1. SOLAR FLARES

2. What is a solar flare? A solar flare is a sudden release of energy
during which magnetic energy is converted to
kinetic energy of fast particles, mass motions,
and radiation across the entire electromagnetic
spectrum.
Energy released up to 1025 J in the largest flares.
Many more much smaller flare-like events (e.g. micro-flares) occur down to ~1017 J (10 × a nano-flare, the observational limit). [nano = 10-9]

3. Solar spacecraft observing solar flares
GOES (Geostationary Operational Environmental Satellites): observe total soft X-ray emission in two bands ( nm, nm) from geostationary positions in western hemisphere.
RHESSI (Ramaty High Energy Solar Spectroscopic Imager):
observes solar flares at high energies (4 keV – 17 MeV (from 2001).
SOHO (SOlar and Heliospheric Observatory): ESA/NASA spacecraft at the L1 Lagrangian point between Earth and Sun, observing Sun in EUV, visible wavelengths (from 1995).
TRACE (Transition Region And Coronal Explorer): observes Sun in Sun-synchronous orbit (orbital plane perpendicular to Sun-Earth direction). EUV bands: 17.1nm (Fe IX, Fe X lines), 19.2nm (Fe XII line), continuum band at 160 nm etc. (from 1998)
Hinode: Japanese spacecraft in Sun-synchronous orbit observing in visible (SOT), soft X-rays (XRT), EUV (EIS) (from 2006).

4. Spacecraft observing solar flares (contd.)
STEREO: Pair of spacecraft, one ahead (A), the other behind (B), the Earth in its orbit, making full-Sun images in EUV (from 2006).
Solar Dynamics Observatory (SDO): Views the Sun in high-Earth orbit in several EUV bands (from 2010).
CORONAS-F, CORONAS-PHOTON: Russian spacecraft carrying X-ray instruments to study flares. Not functional any more.
Yohkoh: Japanese spacecraft with Solar X-ray Telescope and X-ray spectrometers ( ).

5. GOES measured X-ray emission over a 3-day period in 2000.

6. Soft X-ray emission from the Sun as measured
by GOES
GOES measures total soft X-ray emission from Sun in two bands: 0.1—0.8nm, 0.05—4nm (1—8 Å, 0.5—4 Å).
Total X-ray emission in the 0.1—0.8 nm band defined on a logarithmic scale:
X1 = 10-4 W m-2
M1 = 10-5 W m-2
C1 = 10-6 W m-2
B1 = 10-7 W m-2
A1 = 10-8 W m-2
A large flare is typically at X level (e.g. X5). Background emission at solar minimum around A1 or less.

7. Note on X-ray/gamma-ray emission
X-ray wavelengths (λ) normally specified in nm (or Å, where 1Å = 0.1 nm), e.g. strong resonance line of He-line Fe (Fe XXV) is at nm (= 1.85 Å).
But higher-energy X-rays and gamma-rays normally specified by their energies E, expressed in eV or more commonly keV:
λ (nm) = 1.24 / E (keV).
Thermal X-rays have energies up to approximately 20 keV, non-thermal X-rays have energies > ~ 20 keV.
The Fe XXV line at nm has a photon energy of 6.7 keV.
X-ray emission from flares is in the form of emission lines and free-bound and free-free continua. Free-free continuum (or bremsstrahlung) formed when electrons pass near an ion going from one open orbit to another.

8. Chromospheric flare emission
Optical observatories record flares by their H importance:
Flare area measured and classified on a scale S (sub-flare), 1 (small), 2 (medium), 3 (large), 4 (>1200 millionths of a solar hemisphere =
3.6 × 109 km2).
Flare intensity is on a scale from f (faint), n (normal), b (bright).
So a large flare might have a classification 3b

9. Movies of some flares
Movie 1: X17 flare -- Limb flare on 2003 November 4 in the EUV: observations with TRACE in its Fe IX/X, 17.1 nm filter (temp. ~1.0MK). (X17_ _20UT.mov)
Movie 2: “Bastille Day” flare (2000 July 14) near Sun centre in the EUV. An arcade of flare loops on the solar disk observed by TRACE in its Fe XII 19.2 nm filter (temp. ~1.2MK). (Bastilleday.mov)
Movie 3: Another disk flare seen with TRACE (17.1 nm Fe IX/X, temp. ~1.0MK). (TRACE_FeXI_flare.mpg)
Movie 4: Near-limb X14 flare on 2001 April 14 seen with TRACE (17.1 nm Fe IX/X, temp. ~1.0MK). (T171_X14_ avi)
Movie 5: Limb flare seen with TRACE in a continuum channel (about 160 nm, chromospheric emission). (TRACE_cont_flare.mpg)

