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Solar Flares and particle
Eduard Kontar
School of Physics and Astronomy
University of Glasgow, UK
STFC Summer School, Armagh, 2012
radio waves
More prominent in X-rays, UV/EUV
and radio . but can be seen from
radio to 100 MeV
Particles 1AU
Solar flares are rapid localised
brightening in the lower
Solar flares: basics
Figure from Krucker et al, 2007
Solar flares and accelerated particles
Solar flares and accelerated particles
From Emslie
et al., 2004,
Free magnetic
~2 1032 ergs
“Standard” model of a solar flare/CME
Energy release/acceleration
Solar corona T ~ 106 K => 0.1 keV per
Flaring region T ~ 4x107 K => 3 keV per
Flare volume 1027 cm3 => (104 km)3
Plasma density 1010 cm-3
Photons up to > 100 MeV
Number of energetic electrons 1036 per second
Electron energies >10 MeV
Proton energies >100 MeV
Figure from Temmer et al, 2009
Large solar flare releases about 1032 ergs
(about half energy in energetic electrons)
1 megaton of TNT is equal to about 4 x 1022
X-rays and flare accelerated electrons
Observed X-rays
Unknown electron distribution
Emission cross-sections
Thin-target case: For the electron
spectrum F(E)~E-δ ,
bremsstrahlung (free-free
X-ray spectrum of solar flares
Thermal X-rays
Gamma-ray lines
Non-thermal X-rays
July 23, 2002 flare
Ramaty High Energy Solar Spectroscopic Imager (RHESSI) spectrum
Compton scattering in pictures
Observed flux
Reflected flux
Direct flux
How can we image X-rays?
How can we image X-rays?
Grazing Incidence optics:
XMM Newton mirrors
(up to ~10 keV)
Works OK but only up to < a few tens of keV !
RHESSI spacecraft and imaging
RHESSI is designed to investigate particle acceleration and energy release in solar flares
through imaging and spectroscopy of hard X-ray and gamma-rays in the range from 3
keV up to 17 MeV (Lin et al 2002).
Spectroscopy: 9 Ge detectors with energy resolution around 1 keV;
Imaging: rotating modulating collimators allowing angular resolution down to 2.3 arcsec;
Imaging spectroscopy: simultaneous images in various energy ranges
Rotating Modulating Collimators
RHESSI detectors look at the source through
a pair of grids called Rotating Modulating
Collimator (RMC)
Spacecraft spins about once every ~4 sec =>
artificial modulation of incoming X-ray flux
Point source
spin period
RHESSI imaging
RHESSI has 9 RMCs for 9 detectors
Slats/Slits spacing growing with detector
(RMC) number
⇒ angular resolution from ~2.3’’ (RMC #1)
to 180’’ (RMC #9)
RHESSI: ideal modulated lightcurves
Modulation profiles for various ideal sources
for a grid of pitch P with equal slits and slats
Point source
Half flux from the point source => note half
45 degrees angle => note change of phase
Source further from the axis => note change of
modulation frequency
Source size=P/2 => note change of the amplitude
Source size=P => note change of modulation depth
(no modulation for source size >> P)
spin period
Modulation encodes spatial source information:
Phase of the modulation => position angle
Distance from the centre => modulation frequency
Amplitude => source size
Modulated lightcurves
Incoming photon flux from
pixel m of the source
Time interval =
observation time – dead
Point source
Modulated Lightcurve
Detector area
Probability to find a photon
from m-th pixel in i-th time
To find an image is to find the solution:
bin (basically the
response of the
Photons (counts) in i-th time bin
RHESSI imaging
Who is this person ?
X-ray visibilities
Fourier, Joseph, Baron
(sum one roll
bin over a few
periods in )
RHESSI Modulation profile over three periods from (Schmahl and Hurford)
Each period is split into roll bins (here it is 16)
Stacking increasing signal-to-noise ratio and
helps to calculate mean amplitude and phase
=> X-ray Visibilities!
X-ray visibilities
Visibilities amplitude
X-ray Visibilities are two dimensional
spatial Fourier components of X-ray source
Visibilities amplitude
Visibilities phase
Visibilities phase
Note 9 circles (nine RMCs) in U,V
(spatial frequencies) plane
Prato et al, 2008
RHESSI imaging
The fundamental problem of RHESSI imaging is to find the spatial photon
distribution knowing the modulated time profile or visibilities
(solve an inverse problem! ;( ):
To accomplish this task various imaging algorithms to solve this inverse
problem exist:
Back Projection
Maximum Entropy Method MEM based (e.g. MEM NJIT)
Forward Fit
Interpolated (smooth) FFT
You method could be here!
Comparing imaging algorithms
06 - January, 2004 flare
useful URLs
Imaging lecture notes and example IDL scripts:
RHESSI imaging overview (good collection):
RHESSI imaging tutorials (from first steps to advanced level ):
Description of all RHESSI imaging software parameters:
X-ray observations
What do we know from X-ray
and gamma-ray observations
about energetic particles?
