Observations of coronal heating Lidia van DrielGesztelyi UCLMullard

Observations of coronal heating Lidia van Driel-Gesztelyi UCL-Mullard Space Science Laboratory, UK Observatoire de Paris, LESIA, France Konkoly Observatory, Hungary

Solar atmospheric layers and their temperature Atmospheric layers of the Sun from the photosphere to the corona - WL (SOHO/MDI) - SOHO/EIT and - Yohkoh/SXT observations.

Chromosphere: T~104 K During total solar eclipse the Fraunhofer absorption line spectrum of the photosphere is replaced by an emission line spectrum – the flash spectrum. The emission lines have dark counter-parts in the Fraunhofer spectrum but there are differences: • He 5876 Å is seen in the chromospheric flash spectrum. This is collisionally excited and the gas temperature has to be ~2 x 104 K before there are enough free electrons with the required energy. this tells us the chromosphere is HOT.

Corona: T~106 K • The first clue for a hot corona: - spectroscopic study of a total eclipse in 1869 by C. A. Young & W. Harkness - bright emission line at 530. 3 nm (green line) - no identification with spectral lines of known elements coronium • several more unidentified lines found during later eclipses (i. e. 637. 5 nm - red line) • “coronium” did not easily fit in the periodic table of elements discredited • 1939, W. Grotrian: The “red line” was found to be due to Fe. IX + (Fe. X) T ~ 0. 5 million 1942, B. Edlén - laboratory experiment of extremely hot spark sources the “green line” was identified as due to Fe. XIII+ (Fe. XIV) which can only exist if T ~ 1 million. - both are “forbidden” lines resulting of highly improbable quantum-mechanical transitions which can only occur in low- , high-T plasma metastable levels get overpopulated, because collisional de-excitation is rare - other “coronium” lines were identified as due to Fe, Ni, Ca

Temperature profile One expects the temperature to decrease when moving away from the energy source. However, in the Sun where thermonuclear reactor in the core exerts all the energy, not all layers behave that way: Tphotosphere ~ 6000 K Ttemp_min ~ 4300 K, slow rise in the low chromosphere, then dramatically at the top of it reaching Tcorona ~ n x 106 K, then slowly falls in the outer corona and solar wind T 1 AU ~ 105 K. What is heating the corona? Heating by conduction, radiation convection doesn’t work, because they are not allowed by the 2 nd law of thermodynamics!

The coronal heating problem - how to solve it? The way towards solution of the coronal heating problem is to identify and understand the physical mechanisms responsible for heating the corona to temperatures of n x 106 MK, several hundred times hotter than the underlying photosphere. Undoubtedly, there are several different heating mechanisms at work in the corona. The real goal is to determine the dominant one both in general and in specific situations.

Coronal heating flowchart Identify Determine how Predict the spectrum of Predict its manifestation in Klimchuk, 2006, SP 234, 41. Identify Accomplish all of these steps, an integrated approach is needed! Change model parameters to get the best match with real observations!

Coronal heating flowchart Multidimensional MHD models No info No regard for the origin 1 D hydrodynamic models (loop) Most coronal heating models focus on restricted part of the flowchart Klimchuk, 2006, SP 234, 41.

Energy requirement How much energy do we need? · The combined radiative and conductive energy losses from the corona: · Quiet Sun: 3× 105 ergs cm-2 s-1 · Active regions: 107 ergs cm-2 s-1 · Coronal holes: 8× 105 ergs cm-2 s-1 (QS+solar wind!) (Withbroe and Noyes, 1977) • The total energy required to heat the corona is 0. 01% of the Sun’s total luminuous output! Quiet Sun X-ray luminosity: 7 x 1027 ergs/s (Mewe, 1972; Hudson, 1991 ). Active Sun: 2 x 1029 ergs/s (Vaiana and Rosner, 1978)

Heating by acoustic waves? • Biermann (1946) and Schwarschild (1948) proposed acoustic waves for heating the chromosphere and the corona • The convection zone indeed generates sound waves - we see the 5 minute (3’-5’) oscillations. • Athay and White (1978, 1979) UV spectroscopic data from OSO-8: the acoustic wave flux 104 ergs cm-2 s-1 , so it is insufficient to heat the corona. • Upward propagating sound waves steepen into shocks and are dissipated in the chromosphere short-period (40 -60 s) are dissipated in the lower chromosphere long-period waves (300 s) in the upper chromosphere…

The magnetic connection A decade of solar magnetic variability: X-ray levels and T correlate with surface B. Many solar-type stars seem to have X-ray corona.

