3 The Observational Framework

3.1 General properties

Although coronal loops are often well defined and studied in the EUV band, detected by many space mission spectrometers like those on board SoHO and Hinode, and by high resolution imagers such as TRACE and SDO/AIA, the bulk of coronal loops is visible in the X-ray band (Figure 1*). Also, the peak of the coronal emission measure of active regions – where the loops are brightest – is above 2 MK, which is best observed in X-rays (e.g., Peres et al., 2000*; Reale et al., 2009a*; Warren et al., 2011*).

View Image
Figure 1: Images of the same active region, taken in the EUV band with TRACE (top) and in the X-ray band with Hinode/XRT (bottom), on 14 November 2006. The X-ray image shows more clearly that the active region is densely populated with coronal loops.

Coronal loops are characterized by an arch-like shape that recalls typical magnetic field topology. This shape is replicated over a wide range of dimensions. Referring, for the moment, to the soft X-ray band, the main properties of coronal loops are listed in Table 1. The length of coronal loops spans more than two orders of magnitude. As already mentioned, the loops owe their high luminosity and variety to their nature of magnetic flux tubes where the plasma is confined and isolated from the surroundings. Magnetized fully-ionized plasma conducts thermal energy mostly along the magnetic field lines. Due to the high thermal insulation, coronal loops can have different temperatures, from ∼ 105 K up to a few ∼ 107 K (flaring loops). A density of the confined plasma below 107 –108 cm −3 can be difficult to detect, while the density can grow up to 1012 cm −3 in flaring loops. The corresponding plasma pressure in non-flaring loops can typically vary between −3 10 and −2 10 dyne cm, corresponding to confining magnetic fields 0.5 B ∼ 8πp of the order of 0.1 – 10 G in the corona. One characterizing feature of coronal loops is that typically their cross-section is constant along their length above the transition region, at variance from the topology of potential magnetic fields. There is evidence that the cross-section varies across the transition region, as documented in Gabriel (1976*). A simple geometric description is reported in Chae et al. (1998c*):

2 ν 1∕2 A (T )∕A (Th ) = [1 + (Λ − 1)(T ∕Th) ] ∕Λ , (1 )
where A is the cross-section area, T is the temperature, T = 106 K h, Λ = 30, and ν = 3.6.

Table 1: Typical X-ray coronal loop parameters
Type Length Temperature Density Pressure
  [109 cm] [MK] [109 cm–3] [dyne cm–2]
Bright points 0.1 – 1 2 5 3
Active region 1 – 10 3 1 – 10 1 – 10
Giant arches 10 – 100 1 – 2 0.1 – 1 0.1
Flaring loops 1 – 10 > 10 > 50 > 100

3.1.1 Classification

Myriads of loops populate the solar corona and constitute statistical ensembles. Attempts to define and classify coronal loops were never easy, and no finally established result exists to-date. Early attempts were based on morphological criteria, i.e., bright points, active-region loops, and large-scale structures (Vaiana et al., 1973*, Figure 2*), largely observed with instruments in the X-ray band. In addition to such classification, more recently, the observation of loops in different spectral bands and the suspicion that the difference lies not only in the band, but also in intrinsic properties, have stimulated another classification based on the temperature regime, i.e., cool, warm, hot loops (Table 2). Cool loops are generally detected in UV lines at temperatures between 105 and 106 K. They were first addressed by Foukal (1976*) and later explored more with SoHO observations (Brekke et al., 1997*). Warm loops are well observed by EUV imagers such as SoHO/EIT, TRACE, and in most channels of SDO/AIA, and confine plasma at temperature around 1 – 1.5 MK (Lenz et al., 1999*). Hot loops are those typically observed in the X-ray band, and in hot UV and EUV lines (e.g., Fe xvi) and channels (SDO/AIA 335 Å), with temperatures around or above 2 MK (Table 1). These are the coronal loops already identified, for instance, in the early rocket missions (Vaiana et al., 1973*). This distinction is not only due to observation with different instruments and in different bands, but there are hints that it may be more substantial and physical, i.e., there may be two or more classes of loops that may be governed by different regimes of physical processes. For instance, the temperature along warm loops appears to be distributed uniformly and the density to be higher than that predicted by equilibrium conditions. Does this make such loops intrinsically different from hot loops, or is it just the signature that warm loops are a transient conditions of hot loops? New state-of-art methods, like differential emission measure tomography (DEMT), have proposed a new classification of coronal loops based on whether the temperature increases or decreases with height (Huang et al., 2012).

View Image
Figure 2: The X-ray corona contains loops with different spatial scales, e.g., bright points (BP), active region loops (AR), large-scale structures (LSS). The scale unit is labelled. Image credit: Yohkoh mission, ISAS, Japan.

