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The way forward for coronal heating Moortel, Ineke De; Browning, Philippa; Bradshaw, Stephen J.; Pintér, Balázs; Kontar, Eduard P.

Published in: Astronomy & Geophysics DOI: 10.1111/j.1468-4004.2008.49321.x Publication date: 2008 Citation for published version (APA): Moortel, I. D., Browning, P., Bradshaw, S. J., Pintér, B., & Kontar, E. P. (2008). The way forward for coronal heating. Astronomy & Geophysics, 49(3), 21-26. https://doi.org/10.1111/j.1468-4004.2008.49321.x

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Download date: 09. Jul. 2020 De Moortel et al.: Meeting report The way forward for coronal heating Ineke De Moortel, Philippa K Browning, Stephen J Bradshaw, Balázs Pintér and Eduard P Kontar consider approaches to the longstanding and enigmatic problem of coronal heating, as presented at the RAS discussion meeting on 11 January 2008. Downloaded from n the 1940s it was demonstrated that the Abstrt ac for dissipating the wave energy with adequate temperature of the plasma in the Sun’s outer efficiency. Fast waves are totally reflected before atmosphere (the solar corona) is over a mil- The coronal heating problem is one reaching the corona, and the energy flux in I of the major outstanding challenges lion degrees Kelvin (Edlén 1942). This is rather acoustic waves is too low, so attention mainly surprising, given that the Sun’s surface tem- in astrophysics and, while there has focuses on Alfvén waves. It has been suggested http://astrogeo.oxfordjournals.org/ perature is only about 6000 K. Although this been considerable progress in both (Hollweg 1984) that in long loops (>10 000 km), discovery removed the difficulty of an otherwise theory and observations, it remains a enough energy for coronal heating can be trans- unknown element (“coronium”), it presented a subject of controversy. There have been mitted by loop resonances. Efficient dissipation new puzzle, explaining how the coronal plasma exciting developments recently on the requires the generation of small length scales, is heated to such high temperatures. The coronal observational front, with new results with favoured mechanisms, both relying on the heating problem requires us to find a mechanism from, in particular, Ramaty High Energy inhomogeneity of the corona, being phase mix- (or mechanisms) to supply the energy losses of Solar Spectroscopic Imager (RHESSI) ing and resonant absorption. Spatial gradients the hot coronal plasma. These energy losses are (Lin et al. 2002) and Hinode (Kosugi et of Alfvén speed lead to phase mixing of shear due to conduction and radiation – estimated to al. 2007). But there is something of a Alfvén waves (Heyvaerts and Priest 1983). In a be up to 104 W m–2 in active regions. The key to gulf between theory and observations. closed field configuration, with the wavelength at University of Wales Aberystwyth on October 13, 2014 this problem is accepted to be the strong coronal The idea of forward modelling has fixed by the fieldline length, each fieldline oscil- magnetic field, which plays a crucial role in the arisen as a means of bridging this gulf lates with a different frequency; thus, neighbour- and enabling theories to be confronted solar corona (the plasma β – the ratio of thermal ing fieldlines become increasingly out of phase energy density to magnetic energy density – is with observations. The RAS discussion and strong spatial gradients build up, leading to around 10–4). meeting