Implications: structure, heating and dynamics Courtesy A. Winebarger

Evolution of an AR magnetic fields (MDI) high chromosphere ~ 80 000 K (EIT 304 Å) corona ~ 1. 6 106 K (SOHO/EIT 171 Å ) corona ~ 2 -5 106 K (Yohkoh/SXT) Evolution of an active region during six solar rotation from emergence through decay (July-Nov. 1996)

Coronal heating flowchart Identify Klimchuk, 2006, SP 234, 41.

Footpoint shuffling

Energy source and mechanisms Basic requirement from any heating theory is to identify an energy source that can sustain the observed levels of losses. It is widely accepted that mechanical motions in and below the photosphere are the ultimate source of the energy. These motions displace the footpoints of coronal magnetic field lines stress the field (quasi-statically) if timescale of motion is long compared to the end-to-end Alfven travel time generate waves if the timescale of the motion is short compared to the end-to-end Alfven travel time DC (direct current) heating Dissipation of stressed magnetic fields AC (alternating current) heating Dissipation of waves

Importance and role of the magnetic field • It is clear from structuring that the main contribution to the heating is in magnetic form - regions of strong and complex magnetic field are brighter and hotter. • The influence of magnetic field on coronal plasma: - exerts a force which enables it to contain the plasma with enhanced pressure (coronal loops) - provides magnetic energy, which is either stored in additional wave modes that eventually dissipate or released directly in regions where electric currents are strong - it channels the heat along field lines • The coronal heating problem is different from that in the chromosphere heat is not just radiated away as it is there. - coronal hole regions with open field lines allow energy and mass loss to the solar wind. - closed field lines take up various forms from bright points to active regions, where energy is lost through radiation and conduction.

DC heating How much energy is provided by random foot-point motions? Poynting flux: (Note that emerging and submerging flux is not taken into account…) Observational constraints (after Klimchuk, 2006): • Most of the photospheric flux is in small tubes of k. G strength (e. g. Solanki, 1993; Socas-Navarro and Sánchez Almeida, 2002) • Most of the mixed polarity inter- network loops are low; the majority of “magnetic carpet” loops do not reach the corona (Close et al. , 2003) B measurements with modest resolution (pixel size 4”) • Bv = 100 G in AR plage areas (Schrijver and Harvey, 1994) Bv = 5 -10 G in the quiet Sun (López Fuentes, p. c. by Klimchuk, 2006) Vh = 1. 0 x 105 cm s-1(Mueller et al. , 1994; Berger & Title, 1996) assume: Bv = Bh (not really true! Bh tg 20º Bv = 0. 36 Bv) • Use these values in the Eq. Poynting flux into the corona is adequate to cover the observed energy losses both in the quiet Sun (1 -3 x 105) and in ARs (3 -8 x 107 ergs cm-2 s-1)

More shuffling, hotter loop… Support for the role of random footpoint motions in providing energy for coronal heating! Katsukawa & Tsuneta, 2005 Hot (SXR; 2 MK) loops: Lower magnetic filling factor at footpoints, more room to shuffle Cool (TRACE; 1 MK) loops: Higher magnetic filling factor at footpoints, less room to shuffle

AC heating The energetic feasibility of AC heating is less certain… Turbulent convection also generates a large flux of upward propagating waves: acoustic, Alfvén, fast and slow magnetosonic plane waves, torsional, kink and sausage flux tube (both body and surface) waves. Valery’s lecture Theoretical and observational estimates suggest energy fluxes on the top of the convection zone of ~ nx 107 ergs cm-2 s-1 (Narain and Ulmschneider, 1996) adequate? However, only a small fraction of waves can pass through the steep and T gradients in the chromosphere and transition region! - acoustic and slow-mode waves form shocks and are strongly damped - fast-mode waves are strongly refracted and reflected (Narain and Ulmschneider, 1996) Alfvén waves (incl. Alfvén-like torsional and kink tube waves) are best to penetrate into the corona. They don’t form shocks (being transverse) and their energy is channeled along the magnetic field (no refraction). Energy flux of Alfvén waves: ≤ 107 ergs cm-2 s-1 in regions of strong magnetic field. (Ulrich, 1996; based on observed magnetic and velocity fluctuations with the correct phase relationship for Alfvén waves).