Table 2: Thermal coronal loop classification
Type Temperature [MK]
Cool 0.1 – 1
Warm 1 – 1.5
Hot ≥ 2

A real progress in the insight into coronal loops is expected from the study of large samples of loops or of loop populations. Systematic studies of coronal loops suffer from the problem of the sample selection and loop identification, because, for instance, loops in active regions overlap along the line sight. Attempts of systematic studies have been performed in the past on Yohkoh and TRACE data (e.g., Porter and Klimchuk, 1995*; Aschwanden et al., 2000*). A large number of loops were analyzed and it was possible to obtain meaningful statistics. However, it is difficult to generalize the results because of limited samples and/or selection effects, e.g., best observed loops, specific instrument. One basic problem for statistical studies of coronal loops is that it is very difficult to define an objective criterion for loop identification. In fact, loops are rarely isolated; they coexist with other loops that intersect or even overlap along the line of sight. This is especially true in active regions where most of the loops are found. In order to make a real progress along this line, we should obtain loop samples and populations selected on totally objective and unbiased criteria, which is difficult due to the problems outlined above. Some steps are coming in this direction (Aschwanden et al., 2013) and we will see results in the future.

3.2 Morphology and fine structuring

3.2.1 Geometry

Coronal loops are magnetic structures and might therefore be mapped easily and safely by mapping reliably the coronal magnetic field. Unfortunately, it is well-known that it is very difficult to measure the magnetic field in the corona, and it can be done only in very special conditions, e.g., very strong local field (White et al., 1991). In some cases it is possible to use coronal seismology (first proposed by Uchida, 1970) to determine the average magnetic field strength in an oscillating loop, first used by Nakariakov et al. (1999*) and Nakariakov and Ofman (2001*), on TRACE loops, and more recently investigated in a number of studies. In some of these studies, for instance, seismological techniques are used in order to measure flare-induced loop oscillations (Ballai et al., 2011) and waves and flows in active region loops (Wang et al., 2013*; Uritsky et al., 2013). The accuracy of these methods depends on the correct detection of the temporally and spatially resolved mode of oscillation, and on the details of the loop geometry.

View Image
Figure 3: Coronal loops have approximately a semicircular shape. Image: SDO/AIA, 171 Å filter, 24 February 2011. Credit: NASA/LMSAL/SDO.

Since we cannot determine well the coronal magnetic field, coronal loop geometry deserves specific analysis. As a good approximation, loops generally have a semicircular shape (Figure 3*). The loop aspect, of course, depends on the loop orientation with respect to the line of sight: loops with the footpoints on the limb more easily appear as semicircular, as well as loops very inclined on the surface near the center of the disk. The assumption of semicircular shape can be useful to measure the loop length even in the presence of important deformations due to projection effects: the de-projected distance of the loop footpoints is the diameter of the arc. However, deviations from circularity are rather common and, in general, the detailed analysis of the loop geometry is not a trivial task. The accurate determination of the loop geometry is rather important for the implications on the magnetic field topology and reconstruction. It is less important for the structure and evolution of the confined plasma, which follow the field lines whatever shape they have and change little also with moderate changes of the gravity component along the field lines. First works on the accurate determination of the loop geometry date back to the 1960s (Saito and Billings, 1964). More specific ones take advantage of stereoscopic views allowed by huge loops during solar rotation, with the aid of magnetic field reconstruction methods. These studies find deviations from ideal circularity and symmetry, not surprising for such large structures (Berton and Sakurai, 1985). The geometry of a specific loop observed with TRACE was measured in the framework of a complete study including time-dependent hydrodynamic modeling (Reale et al., 2000a*,b*). In that case, the discrepancy between the length derived from the distance of the footpoints taken as loop diameter and the length measured along the loop itself allowed to assess the loop as elongated. Later, a reconstruction of loop geometry was applied to TRACE observation of medium-sized oscillating loops, to derive the properties of the oscillations. In this case, a semicircular pattern was applied (Aschwanden et al., 2002*). The importance of the deviations from circularity on constraining loop oscillations was remarked later (Dymova and Ruderman, 2006).

The STEREO mission is contributing much to the analysis of loop morphology and geometry, thanks to its unique capability to observe the Sun simultaneously from different positions. The three-dimensional shape of magnetic loops in an active region was first stereoscopically reconstructed from two different vantage points based on simultaneously recorded STEREO/SECCHI images (Feng et al., 2007). Five relatively long loops were measured and found to be non-planar and more curved than field lines extrapolated from SoHO/MDI measurements, probably due to the inadequacy of the linear force-free field model used for the extrapolation. A misalignment of 20 – 40 deg between theoretical model and observed loops has been quantified from STEREO results (Sandman et al., 2009; DeRosa et al., 2009). Systematic triangulations and 3D reconstructions using the Extreme UltraViolet Imager (EUVI) telescopes on both STEREO spacecrafts were used to derive loop characteristics, such as the loop plane inclination angles (Aschwanden et al., 2008*, 2009*, 2012). Deviations from circularity within 30%, less significant from coplanarity and twisting below the threshold for kink instability, were found.