held in January this year focused enhanced dissipation. The damping time scales There is a very strong correlation between on new developments in coronal heating with the cube root of the Lundquist number. the brightness of coronal emission and the and the role of forward modelling. The theory has been extended to account for strength of the magnetic field. Indeed, active effects such as the generation of Kelvin–Helm- regions, which are bright in X-ray and EUV holtz instability due to the velocity shear images and hence hotter, have a much greater corona; in the opposite case, we have AC (Browning and Priest 1984), nonlinearities and heating requirement than the quiet Sun, and heating, with coronal magnetohydrodynamic mode coupling (e.g. Nakariakov et al. 1997), also have the strongest magnetic field. There is (MHD) waves. gravitational stratification (De Moortel et al. now a substantial body of evidence from other In both cases, the main challenge is to explain 1999) and a diverging field geometry (Ruder- stars that X-ray coronae are associated with how energy is dissipated in the solar corona: man et al. 1998, De Moortel et al. 2000). More magnetic fields. Indeed, there is a good correla- because the conductivity is extremely high, the recently, phase mixing in collisionless plasmas tion of X‑ray luminosity with magnetic flux over ratio of the ohmic dissipation time to the Alfvén was modelled by Tsiklauri et al. (2005). many orders of magnitude, ranging from solar time (the Lundquist number) is very large, quiet regions through active regions, to dwarf around 1013. Thus, in order to explain coronal Resonant absorption and T Tauri stars (Pevtsov et al. 2003). heating, the energy dissipation must take place Resonant absorption (Ionson 1978) considers on scales smaller than typical MHD scales, resonances of incoming waves where the wave Energy transfer where kinetic effects are likely to be significant. frequency matches the local Alfvén frequency, The basic paradigm of coronal heating is that Moreover, the theories must include the cou- creating narrow layers where the wave ampli- there is an energy transfer from kinetic energy pling between global scales, i.e. on which the tude builds up and energy is dissipated. Interest- of flows below the solar surface into free mag- photospheric driving occurs, and local scales, ingly, resonant absorption may lead to sporadic netic energy in the corona, through motion of where the dissipation must take place. Further heating, more akin to the nanoflare scenario the footpoints of the coronal magnetic fields. difficulties for theory are presented by the cou- described below; since the localized heating at Existing theories can be classified according to pling between the dense interior and tenuous the resonant layer will create a rise in density the ratio of the timescale of this photospheric outer atmosphere, as well as the complex geom- due to chromospheric evaporation, altering the driving and the Alfvén wave transit time along etry and topology of coronal magnetic fields, Alfvén speed profile and creating new resonant a coronal field line. When the driving is slow and the dynamic nature of the corona. layers (Ofman et al. 1998). compared to the Alfvén travel time, we have Theories of wave heating have to account both At the RAS meeting, T Van Doorsselaere DC heating, with quasi-static currents in the for transmission of waves into the corona and (University of Warwick) compared resistive and