X-rays and flare accelerated electrons
Observed X-rays
Unknown electron distribution
Emission cross-sections
Thin-target case: For the electron
spectrum F(E)~E-δ ,
Electron-ion bremsstrahlung
(free-free emission)
Dominant process for energies ~10 – 400 keV
the photon spectrum is I(ε)~ ε-δ-1
X-ray emission processes
For spatially integrated spectrum:
Thin-target case: For the electron spectrum F(E)~E-δ ,
a) Electron-ion bremsstrahlung (free-free emission)
Dominant process for energies ~10 – 400 keV
the photon spectrum is I(ε)~ ε-δ-1
In the simplest form Kramers’ approximation:
b) Electron-electron bremsstrahlung (free-free emission)
Dominant process for energies above 400 keV
the photon spectrum is I(ε)~ ε-δ
c) Recombination emission (free-bound emission)
Could be dominant process for energies up to 20 keV
the photon spectrum is shifted by ionisation potential and I(ε)~ ε-δ-2
(The process requires high temperatures and detailed ionisation calculations)
Solar flares
X-ray emission from typical flares
Soft X-ray coronal source
HXR chromospheric
Coronal Source
Standard fare geometry
Soft X-ray emission up to
~10 - 20 keV
Hard X-ray sources
above ~20 keV
RHESSI spectrum (see
Hannah Lecture)
‘Standard’ flare model picture in 2D (Shibata, 1996)
What do we see in RHESSI?
Standard flare model picture (Shibata, 1996)
Krucker et al, 2007
Mean electron spectra
1 3 5
2 4
12 4 5
Kontar et al, 2005
Typical spectra = thermal + non thermal components
Nonthermal is often a broken power-law
Break energy ~50 keV (lower-energy part is harder) Electron
spectral indices 2-4
Sometimes spectral flattening at 300-500 keV
Energy release inside the loop?
(Xu et al, 2008, Kontar
etal, 2011,Guo et al,2012)
Energetic particles
If the fastest process in the system is collisions we can write:
The flux of the electrons (electrons s-1 cm-2 keV-1) follow:
Thick target model: (Brown, 1971)
Kinetic electron energy as a function of column depth
E ( E0 , N ) = ( E − 2 KN )
1/ 2
K = 2π e Λ
Energetic particles:transport
The local electron flux as a function of
column depth (Brown,71):
F0 ([ E 2 + 2 KN ]1/ 2 )
F (E, N ) =
1/ 2
( E + 2 KN )
K = 2π e 4 Λ
Bremsstrahlung: The photon flux per unit source height range at
I (ε , z ) =
n( z ) ∫ F ( E , N )Q(ε , E )dE
4π D
The role of magnetic reconnection
6-10 keV
14-16 keV
Sui et al, 2004
Local re-acceleration scenario
Are particles accelerated within
the loop?
Vlahos et al 1998, Turkmani et
al, 2005, Hood et al, 2008,
Browning et al 2008
Simulations by Gordovskyy & Browning, 2011
Gamma-lines and accelerated ions
October 28, 2003 Xclass flare
(Share et al, 2004)
Alpha-alpha lines favours forward isotropic
Proton & Alpha power law index is 3.75
2.2MeV line shows ~100 s delay
Gamma ray emission
Imaging of the 2.223 MeV
neutroncapture line (blue
contours) and the HXR
bremsstrahlung (red
contours) of the flare on
October 28, 2003. The
underlying image is from
TRACE at 195 Å. The X-ray
and γ-ray imaging shown
here used exactly the same
selection of detector arrays
and imaging procedure. Note
the apparent loop-top source
in the hard X-ray contours
Hurford et al 2006.
Note shift
Energetic particles at 1AU
Energetic particles at 1AU
But the spectral
indices correlate
but do not match
a simple
From X-rays to electrons
From the analysis of 16 “scatter-free” events
(Lin, 1985; Krucker et al, 2007) :
Although there is correlation between the
electrons total number of electrons at the Sun (thicktarget model estimate) the spectral indices
do not match either thick-target or thintarget models.
Acceleration or transport effects?
How are energetic particles
Electric field acceleration
Let us consider electron in collisional plasma. For simplicity, we
consider fields parallel to electron velocity:
is a collisional frequency.
There is a critical velocity that sets right hand side to zero.
Electrons with the velocities larger than the critical are accelerated.
The process is called electron runaway.
Assuming thermal distribution of electrons, there is critical electric
field, called Dreicer field (Dreicer, 1959):
Acceleration: electric field
Putting the constants, one finds:
where number density is
measured in particles per cubic
meter and temperature in K.
