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FLARING ENERGY RELEASE
Lyndsay Fletcher
University of Glasgow
EPS Plasma Meeting, Sofia, June 2009
1
Overview
Flare observations:
fast electrons, radiation source characteristics
Theoretical basics:
Energy storage and release, ‘standard’ flare model, electron
acceleration
Challenges to the ‘standard’ model and a new idea
Electron beams or Alfvén waves?
Alfvén waves – preliminary calculations
Conclusions
2
Solar magnetism and coronal activity
Convective and rotational energy of solar interior is transferred
to solar atmosphere via stressing of the magnetic field.
Magnetic energy is dissipated in flares, leading to motion of
the bulk plasma, heating and particle acceleration.
3
Electrons in flares
As much as 50% of all the flare energy released goes into
accelerating electrons (Emslie et al ‘04, ‘05)
These electrons
Movie: Gordon Holman
Flare X-ray spectrum:
e- - p+ bremsstrahlung
Movie: Peter Gallagher
Green: hot plasma (Fe emission lines)
Red : 12-25keV (thermal X-rays)
Blue : 25-50keV (nonthermal X-rays)
4
Flare Radiation
X-rays are important diagnostics, but flare radiation is mostly
optical/UV (lines & continuum), from compact sources.
Isobe et al 2007
flare
Woods et al 2005
In some large flares this is visible in the integrated
brightness.
G-band (CH
molecule)
Fe (stokes I)
Fe (Stokes V)
Flare in total solar irradiance
Flare energy = 6 x 1025 J
Power ~ 1022 W
Spatially resolved observations
Source FWHM = 5 x 105 m
Power per unit area ~ 109 W m-2
5
Flare footpoints
Krucker et al. 2008
Typically two strong hard X-ray
footpoints.
HXR and optical emission are spatially
and temporally correlated
Fletcher et al. 2007
Non-thermal electrons collide in
chromosphere, heat and ionise to
produce the optical/UV.
Orange = HXR
grey = Hard X-ray
Blue = optical
black= optical
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Energy storage
Energy is stored in the coronal magnetic field, as currents.
Magnetic reconnection allows magnetic field to reconfigure
to a lower energy state.
Magnetic field and current distribution
Before flare
After flare
Red =
location of
strong
currents
(Schrijver
et al 2008)
Pre-flare currents stored less than 12,000 km above
photosphere, concentrated around polarity inversion line.
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Energy release and eruption
There are many models for a flare eruption. Most involve a
driven ideal MHD instability followed by a resistive instability
e.g. Kink instability
Twisted field embedded
in overlying field
(green)
Kink instability
embedded in an
overlying field (green)
Török & Kliem 2005
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The ‘standard’ flare model
The observations are interpreted in a framework called the
standard flare model
2D ‘standard model’
Ejected plasmoid
1) Magnetic energy liberated
via magnetic reconnection.
Slow shock
Upward reconnection
outflow
Reconnection region
Stand-off shocks
electron beams
Reconnection inflow
Reconnection
outflow (turbulent)
Slow or fast shock
2) Electrons accelerated in
corona carry flare energy to
the chromosphere.
3) Most of energy radiated by
chromosphere (opt-UV).
4) Chromosphere is heated
and expands into corona 
dense, hot flare loops.
Post-flare loops
Ribbons/footpoints
9
Electron acceleration in the corona
There are two main models for coronal acceleration:
E 
B
t
2) Stochastic acceleration
in turbulent E
E
Liu et al 2008.
1) Acceleration in
reconnection E
or..
L~107 m
High efficiency, low volume
Low efficiency, high volume
(Shock acceleration of flare electrons not thought so likely)
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Coronal electrons
Pre-flare coronal electron density is ~ 1015 m-3
Krucker et al. 06
Coronal X-rays flux implies ~ 1-10% are accelerated to >20keV
(energetically, non-thermal electrons dominate thermals).
Coronal source volume ~ 3 × 1021 m3
11
Chromospheric electrons: standard model
accelerator
Accelerated electrons originate in corona.
electrons
Electron beam travelling along coronal B
carries flare energy to chromosphere
Source-averaged
electron spectrum
chromosphere
Holman et al 03
Photon
spectrum
Electrons in the chromosphere
0
5
10
UV, opt.,
HXR
July 23 2003
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Time (mins)
1035 - 1036 electrons/s accelerated. Coronal ne= 1015 cm-3, so
each second, all electrons in V = 1020 - 1021 m3 accelerated.
