PPARC Advanced Summer School in Solar Physics Structure

PPARC Advanced Summer School in Solar Physics Structure of the solar corona Ramón Oliver Universitat de les Illes Balears

Purpose § An 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 concepts § Robertus e-mail message: “… I usually give choco or beer or a poster or a nice picture about the Sun …” 2

Outline § Large-scale structure and physical conditions of the corona § Small-scale structure: active regions & loops § The dynamic corona 3

Solar eclipse totality § Total 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 4

Large-scale structures § Two types of structures: • Thin plumes near the poles • Long streamers near the equator How persistent is this structuring? Just wait! 5

Large-scale structures § Eclipse (blue-ish) + LASCO C 2 image (orange-ish) • LASCO C 2 FOV → 2 -6 R☉ • Streamers extend out many solar radii • Shape of corona changes in time (Δt ≈ 18 months) • Polar plumes? § Note projection on the plane of the sky • Many superposed structures 6

The white light corona (K-corona) § Coronal emission in eclipses and with coronagraphs consists of photospheric radiation scattered off coronal electrons A photon is deflected by an electron A few photons are deflected ~ 90° § This process is equivalent to that responsible for the halo around a street lamp in the fog § By the way… there are free electrons in the corona 7

Coronal density § Observed brightness + theory of Thomson scattering used in the first determinations of coronal density → ne ~ 107 -109 cm-3 • 106 -108 times less dense than the photospheric gas • Less dense than best vacuum in Earth’s laboratories § Variation with height: ne decreases with h ⇨ cause of reduction of brightness with height 8

9 Coronal temperature § Corona emits own light (scattering is not emission!) § Slitless spectrum during eclipse • Chromosphere not completely occulted ⇨ spectral “lines” Hα He. I Hβ Hγ Hδ Ca. II § Slitless spectrum of corona during eclipse • Green, red and yellow coronal lines (5303 Å, 6374 Å, 5694 Å) • Emission from Fe+13, Fe+9 and Ca+14 → Fe. XIV, Fe. X, Ca. XV • Known as E-corona (vs. the K-corona we see in eclipses)

Coronal temperature 10 § Presence of highly ionised atoms possible because of high coronal temperature • Ionisation equilibrium in corona → balance between collisional ionisation ⇔ recombination § Remember: temperature is a measure of average kinetic energy of gas particles • High temperature → large electron velocities → energetic collisions → ionisation

Coronal temperature § Ionisation balance calculations lead to fractional ion abundances as a function of temperature: • Fe+9 most abundant for T ~ 106 K • Fe+13 most abundant for T ~ 2× 106 K • Ca+14 most abundant for T ~ 4× 106 K § Corona is suprathermal and multi-temperature 11

Suprathermal corona 12 § The temperature grows from ~ 5800 K in the photosphere to ~ 106 K in the corona • This 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 PROBLEM” • Solution: unknown, but most probably MAGNETIC • Talks “Coronal heating: observations” & “Coronal heating: theory”

Multi-temperature corona § Existence of the green, red and yellow coronal lines implies corona is not isothermal § Corona 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 Fe. IX/X 171 Å 1 MK Fe. XII 195 Å 1. 5 MK Fe. XV 284 Å 2 -2. 5 MK 13

14 Multi-temperature corona § Simultaneous images with EIT coronal filters 1 MK 2 -2. 5 MK 1. 5 MK

Multi-temperature corona 15 § Yohkoh soft X-ray telescope (SXT) records SXR emission of plasma at 2 -5 MK • Comparison between TRACE (171 Å) and SXT images; SXT has poorer spatially resolution ⇨ different appearance of structures Size of FOV 700 Mm × 350 Mm

Multi-temperature corona § All over the corona gas elements at widely different temperatures are close neighbours § How dynamic is this situation? Do these elements interchange heat until temperature equilibrium is achieved? More about this later 16

Coronal composition 17 § The huge temperature leads to full ionisation of H and partial ionisation of He and metals • Remember: collisions responsible for ionisation § Thus, the corona is made of a mixture of electrons and ions • Protons and electrons are the most abundant § The coronal gas is in a (partially ionised) PLASMA state • Interacts with (electro)magnetic fields • Can be treated as a fluid • Magnetohydrodynamic approximation