Typical values of Dreicer field in
the solar corona ~0.01 V/m
Figure: Dreicer field as
a function of
temperature and density
(Dreicer, 1959)
DC electric field models can
be categorized according
to the electric field:
a) weak sub-Driecer
b) strong super-Driecer
Electric field acceleration: sub-Dreicer field
Runaway acceleration in sub-Dreicer fields has been
applied to solar flares by a number of authors
(Kuijpers (1981), Heyvaerts (1981), Holman (1985), etc)
In principle, such models can
explain observations, e.g.
Benka and Holman (1994)
demonstrate good spectral
Open questions:
1) Stability of the involved DC
2) Large scale fields e.g., the size
of a loop 1010cm
3) Issues with return current
Electric field acceleration: Super-Dreicer field
Models with super-Dreicer require smaller spatial
scales (Martens (1998), Litvinenko (1996, 2003) etc)
The energy spectrum of particles near
an X-point is found to have a power-law
functions N(E)~E-a,a in the range 1.3-2.0
(e.g.Fletcher & Petkaki, 1997, Mori et al,
1998 )
Sub-Dreicer fields might be
responsible for bulk acceleration and
super-Dreicer field from superthermal seed (Aschwanden, 2006).
Figures from Hannah et al, 2002
Open questions:
1) Supply of electrons
2) Consistency of the
Fermi acceleration
Observation of cosmic energetic particles
The story started in 1936. Austrian physicist V. Hess
measured radiation level in 1912 balloon experiment.
Interesting enough, C.T.R. Wilson observed radiation
with cloud chamber experiment (1902) in a railway
tunnel near Peebles, Scotland. However, concluded that
the radiation cannot be cosmic.
Fermi acceleration
Fermi (1949) explained the acceleration of cosmic-ray particles by
reflection on moving magnetic clouds.
Naturally explains inverse power-law distributions.
V’ = V + 2Vs(t)
Vs(t) > 0 => energy gain
Vs(t) < 0 => energy loss
Let Vs(t) =Acos(ωt)
Net energy gain: <V’ >2– <V>2 = 2A2
No energy change in the frame of the racket!
1) Exchange of energy per collision is small
2) Head-on collisions are more frequent
3) Isotropic distribution of particles
Shock acceleration
If csh is the velocity of the shock structure
(e.g. magnetic field acting as a mirror) then
the change in particle energy for one
collision is
The probability of head-on collision is
proportional to v+csh while the probability of
overtaking collision is proportional to v-csh
Taking into account the probabilities the average gain per
collision is
The energy change proportional to the velocity of the shock is first
order Fermi acceleration; proportional to the square is called
second order of Fermi acceleration (original Fermi model).
Power-law distribution
The average rate of energy gain can be written
where we introduced “collisional” time.
Let E=bE0 be the average energy of the particle after one collision and
P be the probability that the particle remains within the acceleration
region after one collision. Then after k collisions, there are N=N0Pk
particles with energies above E=bkE0. Eliminating k one finds
ln P / ln b
N E
=  
N0  E0 
Therefore we find N ( E )dE ∝ E −(1+(ln P / ln b))dE
It can be shown that that the spectral index should be >=2.
Acceleration in flares and CMEs
In solar physics, first-order Fermi acceleration
is often called shock-drift acceleration
(Priest, 1982; Aschwanden, 2006 etc)
Figure: Diffusive shock
acceleration (second-order
Fermi acceleration)
First-order acceleration is viable
for 10-100 keV electrons under
Open questions:
certain conditions and the energy
1) Large areas required
gain is sufficiently fast
2) Number of accelerated electrons
(Tsuneta & Naito, 1980)
Resonant acceleration
Resonant condition
The resonant condition is when the wave has
zero frequency in the rest frame of particle:
Cherenkov resonance (unmagnetised plasma):
Cyclotron resonance (magnetised plasma):
Resonance condition in unmagnetised plasma
Figure: Electron energy spectrum and the spectral density of fast
mode waves (Miller et al., 1996)
Various models have been developed to model acceleration of
electrons by whistler waves (e.g., Hamilton & Petrosian, 1992;
Miller, 1996, 1997)
Doppler resonance:
Solar flare acceleration
Figure: Proton distribution function and Alfven waves (Miller &
Roberts, 1995)
Stochastic acceleration naturally explains enhancement of heavy ions.
Open questions: relatively strong turbulence and its origin
Energetic particles
Instead of conclusions…
Energetic particles at various
cosmic scales
Energetic particles
Scheme of possible emission
mechanism: Positron beam
generating waves => radio
emission via coherent
Figure: Composite Optical/X-ray
image of the Crab Nebula, showing
synchrotron emission in the
surrounding pulsar wind nebula,
powered by injection of magnetic
fields and particles from the central
Energetic particles : Earth ionosphere
RHESSI Terrestrial Gamma-ray Flashes Positions
Visible Lightning Positions
Terrestrial gamma-ray flashes (TGFs) are very brief bursts of
gamma radiation (typically around 1 millisecond long) coming
upwards from the Earth's atmosphere from somewhere in the
vicinity of a thunderstorm (Smith et al, 2005)