Structure of the solar coronaRamn OliverUniversitat de les Illes BalearsPPARC Advanced Summer School in Solar Physics

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PurposeAn hour and a half worth of

some basic observational facts about the solar corona and

some basic understanding about the solar corona

Re-examination of familiar conceptsRobertus e-mail message: I usually give choco or beer or a poster or a nice picture about the Sun

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OutlineLarge-scale structure and physical conditions of the corona

Small-scale structure: active regions & loops

The dynamic coronaLarge-scale structure and physical conditions of the corona

Small-scale structure: active regions & loops

The dynamic corona

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Solar eclipse totalityTotal solar eclipses gave the first glimpse of the solar corona (106 times dimmer than photosphere)

Warning: beware of image processing. During an eclipse, the corona is 100 times brighter at solar limb than at 1 R height

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Large-scale structuresTwo types of structures:Thin plumes near the polesLong streamers near the equatorHow persistent is this structuring? Just wait!

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Large-scale structuresEclipse (blue-ish) + LASCO C2 image (orange-ish)LASCO C2 FOV 2-6 RStreamers extend out many solar radiiShape of corona changes in time (t 18 months)Polar plumes?Note projection on the plane of the skyMany superposed structures

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The white light corona (K-corona)Coronal emission in eclipses and with coronagraphs consists of photospheric radiation scattered off coronal electrons

This process is equivalent to that responsible for the halo around a street lamp in the fogA photon is deflected by an electronA few photons are deflected ~ 90By the way there are free electrons in the corona

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Coronal densityObserved brightness + theory of Thomson scattering used in the first determinations of coronal density ne ~ 107-109 cm-3106-108 times less dense than the photospheric gasLess dense than best vacuum in Earths laboratories

Variation with height: ne decreases with h cause of reduction of brightness with height

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Coronal temperatureCorona emits its own light (scattering is not emission!)Slitless spectrum during eclipseChromosphere not completely occulted spectral linesHHHHCaIIHeISlitless spectrum of corona during eclipseGreen, red and yellow coronal lines (5303 , 6374 , 5694 )Emission from Fe+13, Fe+9 and Ca+14 FeXIV, FeX, CaXVKnown as E-corona (vs. the K-corona we see in eclipses)

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Coronal temperaturePresence of highly ionised atoms possible because of high coronal temperatureIonisation equilibrium in corona balance between

Remember: temperature is a measure of average kinetic energy of gas particlesHigh temperature large electron velocities energetic collisions ionisationcollisional ionisation recombination

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Coronal temperatureIonisation balance calculations lead to fractional ion abundances as a function of temperature:

Fe+9 most abundant for T ~ 106 KFe+13 most abundant for T ~ 2106 KCa+14 most abundant for T ~ 4106 KCorona is suprathermal and multi-temperature

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Suprathermal coronaThe temperature grows from ~ 5800 K in the photosphere to ~ 106 K in the coronaThis is unexpected: the atmosphere does not show the outward temperature decrease of the solar interior (caused by flow of atomic fusion energy)Convective motions below the surface may be the cause of chromospheric heating (but not coronal heating)

Meet THE CORONAL HEATING PROBLEMSolution: unknown, but most probably MAGNETICTalks Coronal heating: observations & Coronal heating: theory

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Multi-temperature coronaExistence of the green, red and yellow coronal lines implies corona is not isothermalCorona emits in a multitude of lines outside the visible spectrum (mostly EUV & soft X-rays SXR)Some spectral lines used by EIT or TRACE and temperature sensitivity

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Multi-temperature coronaSimultaneous images with EIT coronal filters1 MK1.5 MK2-2.5 MK

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Multi-temperature coronaYohkoh soft X-ray telescope (SXT) records SXR emission of plasma at 2-5 MKComparison between TRACE (171 ) and SXT images; SXT has poorer spatially resolution different appearance of structuresSize of FOV 700 Mm 350 Mm

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Multi-temperature coronaAll over the corona gas elements at widely different temperatures are close neighboursHow dynamic is this situation? Do these elements interchange heat until temperature equilibrium is achieved? More about this later

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Coronal compositionThe huge temperature leads to full ionisation of H and partial ionisation of He and metalsRemember: collisions responsible for ionisationThus, the corona is made of a mixture of electrons and ionsProtons and electrons are the most abundant