Coronal composition 18 § Abundances in the coronal gas is similar to photospheric ~ 91% hydrogen atoms (fully ionised) ~ 8. 9% helium atoms ~ 0. 1% metals different ionisation states § But there are some differences: A few elements are more abundant than in photosphere; He is less abundant

Origin of coronal structuring § Classical modelling of the stellar interiors and atmospheres based on gravitational stratification ⇨ balance of pressure gradient and gravity forces • Consequence: physical parameters vary ONLY in the radial direction, NO horizontal structures • Streamers and plumes should not exist! § Some force is shaping the coronal gas… … MAGNETISM § The magnetic field is the dominant organising force in the low corona 19

Solar magnetism § A few keywords: § Convective motions, magnetic field generation in the tachocline & magnetic flux emergence • Talks “Structure of the Sun: the solar interior” & “Dynamo theory” § Photospheric magnetic fields: spatial intermittency, i. e. 100 G to k. G fields very unevenly distributed • Talk: “The structure of the lower solar atmosphere” § Coronal structure is direct consequence of shape of magnetic fields emerging through photosphere 20

Photospheric magnetism § Magnetogram → distribution of photospheric magnetic flux • White/black → strong magnetic field • Grey → 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) 21

Magnetic field structure 22 § Flux tubes expand in chromosphere and transition region and become space-filling in corona • Magnetic field lines connect two opposite photospheric polarities Large flux concentrations Smaller flux concentrations Magnetogram: green instead of grey

Coronal magnetic structure § Field lines often close at very large distance § Magnetic field lines in the corona can be: • Closed: connecting two opposite photospheric polarities • Open: length of field lines is infinite in practice Coronal magnetic field line configuration Magnetogram: yellow & orange instead of white & grey 23

Coronal structure § Coronal 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 plumes • Closed field lines in equatorial region → streamers Plasma maps out coronal magnetic field geometry 24

Coronal structure 25 § The shape of magnetic field lines reflects itself in the structures of the corona; comparison with LASCO C 2 § LASCO image: continuation of streamers and some polar plumes

Coronal structure § And now LASCO C 2 and C 3 • LASCO C 3 FOV → 4 -30 R☉ § Streamers extend radially many R☉ 26

27 Coronal structure § High EUV emission occurs above pairs of strong photospheric magnetic flux → ACTIVE REGIONS • Emergence of fresh magnetic flux gives rise to a host of dynamic phenomena 1. 5 MK 2 -2. 5 MK

28 Coronal structure § EUV & white light corona (LASCO C 2) § Streamers above active regions 1 MK CME 1. 5 MK 2 -2. 5 MK

Coronal structure 29 § Clockwise: 171 Å, 195 Å, 284 Å, Yohkoh SXR & magnetogram § Big image: superposition of the three TRACE EUV images § Corona composed of: § Active regions: the brightest elements, from 1 to 5 MK; closed magnetic fields § Coronal holes: clearly dark in SXR; open magnetic field lines, usually near the poles § Quiet Sun: areas outside active regions & coronal holes; closed field lines; not quiet at all!!

Frozen flux theorem § Because of the very large coronal length-scales, the MHD induction equation dictates that the magnetic flux is “frozen-in” to the fluid • Field lines are like elastic bands • A plasma element moving across a magnetic field is tied to field lines and so drags them • Plasma elements cannot cross the limits of magnetic flux tubes • Plasma elements can only freely move ALONG field lines 30

Density and temperature (once more) § Active regions have the largest n and T • n ~ 108 -109 cm-3, T ~ 2 -6 MK • Activity ⇨ injection of chromospheric material and heating • Closed magnetic topology ⇨ effective plasma confinement § Quiet sun → smaller density and temperature • n ~ 1 -2× 108 cm-3, T ~ 1 -2 MK • Closed magnetic field, but less activity ⇨ reduced mass injection, reduced heat input rate § Coronal holes → rarer and cooler • n ~ 0. 5 -1× 108 cm-3, T ≲ 1 MK • Open field configuration ⇨ particles escape more easily 31

Section summary 32 § Coronal magnetic fields are organised in open and closed configurations § Open fields prevail in the polar regions ⇨ coronal holes & polar plumes § Closed fields connect intense photospheric magnetic pairs ⇨ active regions & streamers § Closed fields (e. g. between neighbouring active regions) ⇨ “quiet Sun” § Plasma in corona is suprathermal & multi-temperature § Hot plasma emits mostly in EUV and X-ray lines

Outline § Large-scale structure and physical conditions of the corona § Small-scale structure: active regions & loops § The dynamic corona 33

Active regions 34 § An 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 Sun’s surface area, but harbour most of coronal activity • Flares, CMEs, plasma heating, flows, waves, etc.

