2What is a solar flare? A solar flare is a sudden release of energy during which magnetic energy is converted tokinetic energy of fast particles, mass motions,and radiation across the entire electromagneticspectrum.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]
3Solar 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).
4Spacecraft 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 ( ).
5GOES measured X-ray emission over a 3-day period in 2000.
6Soft X-ray emission from the Sun as measured by GOESGOES 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-2M1 = 10-5 W m-2C1 = 10-6 W m-2B1 = 10-7 W m-2A1 = 10-8 W m-2A large flare is typically at X level (e.g. X5). Background emission at solar minimum around A1 or less.
7Note 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.
8Chromospheric 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
9Movies of some flaresMovie 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)
10Limb flare seen with TRACE (2001 April 15): 171Å filter (Fe IX/Fe X) Solar flare imagesLimb 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)
11Playing 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
12Energy 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 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: – JTotal energy in a large flare: ~ 3×1025 J
13Fundamental 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.
14Fundamental questions in flares (contd.) Where is the energy released?Practically impossible to determine – it appears that energetic particles are accelerated at the energy release siteWhat 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.
15Flare 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.
16Flare 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 ionssuch 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-relativisticelectron bremsstrahlung>10 MeV continuum is due to relativistic electronbremsstrahlung.
17Flare radiation and emission mechanisms (contd.) γ-ray emission (contd.)- continuum in the 4-7 MeV range due to merging ofbroad nuclear de-excitation lines when ambient H and Henuclei are bombarded by heavy nuclei.- narrow lines in 4-7 MeV range produced whenaccelerated protons and particles interact with ambientheavy nuclei.- strongest -ray line is the neutron capture line at2.23 MeV, with another strong line at MeV dueto electron-positron (e- - e+) annihilation.
19Flare evolution Flare evolution is in three main phases: Pre-flare: build-up of stored energy and initial energyrelease in a pre-cursor or trigger phaseImpulsive: most evident in HXR and radio, but intenseemission is also seen in optical, UV and EUV.The impulsive nature of the HXR and -wavesargues for electron beam acceleration.Gradual: characterised by a slow rise in SXR caused byfilling of loops with hot material on a timescaleof tens of minutes.
20Soft, Hard X-rays and Gamma rays for a typical flare
21Energy Source of Flares The possible alternatives for the source of flares include:Thermal energy derived from the pre-flare plasmaGravitational potential energy of the pre-flare plasmaEnergy 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.
22Assumed 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).
23Pre-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 JSo only magnetic energy can explain the energy released in the largest flares.
25Maxwell’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:
26Potential 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).
27Energy release Energy release occurs in stressed magnetic fields, but there is much difficulty in accounting for the rapidnature of the release.The basic problem is that high-temperature coronal plasma,especially for flares, has an extremely large electricalconductivity σ (comparable to the conductivity of solidcopper at room temperature) or equivalently small magneticdiffusivity η = 1/(σ μ0) .The energy release timescale appears to be of the orderof years rather than the observed seconds or minutes.
28Induction 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) isSo (3)
29Diffusive, 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 / L2or diffusion time, τD = L2 / η (4)The “classical” value of the magnetic diffusivity (Spitzer) isη = 109 Te-3/2 m2 s-1where 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.)
30Diffusive, 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 approximatelyB / 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 byRm = 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.
31Diffusive, 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.
32Magnetic reconnection Magnetic 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 theinduction equation dominates and results in a changeof magnetic field morphology, converting magneticenergy into heat and kinetic energy.
33Reconnection region (few m wide) X-type reconnectionReconnection region (few m wide)Plasma flow: reconnection “jet”Field linesStage 1Stage 2
34Solar Flares: two reconnection schemes Flare model of Sturrock (1980)Flare model of Heyvaerts et al. (1977)
35Effects 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.
36The flare impulsive phase Most strong particle acceleration occurs during theimpulsive phase and it is most obviously characterized byimpulsive hard X-rays (HXR) and microwave emissionwhich suggests the presence of accelerated electrons.HXR emission (photon energies > ~20 keV) occurs inimpulsive bursts, which are fractions of seconds long.It correlates well with impulsive microwave radio emissionin the 3-10 GHz range.Both HXR and microwaves show complex fluctuations onshort timescales, implying multiple short accelerationbursts.
37The flare’s hard X-ray spectrum The HXR photon spectrum can be described by apower law:photons m-2 s-1 keV-1where I(E) is the measured photon flux and is thespectral hardness where 2.5 < < 5.0 usually. (Thespectral constant C ranges between ,increasing with higher values of .)
38Flare 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.
39The ‘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.
40Other 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.
41Schematic 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
42Gradual 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
43X-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.
44Gradual 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.
45Neupert 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
46Concluding 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.