The coronal gas is in a (partially ionised) PLASMA stateInteracts with (electro)magnetic fieldsCan be treated as a fluidMagnetohydrodynamic approximation

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Coronal compositionAbundances in the coronal gas is similar to photospheric~ 91% hydrogen atoms (fully ionised)~ 8.9% helium atoms~ 0.1% metals

But there are some differences:different ionisation statesA few elements are more abundant than in photosphere; He is less abundant

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Origin of coronal structuringClassical modelling of the stellar interiors and atmospheres based on gravitational stratification balance of pressure gradient and gravity forcesConsequence: physical parameters vary ONLY in the radial direction, NO horizontal structuresStreamers and plumes should not exist!

Some force is shaping the coronal gas MAGNETISMThe magnetic field is the dominant organising force in the low corona

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Solar magnetismA few keywords:Convective motions, magnetic field generation in the tachocline & magnetic flux emergenceTalks Structure of the Sun: the solar interior & Dynamo theory

Photospheric magnetic fields: spatial intermittency, i.e. 100 G to kG fields very unevenly distributedTalk: The structure of the lower solar atmosphere

Coronal structure is direct consequence of shape of magnetic fields emerging through photosphere

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Photospheric magnetismMagnetogram distribution of photospheric magnetic fluxWhite/black strong magnetic fieldGrey weak/no mag. field

Large-scale structures dominate, but intense flux concentrations present at 1 Mm scales (i.e. spatial resolution limit maybe flux tubes are thinner than 1 Mm)

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Magnetic field structureFlux tubes expand in chromosphere and transition region and become space-filling in coronaMagnetic field lines connect two opposite photospheric polaritiesLarge flux concentrationsSmaller flux concentrationsMagnetogram: green instead of grey

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Coronal magnetic structureField lines often close at very large distanceMagnetic field lines in the corona can be:Closed: connecting two opposite photospheric polaritiesOpen: length of field lines is infinite in practice Coronal magnetic field line configuration

Magnetogram: yellow & orange instead of white & grey

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Coronal structureCoronal magnetic topology based on magnetogram data for 03/17/2006 & used to PREDICT magnetic configuration on 03/26/2006 (total eclipse!)Open field lines in polar regions polar plumesClosed field lines in equatorial region streamersPlasma maps out coronal magnetic field geometry

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Coronal structureThe shape of magnetic field lines reflects itself in the structures of the corona; comparison with LASCO C2LASCO image: continuation of streamers and some polar plumes

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Coronal structureAnd now LASCO C2 and C3LASCO C3 FOV 4-30 R

Streamers extend radially many R

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Coronal structureHigh EUV emission occurs above pairs of strong photospheric magnetic flux ACTIVE REGIONSEmergence of fresh magnetic flux gives rise to a host of dynamic phenomena1.5 MK2-2.5 MK

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Coronal structureEUV & white light corona (LASCO C2)Streamers above active regions1 MK1.5 MK2-2.5 MKCME

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Coronal structureClockwise: 171 , 195 , 284 , Yohkoh SXR & magnetogramBig image: superposition of the three TRACE EUV imagesCorona composed of:Active regions: the brightest elements, from 1 to 5 MK; closed magnetic fieldsCoronal holes: clearly dark in SXR; open magnetic field lines, usually near the polesQuiet Sun: areas outside active regions & coronal holes; closed field lines; not quiet at all!!

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Frozen flux theoremBecause of the very large coronal length-scales, the MHD induction equation dictates that the magnetic flux is frozen-in to the fluidField lines are like elastic bandsA plasma element moving across a magnetic field is tied to field lines and so drags themPlasma elements cannot cross the limits of magnetic flux tubesPlasma elements can only freely move ALONG field lines

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Density and temperature (once more)Active regions have the largest n and Tn ~ 108-109 cm-3, T ~ 2-6 MKActivity injection of chromospheric material and heatingClosed magnetic topology effective plasma confinementQuiet sun smaller density and temperaturen ~ 1-2108 cm-3, T ~ 1-2 MKClosed magnetic field, but less activity reduced mass injection, reduced heat input rateCoronal holes rarer and coolern ~ 0.5-1108 cm-3, T 1 MKOpen field configuration particles escape more easily