Active regions 35 § Origin of this activity • Magnetic flux emergence, magnetic flux cancellation, magnetic reconfiguration, magnetic reconnection § Consequence of activity → chromospheric upflows inject material in the corona Composite of TRACE 171 Å images • Many loops filled with hot, dense plasma • Emission in EUV & SXR

Active regions & loops 36 § Close look at an active region using TRACE: • three dimensional structure extending to great heights • complex 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

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 37

Loop emission 38 § Coronal loops are detected because: • They have the right temperature to emit in the filter passband • Emitted intensity roughly proportional to ne 2 ⇨ loops are visible only if they are dense enough

Loop thickness 39 § Why are loops so thin? • Small loop widths are a consequence of the transverse size of photospheric magnetic fields § But then, why doesn’t 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

Loops & equilibrium 40 § We know very well that some loops are dynamic objects § However, why not assume some of them are in some sort of equilibrium? § Let us introduce some theoretical concepts • Hydrostatic equilibrium • Magnetohydrostatic equilibrium § Robertus e-mail message: “… do not have too much maths, but SOME maths can be delivered for those interested in theory…” → Here we go!

Hydrostatic equilibrium § Let us consider a gas in hydrostatic equilibrium ⇨ no time variations + balance of –∇p and ρg –∇p + ρg = 0 § Assume only dependence with height (z = r–R☉) –dp/dz – ρg = 0 § Assume ideal gas law → p = ρRT/ξ • ξ comes from adding together the pressure of electrons, protons & ions • ξ = 0. 5 in a fully ionised H plasma • ξ ~ 0. 635 in corona (mostly because of 4 He) § Assume uniform temperature (really? ) § Gravitational acceleration: g = g☉(R☉/r)2 (g☉=274 m s-1) 41

Hydrostatic equilibrium § Neglect radial variation of g (so take g = g☉) § p, ρ decrease exponentially with height p(z) = p 0 exp(–z/Λ), Λ = RT/ξg☉ § Λ is the gravitational scale-height: Λ = 47. 7 T 6 Mm T 6=T/106 K § If radial variation of g not neglected p(z) = p 0 exp[–z/Λ(1+z/R☉)] § Some remarks: • p ~ const. for small variations of z or large T • Close to surface z ≪ R☉ and the two expressions agree • For T = 1 MK and z = 100 Mm the exponential approximation 42

Magnetohydrostatic equilibrium § A magnetic field B exerts a force j×B per unit volume on a plasma element • j = ∇×B/μ (from Ampere’s law) is the current density • j×B is called the Lorentz force • Comes from the force qv×B on a charge q with velocity v § The force balance equation now is –∇p + ρg + j×B = 0 § Does the equilibrium solution differ too much from the hydrostatic one? 43

Magnetohydrostatic equilibrium 44 § Scalar product by B (⇨ we follow the loop field line) –B⋅∇p + ρB⋅g = 0 ⇨ –B dp/ds – B ρg cosθ =0 ⇨ dp/dz + ρg = 0 § Same equation of hydrostatic case • Same vertical dependence of density and pressure • BUT each loop can have its own T ⇨ its own Λ ⇨ different loops may behave in a different manner • Loops are like mini-atmospheres

Are loops in hydrostatic equilibrium? § TRACE image in 171 Å filter • Sensitive to 106 K temperature § If hydrostatic equilibrium ⇨ n(z) = n 0 exp(–z/Λ) with Λ ~ 47. 7 Mm § The line intensity is proportional to n 2 ⇨ I(z) = I 0 exp(– 2 z/Λ) ⇨ scale-height is Λ / 2 ~ 25 Mm • Intensity decreases by almost 40% every 25 Mm § Is this what we observe? • Very probably not 45