Another interesting issue regarding coronal loop geometry is the analysis of the loop cross-section, which also provides information about the structure of the coronal magnetic field. Yohkoh/ SXT allowed for systematic and quantitative studies of loop morphology and showed that the cross-section of coronal loops is approximately constant along their length and do not increase significantly. More in detail, a systematic analysis of a sample of ten loops showed that the loops tend to be only slightly (∼ 30%) wider at their midpoints than at their footpoints, while for a bipolar field configuration we would expect expansions by factors. One possible explanation of this effect is the presence of significant twisting of the magnetic field lines and, therefore, the development of electric currents and strong deviations from a potential field. The effect might be seen either as a twisting of a single loop or as a “braiding” of a bundle of unresolved thin loops (see Section 3.2.2). At the same time it was found that the variation of width along each loop tends to be modest, implying that the cross section has an approximately circular shape (Klimchuk et al., 1992).

View Image
Figure 4: Magnetic field lines extrapolated from optical magnetogram superposed on a composite SDO/AIA (211 Å, 193 Å, 171 Å) image, on 7 April 2014. Credit: NASA/LMSAL/SDO.

Implications of these results on the theory of coronal heating were discussed in Klimchuk (2000*),but the conclusion was that none of the models alone is able to explain all observed properties. Important information about the internal structuring of coronal loops comes from the joint analysis of the photospheric and coronal magnetic field (Figure 4*). TRACE loops are quite symmetric and their cross-section is constant to a good degree of approximation, at variance from the prediction by linear force-free extrapolation on SoHO/MDI data (López Fuentes et al., 2006). The magnetic field lines starting from the same footpoint can diverge to different end footpoints, and thus be very complicated with strong tangling of the magnetic flux strands driven by the photospheric convection. This is not observed at high-resolution in the quiescent corona, possibly because of braiding-induced interchange reconnection of the magnetic field (Schrijver, 2007). Other approaches address also the density values and stratification, and explain the evidence with a combination of high plasma density within the structures, which greatly increases the emissivity of the structures, and geometric effects that attenuate the apparent brightness of the feature at low altitudes (DeForest, 2007). More recent MHD modeling finds that the temperature distribution across the loop naturally leads to the appearance of constant cross-section in EUV band (Peter and Bingert, 2012*). Another model shows that the apparent constant loop cross section is a result of the non-circular shape of the loops (Malanushenko and Schrijver, 2013).

An alternative analysis of the magnetic field at the footpoints of hot and cool loops showed that the magnetic filling factor is lower in hot loops (0.05 – 0.3 out of sunspots) than in warm loops (0.2 – 0.6) (Katsukawa and Tsuneta, 2005). The multispectral analysis of solar EUV images has showed the possibility of separating the different solar structures from a linear combination of images to emphasise the structures (Dudok de Wit and Auchère, 2007).

The general impression is that, although moderate deviations from the ideal circular shape with constant cross-section are often observed, they probably do not affect the description of loops with a simplified geometry.

3.2.2 Fine structuring

It has been long claimed that coronal loops consist of bundles of thin strands, to scales below the instrumental resolution (e.g., Gómez et al., 1993). The issue of fine loop structure is of critical importance because it constrains the elementary processes that determine the loop ignition. The task to investigate this substructuring is not easy. Studies based both on models and on analysis of observations independently suggest that elementary loop components should be very fine with typical cross-sections of the strands on the order of 10 – 100 km (Beveridge et al., 2003; Cargill and Klimchuk, 2004*; Vekstein, 2009*). First limited evidence of fine structuring was the low filling factor inferred for loops observed with NIXT (Di Matteo et al., 1999*, see Section 3.3.2). The high spatial resolution achieved by the TRACE normal-incidence telescope allowed to address the transverse structure of the imaged coronal loops. EUV images visibly show that coronal loops are substructured (Figure 5*).

View Image
Figure 5: SDO/AIA (193 Å channel) image of finely-structured coronal loops (14 October 2011, 22:56 UT). The image was treated with a Gaussian sharpening filter with a radius of 3 pixels. Image reproduced with permission from Brooks et al. (2012*), copyright by AAS.