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1: Comparison between SXT/ Yohkoh (top row) and EIT/SOHO (bottom row) observations and synthesized emission for different values of the parameters α and β. (Taken from Warren and Winebarger 2006) Downloaded from

viscous dissipative effects on footpoint heating Nakariakov and Verwichte 2005). which are significant at small length scales. For by waves. According to analytical and numeri- Consider now the alternative scenario, DC example, the Hall effect, which allows separa- http://astrogeo.oxfordjournals.org/ cal results, ohmic heating has to dominate any heating: the Poynting flux of energy into the tion of electron and ion fluids, can significantly wave heating mechanisms in order to accom- corona can be expressed as: affect the reconnection rate (Vekstein and Bian modate the constraint of footpoint heating (Van 2006). Magnetic reconnection during collision- ​F = __1 ​ B B v Doorsselaere et al. 2007). µ v h ph less X‑point collapse is also an efficient source

Both ground- and space-based observa- where Bv and Bh are the vertical and horizon- of heat, according to the computational simula- tions have recently found evidence that waves tal magnetic field components, respectively, tions by D Tsiklauri (Salford), presented at the are omnipresent in the solar atmosphere. For and vph is the photospheric footpoint velocity. meeting. example, Tomczyk et al. (2007) report observa- Taking typical coronal values, Bv = 0.01 T and Parker (1988) proposed that the corona is –1 tions of upwardly propagating coronal waves vph =m 1 k s , gives a Poynting flux of about heated by the combined effect of many small from intensity, line-of-sight velocity and linear 104 W m–2: sufficient for active region heating, as (and currently unobservable) nanoflares – tiny at University of Wales Aberystwyth on October 13, 2014 polarization measurements obtained with the long as the horizontal field component is around heating events with the same energy release Coronal Multi-Channel Polarimeter (CoMP) 10% or more of the vertical field in magnitude. mechanism as large-scale flares, namely mag- instrument. However, the detected waves have The latter condition imposes an important con- netic reconnection, but much weaker (of the an energy flux much too low for coronal heating straint on theories, since it is required to explain order of 1024 ergs). Typical solar flares, releasing requirements, although unresolved waves may why dissipation only “switches on” when this 1029–1031 ergs, are not frequent and therefore have more energy. value is reached. While energy flux is sufficient, they have inadequate total energy output for Early results from Hinode show similar evi- global ohmic dissipation of the DC currents in coronal heating purposes. However, if small dence for the ubiquitous nature of waves in the the corona is far too inefficient for coronal heat- events occur sufficiently frequently, their com- solar corona. Using the Hinode Solar Optical ing purposes. However, there is strong evidence bined effect may be more significant; the issue Telescope (SOT), De Pontieu et al. (2007) find that current sheets or filaments are omnipresent depends on whether the spectrum of the fre- strong transverse displacements of spicules in in the corona, and these form sites for local- quency of occurrence vs energy is steep enough the upper chromosphere, with an energy flux ized efficient dissipation of energy by magnetic (Hudson 1991). Hugh Hudson (University of (~100 W m–2) that does appear sufficient to reconnection (see, for example, Priest and California, Berkeley) in his invited review talk heat the quiet Sun corona or drive the solar Forbes 2000 and Biskamp 2000 for an overview proposed the interesting and rather controver- wind. Similarly, Okamoto et al. (2007) report of this important physical process). sial idea that flares and microflares actually cool transverse oscillations of filamentary struc- the corona. The argument is that flares reduce tures in prominences observed by SOT. All the Reconnection models the mean magnetic energy and hence, because above authors have interpreted their respective Models of magnetic reconnection may be clas- heating is known to correlate with magnetic observed oscillations as Alfvén waves. How- sified as: spontaneous linear instability (such field strength, reduce the coronal heating. ever, this interpretation was recently challenged as tearing mode), steady driven reconnection A theoretical model by Browning et al. (2003) by Van Doorsselaere et al. (2008), who claim (such as Sweet-Parker or Petschek) and forced predicts sporadic heating of a single coronal that an explanation in terms of guided kink reconnection (triggered by an external dis- loop by a series of discrete events of varying magneto-acoustic waves is more appropriate. turbance; Hahm and Kulsrud 1985). The lat- magnitude, which may be regarded as nano- Wave heating is a strong candidate for open ter could be most relevant to coronal heating, flares. Each heating event is triggered by kink field regions but is probably less viable for closed with disturbances arising from photospheric instability, while the energy release is predicted field regions, partly due to the short Alfvén footpoint motions, for example. An analyti- by assuming a helicity conserving relaxation to time in active region loops (1–30 s). Even if not cal theory of coronal heating by forced recon- a minimum energy state. The theory has been the prime source of coronal heating, coronal nection has been presented by Vekstein and confirmed recently by 3-D numerical simula- waves are important as a diagnostic of coronal Jain (1998), with numerical simulations of the tions of a kink unstable loop (Browning et al. parameters, through the burgeoning science of nonlinear effects recently performed by Jain et 2008). This approach allows for the distribution coronal seismology (see, for example, reviews al. (2006). An important challenge for recon- of nanoflares to be predictedab initio. by Chaplin and Ballai 2005, De Moortel 2005, nection theory is to incorporate kinetic effects, New results from RHESSI have put significant

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observational data is subject to many possi- ble sources of error and confusion, such as the optically thin radiation in the solar corona or the unknown filling factor. To compare theory and observations, one could try to deduce basic parameters such as temperature or density from the observational data (e.g. Prato et al. 2006). However, it has long been known that the inversion of data is often an “ill-posed” problem, i.e. that the solutions are non-unique and additional constraints are needed to resolve this non-uniqueness. Various inversion algo- rithms for model-independent reconstruction of electron spectra have proved to work well for continuum X-ray emission (Piana et al.