AC heating Energy flux of Alfvén waves: ≤ 107 ergs cm-2 s-1 in regions of strong magnetic field. Would be ~ sufficient to heat ARs, and more than sufficient to heat QS areas in case of 100% transmission efficiency. However, Alfvén waves are strongly reflected in the chromosphere and TR, where v. A changes dramatically with height. Significant transmission is possible in narrow frequency ranges, where loop resonance conditions are satisfied (Hollweg, 1984; Ionson, 1982) Enough for long loops (>100 Mm), but insufficient wave flux to heat the short ones (unless they are twisted)! (Hollweg, 1985; Litwin & Rosner, 1998). Waves generated in the corona by e. g. magnetic reconnection events have no transmission problem (e. g. Moore et al. , 1991, Longcope, 2004). Energy in stressed m. f. is converted to wave energy in such case… DC AC Such waves can be very important in heating the corona away from DC energy release sites and provide heating to the “diffuse corona”.

Coronal heating flowchart Identify Klimchuk, 2006, SP 234, 41.

Energy conversion Since classical dissipation coefficients are very small in the corona, significant heating requires: • very steep gradients - magnetic gradients strong currents Ohmic dissipation, reconnection - velocity gradients heating by viscous dissipation • very small spatial scales Steep gradients are linked to: • magnetic topology (separatrix surfaces, nulls, QSLs, separators) • complex flow patterns • instabilities (e. g. kink) • loss of equilibrium • turbulence • resonant absorption • phase mixing Anomalously large transport coefficients (e. g. electrical resistivity) may be required for significant heating (even if steep gradients are present). Petschek-type fast reconnection requires >1000 x electrical resistivity increase (Parker, 1973, Bishkamp, 1993), and it must be spatially localised (Kulsrud, 2001).

Coronal heating flowchart May affect the subsequent heating! Close coupling between the corona and the transition region (moss, flows during flares…) Resonant wave absorption is affected by the plasma response! Klimchuk, 2006, SP 234, 41.

Coupling with the TR In static equilibrium thermal conduction transports more than half of coronal heating energy down to the transition region, where it is more efficiently radiated away (> , <T). (Vesecky et al. , 1979). The corona can not be treated in isolation! e. g. moss! Katsukawa & Tsuneta, 2005 Time-dependent heating ((nano)flares): suddenly increased downward heat-flux + radiation saturation chromospheric evaporation (heated upward plasma flow) decreasing heating cool condensations flow down. Field-aligned thermal conduction is an important factor… Chromospheric evaporation: highest-speed upflows are short-lived and faint small Doppler (blue) shift (Warren & Doschek, 2005) Solar-B: look in the hottest lines!

Coronal heating flowchart If plasma is in ionisation equilibrium state, CHIANTI can be used; problems: Doppler shifts integrated, elemental abundances unknown… Even more complicated in non-equilibrium case. Klimchuk, 2006, SP 234, 41.

Observables • Real data detect bits of pieces of the emitted spectrum, average it over space, time and wavelength ambiguity leading to confusion. Care is needed! • Sub-resolution structures in , T (Orall et al. , 1990; Brosius et al, 1996; Schmelz, 2002) • Line-of-sight path in the optically thin corona can cross different large-scale structures with different properties. • T determination (filter-ratio method) is only valid, if the plasma is isothermal (it is not!) (Reale & Peres, 2000; Martens et al. , 2002; Schmelz et al, 2003; also Noglik et al. , 2004, 2005, Patsourakos and Klimchuk, 2005) • Simulated observations (with model parameters varied) matched with real observations.

DC heating

Nanoflares Parker (1983) • Parker (1988) proposed that the corona would be heated by the dissipation of many tangential discontinuities arising spontaneously in the coronal magnetic field that is stirred by random photospheric footpoint motions. The theoretically estimated energy dissipated in a single burst was 3 x 1023 ergs, 10 -9 times the energy of a great flare of 1032 -1033 ergs nanoflares • Parker noted that the mean input to the gas is not large: 3 ergs/cm 3 over the reconnected volume, 1/3 of thermal energy density, but it is concentrated… At the heating rate required, this would mean 30 nanoflares over a granule-size area (1016 cm 2) are present at different stages of development at any one time… • It is beyond doubt that reconnection events occur in the corona, but also in the transition region and chromosphere. • A key question: Can we detect unambiguous observational signatures of the reconnection events and quantify their energy input and realise their efficiency for coronal heating?