There were some early attempts to study the structure along the single strands in TRACE observations (Testa et al., 2002*). Later, it was shown that in many cases, hot loop structures observed in active regions with the Yohkoh/SXT (T > 3 MK) are not exactly co-spatial with warm structures (T ∼ 1– 2 MK) observed in the EUV bands (195 Å) of the SoHO/EIT, nor they cool down to become visible with EIT (Nagata et al., 2003; Schmieder et al., 2004). In another study, hot monolithic loops visible with the Yohkoh/SXT were instead resolved as stranded cooler structures with TRACE at later times (Winebarger and Warren, 2005*), although the large time delay (1 to 3 hours) is hardly compatible with the cooling time from SXT to TRACE sensitivity. More systematic studies of TRACE images proposed that about 10% of the positions across loops can be fitted with an isothermal model, indicating coherent loop components about 2000 km wide (Aschwanden and Nightingale, 2005*; Aschwanden et al., 2007).

More recent studies have found other indirect evidence for loop fine structuring. For instance, the different fuzziness measured in spectral lines forming at different coronal temperatures (Tripathi et al., 2009*) has been modeled with loops made of tens of independently pulse-heated strands (Guarrasi et al., 2010*; Reale et al., 2011*). Other indirect evidence might come from optical observations of relatively dense and cool (∼ 7000 K) downfalling elongated blobs above the solar limb, the so-called “coronal rain” (Antolin and Rouppe van der Voort, 2012), with widths of the order of 500 km. Upflows in even narrower channels (∼ 100 km) were resolved in the optical band, correlating with brightenings in SDO/AIA observations (Ji et al., 2012).

New direct measurements of the loop fine structure are stimulated by the new observations with normal-incidence telescopes (SDO/AIA, Hi-C) and by indications that the elementary components of most loops might be small scale and close to be resolved (Brooks et al., 2012). Some quantitative constraints come from the very high spatial resolution of the Hi-C sounding rocket, with cross-sections that range between about 300 km (Brooks et al., 2013) to over 1000 km (Peter et al., 2013) for long loops, with possibility of further substructuring well below 100 km.

Evidence for fine structure can come also from studies of thermal structuring; in general, an emission measure distribution extending over a broad temperature range along the line of sight is retained to be a signature of the presence of multi-stranded structure, because of the coexistence of many thermal components. See Section 3.3 for more details.

In general, there is converging evidence for fine loop structuring to scales on the order of 100 km or below. Ultimate information could be provided by higher resolution future instruments.

3.3 Diagnostics and thermal structuring

The investigation of the thermal structure of coronal loops is very important for their exhaustive physical comprehension and to understand the underlying heating mechanisms. For instance, one of the classifications outlined above is based on the loop thermal regime, and, we remark, it is debated whether the classification indicates a real physical difference.

Diagnostics of temperature are not trivial in the corona. No direct measurements are available. Since the plasma is optically thin, we receive information integrated on all the plasma column along the line of sight. The problem is to separate the distinct contributing thermal components and reconstruct the detailed thermal structure along the line of sight. However, even the determination of global and average values deserves great attention. Exploratory measurements have shown that the ion temperature can be different from the electron temperature in the quiet corona (Landi, 2007).

Moderate diagnostic power is allowed by imaging instruments, by means of multifilter observations. Filter ratio maps (Figure 6*) provide information about the spatial distribution of temperature and emission measure (e.g., Vaiana et al., 1973). The emission of an optically thin isothermal plasma as measured in a j-th filter passband is:

Ij = EM Gj (T) , (2 )
where T is the temperature and EM is the emission measure, defined as
∫ 2 EM = V n dV ,

where n is the particle density, and V the plasma volume. The ratio Rij of the emission in two different filters i,j is then independent of the density, and only a function of the temperature:

Ii Gi (T) Rij = I- = G--(T) . (3 ) j j
The inversion of this relationship provides a value of temperature, based on the isothermal assumption.

The limitations of this method are substantial. In particular, one filter ratio value provides one temperature value for each pixel; this is a reliable measurement, within experimental errors, as long as the assumption of isothermal plasma approximately holds for the plasma column in the pixel along the line of sight. If the plasma is considerably multithermal, the temperature value is an average weighted for the instrumental response. Since the response is a highly nonlinear function of the emitting plasma temperature, it is not trivial to interpret the related maps correctly. In addition, it is fundamental to know the instrument response with high precision, in order to avoid systematic errors, which propagate dangerously when filter ratios are evaluated. In this respect, broadband filters provide robust thermal diagnostics, because they are weakly dependent on the details of the atomic physics models, e.g., on the presence of unknown or not well-known spectral lines, on the choice of element abundances. Narrowband filters can show non-unique dependencies of filter ratio values on temperature (e.g., Patsourakos and Klimchuk, 2007*), due to the presence of several important spectral lines in the bands, but a more general problem can be the bias to detect narrow ranges of temperatures forced by the specific instrument characteristics (Weber et al., 2005*). This problem can be important especially when the distribution of the emission measure along the line of sight is not simple and highly nonlinear (e.g., Reale et al., 2009a*). New methods for thermal diagnostics with narrow band instruments have been proposed (Dudok de Wit et al., 2013).