Are loops in hydrostatic equilibrium? 46 § Analysis of 40 loops, measure scale-height (Λm) § Loops selected if intensity contrast is significant along their whole length § But, 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

Are loops in hydrostatic equilibrium? Λm/Λ § Results: only a few loops have Λm ~ Λ, all other loops are not in (magneto)hydrostatic equilibrium No long loops in hydrostatic equilibrium found (as expected) Moreover, many loops not in hydrostatic equilibrium § What is wrong? Our assumption of force balance • Dynamics (flows, waves, …), but also energetics (heating & cooling ) must be taken into account 47

Are loops in hydrostatic equilibrium? § Forces required to lift up the large quantities of plasma illustrated by simulated image based on hydrostatic balance How active region looks like How it would look like if in hydrostatic equilibrium 48

Plasma beta § Relative importance of forces through dimensional analysis: |–∇p| / |ρg| ~ p/L / ρg = Λ/L • Pressure force dominates over gravity on short vertical distances (Λ/L≫ 1); gravity important in high structures (Λ/L≪ 1) § Lorentz force j×B = 1/μ(∇×B)×B: |–∇p| / |j×B| ~ p/L / (B 2/μL) ~ 2μp/B 2 = β • Magnetically dominated plasma for β≪ 1 § Lorentz force: j×B = 1/μ(∇×B)×B = 1/μ(B⋅∇)B – ∇(B 2/2μ) 1/μ(B⋅∇)B → magnetic tension force 49

Coronal magnetic field modelling § Little observational information about coronal magnetic field ⇨ numerical modelling § The solar corona is usually described as a low-β plasma • The magnetic Lorentz force then is said to shape the coronal plasma • The influence of gravity is neglected (is this realistic? ) § Force balance equation reduces to j×B = 0 ! • j = 0 ⇨ ∇×B = 0 potential solution • j ≠ 0 ⇨ (∇×B)×B = 0 force-free solution § Partial differential equations for B solved; boundary conditions = photospheric magnetic field distribution • Real b. c. should be chromospheric magnetic field 50

Coronal magnetic field modelling § Results: • Magnetic field is non-potential ⇨ currents flow in the coronal plasma • No unique force-free configuration from given boundary conditions! § Comparison between different numerical models • Fix magnetic flux distribution at coronal base • Feed the numerical models with these data • Compare numerical solutions with analytical one 51

Coronal magnetic field modelling § Centre of domain → some agreement between computations and analytical solution 52

Section summary § Active regions are mainly composed of closed magnetic field lines connecting two strong magnetic flux concentrations on the photosphere § Flux tubes in active regions reflect the fibril nature of the very thin photospheric magnetic fields § A few flux tubes are the sites of enhanced density & temperature and emit EUV and SXR → coronal loops § The intensity of some very large loops in 171 Å indicates that they are not in hydrostatic or magnetohydrostatic equilibrium § Modelling of coronal structures is tough and needs improvement 53

Outline § Large-scale structure and physical conditions of the corona § Small-scale structure: active regions & loops § The dynamic corona 54

Temporal variability § We have described the spatial complexity of corona; dynamic behaviour equally (or more) important • Changes in time scales from years to seconds (or less, given the time cadence of observations) § Keywords and phenomena: • Very long time scale: solar cycle • Impulsive & extremely energetic: eruptive filaments, CMEs, flares, shock waves • Not so energetic (where is the boundary? ): flows, jets, brightenings, blinkers, oscillations, … • In two words → SOLAR ACTIVITY 55

56 Solar cycle § During the solar cycle the strong bipolar magnetic flux concentrations creating sunspots grow and decrease in number and importance January 1992 (cycle 22) July 1999 (cycle 23)

57 Solar cycle § Active regions follow the same trend; the same happens with all manifestations of solar activity January 1992 (cycle 22) July 1999 (cycle 23)

Solar cycle & X-rays § Yohkoh SXT movie during 1993 -94 • Declining phase of cycle 22 • Less and less active regions • Active regions become less bright (less active!) • Coronal holes cover larger portion of corona 58

Solar cycle & EUV § Duration = 1 month; EIT 171 Å § Sun is more active in rising phase than in minimum 59