Surface magnetic field Footpoint shuffling…

The magnetic “carpet” Démoulin & Priest (1997) QSLs in a bipolar region formed by 200 magnetic field concentrations. At QSL location, the field line linkage changes drastically, and these are preferred places for magnetic current formation. reconnection, dissipation of currents

Conditions for current generation and dissipation • A slow random walk of flux tubes can lead to distortion of the coronal magnetic field, producing field aligned currents that can dissipate resistively. This only applies to closed magnetic structures where stresses can build up over time. Field aligned currents appear when <<1 recall: = L 2/ diffusion time in the corona is only effective at length scales of a few meters, then it is a few seconds. • Currents may dissipate - directly by Joule heating - by a chain of events involving reconnection

Tangled coronal magnetic field TRACE Electric current sheet

Impulsive energy release: nanoflare in loops Nanoflare can also be defined as impulsive heating in a single, probably unresolvable, loop strand. frequency of recurrence in a given strand relative to the cooling time define the plasma properties , T (e. g. Kopp & Poletto, 1993, Tesla et al. , 2005) could result in loops in quasi-equilibrium. When thinking of micro- and nano-flares, do not only consider brightenings in small-scale loops: XBPs or EUV BPs…

Small-scale EUV brightenings 30, 000 x 74, 000 km, t= 1 min. Simultaneous observations of the distribution and mixing of magnetic polarities as observed by MDI (displayed as yellow and blue in the left panel) and the EUV emission observed by CDS from plasma at the temperature of 250 000 K. The field of view is 5’ x 4’ and the actual duration is 1. 5 hours. The observations were obtained at disk center on 15 August 1996.

Explosive events and nanoflares • Explosive events: just velocity events (red- and blueshift in spectral lines, with no observable brightening - they also result from magnetic reconnection (Innes et al, 1997).

Energy and T of different flare classes Eth (erg) T (MK) ne (cm-3 ) detection (Tmax) Large flares 1030 - 1032 8 - 40 0. 2 -2 x 1011 HXR, SXR, EUV Microflares 1027 - 1030 2 -8 0. 2 -2 x 1010 SXR, EUV (HXR!) Nanoflares 1024 - 1027 1 -2 0. 2 -2 x 109 EUV

Flare distribution function The number of flares falls off with increasing power as a flat power law with a slope of ~-1. 8 (SXR, EUV, microwave, HXR bursts, optical flares) (e. g. Drake, 1971; Dennis, 1985, see refs. in Hudson, 1991) d. N/d. W=A. W- (ergs s)-1 the normalisation factor A varies with the level of activity (Kreplin et al, 1977, Wagner, 1988) Then the total power released by flares is: If the power is flat (distribution of microflares have the same distribution as large flares) and < 2, then the total power depends on the most energetic events and Microflares or nanoflares do not contribute much to the total power (Hudson, 1991).

Scaling laws From physical parameters of flares, microflares and nanoflares in the EUV, SXR and HXR wavelength groups the deduced approximate scaling laws are: L(T) T 1 ne(T) T 2 (ne. L T 2 ) p(T) T 3 (p nex. T T 2 x. T=T 3) EM(T) T 5 (EM ne 2 x L (T 2)2 x. T= T 5) Eth(T) T 6 (Eth=3 nek. BTe. V) Aschwanden et al (2000) Consequences: • Correlated increase of T and EM • Nano- and pico-flare events would be much cooler, so it is a question whether they remain relevant for coronal heating. However, it is the energy added which counts!!!

Flare statistics Results are controversial, values found range between -1. 5 and -2. 6. Are the slopes based on data obtained in a narrow T range overestimated? <1 -hour dataset! (Aschwanden & Charbonneau, 2002) =-1. 8 Aschwanden et al, (2000) Discrepancies could be due to • systematic errors in the conversion to total flare energy and/or to • actual variability of the solar event rate. • Integration over the l. o. s. decrease of slope. Note that such statistics can only be valid over a long time… Is the power law really flat? ?

Uncertainties: event definition Moving plasma clouds (in emission and absorption), oscillating and swaying loops, propagating sound waves, rotating helical spicules, coronal dimming, temperature changes due to cooling and thermal conduction introduce time variability which may be completely unrelated to flare/microflare/nanoflare processes. Moving absorption features Oscillating loops Not every detected brightness change is a nanoflare !

The power-law slope is different for all events (2. 08) and for “flares” (1. 80 -1. 85). Aschwanden et al. 2000.