10. Limb flare seen with TRACE (2001 April 15): 171Å filter (Fe IX/Fe X)
Solar flare images
Limb flare seen with TRACE (2001 April 15): 171Å filter (Fe IX/Fe X)
Disk flare seen with TRACE (2000 July 14): 195 Å filter (Fe XII/Fe XXIV)

11. Playing movies from KJHP web site
Go to:
You’ll find all the movies illustrating this course there. Quick time should open all of them. If not, try IrfanView.
Flare movies include Bastilleday.mov, TRACE_cont_flare.mpg, TRACE_FeXI_flare.mpg, X17_ _20UT.mov, xflares_Nov2003.mpg

12. Energy Budget for a large flare
A large flare’s energy is roughly divided up as:
Soft X-ray emission (lines and continua):  > 0.5nm – 1025 J
Interplanetary blast wave – 1025 J
Hard X-rays (continuum) – 5×1024 J
Accelerated nuclei (relativistic: gives rise to gamma-ray emission >10MeV) – 2×1024 J
Accelerated nuclei (non-relativistic: gives rise to gamma-ray line and continuum emission <10MeV) – 3×1024 J
Optical and UV emission: – J
Total energy in a large flare: ~ 3×1025 J

13. Fundamental questions in flares
Where and how is the energy stored?
The location of the stored energy is unobservable – it is presumed to be in a non-potential magnetic field region (but coronal fields as such cannot be seen or measured).
Why is the energy released?
It is widely assumed that magnetic reconnection results in a sudden release of energy in the way observed.

14. Fundamental questions in flares (contd.)
Where is the energy released?
Practically impossible to determine – it appears that energetic particles are accelerated at the energy release site
What happens after the energy is released?
There are bursts of hard X-rays followed by a gradual increase of soft X-rays and radio emission which is well observed.

15. Flare radiation and emission mechanisms
Radio – microwave to metre wavelengths, produced by gyrosynchrotron (electrons gyrating round magnetic fields), bremsstrahlung and collective plasma processes.
Optical line emission – H and other Balmer lines seen in emission (due to collisional excitation in hot, flare-produced plasma).
White-light continua probably produced by H recombination following electron bombardment and H- emission.
UV lines and continua – excitation by hot flare-produced plasma. Impulsive contribution due to non-thermal e’s.

16. Flare radiation and emission mechanisms (contd.)
EUV lines -- excitation by hot flare-produced plasma.
Soft X-ray – lines and continua (thermal bremsstrahlung,
free--bound continuum). Lines are due to highly ionized ions
such as Fe+24 (He-like Fe, formed at T>15×106K=15MK).
Hard X-rays– non-thermal e- - proton bremsstrahlung
(featureless continuum, intensity decreasing with energy).
-ray lines and continua:
continuum up to 1 MeV produced by non-relativistic
electron bremsstrahlung
>10 MeV continuum is due to relativistic electron
bremsstrahlung.

17. Flare radiation and emission mechanisms (contd.)
γ-ray emission (contd.)
- continuum in the 4-7 MeV range due to merging of
broad nuclear de-excitation lines when ambient H and He
nuclei are bombarded by heavy nuclei.
- narrow lines in 4-7 MeV range produced when
accelerated protons and  particles interact with ambient
heavy nuclei.
- strongest -ray line is the neutron capture line at
2.23 MeV, with another strong line at MeV due
to electron-positron (e- - e+) annihilation.

18. Flare gamma-rays

19. Flare evolution Flare evolution is in three main phases:
Pre-flare: build-up of stored energy and initial energy
release in a pre-cursor or trigger phase
Impulsive: most evident in HXR and radio, but intense
emission is also seen in optical, UV and EUV.
The impulsive nature of the HXR and -waves
argues for electron beam acceleration.
Gradual: characterised by a slow rise in SXR caused by
filling of loops with hot material on a timescale
of tens of minutes.

20. Soft, Hard X-rays and Gamma rays for a typical flare

21. Energy Source of Flares
The possible alternatives for the source of flares include:
Thermal energy derived from the pre-flare plasma
Gravitational potential energy of the pre-flare plasma
Energy contained in the magnetic field of the pre-flare plasma.
To evaluate which is important, we consider likely values for physical parameters of pre-flare plasma.