The problem of diagnostics of loop plasma from filter ratios, and, more in general, the whole analysis of loop observations, are made even more difficult by the invariable presence of other structures intersecting along the line of sight. A uniform diffuse background emission also affects the temperature diagnostics, by adding systematic offsets that alter the filter ratio values. The task of subtracting this “background emission” from the measured emission is non-trivial and can seriously bias the results of the whole analysis. This problem emerged dramatically when the analysis of the same large loop structure observed with Yohkoh/SXT on the solar limb led to three different results depending mostly on the different ways to treat the background (Priest et al., 2000*; Aschwanden et al., 2001; Reale, 2002a*). The amount of background depends on the instrument characteristics, such as the passband and the point response function: it is most of the signal in TRACE UV filterbands, for instance, and its subtraction becomes a very delicate issue (e.g., Del Zanna and Mason, 2003*; Reale and Ciaravella, 2006*; Aschwanden et al., 2008*; Terzo and Reale, 2010*). The problem can be mitigated if one analyzes loops as far as possible isolated from other loops, but this is not easy, for instance, in active regions. If this is not the case, broadband filters may also include contamination from many structures at relatively different temperature and make the analysis of single loops harder. The problem of background subtraction in loop analysis has been addressed by several authors, who apply different subtraction ranging from simple offset, to emission in nearby pixels or subregions, to values interpolated between the loop sides, to whole images at times when the loop is no longer (or not yet) visible (Testa et al., 2002; Del Zanna and Mason, 2003*; Schmelz et al., 2003*; Aschwanden and Nightingale, 2005*; Reale and Ciaravella, 2006*; Aschwanden et al., 2008; Terzo and Reale, 2010).

More accurate diagnostics, although with less time and space resolution, are in principle provided by spectrometers and observations in temperature-sensitive spectral lines, which are being constantly improved to provide better and better spatial information. Early results from UV spectroscopy already recognized the link between transition region and coronal loops, for instance, from Skylab mission (Feldman et al., 1979; Mariska et al., 1980). There is a considerable effort to develop and update continuously the spectral codes and databases, in particular the CHIANTI spectral line database (Dere et al., 1997; Landi et al., 1999; Dere et al., 2001; Landi et al., 2006; Dere et al., 2009; Landi et al., 2012a; Del Zanna, 2012; Landi et al., 2013). Together with background subtraction, one major difficulty met by spectroscopic analysis is that, in the UV band, the density of lines is so high that they are often blended and, therefore, it is hard to separate the contribution of the single lines, especially the weak ones. Fine diagnostics, such as Doppler shifts and line broadening, can become very tricky in these conditions and results are subject to continuous revisitation and warnings from the specialized community. The problem of background subtraction is serious also for spectral data, because their lower spatial and temporal resolution determines the presence of more structures and, therefore, more thermal components, along the line of sight in the same spatial element.

View Image
Figure 6: Temperature map of an active region obtained from the ratio of two images in different broadband filters with Hinode/XRT (12 November 2006, 12 UT).

Care should be paid also when assembling information from many spectral lines into a reconstruction of the global thermal structure along the line of sight. Methods are well-established (e.g., Gabriel and Jordan, 1975) and several approaches are available. The so-called method of the emission measure loci (Pottasch, 1963; Jordan et al., 1987; Landi et al., 2002) is able to tell whether plasma is isothermal of multithermal along the line of sight (Figure 7*), but less able to add details. Detailed emission measure distributions can be obtained from differential emission measure (DEM) reconstruction methods (e.g., Brosius et al., 1996*; Kashyap and Drake, 1998), but this is an ill-posed mathematical problem, and, therefore, results are not unique and are subject to systematic and unknown errors.

There is no wide convergence on the reconstruction of the temperature distribution of the emission measure along the line of sight. So several works have been devoted to develop new methods (e.g., Hannah and Kontar, 2012) and to investigate the limits and capabilities of the methods themselves. One important question is how far can we push the temperature resolution of the methods. We expect better resolution switching from narrow-band instruments with few channels (Weber et al., 2005*) to spectrometers (Landi and Klimchuk, 2010; Landi et al., 2012b*), but it is difficult to achieve a temperature resolution better than Δ logT ≈ 0.05 (Landi et al., 2012b*). Reconstructions from narrow-band data may suffer from biases that affect their reliability (Weber et al., 2005*) and produce clustering (Guennou et al., 2012a,b). Not only the width and sensitivity of the spectral band is important, but also its position in the temperature range. It has been remarked that, with the available instruments, it is difficult to constrain emission from plasma at temperature above about 6 MK and emission measures less than ∼ 1027 cm −5 (Winebarger et al., 2012*). Under some conditions, these limitations might be overcome, as described in Section 3.3.1. It is also useful to assess unknown uncertainties in the atomic data (Landi et al., 2012b). All-encompassing 3D MHD simulations allow to build a complete cycle from true values to observables back to reconstructed values and comparison with true values (Testa et al., 2012). It is important to test the combination of all possible uncertainties, the overall capability of the methods, indicating that a highly non-uniform density distribution along the line of sight can mislead the methods.