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Section summaryCoronal magnetic fields are organised in open and closed configurationsOpen fields prevail in the polar regions coronal holes & polar plumesClosed fields connect intense photospheric magnetic pairs active regions & streamersClosed fields (e.g. between neighbouring active regions) quiet SunPlasma in corona is suprathermal & multi-temperatureHot plasma emits mostly in EUV and X-ray lines

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OutlineLarge-scale structure and physical conditions of the corona

Small-scale structure: active regions & loops

The dynamic corona

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Active regionsAn active region is a portion of the corona overlying two opposite strong magnetic polarities visible here as a sunspot pair

Active regions occupy only a fraction of the Suns surface area, but harbour most of coronal activityFlares, CMEs, plasma heating, flows, waves, etc.

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Active regionsOrigin of this activityMagnetic flux emergence, magnetic flux cancellation, magnetic reconfiguration, magnetic reconnection

Consequence of activity chromospheric upflows inject material in the coronaMany loops filled with hot, dense plasmaEmission in EUV & SXRComposite of TRACE 171 images

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Active regions & loopsClose look at an active region using TRACE:three dimensional structure extending to great heightscomplex arrangement of tubular arches (loops)Loops merge large and small scales: length and thickness (~ 1 Mm), respectively

Are loops resolved by TRACE observations (0.5 spatial resolution)?Loops delineate path of magnetic fields

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Ubiquitous loops?Despite the omnipresence of loop structures in coronal EUV images, loops are actually relatively rare

If many more loops were present in a given area, then isolated loops would not be so clearly visible

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Loop emissionCoronal loops are detected because:They have the right temperature to emit in the filter passbandEmitted intensity roughly proportional to ne2 loops are visible only if they are dense enough

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Loop thicknessWhy are loops so thin?Small loop widths are a consequence of the transverse size of photospheric magnetic fieldsBut then, why doesnt the loop material spread in the transverse direction?

Because of frozen flux theorem, plasma elements are confined to the limits of the magnetic flux tube and can only freely move ALONG the loop

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Loops & equilibriumWe know very well that some loops are dynamic objectsHowever, why not assume some of them are in some sort of equilibrium?Let us introduce some theoretical conceptsHydrostatic equilibriumMagnetohydrostatic equilibrium

Robertus e-mail message: do not have too much maths, but SOME maths can be delivered for those interested in the theory Here we go!

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Hydrostatic equilibriumLet us consider a gas in hydrostatic equilibrium no time variations + balance of p and gp + g = 0Assume only dependence with height (z = rR) dp/dz g = 0Assume ideal gas law p = RT/ comes from adding together the pressure of electrons, protons & ions = 0.5 in a fully ionised H plasma ~ 0.635 in corona (mostly because of 4He)Assume uniform temperature (really?)Gravitational acceleration: g = g(R/r)2 (g=274 m s-1)

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Hydrostatic equilibriumNeglect radial variation of g (so take g = g)p, decrease exponentially with height p(z) = p0exp(z/), = RT/g is the gravitational scale-height: = 47.7 T6 MmT6=T/106 KIf radial variation of g not neglected p(z) = p0exp[z/(1+z/R)]Some remarks:p ~ const. for small variations of z or large TClose to surface z R and the two expressions agreeFor T = 1 MK and z = 100 Mm the exponential approximation underestimates the pressure by 23%

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Magnetohydrostatic equilibriumA magnetic field B exerts a force jB per unit volume on a plasma elementj = B/ (from Amperes law) is the current densityjB is called the Lorentz forceComes from the force qvB on a charge q with velocity vThe force balance equation now is p + g + jB = 0

Does the equilibrium solution differ too much from the hydrostatic one?