12
Electron number and current
Standard model beam rate is ~ 1036 el. s-1 (leaving corona)
Beam area from HXR and optical is < 1013 m2
Beam flux ~ 1023 el. m-2 s-1
Beam speed vbeam ~ 1-2 × 108 m s-1 (electrons at 30-100
keV)
Beam density nbeam ~ few × 1014 m-3
Self field ~ 104 T
Return current
(large fraction of ncorona)
(~ 105 - 106 x ambient)
nbeamvbeam = ncoronavrc
So vrc ~ few × 107 ms-1
cs = 3×105 ms-1 and vth,e ~ 1.2 ×107 m s-1  beam
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Energy transport in our magnetosphere
Following substorm
reconnection, energy stored in
the Earth’s magnetic field
propagates as Alfvén waves.
- Cascades to small k
- Generates field-aligned electric
field which accelerates auroral
electrons. (e.g. Chaston et al.
2008)
- Energy ultimately dissipates in
the ionosphere
Could there be an analogous process in flares?
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Flare energy transport by Alfvén pulse
• Before the flare, energy is stored in twisted magnetic field.
• Field reconfigures, twist redistributes and energy is released
• Wave pulse carries energy as Poynting flux S  v aB 2 / o
Nb. twist greatly exaggerated in
this cartoon.

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Brosius & White 2006
Wave speed and Poynting flux
|B| measured from gyrosynchrotron
emission:
Typical magnetic field strength at
10,000 km altitude:
~ 0.05T (500 G) average over region
~ 0.1T (1kG) above a sunspot
Gyrosynchrotron emission
(contours) above a sunspot
Pre-flare coronal density ~ 1015 m-3  vA ~ 0.1c – 0.3c
Observed chromospheric output = 109 W m-2
10,000
Needs a wave Poynting flux with
Bkm~ 0.006T (60G )
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Inertial Alfven waves
b < me/mp, i.e. vA > vth in flare
corona and upper chromosphere
So waves are in ‘inertial’ regime
and generate an E||
where
For typical solar k|| and k, the E|| is small.
But if ||~ 100 km, ~ 10 km then E|| > Dreicer field and
electrons can be accelerated.
Electrons unable to surmount wave potential barrier reflect and
are energised to 2mvA2 ~ 25 - 100 keV.
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Electron acceleration in a shear pulse
Uniform equilibrium with B = (0,0,B0), electric potential  = 0.
Shear wave perturbation in magnetic potential A is
Modification for
electron inertia
Solutions:
Choose:
giving
(McClements & Fletcher 2009)
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Accelerated fraction and distribution
Calculate fraction of initially Maxwellian electrons reflected
by this pulse and accelerated:
ne = 1015 m-3, B0 = 0.1T, B = 0.01T
x = 3m, initially
Maxwellian
T = 4106 K
T = 4 106 K
T = 3 106 K
T = 2106 K
T = 106 K
T = 3106 K
T = 2106 K
T = 106 K
Electron distribution in this simple case does not look like
the observed power-law. Can try spatially varying plasma
and field properties, and broader spectrum wave pulse.
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MHD simulations of wave propagation
3D MHD simulations of reconnection in coronal field
Diffusion region assumed small
Poynting flux and enthalpy flux tracked.
x
z
Sheared low-b
arcade, erupting
(Birn et al.
y=0 plane:
Poynting
flux in x
direction
y = 0 plane
Poynting
flux in z
direction
Photospheric
projection:
Temperature (grey)
Poynting flux (red)
20
Wave dissipation in the chromosphere
Ion-neutral damping is strong in low chromosphere
 heating and WL, UV production (Emslie & Sturrock 82)
Also with higher viscosity and higher gradients, a
(perpendicular) turbulent wave cascade may develop as
wave pulse crosses chromosphere.
stochastic electron acceleration in the chromosphere? (e.g.
Hamilton & Petrosian 1992).
e.g. Transit time acceleration optimal when vA ~ vth,e, which
happens in upper chromosphere.
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Conclusions
During a flare, stored magnetic energy is distributed through
corona and efficiently converted to KE of fast particles.
Flare ‘standard model’ does a pretty good job at providing a
framework for the whole flare phenomenon.
However, theory of energy transport by electron beams runs
into some trouble compared with recent observations.
Proposal – energy transport by Alfven wave pulse
Electron acceleration
in wave E field?
Pulse dissipation in
chromosphere & local
acceleration?
Much remains to be worked out….
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