Forward modeling and simulations can be ways to escape from these problems, but they require non-trivial computational efforts and programming, and it is not always possible to provide accurate confidence levels. All these approaches are constantly improved and, probably, the best way to proceed is to combine different approaches and multiband observations and to finally obtain a global consistency.

Interesting issues come from global thermal analysis of the confined solar corona. The analysis of full-disk data from spatially-unresolved SphinX spectral data at the solar minimum of 2009 shows temperatures of 1.7 – 1.9 MK and emission measures between 47 − 3 4 × 10 cm and 48 −3 1.1 × 10 cm. Most of the emission comes from the large-scale corona rather than localized and bright structures, e.g., bright points (Sylwester et al., 2012).

In addition to the problems intrinsic to diagnostic techniques, we have to consider that loops appear to have different properties in different bands, as mentioned in Section 3.1.1. It is still debated whether such differences originate from an observational bias due to the instruments or from intrinsic physical differences, or both. In view of this uncertainty, in the following we will make a distinction between hot and warm loops, which will generally correspond to loops observed in the X-ray (and hot UV lines, e.g., Yohkoh/SXT, Hinode/XRT, SoHO/CDS Fe xvi line) and in the UV band (e.g., SoHO/EIT, TRACE), respectively. Cool loops are also observed in the UV band. The boundary between hot and warm loops is, of course, not sharp, and it is not even clear whether they are aspects of the same basic structure, or they really are physically different and are heated differently (see also Section 3.3.3). We will now devote our attention to the comparison between hot and warm loops.

3.3.1 Hot loops

After the pioneering analyses driven by the Skylab X-ray instruments (Section 2), Yohkoh/SXT allowed to conduct large-scale studies on the thermal and structure diagnostics of hot loops, mostly located in active region, and the comparison with other instruments, for instance on-board SoHO, allowed to obtain important cross-checks and additional information. Filter ratio maps of flaring loops were shown early after the mission launch (Tsuneta et al., 1992).

Systematic measurements of temperature, pressure, and length of tens of both quiescent and active region coronal loops were conducted on Yohkoh observations in the 1990s (Porter and Klimchuk, 1995*) using the filter ratio method. Steady and isolated loops were selected with a length in a decade between 9 10 5 × 10 < 2L < 5 × 10 cm. Their average temperature was high, ranging in a decade (2 < T < 30 MK), with a mean of about 6 MK and with large uncertainties in the hot tail of the distribution. Pressure was estimated to span over two decades (0.1 < p < 20 dyne cm− 2). The temperature and length were uncorrelated, while the pressure was found overall to vary inversely with the length (as overall expected for a thermally homogeneous sample from loop scaling laws, see Section 4.1.1), allowing to constrain the dependence of the magnetic field intensity on the loop length (Klimchuk and Porter, 1995), and the data uncertainties (Klimchuk and Gary, 1995). Another systematic analysis on another sample of Yohkoh loops in active regions (Kano and Tsuneta, 1995*) confirmed some of the correlations in Porter and Klimchuk (1995), but also found a correlation between the loop length and the temperature, and deviations from RTV scaling laws (Section 4.1.1). The correlations might depend on the loop sample, as a single scaling law links three parameters. Very hot Yohkoh/SXT loops were found to have short lifetimes (less than few hours), and often to exhibit cusps (Yoshida and Tsuneta, 1996).

Density diagnostics through density-sensitive line ratio led to measure directly density values in active regions (e.g., Doschek et al., 2007*). The hot core of the active region is densest, with values as high as 1010.5 cm −3. Density in active regions has been measured also using Fe lines, with values in the range 8.5 ≤ log (Ne ∕cm −3) ≤ 11.0 (Young et al., 2009), or in a smaller range (from 108.5 to 9.5 − 3 10 cm) (Watanabe et al., 2009). Diagnostics of high density structures are also possible from the analysis of absorbed structures observed with narrow-band imagers (e.g., Landi and Reale, 2013).

