D flare geometry:Hanaoka, Nishio, Aschwanden

Localization of Acceleration Region

Volume of field-lineshrinking (relaxation)after magn. reconnectiondefines geometry ofacceleration region :

-cusps-double cusps-jets-curved hyperboloids-spines

MACROSCOPIC SCALES :

Anatomy of hard X-ray sourcesin a solar flare:

How do we localize the particle acceleration sources from this ?

Acceleration regions are expected in locations where newlyreconnected field lines relax into a force-free configuration.

)( Bc

vEq

dt

dvm ×+=

Force on acceleratedparticles :

Energy gain from shortened(relaxed) force-free field line:

dssBdssBWfreeforcecusp

]8/)([]8/)([ 22 ππ ∫∫−

−=Δ

Measurements ofratio ofelectron time-of-flightdistance L toflare loop half length s

L/s = 1.43 +/- 0.30(Aschwanden et al. 1996)

L/s = 1.6 +/- 0.6 (Aschwanden et al. 1998, 1999)

Reconstruction of heightof electron acceleration regionin Masuda flare: L/s ~ 1.5-2.0(Aschwanden et al. 1996)

Measurement of electron time-of-flight distance :-velocity dispersion from hard X-ray energy-time delay t=L/v-pitch angle correction (vparallel/v = cos )-magnetic field line twist correction (Lprojected/LTOF)

Altitudes averaged from northern and southern footpoints :(error bars correspond to difference between N and S)

00 32.1,3.2,)20

()( −=== − aMmzkeV

zz aεε

The height distribution of HXR emission dI/dz(z) is shownfor 5 different HXR photon energies e=5, 10, 20, 30, 40 keV

Acceleration sources of electrons versus ions:

The standard flare scenarios predict identical sourcesbut the observations reveal different locations for hard X-ray electrons and 2.2 MeV producing neutrons !

Hurford et al. (2006)

The gamma-ray source of the 2.2 MeV neutron-capture linewas found to be displaced by 20”+/- 6” from the 25 keV hardX-ray footpoints during the 2002 Jul 23 flare. A similarresult was found for the Oct/Nov 2003 flares.

Energized electrons and ions show displaced energy loss sites (1) different acceleration sites for electrons and ions ? - different path lengths for stochastic accleration (Emslie 2004)

- charge separation in super-Dreicer electric field (Zharkova & Gordovskyy 2004) (2) different propagation paths for electrons and ions ?

Physics of Particle Acceleration

Fast (subsecond) time structures of hard X-ray and radiopulses in solar flares suggest small-scale, fragmented,bursty magnetic reconnection mode.

MICROSCOPIC SCALES :

Basic Particle Motion

Particle orbits in magnetic fields: Electrons and ionsexperience Lorentz force that makes them to gyratearound the guiding magnetic field.

€

d(mγr v )

dt(r x , t) = q

r E (

r x , t) +

1

cr v ×

r B (

r x , t)

⎡ ⎣ ⎢

⎤ ⎦ ⎥

A force perpendicular to the magnetic field (e.g., electric force, polarization drift force, magnetic field gradient force,curvature force) produces a drift of the charged particle, while a force parallel to the magnetic field accelerates the particle.

€

rv Drift =

q

c

Fperp ×r B

B2 =1

Ωg

Fperp

m×

r B

B

⎛

⎝ ⎜

⎞

⎠ ⎟

Magnetic island formation by tearing mode instability(Furth, Killeen, & Rosenbouth et al. 1963)

Magnetic X-point and O-points form coalescence instability (Pritchett & Wu 1979)

Magnetic island formation + coalescence instability regime of impulsive bursty reconnection(Leboef et al. 1982; Tajima et al. 1987; Kliem 1998, 1995)

Karpen et al. 1995, 1998Schumacher & Kliem 1997Kliem et al. 1995, 1998Kliem, Karlicky, & Benz 2000

Electric field at X-point inimpulsive bursty reconnection mode(Kliem et al. 2000)

Hard X-ray pulses resulting fromaccelerated electrons dt ~ 0.1-0.3 s(Aschwanden et al. 1996)

Observations show a scaling law between Hard X-ray pulse durations and flare loop size : Tpulse ~ 0.5 s [rloop/10 Mm] scale invariance of magnetic reconnection region (Aschwanden et al. 1998)

Lower limit of pulse durations: collisional deflection time

MICROSCOPIC & MACROSCOPIC SCALES :

a) Electric DC field acceleration :-Sub-Dreicer field needs too large current sheets (Holman 1985; Tsuneta 1985)

-Super-Dreicer field applicable in magnetic islands (Litvinenko 1996)

-Generalization to dynamics of filamentary current sheets (Tajima et al. 1987; Kliem 994)

Sub-Dreicer DC electric field:

Under the action of an electric DC field, the bulk of the electron distribution drifts with a velocity vd, but is notaccelerated because of the frictional drag force is stronger than the electric field. Above the critical velocityvr defined by the Dreicer field, the electric force overcomesthe frictional force and electrons can be accelerated freelyout of the thermal distribution (runaway accleration regime).