2003, Kontar et al. 2005), although the situa- Downloaded from tion is more complicated for line emission. For example, Wikstøl et al. (1998) argued that line emission observations alone are not sufficient to explain the nature of the solar transition region and additional information is needed. The other http://astrogeo.oxfordjournals.org/ approach, often termed “forward modelling”, is to calculate observable parameters (for example, intensities or Doppler shifts) for instruments from theoretical models. These “synthesized” observations can then be directly compared to real observational data. Forward modelling 2: XRT/Hinode image of a coronal active region. (Courtesy SAO/NASA/JAXA/NAOJ) Forward modelling provides a robust link between theory and observations, allowing at University of Wales Aberystwyth on October 13, 2014 limits on heating by microflares with typical advanced version is to create synthetic images us to start from a certain physical model and energies of 1028–1029 ergs. A study of 25 000 of extrapolated coronal loops from measured subsequently to examine the observable conse- microflares by Hannahet al. (2008) shows that photospheric magnetograms, using different quences of this model. This then provides a way α β these events, like ordinary flares, exhibit high scalings for the heating rate (εH ~ B L ), as to test the sensitivity of the observables on the temperatures and a non-thermal component shown in figure 1. By comparing with actual input parameters of the model or to compare correlated with the thermal component. All images, the best fit exponents α( and b) can be the observational consequences of different occur within active regions and are thus con- found (Warren and Winebarger 2006). Using theoretical models put forward to explain the centrated in bands of latitude. The frequency the same empirical scaling laws for the heat- same solar phenomenon. At best, this will allow distribution has a similar exponent to flares, ing function, Stéphane Régnier (St Andrews) us to distinguish between different theoretical with the spectrum being insufficiently steep for presented recent work at the meeting on a com- suggestions or even to eliminate those models coronal heating requirements. However, this parison between potential and nonlinear force- that cannot “reproduce” the observations. On still leaves open the possibility that smaller free magnetic field extrapolations, showing the the other hand, it is of course possible that nanoflares, with somewhat different physics, importance of both currents and the complexity substantially different theoretical models yield may be responsible for heating the corona. of the field in studying the heating mechanism. observable parameters which are too similar Investigating the observational consequences of The approach seems very promising but, as to distinguish the different models confidently. nanoflare heating is thus very important. SXT/ pointed out by Hudson in his review, there However, the strength of forward modelling lies Yohkoh and TRACE observations have recently are some difficulties: the active region filling in its predictive character: predicting observa- been analysed by G Vekstein (Manchester) and factor is small (i.e. how much of the coronal tional consequences of theoretical models at co-workers to find evidence for significant nano- volume is actually contributing to the emis- its most basic level, providing guidance for the flare heating, and to determine the properties of sion observed in a particular wavelength?) and design of specific observing programmes, but nanoflares, extending the methodology outlined adjacent flux tubes have almost identicalB and also predicting the potential achievement and in Vekstein and Katsukawa (2000). L, while having very different emission (see for hence guiding the development of future instru- A promising approach is to discriminate obser- example, the image from XRT/Hinode in fig- ment design. Crucial to forward modelling of vationally between different heating models by ure 2). Simple scaling models cannot account line emission are atomic data packages, such comparing the predicted scaling of the heating for filamentary structure! as CHIANTI (Dere et al. 1997, Young et al. rate of various models (particularly in terms Comparing theory and observations is obvi- 2003), which provide essential parameters such of the field strengthB and loop length L, since ously crucial to “proving” any coronal heat- as element abundances, ion population fractions other parameters can be expressed in terms of ing theory. However, this task is not always and ion emissivities. these) and to see which fits best with observa- as straightforward as it may sound. Theoreti- Generating observable quantities from theo- tions (Mandrini et al. 2000). Unfortunately, cal models do not often yield parameters that retical models through forward modelling has the initial results are inconclusive, in that most are easily compared to observed quantities been successfully demonstrated in the past by models are consistent with the data. A more and, at the same time, the interpretation of numerous authors, for various solar phenomena,

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4000 1.0 4000 1.0

0.8 0.8 3000 3000

0.6 0.6 2000 2000 time (s) time (s) 0.4 0.4 normalized intensity normalized intensity 1000 1000 0.2 0.2

0 0 0 0 –200 –100 0 100 200 –200 –100 0 100 200 –300 –200 –100 0 100 –200 –100 0 100 velocity (kms–1) velocity (kms–1) velocity (kms–1) velocity (kms–1) Downloaded from 3: Synthetic line profiles for Mg x (left pair) and Fe xvii (right pair) taken from Patsourakos and Klimchuk (2006). The contour plots show the temporal evolution averaged over the coronal section of the loop strand, whereas the line plots show the temporally averaged profiles (where the solid line corresponds to the coronal section, the dashed line to the loop footpoint and the dot-dashed line to the entire loop).