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Magnetohydrostatic equilibriumScalar product by B ( we follow the loop field line) Bp + Bg = 0 B dp/ds B g cos = 0 dp/dz + g = 0

Same equation of hydrostatic caseSame vertical dependence of density and pressureBUT each loop can have its own T its own different loops may behave in a different mannerLoops are like mini-atmospheres

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Are loops in hydrostatic equilibrium?TRACE image in 171 filterSensitive to 106 K temperatureIf hydrostatic equilibrium n(z) = n0exp(z/) with ~ 47.7 MmThe line intensity is proportional to n2 I(z) = I0exp(2z/) scale-height is / 2 ~ 25 MmIntensity decreases by almost 40% every 25 Mm

Is this what we observe?Very probably not

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Are loops in hydrostatic equilibrium?Analysis of 40 loops, measure scale-height (m)Loops selected if intensity contrast is significant along their whole lengthBut, suppose a long loop is in hydrostatic equilibrium intensity decreases substantially from bottom to top loop is discarded !Long loops in hydrostatic equilibrium cannot be detected with this selection criterion

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Are loops in hydrostatic equilibrium?Results: only a few loops have m ~ , all other loops are not in (magneto)hydrostatic equilibriumNo long loops in hydrostatic equilibrium found (as expected)Moreover, many loops not in hydrostatic equilibriumWhat is wrong? Our assumption of force balanceDynamics (flows, waves, ), but also energetics (heating & cooling ) must be taken into accountm/

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Are loops in hydrostatic equilibrium?Forces required to lift up the large quantities of plasma illustrated by simulated image based on hydrostatic balanceHow active region looks likeHow it would look like if in hydrostatic equilibrium

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Plasma betaRelative importance of forces through dimensional analysis: |p| / |g| ~ p/L / g = /LPressure force dominates over gravity on short vertical distances (/L1); gravity important in high structures (/L1)Lorentz force jB = 1/(B)B: |p| / |jB| ~ p/L / (B2/L) ~ 2p/B2 = Magnetically dominated plasma for 1Lorentz force: jB = 1/(B)B = 1/(B)B (B2/2) 1/(B)B magnetic tension force(B2/2) gradient of magnetic pressure

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Coronal magnetic field modellingLittle observational information about coronal magnetic field numerical modellingThe solar corona is usually described as a low- plasmaThe magnetic Lorentz force then is said to shape the coronal plasmaThe influence of gravity is neglected (is this realistic?)Force balance equation reduces to jB = 0 !j = 0 B = 0potential solutionj 0 (B)B = 0force-free solutionPartial differential equations for B solved; boundary conditions = photospheric magnetic field distributionReal b.c. should be chromospheric magnetic field

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Coronal magnetic field modellingResults:Magnetic field is non-potential currents flow in the coronal plasmaNo unique force-free configuration from given boundary conditions!

Comparison between different numerical modelsFix magnetic flux distribution at coronal baseFeed the numerical models with these dataCompare numerical solutions with analytical one

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Coronal magnetic field modellingCentre of domain some agreement between computations and analytical solution

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Section summaryActive regions are mainly composed of closed magnetic field lines connecting two strong magnetic flux concentrations on the photosphereFlux tubes in active regions reflect the fibril nature of the very thin photospheric magnetic fieldsA few flux tubes are the sites of enhanced density & temperature and emit EUV and SXR coronal loopsThe intensity of some very large loops in 171 indicates that they are not in hydrostatic or magnetohydrostatic equilibriumModelling of coronal structures is tough and needs improvement

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OutlineLarge-scale structure and physical conditions of the corona

Small-scale structure: active regions & loops

The dynamic corona

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Temporal variabilityWe have described the spatial complexity of corona; dynamic behaviour equally (or more) importantChanges in time scales from years to seconds (or less, given the time cadence of observations)Keywords and phenomena:Very long time scale: solar cycleImpulsive & extremely energetic: eruptive filaments, CMEs, flares, shock wavesNot so energetic (where is the boundary?): flows, jets, brightenings, blinkers, oscillations,

In two words SOLAR ACTIVITY

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Solar cycleDuring the solar cycle the strong bipolar magnetic flux concentrations creating sunspots grow and decrease in number and importanceJanuary 1992(cycle 22)July 1999(cycle 23)

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Solar cycleActive regions follow the same trend; the same happens with all manifestations of solar activityJanuary 1992(cycle 22)July 1999(cycle 23)

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Solar cycle & X-raysYohkoh SXT movie during 1993-94Declining phase of cycle 22

Less and less active regionsActive regions become less bright (less active!)Coronal holes cover larger portion of corona