€

eE =mevr

tse,i(vr)

,

tse,i = v / < Δv parallel /Δt)

mv=change of momentumts

e,i=collisional slowing-down time

Super-Dreicer fields require much smaller spatial scalesbut higher electric fields. Energy gain in an electric fieldperpendicular to the guiding magnetic field:

€

W =Bparallel

Bperp

eΔwy E parallel

Sub-Dreicer: particle acclerated along full length of current sheetSuper-Dreicer: particle drifts perpendicularly out of current sheet

Convective electric field : Econv = - u/c B (convective flow speed u ~ (0.01-0.1) vA

Particle orbit near magnetic O-point in magnetic island shows largest acceleration kick due to B-drift next X-point

(Kliem 1994)

Particle acceleration near X-point (chaotic orbits)(Hannah et al. 2002)

b) Stochastic acceleration- Wave turbulence spectrum (Kolmogorov, Kraichnan)- Particle randomly gains energy by wave-particle interactions (Doppler gyroresonance condition)

0/ =−Ω− ⇑⇑vks γω

Gyroresonant wave-particle interactions are describedby coupled equation system for changes of photonwave spectrum N(k,t) and particle distribution f(p).

€

Γ(k,f[p])=wave amplification growth rateΓColl(k)=wave damping rate due to collisionDij(N[k])=quasi-linear diffusion tensor of particles

Miller et al. (1996)

-Electron acceleration by whistler waves-Ion acceleration by Alfven waves-Enhanced ion abundances in flares reproduced by stochastic acc. (C, O, Ne, Mg, Si, Fe, but some problems with He3/He4)

ep Ω<<<Ω ω

⇑⇑Ω vkH ~

c) Shock acceleration

-First-order Fermi acceleration (electric field E=-(vshock/c)xB in deHoffman-Teller frame)-Diffusive (second-order Fermi) (multiple shock crossings)

Shock-Drift (First-Order Fermi) Acceleration

Adiabatic particle orbity theory can beapplied to collisionless shocks.Particle gains perpendicular momentumdue to the conservation of magneticmoment across shock front:

De Hoffman-Teller frame:ratio of reflected to incidentkinetic energy:

Diffusive shock acceleration

Particles encounter multiple transversals of shock frontsand pick up each time an increment of momentum thatis proportional to its momentum. Momentum after N shockcrossings is:

leading to a powerlaw spectrum for the particle momentum

General treatment: diffusion convection equation:

Particle orbit undergoes diffusive shock accelerationin a quasi-perpendicular shock (60 deg) by multiple crossings of the shock frontwith magnetic mirroring upstream the shock front (x<0)Decker & Vlahos (1986)

Somov & Kosugi (1997) Tsuneta & Naito (1998)

Applications of shock acceleration to solar flares :-First-order Fermi in mirror trap in flare loop cusp-Fast shock in reconnection outflow above flare loop-Type II as shock front signature in interplanetary space

Classification of acceleration mechanisms :

Particle Kinematics and Propagation

Each particle transportprocess has its characteristicenergy-dependent timingthat can be used for diagnostic

-acceleration dE/dt > 0-injection [pitch angle, (t)]-time-of-flight t(E) ~ t/v(E)-trapping: collisional deflection time t(E) ~ E 3/2 / ne

-energy loss: tloss << tTOF

MICROSCOPIC & MACROSCOPIC SCALES :

Electron velocityDispersion:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=Δ

21 v

l

v

lt TOFTOF

prop

Pitch angle:

v

vlll TOFTOFmag

||)cos( ==

Magnetic twist:

)cos(θmagloop ll =Electron energy:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−=

2

2

)/(1

1

cvcmeε

Photon energy:

eHXRE ε≤(Bremsstrahlung cross-section)

Electron time-of-flight(velocity dispersion)

t1-t2 = L/v1 – L/v2

v(E) = c [ 1 – 1/γ2] 1/2

EHXR ~ 0.5 Ekin

pitch angle correction

magnetic field twist corr.

Electron vs. ion acceleration :- gamma ray pulses delayed with respect to hard X-rays by few sec- time-of-flight difference between ions and electrons dt=L/ve-L/vion

(vion ~ ve/42)

Electron trapping:Weak-diffusion limit : collisional deflection time ttrap (E) ~ E 3/2 / ne ne ~ 1010-1012 cm -3

Krucker et al. (2008)

RHESSI showed coronal 250-500 keV gamma-rayContinuum emission ar the looptop later in the flarewith decay times progressively increasing with energy.