10–22 10–3 input energy distribution intensity distribution for Fe XII http://astrogeo.oxfordjournals.org/

10–4 10–24 10–5 α=–1.62 α=–4.6 10–26 10–6 PDF PDF

10–7 10–28 at University of Wales Aberystwyth on October 13, 2014 10–8

10–30 10–9 1019 1020 1021 1022 1023 1024 1025 103 104 105 106 E (erg) Fe XII (ergcm–2s–1sr–1) 4: Distribution functions (with estimated slopes) for the “input” 10–1 nanoflare energy heating the loop and for the resulting (synthetic) Fe xii intensity distribution for Fe XIX and Fe xix intensity from Parenti et al. (2006).

10–2

α=–1.6 10–3 PDF

10–4

10–5

10–6 1 101 102 103 104 Fe XIX (ergcm–2s–1sr–1) but the greatest effort has focused on the effects that the redshifts observed in transition-region redshifts. Demonstrating the predictive power of of coronal nanoflares. With a few selected exam- spectral lines can be explained in terms of forward modelling, Wikstøl et al. (1997) look ples, we will try to demonstrate the potential of downward propagating, compressive (acoustic) for observable signatures of wave energy, propa- forward modelling. During the 1990s, a series waves, generated at the apex of coronal loops by gating in different directions through the solar of papers by Wikstøl and Hansteen determined nanoflares (or some other form of episodic heat- atmosphere, which survive spatial and temporal a range of observables associated with wave ing). More recently, modelling of the response of averaging. As a basic model, the flow of wave propagation in the solar atmosphere. Using a transition region lines to nanoflares by Taroyan energy in different directions can be associated basic, 1-D model (including the effect of non- et al. (2006) also suggests that nanoflares might with two different coronal heating models, equilibrium ionization), Hansteen (1993) shows be responsible for the observed transition-region namely upward propagating acoustic waves

3.24 A&G • June 2008 • Vol. 49 De Moortel et al.: Meeting report De Moortel et al.: Meeting report

and nanoflare heating (generating downward 5: Comparison Doppler propagating waves). In particular, these authors between observed C IV shift C III O V predict that the associated spectral signatures and synthesized should be observable by the SUMER instrument Doppler shifts (top) 10 Ne VIII Mg X onboard SOHO, both in line profiles and line and differential red O VI emission measures ratios of density-sensitive line pairs. Such an ) → (bottom). (From –1 C II Si II approach could not only be applied to the solar Peter et al. 2006) 5 corona, but also to (unresolved) stellar sources. Si IV O IV Nanoflare heating 0 Other authors have also considered forward Doppler shift (kms modelling of nanoflare heating in the solar observations corona, in particular Cargill, Klimchuk and line shifts from average synthetic spectra –5 co-authors (Cargill 1993, 1994, Cargill and (two time steps 7 min apart) Klimchuk 1997, Klimchuk and Cargill 2001, CHIANTI inversion fit

Cargill and Klimchuk 2004, Patsourakos and Downloaded from 27 of synthetic spectra Klimchuk 2006, Sarkar and Walsh 2006, Buch- Si II lin et al. 2007, 2008). Often using basic 0‑D or directly from MHD 26 1 ‑D hydro-models, the effect of nanoflare heat- 2 × observed QS DEM ) –1

ing on observable parameters such as emission K

–5 25 measure, line profiles and intensities is investi- C II http://astrogeo.oxfordjournals.org/ gated in detail and again, the predictive power 24 of forward modelling is exploited. For example, C III