22. Assumed pre-flare plasma parameters
Spherical volume with radius R ~ 10,000 km:
V = (4/3) π R3 ~ 4 × 1021 m3.
Electron temperature ~ coronal temperature = 1 MK.
Particle number density ~ 1016 m-3 (proton mass mH = 1.7×10-27 kg).
Height of plasma above photosphere H ~ 10,000 km (note acceleration due to solar gravity is gʘ = 274 m s-2).
Magnetic field ~ T (note permeability of free space µ0 = 4 π × 10-7 H m-1 = 1.26×10-6 H m-1).

23. Pre-flare energies Thermal energy = (3/2) (np + ne) kB Te V
= 3 np kB Te V = 1.7 × 1021 J. (kB = 1.38 × J K-1)
Potential energy = np V mH gʘ H = 1.9 × 1020 J.
Magnetic energy = (B2/2µ0) V = 4 × 1024 – 1.6 × 1025 J.
Observed total energy (large flare) = 3 × 1025 J
So only magnetic energy can explain the energy released in the largest flares.

24. Vector identities and operators

25. Maxwell’s Equations We neglect electric displacement field D.
B is the magnetic induction (or magnetic field)
E is the electric field.
ε0 = permittivity of free space.
Gauss’s law:
Faraday’s law:
No magnetic monopoles:
Ampère’s law:

26. Potential and non-potential magnetic field
From Maxwell’s equations (neglecting displacement current):
curl B = µ0J
where B = magnetic flux density and J is the current.
When there is no current,
curl B = 0, so B = grad φ
i.e. B can be expressed in terms of a potential φ.
There is zero energy available from a potential field. Flares derive their energy from non-potential magnetic fields (i.e. from currents).

27. Energy release Energy release occurs in stressed magnetic fields,
but there is much difficulty in accounting for the rapid
nature of the release.
The basic problem is that high-temperature coronal plasma,
especially for flares, has an extremely large electrical
conductivity σ (comparable to the conductivity of solid
copper at room temperature) or equivalently small magnetic
diffusivity η = 1/(σ μ0) .
The energy release timescale appears to be of the order
of years rather than the observed seconds or minutes.

28. Induction equation for flare plasma
Ohm’s law for a plasma:
(1)
where J = current density, E = electric field, B = magnetic induction (field); η = magnetic diffusivity.
Take the curl of both sides:
η curl J = curl E + curl (v × B) (2)
(1/ η) × L.H.S. of (2) is, by Maxwell’s equations,
R.H.S. of (2) is
So (3)

29. Diffusive, advective timescales
Eq. (3):
can be expressed in words by:
Rate of change of magnetic field in a flare volume =
diffusive term + advective term.
Get an order-of-magnitude estimate of quantities by approximating:
If there is no advective term,
B / τD = η B / L2
or diffusion time, τD = L2 / η (4)
The “classical” value of the magnetic diffusivity (Spitzer) is
η = 109 Te-3/2 m2 s-1
where Te = electron temperature. For the quiet corona, Te = 2 MK, so η = 0.35 m2 s-1.
(Solid copper is only a factor 10 smaller.)

30. Diffusive, advective timescales (contd.)
So the diffusive time scale τD for the pre-flare volume (take this to be L = 10,000 km = 107 m) is possibly as high as τD ~ s
(10 million years).
If there is no diffusion, only advection, then approximately
B / τA = (v B) / L2 or advective time scale, τA = L / v (5)
and with v ~ 100 km/s, L = 107 m, τA = 100 seconds.
Magnetic Reynolds number (dimensionless) is defined by
Rm = τD / τA (6)
which is therefore ~ for coronal material.
However, these simple estimates must be wrong for actual flares. It is likely that L ~ a few metres, not the observed flare dimensions which represent the “aftermath” of a flare, not the magnetic field diffusion region.

31. Diffusive, advective timescales (contd.)
As well as a much smaller diffusion length scale, magnetic diffusivity η is probably not given by the simple dependence on Te but instead is described by an “anomalous” value in which the resistivity is due, not to electrons colliding with other electrons, but electrons colliding with plasma waves.
Observations of an oscillating loop (Nakariakov et al.) in solar flare images from the TRACE spacecraft suggest that Rm is in fact more like
(1-6)×105, not ~3×1012.

32. Magnetic reconnection
Magnetic reconnection is the most promising
way of reducing the dissipation timescale. It
occurs when oppositely directed field lines approach one
another.
Reconnection occurs when the diffusion term in the
induction equation dominates and results in a change
of magnetic field morphology, converting magnetic
energy into heat and kinetic energy.