Evidence for trapping? - tcoll(E) ~ E3/2

Radio: electron beams along open and/or closed field lines produce plasma emission (radio type III, J, U, N, RS bursts)Predictions: bi-directional beams (type III+RS pairs) correlated pulses in radio (type III) and hard X-rays

Upward versus downward acceleration in flares

Electron beam trajectories diagnosis for radio dynamic spectra: - open magnetic field lines (type III) - closed magnetic field lines (type J, U) - downward propagating electron beams (type RS)

Acceleration region bracketed by upward/downward electron beams:--> triple correlations between radio type III, RS and HXR pulses

CGRO

Zurichradio

Aschwanden et al. (1993)

Aschwanden, Bastian, Benz, & Brosius (1992)

Spatial reconstruction of electron beam propagation:radio dynamic spectra: type U burst turnover frequency 1.445 GHz --> electron density ne=(2*1010 cm-3) at loop topradio image at 1.445 GHz (with VLA) --> spatial location of loop topmagnetic field extrapolation (KPNO) --> footpoints and origin of electron beam acceleration

Lee & Gary (2000) Kundu, White, Shibasaki et al. (2001)

Gyrosynchrotron emission of trapped electrons : pitch angle distribution of accelerated/injected electrons

Time profile components and e-folding deconvolution : separation of direct-precipitating and trap-precipiting electrons

Hard X-ray and Gamma-ray Emission Mechanisms

Observed Primary photons particle energy____________________________________________________Bremsstrahlung continuum 20 keV-1 MeV 20 keV-1 MeV >10 MeV 10 MeV-1 GeVNuclear de-exitation lines 0.4…6.1 MeV 1-100 MeV/nuclNeutron capture line 2.2 MeV 1-100 MeV/nuclPositron annihilation radiation 0.511 MeV 1-100 MeV/nuclPion decay radiation 10 MeV-3 GeV 0.2-5 GeVNeutrons in space 10-500 MeV 10 MeV-1 GeVNeutrons induc.atmos. cascades 0.1-10 GeV 0.1-10 GeVNeutron decay protons in space 20-200 MeV 20-400 MeV

Energy spectrum of the largest flares

1 GeV1 MeV1 keV

Electron-dominated bremsstrahlung spectrum observed up to 50 MeV in 1991-Jun-30 flare, gamma rays detected up to >1 GeV in 1991-Jun-11 flare (Kanbach et al. 1992)

Gamma rays detected with EGRET/CGRO during 1991-Jun-11flare up to >1 GeV (Kanbach et al. 1993; Mandzhavidze & Ramaty 1992)

Grechnev et al. 2008

The 2005-Jan-20 flare shows up to >200 MeV gamma rays.The impulsive phase of GLE, pion-decay gamma raysclosely correspond in time.

Temporal coincidence of hard X-ray and gamma-rays.

Grechnev et al. (2008)

Impulsive gamma-rays and GLE coincide within ~1 minute.

What are the maximum energies to which particles can be accelerated in solar flares ?

* No known high-energy cutoff of electron bremsstrahlung spectrum* Highest energies of observed bremsstrahlung >100 MeV* Highest gamma-rays reported >1 GeV with EGRET/CGRO in 1991-Jun-11 flare: spectrum could be fitted with a composite of a proton generated pion neutral spectrum and a primary electron bremsstrahlung component

SOC in Solar Physics

-Flare gamma rays, hard X-rays, soft X-raysFlare gamma rays, hard X-rays, soft X-rays-Solar flare, microflares, nanoflaresSolar flare, microflares, nanoflares

-Flare ultraviolet, EUV, HFlare ultraviolet, EUV, H--alphaalpha-Solar energetic particle events (SEP)Solar energetic particle events (SEP)-Coronal mass ejectionsCoronal mass ejections-Solar wind fluctuationsSolar wind fluctuations

Dennis (1985), Crosby et al. (1993)

SOC in Stellar Physics

-Stellar flares (dME stars)-Cataclysmic Variable (CV) stars-Accretion disks-Black holes-Pulsar glitches-Soft gamma repeaters (SGR)

Audard et al. (2000)

From the smallest nanoflareFrom the smallest nanoflareto the largest flare ...to the largest flare ...

… … there are 8 ordersthere are 8 ordersof magnitude differenceof magnitude differencein (thermal) energy !in (thermal) energy !

1) Macroscopic scales that organize particle acceleration in solar flares are controlled by the magnetic topology (dipolar, tripolar, quadrupolar), which scales the size of acceleration regions in magnetic reconnection sites and causes sequential local reconnection events that propagate in parallel, perpendicular, and vertical direction to the neutral line.

2) Microscopic scales in the magnetic reconnection region (electric fields caused by convective (v x B) drift, wave turbulence, shocks) determine the size of local fragmented acceleration regions (e.g., tearing and coalescing magnetic islands).

3) A scaling law between microscopic (sub-second hard X-ray pulses) and macroscopic scales (soft X-ray flare loop size) has been found that is consistent with a scale-invariant (self-similar) reconnection geometry and Alfvenic (coalescence) time scales.

4) Self-similar expansion of CME bubbles and erupting filaments produce naturally a scale-invariant geometry of current sheets in the trailing magnetic reconnection regions.

CONCLUSIONS :

http://www.lmsal.com/~aschwand/ppt/2011_SLAC_solar.ppt