log DEM (cm Ne VIII observations of the filling factor (the ratio of C IV volume radiating in EUV or X-ray to total vol- 23 O V O VI ume) could be used to deduce the average size differential Mg X of the energy-release site. Modelling a coronal 22 emission Si IV measure (DEM) O IV active region as a collection of several hundred thin loops, heated randomly by thousands of 4.0 4.5 5.0 5.5 6.0 log line formation temperature (K) nanoflares, predictions are made in terms of the 10 emission measure (which is shown to exhibit a at University of Wales Aberystwyth on October 13, 2014 sharp change in gradient above temperatures of providing another powerful test for the nanoflare flare energy and whether this will be reflected in about 1 MK) and filling factors for both broad- model, as this line is observable with EIS/Hinode. the observations. This question was addressed band instruments such as SXT/Yohkoh and nar- Going one step further still, recent work of Buch- by Parenti et al. (2006), who looked at the sta- rowband (spectroscopic) instruments. lin and co-authors (Buchlin et al. 2007, 2008) tistical properties of coronal loops, subject to Understanding the (differential) emission couples physical models of nanoflare heating turbulent heating, to test whether the plasma measure is an important step towards identi- (anisotropic turbulence driven by Alfvén waves) response simply transmits the statistical distri- fying the distribution of coronal densities and and cooling processes (convection, conduction, bution of events, without modifying it (in other temperatures. Klimchuk and Cargill (2001) and radiation based on atomic physics) in a coro- words, whether the injected and radiated ener- actually provide tabulated values for line nal loop. The heating is found to be intermittent gies follow the same power-law). Two different intensity and emission measure for a range of and sufficient to heat the loop to temperatures of cooling mechanisms are taken into account, spectral lines, which can directly be compared more than a million degrees, with realistic values namely conduction and radiation, which both with spectroscopic observations from, e.g. of the amplitude of the forcing (corresponding turn out to play an important role. So how does CDS onboard SOHO, or EIS on Hinode. Such to motions of the photospheric footpoints of the coronal energy transport affect the event dis- a comparison would be a profound test for the loop). Spectral line profiles of the UV emission tribution, for a known distribution of energy nanoflare heating model! One of the predictions and their time evolution are obtained by forward input? It appears that the resulting distribution of the studies by Cargill and Klimchuk is the modelling, and are used to identify signatures of of intensities strongly depends on the chosen possibility of very low filling factors in the solar heating processes in observations by, for exam- spectral lines (see figure 4); for cool (EUV) lines, corona. Numerical simulations by Bradshaw ple, Hinode and STEREO. the power-law index of the output distribution and Cargill (2006) investigate how nanoflares is strongly modified. However, for hotter lines might heat such a tenuous plasma to very high Beyond simple models (T ~ 107 K, i.e. those lines where thermal con- temperatures and whether any specific observa- The advantage of using relatively simple 0‑D or duction is the dominant cooling mechanism), tional signatures exist. Departures from ioniza- 1 ‑D hydro-models is that it allows one to vary the distribution is well preserved, highlighting tion equilibrium of up to an order of magnitude many of the model input parameters such as the the importance of choosing the “right” emission are found for iron and the authors suggest that number of loop strands and the location and size lines for the analysis of the statistical distribu- an associated blue-shift at the loop footpoints (or distribution of sizes) of the heating events. tion of observed nanoflares. might be observable by EIS/Hinode. As already mentioned before, the frequency Although many studies have focused on nano- The study of Patsourakos and Klimchuk (2006) of occurrence of nanoflares vs their energy is flares, one of the strengths of forward mod- calculates nanoflare line profiles for Ne viii, Mg x thought to follow a power-law, based on the elling is that it can be applied to almost any and Fe xvii (see figure 3). The Ne viii and Mg x extension of the observed power-law distribu- theoretical model. Substantial progress can be profiles agree well with existing observations. tion of larger flares down to nanoflare energies made by forward modelling of large-scale, 3‑D The predicted profile for the hot Fe xvii line (see e.g. Hudson 1991). Hence, of particular MHD simulations such as those by Gudiksen shows distinct enhancements in the line wings, interest is the distribution of the (input) nano- and Nordlund (2005), from which a range of