Solar cycle & eclipses § Near the minimum there are less streamers and polar plumes are emphasised Corona has a “bipolar” configuration § At maximum, there are many active regions and streamers overlap Streamers burst in all directions 60

Dynamics of an active region § TRACE observation through 171 Å passband • • Duration ~ 6 hours, spatial resolution ~ 750 km per pixel Rapid evolution even though there are no obvious flares A front near the left sunspot moves from north to south Sunspot on the right rotates anti-clockwise → magnetic reconfiguration → many rapidly evolving loops between the two sunspots If you cannot see all these phenomena, play the movie more slowly 61

Dynamics of an active region § TRACE observation; duration ~ 8 hours • Flows along field lines • Heating and cooling of successively longer loops 62

Dynamics of an active region § Remarkable vertical ejection of plasma (TRACE) • Often activity originates at the chromosphere or bottom of corona 63

Full disk solar activity § EIT at 195 Å for 3. 5 days § Activity signs in active regions near the disk centre and on the east limb § Large dark filaments across the disk 64

Flows § TRACE 1550 Å (transition region line!) § Material flows in low-lying loops § Flow to the left: ejection? 65

Shock waves § EIT 195 movie of active region transiting into the disk § Continuous morphological loop changes § A few shock waves (aka EIT waves) produce emission dimming in and around the active region 66

Waves and oscillations § These are but two examples of waves and oscillations detected in EUV and X-rays • Talk: “MHD waves” Transverse coronal loop oscillations Propagating compressive waves along loop footpoint 67

Prominences/filaments 68 § Two names for the same kind of object Filament Prominence § Plasma with chromospheric properties suspended in the corona § Emission and absorption in chromospheric lines (e. g. Hα)

Prominences/filaments § Yet another EIT filter! → He line at 304 Å • 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 69

Eruptive filament § Filaments block some EUV emission (TRACE 195 Å) Small, low-lying active region filament ejected into the interplanetary space Look at the time for destabilisation! Later on, heated and cooling loops 70

Eruptive filament § Eruptive filament followed by the formation of arcade loops Eruption seems to be caused by instability linked to emergence of new magnetic flux Talk: “MHD instabilities” 71

72 Flares § The most energetic (1029 -1032 erg) and rapid (well below the instrumental acquisition cadence) phenomena observed in the solar corona The large photon flux causes EIT CCD saturation (horizontal bar) “Snow shower” due to particles accelerated to extremely high speeds

Bastille day flare § Same event with smaller FOV • Duration of movie: 7 hours • Flare takes place around 10: 00 (accompanied by ejection) • Two-ribbon structure & post-flare arcade develop Talks: “MHD instabilities”, “Coronal heating: observations”, “Coronal heating: theory” 73

Coronal mass ejections § CMEs are huge plasma “bubbles” ejected into the interplanetary medium • Ejected mass up to 1010 tonnes; speed up to 1000 km s-1 § LASCO C 1 ⇨ CME initiation can be appreciated 74

75 Coronal mass ejections § CME associated to filament eruption Talk: “MHD instabilities”

Section summary § All solar activity manifestations vary in intensity along the 11 -year solar cycle § Solar activity consists of dynamic phenomena covering many spatial, temporal and energy scales § Solar activity is triggered by magnetism AND ALL THIS THANKS TO CONVECTION! 76

Bibliography 77 § M. J. Aschwanden (2006) “Physics of the Solar Corona”, Springer-Praxis • Observations, data analysis, theory, … § H. P. Goedbloed & S. Poedts (2004) “Principles of magnetohydrodynamics”, Cambridge Univ. Press • Theory, theory § L. Golub & J. M. Pasachoff (1997) “The Solar Corona”, Cambridge Univ. Press • Observations, theory, instruments, history, … § E. R. Priest (1982) “Solar magnetohydrodynamics”, Reidel • Theory, theory

Web resources § SOHO web page http: //sohowww. nascom. nasa. gov/ § SOHO realtime images http: //sohowww. nascom. nasa. gov/data/realtime-images. html § TRACE web page http: //sunland. gsfc. nasa. gov/smex/trace/mission/trace. htm § Yohkoh SXT instrument http: //www. lmsal. com/SXT/ § Etc. , etc. 78