Observing cadence and exposure time Data with full time resolution Flux Data with limited cadence Typical cadences: 30 -200 sec (TRACE, EIT) Typical exposure times: 5 -20 sec (TRACE, EIT) Time - The exposure time smears fast time scales out - Poor time cadence under-samples the data àflux and number of small events is underestimated

Multi-Temperature structure of the Sun Blue: EIT 171 A T=1. 0 MK Green: EIT 195 A T=1. 5 MK Red: EIT 284 A T=2. 0 MK

T True peak temperature Detected temperature in 171 A What temperature response do we see in the filters ? The flux peaks when flare temperature matches the filter peak temperature !

Correction of Temperature bias power-law slopes (of narrowband EUV filters) Observations: Uncorrected Corrected TRACE 171 (Aschwanden & Parnell 2002) TRACE 171 (Parnell & Jupp 2000) EIT 171 (Krucker & Benz 1988) 1. 86+0. 06 1. 84 -2. 08 1. 77 -1. 94 1. 62+0. 06 1. 69+0. 09 1. 62+0. 07 TRACE 195 (Aschwanden & Parnell 2002): 1. 81+0. 10 1. 59+0. 09 SXT (Aschwanden & Parnell 2002) SXT (Shimizu 1995) 1. 57+0. 05 1. 6 -1. 7 1. 57+0. 05 1. 65+0. 05

Nanoflares - verdict (by Marcus Aschwanden) Since the observational value is below the critical limit of =2, this implies that there is more total energy content in the large (catastrophic) flare events than in small-scale energy releases, and thus the small-scale events can be neglected in the total energy budget of energy releases, as possible power source for coronal heating. However, many researchers do not agree with this! Marcus also remarks (Aschwanden, 2003): The integrated energy flux of dissipation events should be a better measure of the effectiveness of nanoflare heating, so the finding that the powerlaw slope <2 is not decisive for the heating budget.

Gudiksen & Nordlund (2002) MHD simulations of magnetic reconnection, driven by (convective) random motion of chromospheric loop footpoints, reproduces the filling of coronal loops with heated plasma a likely mechanism for coronal heating Does this contradict Marcus’ conclusion?

Marcus: There is a continuous distribution from large-scale loops (L>600, 000 km) to small-scale loops (L<2000 km) that show brightening (emission measure increase) as a result of filling with heated plasma. The basic heating mechanism has therefore to occur in the transition region, driven by either magnetic reconnection or particle precipitation. Unresolved coronal nanoflares (Parker 1988) cannot explain the emission measure increase in isothermal coronal loops.

Nanoflares are important: loop argument • Warm (TRACE and EIT) loops are over dense to what is expected for static equilibrium (Aschwanden et al. , 1999, 2001; Winebarger et al. , 2003) or steady flow equilibrium (Patsourakos et al. , 2004). • Hot (> 2 MK; Yohkoh) loops are under dense to what is expected for static equilibrium (Porter & Klimchuk, 1995). • Loops of intermediate T (SXI on GOES-12) have ~ the right density (Lopez-Fuentes et al. , 2004) Are they physically different classes of loops? There may be a different explanation… Over and under densities are related to the ratio of the radiative and conductive cooling times: where (T) is the optically-thin radiative loss function. For loops in equilibrium the ratio is 1 (Vesecky et al. , 1979).

Cooling Time Ratio vs. Temperature (multi-stranded loop) Hot loops: thermal conduction dominates over radiation Simulated observations Static Equilibrium Cooling track Cooler loops: radiation dominates over thermal conduction TRACE Yohkoh rad/ cond = T 4 / (n. L)2 + Actual observations Klimchuk (2006)

Cooling loops? However, both SXR and EUV loops live longer than their cooling times!!! (Porter & Klimchuk, 1995; Winebarger et al. , 2003; Lopez Fuentes et al. , 2004) Loops are not monolitic structures, but a bunch of individually heated strands, which evolve rapidly, while their ensemble is slowevolving… Yohkoh detects the hottest strands in their early, conduction-dominated phase of cooling TRACE detects the warm strands in the later, radiation-dominated phase. Problem: Yohkoh and TRACE loops should be co-spatial… Large literature to show the opposite!

Cooling loops? Repetition of nanoflare along each strand quasi-static equilibrium conditions • Larger events and frequencies maintain hot strands • Smaller events and lower frequencies warm strands Hot and warm loops are not at the same place! However, this does not explain the under densities of hot and over densities of warm loops… Aschwanden & Nightingale (2005): thin TRACE loops are isothermal. Where is the truth?

