SOLAR FLARES

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What is a solar flare?A solar flare is a sudden release of energyduring which magnetic energy is converted tokinetic 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]

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Solar spacecraft observing solar flares

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GOES (Geostationary Operational Environmental Satellites): observe total soft X-ray emission in two bands (0.1-0.8nm, 0.05-0.4nm) 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).

Spacecraft observing solar flares (contd.)

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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 (1991-2001).

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

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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.

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 0.185 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 0.185 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. 7

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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

Movies of some flares

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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_20031104_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_010415.avi)

Movie 5: Limb flare seen with TRACE in a continuum channel (about 160 nm, chromospheric emission). (TRACE_cont_flare.mpg)

Solar flare imagesLimb flare seen with

TRACE (2001 April 15): 171Å filter (Fe IX/Fe X)

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Disk flare seen with TRACE (2000 July 14): 195 Å filter (Fe XII/Fe XXIV)

Playing movies from KJHP web site

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Go to: http://www.mssl.ucl.ac.uk/~kjhp/SOLAR_PHYSICS_COURSE_2011/MOVIES/

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_20031104_20UT.mov, xflares_Nov2003.mpg

A large flare’s energy is roughly divided up as:Soft X-ray emission (lines and continua): > 0.5nm – 1025 JInterplanetary blast wave – 1025 JHard X-rays (continuum) – 5×1024 JAccelerated nuclei (relativistic: gives rise to gamma-ray emission >10MeV) – 2×1024 JAccelerated nuclei (non-relativistic: gives rise to gamma-ray line and continuum emission <10MeV) – 3×1024 JOptical and UV emission: – 1024 J Total energy in a large flare: ~ 3×1025 J

Energy Budget for a large flare

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Fundamental questions in flaresWhere 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.

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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.

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Flare radiation and emission mechanismsRadio – 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.

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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.

Flare radiation and emission mechanisms (contd.)

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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 0.511 MeV due to electron-positron (e- - e+) annihilation.

Flare radiation and emission mechanisms (contd.)

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Flare gamma-rays

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 phaseImpulsive: 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.

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

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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. 21

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 ~ 0.05-0.1 T (note permeability of free space µ0 = 4 π × 10-7 H m-1 = 1.26×10-6 H m-1). 22

Pre-flare energiesThermal energy = (3/2) (np + ne) kB Te V = 3 np kB Te V = 1.7 × 1021 J. (kB = 1.38 × 10-23 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.

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Vector identities and operators

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grad

.AA div

AA curl

0)( ) (grad curl 2) div( grad curl curl AAA

del""

zyx

squared"-del"2

2

2

2

2

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zyx

Maxwell’s Equations

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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:

0

.E

0.Bt

BE

JB 0

Potential and non-potential magnetic field

From Maxwell’s equations (neglecting displacement current):

curl B = µ0Jwhere B = magnetic flux density and J is the current.When there is no current,

curl B = 0, so B = grad φi.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). 26

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.

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Induction equation for flare plasmaOhm’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)

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BBBBJ 22) div( grad curl curl curl

) (v curl B

t

B

) 2 B(vcurlBB

t

BvEJJ 0

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Diffusive, advective timescalesEq. (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.)29

) 2 B(vcurlBB

t

22 1

;1

curl ;1

LLtt

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 ~3.1014 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 ~ 3.1012 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. 30

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. 31

Magnetic reconnectionMagnetic reconnection is the most promisingway of reducing the dissipation timescale. Itoccurs when oppositely directed field lines approach oneanother.

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.

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X-type reconnection

Field lines

Reconnection region (few m wide)

Plasma flow: reconnection “jet”

Stage 1 Stage 233

Solar Flares: two reconnection schemes

Flare model of Sturrock (1980) Flare model of Heyvaerts et al. (1977)34

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.

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The flare impulsive phaseMost 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. 36

The flare’s hard X-ray spectrum

The HXR photon spectrum can be described by apower law:

CEdE

EdI )(photons m-2 s-1 keV-1

where I(E) is the measured photon flux and is thespectral hardness where 2.5 < < 5.0 usually. (Thespectral constant C ranges between 103-107, increasing with higher values of .)

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Flare hard X-ray emission sources

A common configuration is double footpointsources. These are seen at the footpoints of soft X-ray loops. They are compatible with the standard thick-target theory of flares.

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The ‘standard’ thick-target flare modelPreceding 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.

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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.

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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 41

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 42

X-ray lines showing flare short-wavelength shifts

Spectra of the Ca XIX resonance line at 0.318 nm (3.18 Å) at four times during a large solar flare: note short-wavelength component to each spectral line.

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.

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Neupert effect for microwave & soft X-ray emission in a solar flare

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Impulsive microwave burst (2695 MHz = 11 cm)

Soft X-ray emission (0.187nm = 1.87 Å)

Time-integrated microwave emission ~ soft X-ray emission

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.

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