A&G • June 2008 • Vol. 49 3.25 De Moortel et al.: Meeting report observables can be predicted. These particular events in the chromospheric network. The latter References simulations model the solar corona ab initio, authors pay particular attention to the effects of Aiouaz T et al. 2005 A&A 442 L35. where the necessary energy to heat the model non-equilibrium ionization. Observables associ- Biskamp D 2000 Magnetic Reconnection in Plasmas (CUP, Cambridge). corona is provided through slow braiding of ated with catastrophic cooling and downflows Bradshaw S J and Cargill P J 2006 A&A 458 987. magnetic field lines by photospheric footpoint in coronal loops are investigated by Müller et Browning P K and Priest E R 1984 A&A 131 283. motions. Peter et al. (2004, 2006) calculate al. (2004, 2005), Lundquist et al. (2004) dem- Browning P K et al. 2003 A&A 400 355. both intensity and Doppler shifts, providing a onstrate how forward modelling can lead to Browning P K et al. 2008 A&A submitted. range of different diagnostics which can be com- observational constraints for coronal heating Buchlin E et al. 2007 A&A 469 347. Buchlin E et al. 2008 A&A in preparation. pared to both imaging and spectroscopic obser- mechanisms and Aiouaz et al. (2005) show that Cargill P J 1993 Sol. Phys. 147 263. vations. The synthesized emission shows a nice different heating profiles in coronal funnels lead Cargill P J 1994 Ap. J. 422 381. qualitative agreement with the general appear- to different Doppler shifts in the Ne viii line. Cargill P J and Klimchuk J A 1997 Ap. J. 478 799. ance of the solar corona, whereas the Doppler Martínez-Sykora et al. (2008) describe the Cargill P J and Klimchuk J A 2004 Ap. J. 605 911. maps show an intriguing amount of detail. In response of the solar atmosphere to magnetic Chaplin B and Ballai I 2005 A&G 46 4.27. fact, there seems to be substantially more spa- flux emergence with magnetograms, synthe- De Moortel I et al. 1999 A&A 346 641. De Moortel I et al. 2000 A&A 354 334. tial variability in the (coronal) Doppler shifts sized continuum and Ca ii H-line images. De Moortel I 2005 Roy. Soc. Phil. Trans. A 363 2743. than in the associated intensity, emphasizing De Moortel I and Bradshaw S J 2008 Sol. Phys. Downloaded from again the need for combined imaging and spec- For the future submitted. troscopic observations. For a range of spectral From the theoretical point of view, a number De Pontieu B et al. 2007 Science 318 1574. lines, a direct comparison is made between the of areas of future work are required in order Dere K P et al. 1997 A&A Suppl. Ser. 125 149. observed Doppler shifts and emission measures to make progress on coronal heating: further Edlén B 1942 Z. Astrophys. 22 30. Gudiksen B V and Nordlund A 2005 Ap. J. 618 1020. and the corresponding values derived from their studies of reconnection (including 3‑D models, Hahm T H and Kulsrud R S 1985 Phys. Fluids 28 2412. http://astrogeo.oxfordjournals.org/ synthesized spectra (see figure 5). Taking into kinetic effects and relation to external driving) Hannah I G et al. 2008 Ap. J. 677 704. account the limitations of the underlying 3‑D and waves (including nonlinear studies, kinetic Hansteen V H 1993 Ap. J. 402 741. MHD model, these graphs show a remarkable effects, more realistic geometries and coronal Heyvaerts J and Priest E R 1983 A&A 117 220. agreement for both parameters, in almost the seismology). Observational challenges include Hollweg J 1984 Ap. J. 277 392. Hudson H S 1991 133 357. entire range of calculated spectral lines. a better understanding of the fine structure of Sol. Phys. Innes D E and Tóth G 1999 Sol. Phys. 185 127. A lot of forward modelling so far has in some coronal plasma: what are the minimum temper- Ionson J 1978 Ap. J. 226 650. way or another been related to the long-stand- ature and density in an active region loop? Also, Jain R et al. 2006 Phys. Plas. 13 52902. ing coronal heating problem. However, a few further consideration must be given to the time Klimchuk J A and Cargill P J 2001 Ap. J. 553 440. recent studies have focused on forward model- series analysis of X-ray brightness, and to the Kontar E P et al. 2005 Sol. Phys. 226 317. ling of MHD wave behaviour in the solar atmo­ electrodynamics of the chromosphere. Clearly, Kosugi T et al. 2007 Sol. Phys. 243 3. at University of Wales Aberystwyth on October 13, 2014 Lin R P et al. 2002 Sol. Phys. 210 3. sphere, which is of particular relevance to the furthering our understanding of the elusive Lundquist L L et al. 2004 ESA-SP 575 306. rapidly developing field of coronal seismology coronal heating mechanism depends on progress Mandrini C H et al. 2000 Ap. J. 530 999. (De Moortel 2005, Nakariakov and Verwichte in both observations and theoretical modelling Martínez-Sykora J et al. 2008 Ap. J. submitted. 