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Solar cycle & EUVDuration = 1 month; EIT 171 Sun is more active in rising phase than in minimum

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Solar cycle & eclipsesNear the minimum there are less streamers and polar plumes are emphasised

At maximum, there are many active regions and streamers overlapCorona has a bipolar configurationStreamers burst in all directions

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Dynamics of an active regionTRACE observation through 171 passbandDuration ~ 6 hours, spatial resolution ~ 750 km per pixelRapid evolution even though there are no obvious flaresA front near the left sunspot moves from north to southSunspot on the right rotates anti-clockwise magnetic reconfiguration many rapidly evolving loops between the two sunspotsIf you cannot see all these phenomena, play the movie more slowly

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Dynamics of an active regionTRACE observation; duration ~ 8 hoursFlows along field linesHeating and cooling of successively longer loops

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Dynamics of an active regionRemarkable vertical ejection of plasma (TRACE)Often activity originates at the chromosphere or bottom of corona

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Full disk solar activityEIT at 195 for 3.5 days

Activity signs in active regions near the disk centre and on the east limb

Large dark filaments across the disk

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FlowsTRACE 1550 (transition region line!)Material flows in low-lying loopsFlow to the left: ejection?

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Shock wavesEIT 195 movie of active region transiting into the diskContinuous morphological loop changesA few shock waves (aka EIT waves) produce emission dimming in and around the active region

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Waves and oscillationsThese are but two examples of waves and oscillations detected in EUV and X-raysTalk: MHD wavesTransverse coronal loop oscillationsPropagating compressive waves along loop footpoint

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Prominences/filamentsTwo names for the same kind of objectFilamentProminence

Plasma with chromospheric properties suspended in the coronaEmission and absorption in chromospheric lines (e.g. H)

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Prominences/filamentsYet another EIT filter! He line at 304 Chromosphere - transition region

Most prominences in this movie are active; the large one near the south pole seems quiescent except at the end of the movie

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Eruptive filamentFilaments block some EUV emission (TRACE 195 )Small, low-lying active region filament ejected into the interplanetary space

Look at the time for destabilisation!

Later on, heated and cooling loops

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Eruptive filamentEruptive filament followed by the formation of arcade loopsEruption seems to be caused by instability linked to emergence of new magnetic flux

Talk: MHD instabilities

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FlaresThe most energetic (1029-1032 erg) and rapid (well below the instrumental acquisition cadence) phenomena observed in the solar coronaThe large photon flux causes EIT CCD saturation (horizontal bar)

Snow shower due to particles accelerated to extremely high speeds

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Bastille day flareSame event with smaller FOVDuration of movie: 7 hoursFlare takes place around 10:00 (accompanied by ejection)Two-ribbon structure & post-flare arcade developTalks: MHD instabilities, Coronal heating: observations, Coronal heating: theory

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Coronal mass ejectionsCMEs are huge plasma bubbles ejected into the interplanetary mediumEjected mass up to 1010 tonnes; speed up to 1000 km s-1LASCO C1 CME initiation can be appreciated

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Coronal mass ejectionsCME associated to filament eruptionTalk: MHD instabilities

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Section summaryAll solar activity manifestations vary in intensity along the 11-year solar cycleSolar activity consists of dynamic phenomena covering many spatial, temporal and energy scalesSolar activity is triggered by magnetism

AND ALL THIS THANKS TO CONVECTION!

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BibliographyM. J. Aschwanden (2006) Physics of the Solar Corona, Springer-PraxisObservations, data analysis, theory, H. P. Goedbloed & S. Poedts (2004) Principles of magnetohydrodynamics, Cambridge Univ. PressTheory, theory, theoryL. Golub & J. M. Pasachoff (1997) The Solar Corona, Cambridge Univ. PressObservations, theory, instruments, history, E. R. Priest (1982) Solar magnetohydrodynamics, ReidelTheory, theory, theory

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Web resourcesSOHO web pagehttp://sohowww.nascom.nasa.gov/SOHO realtime imageshttp://sohowww.nascom.nasa.gov/data/realtime-images.htmlTRACE web pagehttp://sunland.gsfc.nasa.gov/smex/trace/mission/trace.htmYohkoh SXT instrumenthttp://www.lmsal.com/SXT/

Etc., etc., etc.