33. Reconnection region (few m wide)
X-type reconnection
Reconnection region (few m wide)
Plasma flow: reconnection “jet”
Field lines
Stage 1
Stage 2

34. Solar Flares: two reconnection schemes
Flare model of Sturrock (1980)
Flare model of Heyvaerts et al. (1977)

35. Effects of magnetic reconnection
Global topology and connectivity of the field lines change, affecting processes that are directed along field lines, e.g. particle transport and heat conduction.
Magnetic energy is converted to heat, kinetic energy, and fast particles.
Large currents, electric fields and shock waves are generated which help to accelerate particles.

36. The flare impulsive phase
Most strong particle acceleration occurs during the
impulsive phase and it is most obviously characterized by
impulsive hard X-rays (HXR) and microwave emission
which suggests the presence of accelerated electrons.
HXR emission (photon energies > ~20 keV) occurs in
impulsive bursts, which are fractions of seconds long.
It correlates well with impulsive microwave radio emission
in the 3-10 GHz range.
Both HXR and microwaves show complex fluctuations on
short timescales, implying multiple short acceleration
bursts.

37. The flare’s hard X-ray spectrum
The HXR photon spectrum can be described by a
power law:
photons m-2 s-1 keV-1
where I(E) is the measured photon flux and  is the
spectral hardness where 2.5 <  < 5.0 usually. (The
spectral constant C ranges between ,
increasing with higher values of .)

38. Flare hard X-ray emission sources
A common configuration is double footpoint
sources. These are seen at the footpoints of soft X-ray loops. They are compatible with the standard thick-target theory of flares.

39. The ‘standard’ thick-target flare model
Preceding the flare, an Hα prominence (or filament) may be activated, becomes unstable and starts to rise (“disparition brusque”).
Following its eruption the opened magnetic field lines reconnect below, producing a reconnection “jet” of fast-moving material.
Particles are accelerated, the reconnection jet collides with the SXR loop below producing an MHD fast shock producing the HXR loop-top source and further acceleration.
Electrons and ions stream down the legs of the loop producing HXR emission when they meet the dense chromosphere.

40. Other features of the thick-target model
Chromospheric material is heated so rapidly that energy cannot be radiated away; plasma expands or “evaporates” to fill the SXR loops.
As the reconnection proceeds, more and more field lines reconnect producing an arcade of loops seen in SXR.
The flare footpoints seen in H as “ribbons” can be seen to move apart. Similar motion seen at HXR footpoints.

41. Schematic model of a flaring magnetic loop (Dennis & Schwartz 1989).
A reconnection of fields occurs along the loop length which accelerates electrons down to the chromosphere.
They dump their energy in the chromosphere which “evaporates” upwards

42. Gradual phase and the Neupert effect
The energy of accelerated electrons provides heating of the ambient atmosphere which sets up pressure gradients leading to hydrodynamic flows & density variations: there is a rapid upflow of heated material, i.e. chromospheric evaporation.
As a result, Doppler shifts are detectable in soft X-ray lines (short-wavelength components to main lines for disk flares): velocities are hundreds of km/s.
See movie bcsmov_16dec_f.avi

43. X-ray lines showing flare short-wavelength shifts
Spectra of the Ca XIX resonance line at nm (3.18 Å) at four times during a large solar flare: note short-wavelength component to each spectral line.

44. Gradual phase and the Neupert effect (contd.)
A critical test of the thick-target model is the SXR line profile during the first 10-20s before the stationary component has had a chance to develop – the model predicts that it should be shifted by 3—4 × 10-4 nm. But observations show a profile where the principal component is stationary.
The peak of the gradual phase is generally observed to occur later than the peak of the impulsive phase in microwaves. Neupert found that the integral of the microwave emission gives a curve closely following the SXR emission.

45. Neupert effect for microwave & soft X-ray emission in a solar flare
Impulsive microwave burst (2695 MHz = 11 cm)
Soft X-ray emission (0.187nm = 1.87 Å)
Time-integrated microwave emission ~ soft X-ray emission

46. Concluding remarks about solar flares
Like the coronal heating problem, the sudden release of energy in a solar flare is still not understood, 150 years after a flare was first observed. The flare problem is similar to the coronal heating problem in that magnetic energy is almost certainly converted to the observed energy forms, but estimates of the magnetic diffusion are far too small to explain the suddenness of the energy release. Most likely the distance scales are very small and/or there are anomalous processes occurring.