2005). For example, the interpretation of loop but most importantly, by successfully compar- Müller D et al. 2004 A&A 424 289. oscillations observed by SUMER/SOHO and ing and linking theory and observations. This Müller D et al. 2005 A&A 436 1067. SXT/Yohkoh in terms of slow standing modes, necessary link can be provided by forward mod- Nakariakov et al. 1997 Sol. Phys. 175 93. Nakariakov V M and Verwichte E 2005 Living Reviews initiated by a microflare at the loop footpoint, is elling as its predictive power is an excellent tool in Sol. Phys. 2 3. investigated by Taroyan et al. (2007). Synthetic to study a wide variety of physical processes. Ofman L et al. 1998 Ap. J. 493 474. spectra are produced for the Fe xix, Ca xv and Forward modelling can both aid the (correct) Okamoto S et al. 2007 Science 318 1577. Ca xiii lines, which are directly comparable interpretation of observational data to allow Parenti S et al. 2006 Ap. J. 651 1219. with SUMER observations. The time profiles comparison with theoretical models and provide Parker E N 1988 Ap. J. 330 474. Patsourakos S and Klimchuk J A 2006 647 of the synthesized intensity and Doppler shifts guidance and constraints derived from theoreti- Ap. J. 1452. show a good qualitative agreement with the cal modelling on observational campaigns and Peter H et al. 2004 Ap. J. 617 L85. observed oscillations and confirm that these the design of future instrumentation. ● Peter H et al. 2006 Ap. J. 638 1068. particular hot loop oscillations will show up Pevtsov A A et al. 2003 Ap. J. 598 1387. much stronger in Doppler shift than in inten- Ineke De Moortel, University of St Andrews Piana M et al. 2003 Ap. J. 595 L127. sity. Although not modelling a particular physi- ([email protected]); Philippa Browning, Prato M et al. 2006 Sol. Phys. 237 61. Priest E R and Forbes T 2000 Magnetic Reconnection cal process, De Moortel and Bradshaw (2008) University of Manchester; Stephen J Bradshaw, (CUP, Cambridge). investigate intensity perturbations associated Imperial College, London; Balázs Pintér, Ruderman M et al. 1998 A&A 338 1138. with coronal density oscillations and show that University of Aberystwyth; Eduard P Kontar, Sarkar A and Walsh R W 2006 ESA-SP 617 118. care has to be taken with the interpretation of University of Glasgow. Sarro L M et al. 1999 A&A 351 721. some parameters derived from observed (inten- Acknowledgments. The authors would like Taroyan Y et al. 2006 A&A 446 315. Taroyan Y et al. 2007 Ap. J. 659 L173. sity) oscillations. In particular, it is found that to thank all the participants and speakers, in Tomczyk S et al. 2007 Science 317 1192. the damping rate of the “input” density pertur- particular the invited speakers, P Cargill (Imperial Tsiklauri D et al. 2005 New J. Phys. 7 79. bations and the resulting, synthesized intensity College, London), V Hansteen (University of Van Doorsselaere T et al. 2007 A&A 471 311. oscillations can be substantially different. Oslo) and H Hudson (University of California, Van Doorsselaere T et al. 2008 Ap. J. 676 L73. Many other examples of forward modelling Berkeley). IDM and SB acknowledge support of Vekstein G and Jain R 1998 Phys. Plas. 5 1506. can be found in the literature. To mention but a Royal Society University Research Fellowship Vekstein G and Bian N 2006 Phys. Plas. 13 122 105. Vekstein G and Katsukawa Y 2000 Ap. J. 501 1096. a few, Innes and Tóth (1999) and Sarro et al. and STFC Postdoctoral Fellowship, respectively. Warren H P and Winebarger A R 2006 Ap. J. 645 711. (1999) study the dynamical response of several EPK acknowledges support of an STFC Advanced Wikstøl O et al. 1997 Ap. J. 483 972. different spectral lines to Petschek-like recon- Fellowship. BP acknowledges the financial support Wikstøl O et al. 1998 Ap. J. 501 895. nection and apply their results to explosive from STFC. Young et al. 2003 A&A Suppl. Ser. 144 135.

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