A big effort has been devoted to the possible detection of hot plasma outside of evident flares. This would be a conclusive evidence of the presence of impulsive heating mechanisms in coronal loops (e.g., Klimchuk, 2006*, see Section 4.4). Hinode instruments appear to be able to provide new interesting contributions to this topic. The analysis of spectroscopic observations of hot lines in solar active regions from Hinode/EIS allows to construct emission measure distributions in the 1 – 5 MK temperature range, and shows that the distributions are flat or slowly increasing up to approximately 3 MK and then fall off rapidly at higher temperatures (Patsourakos and Klimchuk, 2009). Emission from very hot lines has been early found in other Hinode/EIS observations, and in particular from the Ca xvii at 192.858 Å, formed near a temperature of 6 6 × 10 K, in active regions (Ko et al., 2009).

Thanks to its multifilter observations, also Hinode/XRT is providing useful information about the thermal structure of the bright X-ray corona. Temperature maps derived with combined filter ratios show fine structuring to the limit of the instrument resolution and evidence of multithermal components (Reale et al., 2007), as complemented by TRACE images. Observations including flare filters show evidence of a hot component in active regions outside of flares (Schmelz et al., 2009*), and data in the medium thickness filters appear to constrain better this component of hot plasma as widespread, although minor, and peaking around logT ∼ 6.8– 6.9, with a tail above 10 MK (Reale et al., 2009b). Further support comes from RHESSI data (Reale et al., 2009a*; McTiernan, 2009).

Further evidence for minor components of hot plasma in non-flaring active regions have been found from various other instruments. Analysis in the waveband 3.3 – 6.1 Å and 280 – 330 Å with the RESIK and SPIRIT instruments, respectively, confirm the presence of a 0.1% ∼ 10 MK component at various activity levels (Sylwester et al., 2010; Shestov et al., 2010). Low-resolution SphinX spectra integrated on 17 days in the 2 – 10 Å band still show a small but highly-significant component at about 7 MK from active regions outside of microflares (Miceli et al., 2012). The separation of the hot from the cool components in the SDO/AIA 94 Å channel indicates finely-structured Fe xviii line emission in the core of bright active regions (Reale et al., 2011*). This filamented emission at high temperature has been previously predicted with a model of multi-stranded pulse-heated loops (Guarrasi et al., 2010*). The emission from hot emission lines (Ca xvii and Fe xviii) has been confirmed from simultaneous observations with SDO/AIA and with the Hinode/EIS spectrometer (Testa and Reale, 2012*; Teriaca et al., 2012*). However, while it has been proposed that AIA imaging observations of the solar corona can be used to track hot plasma (6 – 8 MK), it has been questioned that such emission is really at the temperature of the line sensitivity peak (Teriaca et al., 2012*). Other analysis of a limb active region with EUV spectral data from Hinode/EIS does not find evidence for plasma at temperature log T > 7 (O’Dwyer et al., 2011) and puts an upper limit on the same track as remarked by Winebarger et al. (2012). So a final conclusion on this topic is still to be reached. There is some evidence that the amount of high-temperature plasma might correlate with the intensity of the active region magnetic fields because of increasing frequency of energy release (Warren et al., 2012).

3.3.2 Comparison of hot and warm loops

Before the SoHO/EIT and TRACE observations, warm loops had been imaged in a similar spectral band and with similar optics by the rocket NIXT mission (see Section 2). Studies of NIXT loops including the comparison with hydrostatic loop models (Section 4.1.1) pointed out that bright spots also visible in Hα band were the footpoints of hot high-pressure loops (Peres et al., 1994*). This result was confirmed by the comparison of the temperature structure obtained from Yohkoh with NIXT data (Yoshida et al., 1995, see also Section 3.3.3).

Another comparison of loops imaged with NIXT and Yohkoh/SXT showed that the compact loop structures (length 9 ∼ 10 cm) have a good general morphological correspondence, while larger scale NIXT loops (10 ∼ 10 cm) have no obvious SXT counterpart (Di Matteo et al., 1999). Comparison with static loop models (see Section 4.1.1) allowed to derive estimates of the loop filling factors, important for the loop fine structure (Section 3.2.2). In the NIXT band, the filling factor of short loops was found to be very low (10 −3– 10−2), but of the order of unity in the SXT band and for the largest structure. Simultaneous SoHO and Yohkoh observations of a small solar active region suggested a volume filling factor decreasing with increasing density and possible differences between emitting material in active regions and the quiet Sun (Griffiths et al., 2000). Other measurements of the filling factor come from density sensitive lines and images in the EUV band. For bright points the plasma-filling factor has been found to vary from 3 × 10− 3 to 0.3 with a median value of 0.04, which may indicate considerable subresolution structure, or the presence of a single completely-filled unresolved loop with subarcsec width (Dere, 2008, 2009).