AC Heating

Detectability of various MHD Wave Types MHD wave type Observables of Oscillations Fast MHD kink mode x(t), transverse displacements Fast MHD sausage mode A(t), n_e(t), EM(t) cospatial flux variations Slow MHD (acoustic mode) Acoustic waves n_e(x-vt), EM(x-vt) propagating density compression Alfvenic waves B(x-v_A*t), v 1(x-v_A*t) line broadening Magnetoacoustic waves (intermediate between acoustic and Alfvenic waves) n_e(x-vt), EM(x-vt) (but weaker signal than for acoustic waves)

Wave observations Most of theoretically known MHD oscillation and propagating wave modes have been detected recently (since 1999), except for the torsional mode. We can know identify the modes and measure the periods, amplitudes, phase speeds, and propagation speeds.

Energy flux carried by MHD waves Kinetic energy associated with a wave disturbance propagating with v 1 Energy flux flowing through volume d. V with footpoint area d. A along field line ds with phase speed vph Energy flux F per unit area d. A and time dt :

mass density (mean molecular weight m=1. 27 for H: He=10: 1) mean velocity v 1 of disturbed mass is quantified by displacement amplitude a and period P, phase speed of wave vph propagating over 4 node half-lengths L: define velocity ratio wave energy flux

Radiative loss rate: Thermal conduction rate: Wave energy flux compared with radiative and conductive loss rates : in out

Alfvenic MHD Oscillations and Waves Fast MHD kink mode Fast MHD Propagating sausage mode Alfven wave Aschwanden et al. 2002 Asai et al. 2001 Nakariakov et al. 2003 Doyle et al. 1999 Electron density ne [cm-3] 0. 6 x 109 0. 7 x 1011 0. 11 x 109 Loop half length L = 110 Mm 47 Mm Electron temperature T= 1. 0 MK 15 MK Displacement qa=a/L 0. 02 0. 01 Phase speed vph~v. A 1. 0 MK 0. 015 1400 km/s 4600 km/s Wave energy flux Fwave 7 x 105 7 x 108 1. 6 x 105 Radiative loss rate 2 Frad 8 x 105 4 x 108 6 x 103 0. 5 x 105 7 x 109 6 x 104 Conductive loss rate 2 Fcond Solar wind flux Fwind Input/output 1800 km/s 7 x 105 0. 82 0. 09 0. 21

Acoustic MHD Oscillations and Waves Slow MHD (acoustic) mode Wang, T. J. et al. 2002 Propagating acoustic wave De. Moortel et al. 2002 Electron density ne [cm-3] 1. 0 x 109 0. 24 x 109 Loop half length L = 95 Mm 8. 9 Mm Electron temperature T= 6. 3 MK 1. 0 MK Displacement qa=a/L 0. 05 0. 02 Phase speed vph~v. A 370 km/s 147 km/s Wave energy flux Fwave 1. 3 x 105 3. 2 x 102 Radiative loss rate 2 Frad 0. 8 x 106 5 x 103 Conductive loss rate 2 Fcond 3. 4 x 107 3 x 105 Solar wind flux Fwind Input/output 0. 09 0. 04

Wave heating - verdict Alfvenic MHD waves carry a wave energy flux that is comparable with radiative and conductive losses, and thus could potentially account for coronal heating, while acoustic waves and oscillations fall short of the heating rate requirement by ~2 orders of magnitude.

Conclusions • The exact details of the mechanisms heating the solar corona are still unclear, but the heating must have a magnetic origin. • Different mechanisms may dominate in different regions. • Coronal heating is probably due to a combination of wave and electric current dissipation - both have ~ enough energy flux… - (nano)flares heat the corona supplying a large fraction of the energy - they also generate waves that propagate into extended loops and dissipate there to provide extra heat for these large-scale structures - waves generated by (nano)flares help to dissipate other MHD waves.

Useful observables with new instruments: current heating • Search for twisting and braiding of loops at all T. • Search for evidence of small-scale reconnection. • Relate the observed coronal structures to magnetic structure predicted by extrapolation of photospheric field: Does heating occur in sheets located at separatrix or QSL surfaces? • Determine how average heating depends on loop parameters (B, L, …). • Determine how heating varies along loops. • Evidence for energetic particles? Compare with theories coronal heating.

Useful observables with new instruments: waves • Search for waves and oscillations in all SOLAR-B and AIA passbands. High cadence allows study of high-frequency waves. • Search for Alfven waves: track transverse motion of features in closed and open fields. • Study evolution of coronal structures on quiet Sun: Does reconnection in “magnetic carpet” produce waves that can drive the solar wind?

I thank Jim Klimchuk and Marcus Aschwanden for their help with the preparation of this lecture…