Magnetic Reconnection
& Particle Acceleration
in Solar Flares
Markus Aschwanden
Lockheed Martin Solar and Astrophysics Laboratory
Magnetic Reconnection in Relativistic Wind Workshop
Stanford 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
Contents:
Magnetic Reconnection & Particle Acceleration in solar flares
1)
2)
3)
4)
5)
6)
Refs :
Magnetic Topology in Solar Flares
Localization of Acceleration Region
Physics of Particle Acceleration
Particle Kinematics and Propagation
Largest flares (SEP and GLE events)
Self-organized criticality
(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”
MACROSCOPIC SCALES :
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.
Energy argument for
location of particle
accelerator in solar
flares:
Free magnetic energy
is available in a
reconnection region
where the magnetic
field lines shrink:
dW 

B
before
(s)ds Bafter(s)ds  0
Bipolar reconnection (examples from Yohkoh)
Bipolar topologies
Tripolar topologies
Bastille-Day flare
2000 Jul 14:
The footpoints
In two-ribbon
flares separate
Consequence
of magnetic
reconnecion
to progress in
altitude
Aschwanden & Alexander (2001)
Discovery of symmetrc dual coronal hard X-ray sources
confirm the X-point geometry with upward/downward
acceleration of hard X-ray producing electrons.
6-8 keV
10-12 keV
6-20 keV
TRACE 1600 A on 2002 Apr 15, 23:07 UT, overlaid with RHESSI
10-15 keV contours. The energies of the symmetric coronal sources
decrease progressively with distance from X-point, as expected from
the temperature drop of conductive cooling (Sui & Holman 2003).
Sui & Holman (2003)
Coronal hard X-ray source is found to initally drop in altitude
before 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 !
The hard X-ray flux F(t) is correlated with the acceleration d2h/dt2(t) of
the CME (Temmer et al. 2008). The upward-directed CME acceleration
could push the X-point initially down, while it sucks it in upward direction
after the pressure drops when the CME expands into interplanetary space.
Does a simple HXR double footpoint source mean a single flare loop?
Time profiles indicate multiple loops with different timing
Krucker & Lin (2002)
Propagation of
reconnection sites
2002 July 23 flare:
Motions of footpoints
are observed to
increase in size and
to move systematically
along the ribbons.
see simulations
of zipper effect by
Mark Linton
Krucker, Hurford & Lin (2003)
Grigis & Benz (2005)
The footpoints of conjugate hard X-ray footpoints are observed
to systematically propagate along the flare ribbons (in 2002 Nov 9 flare),
rather than apart as predicted in the Kopp-Pneuman model
reconnection propagates along neutral line
Where are the hard X-ray double ribbons ?
(Chang) Liu et al. (2007)
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.
3D nullpoint spine reconnection
Krucker et al. (2004)
Quadrupolar topologies
Magnetic flux transfer (Melrose)
3D flare geometry:
Hanaoka, Nishio, Aschwanden
MACROSCOPIC SCALES :
Localization of Acceleration Region
Volume of field-line
shrinking (relaxation)
after magn. reconnection
defines geometry of
acceleration region :
-cusps
-double cusps
-jets
-curved hyperboloids
-spines
Anatomy of hard X-ray sources
in a solar flare:
How do we localize the particle acceleration sources from this ?
Force on accelerated
particles :
dv
v
m  q( E   B)
dt
c
Energy gain from shortened
(relaxed) force-free field line:
W 
2
[
B
 (s) / 8 ]ds 
cusp
2
[
B
 (s) / 8 ]ds
force  free
Acceleration regions are expected in locations where newly
reconnected field lines relax into a force-free configuration.
Measurements of
ratio of
electron time-of-flight
distance L to
flare 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 height
of electron acceleration region
in 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)
z ( )  z0 (

20 keV
)  a , z  2.3Mm , a  1.32 0
The height distribution of HXR emission dI/dz(z) is shown
for 5 different HXR photon energies e=5, 10, 20, 30, 40 keV
Hurford et al. (2006)
Acceleration sources of electrons versus ions:
The standard flare scenarios predict identical sources
but the observations reveal different locations for
hard X-ray electrons and 2.2 MeV producing neutrons !
The gamma-ray source of the 2.2 MeV neutron-capture line
was found to be displaced by 20”+/- 6” from the 25 keV hard
X-ray footpoints during the 2002 Jul 23 flare. A similar
result 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 ?
MICROSCOPIC SCALES :
Physics of Particle Acceleration
Fast (subsecond) time structures of hard X-ray and radio
pulses in solar flares suggest small-scale, fragmented,
bursty magnetic reconnection mode.
Basic Particle Motion
Particle orbits in magnetic fields: Electrons and ions
experience Lorentz force that makes them to gyrate
around the guiding magnetic field.
r
r r
d(mv ) r
1 r r r 
( x,t)  q E ( x,t)  v  B( x,t) 


dt
c
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.
r
r

q Fperp  B 1 Fperp B 
r
v Drift 

 

2
c
B
g  m
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, 1998
Schumacher & Kliem 1997
Kliem et al. 1995, 1998
Kliem, Karlicky, & Benz 2000
Electric field at X-point in
impulsive bursty reconnection mode
(Kliem et al. 2000)
Hard X-ray pulses resulting from
accelerated electrons dt ~ 0.1-0.3 s
(Aschwanden et al. 1996)
MICROSCOPIC & MACROSCOPIC SCALES :
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
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:
me v r
eE  e,i
,
t s (v r )
tse,i  v /  v parallel /t)
mv=change of momentum
tse,i=collisional slowing-down time

Under the action of an electric DC field, the bulk of the
electron distribution drifts with a velocity vd, but is not
accelerated because of the frictional drag force is
stronger than the electric field. Above the critical velocity
vr defined by the Dreicer field, the electric force overcomes
the frictional force and electrons can be accelerated freely
out of the thermal distribution (runaway accleration regime).
Super-Dreicer fields require much smaller spatial scales
but higher electric fields. Energy gain in an electric field
perpendicular to the guiding magnetic field:
W 
Bparallel
Bperp
ewy E parallel
Sub-Dreicer: particle acclerated along full length of current sheet
Super-Dreicer: particle drifts perpendicularly out of current sheet
(Kliem 1994)
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
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)
  s /   kv  0
Gyroresonant wave-particle interactions are described
by coupled equation system for changes of photon
wave spectrum N(k,t) and particle distribution f(p).

Γ(k,f[p])=wave amplification growth rate
ΓColl(k)=wave damping rate due to collision
Dij(N[k])=quasi-linear diffusion tensor of particles
Miller et al. (1996)
 p    e
-Electron acceleration by whistler waves
 H ~ k v
-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)
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 be
applied to collisionless shocks.
Particle gains perpendicular momentum
due to the conservation of magnetic
moment across shock front:
De Hoffman-Teller frame:
ratio of reflected to incident
kinetic energy:
Diffusive shock acceleration
Particles encounter multiple transversals of shock fronts
and pick up each time an increment of momentum that
is proportional to its momentum. Momentum after N shock
crossings is:
leading to a powerlaw spectrum for the particle momentum
General treatment: diffusion convection equation:
Particle orbit undergoes diffusive shock acceleration
in a quasi-perpendicular shock (60 deg)
by multiple crossings of the shock front
with 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 :
MICROSCOPIC & MACROSCOPIC SCALES :
Particle Kinematics and Propagation
Each particle transport
process has its characteristic
energy-dependent timing
that 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
Electron velocity
Dispersion:
t prop
 lTOF
lTOF


 v
v2
 1




Pitch angle:
lmag  lTOF cos( )  lTOF
v||
v
Magnetic twist:
lloop  lmag cos( )
Electron energy:

  me c 


1
2
1  (v / c ) 2




Photon energy:
EHXR   e
(Bremsstrahlung cross-section)
Electron time-of-flight
(velocity dispersion)
t1-t2 = L/v1 – L/v2
v(E) = c [ 1 – 1/2] 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-ray
Continuum emission ar the looptop later in the flare
with decay times progressively increasing with energy.
Evidence for trapping? - tcoll(E) ~ E3/2
Upward versus downward acceleration in flares
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
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)
Zurich
radio
CGRO
Aschwanden et al. (1993)
Acceleration region bracketed by upward/downward electron beams:
--> triple correlations between radio type III, RS and HXR pulses
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 top
radio image at 1.445 GHz (with VLA)
--> spatial location of loop top
magnetic 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 GeV
Nuclear de-exitation lines
0.4…6.1 MeV 1-100 MeV/nucl
Neutron capture line
2.2 MeV
1-100 MeV/nucl
Positron annihilation radiation
0.511 MeV
1-100 MeV/nucl
Pion decay radiation
10 MeV-3 GeV 0.2-5 GeV
Neutrons in space
10-500 MeV 10 MeV-1 GeV
Neutrons induc.atmos. cascades 0.1-10 GeV
0.1-10 GeV
Neutron decay protons in space 20-200 MeV
20-400 MeV
Energy spectrum of the largest flares
1 keV
1 MeV
1 GeV
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-11
flare 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 rays
closely 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
Dennis (1985), Crosby et al. (1993)
-Flare gamma rays, hard X-rays, soft X-rays
-Solar flare, microflares, nanoflares
-Flare ultraviolet, EUV, H-alpha
-Solar energetic particle events (SEP)
-Coronal mass ejections
-Solar wind fluctuations
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 nanoflare
to the largest flare ...

… there are 8 orders
of magnitude difference
in (thermal) energy !

CONCLUSIONS :
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.
http://www.lmsal.com/~aschwand/ppt/2011_SLAC_solar.ppt