Some similarity between loops observed in the TRACE EUV band and Yohkoh X-ray band was found in outer active region loops (Nitta, 2000) and interpreted as evidence of loops with a broad range of temperatures. Core loops were instead observed only in the X-rays and found to be variable, indicating that probably they are not steady.

Density and temperatures in two active regions were accurately determined from SoHO-CDS observations (Mason et al., 1999) and it was confirmed quantitatively that the AR cores are hotter than larger loop structures extending above the limb. The analysis of a single loop observed on the solar limb with SoHO/CDS showed a bias to obtain flat temperature distributions along the loop from ratios of single lines or narrow band filters (TRACE), while a careful DEM reconstruction at selected points along the same loop was inconsistent with isothermal plasma, both across and along the loop (Schmelz et al., 2001*). A whole line of works started from this analysis reconsidering and questioning the basic validity of the temperature diagnostics with TRACE and emphasizing the importance of the background subtraction, but also the need to obtain accurate spectral data (Schmelz, 2002; Martens et al., 2002; Aschwanden et al., 2002; Schmelz et al., 2003). Similar results but different conclusions were reached after the analysis of a loop observed with SoHO, invoking a non-constant cross-section to explain the evidence of isothermal loop (Landi and Landini, 2004*; Landi and Feldman, 2004*). On the other hand, evidence of non-uniform temperature along loops observed with TRACE was also found (Del Zanna and Mason, 2003*; Reale and Ciaravella, 2006*), emphasizing that the temperature diagnostic with narrow band instruments is a delicate issue.

View Image
Figure 7: EM-loci plots for two different loop systems, one showing a multi-thermal structure (top, from Schmelz et al., 2005*, reproduced with permission, copyright by AAS), the other an almost isothermal one (bottom, from Di Giorgio et al., 2003*, reproduced with permission, copyright by ESO). The EM is per unit area in the top panel.

An interesting debate focussed on the question whether the loops observed with TRACE and CDS have a uniform transverse thermal distribution, i.e., a narrow DEM, or a multi-thermal distribution, i.e., a wide DEM that may group together warm and hot loops. Although tackled from a different perspective, this question also concerns the fine longitudinal structuring of the loops and of their heating and is therefore strictly connected to the subject of Sections 3.2.2 and 4.4. A loop imaged by TRACE was found to be isothermal (with temperatures below 1 MK) along the line of sight from diagnostics of spectral lines obtained with SoHO/CDS (Del Zanna and Mason, 2003*). The distribution across another loop observed on the limb with SoHO/CDS was found multi-thermal, with a DEM reconstruction and a careful analysis of background subtraction (Schmelz et al., 2005). From the comparison with the isothermal structure of hot loops derived from CDS data (Di Giorgio et al., 2003*; Landi and Landini, 2004*) and a systematic inspection of the CDS atlas, the conclusion was that there might be two different classes of loops, multi-thermal and isothermal (Figure 7*).

Comparative studies of active region loops in the transition region and the corona (Ugarte-Urra et al., 2009) observed with Hinode seem to point out the presence of two dominant loop populations, i.e., core multitemperature loops that undergo a continuous process of heating and cooling in the full observed temperature range 0.4 – 2.5 MK shown by the X-Ray Telescope, and peripheral loops that evolve mostly in the temperature range 0.4 – 1.3 MK.

Multiband observations are able to provide more information and constraints. The analysis of an isolated loop in a time-resolved observation in several spectral bands, namely three TRACE UV filters, one Yohkoh/SXT filter, two rasters taken with SoHO/CDS in twelve relevant lines (5.4 ≤ log T ≤ 6.4), supported a coherent scenario across the different bands and instruments, i.e., a globally cooling loop and the presence of thermal structuring (Reale and Ciaravella, 2006*). The analysis overall indicated that the loop analysis can be easily affected by a variety of instrumental biases and uncertainties, for instance due to rough background subtraction. The fact that the loop that could be well analyzed across several bands and lines is a cooling loop may not be by chance (see end of Section 3.3.3).

SoHO spectrometric data have contributed to investigate the loop thermal structure for a long time. From a differential emission measure (DEM) analysis with a forward-folding technique on SoHO/CDS data, some loops were found to be isothermal and others to have a broad DEM (Schmelz et al., 2007*, 2008). Three distinct isothermal components, reminiscent of coronal hole, quiet-Sun, and active region plasmas, were found from the analysis of an active region spectrum observed by the SoHO/SUMER (Landi and Feldman, 2008).

Hinode/EIS observations of active region loops show that contrasted structures in cooler lines (∼ 1 MK) become fuzzy at higher temperatures (∼ 2 MK, Tripathi et al., 2009*), Figure 8*), as already pointed out by Brickhouse and Schmelz (2006). This issue is addressed by multi-thread loop modeling (Guarrasi et al., 2010*).

View Image
Figure 8: Loop system observed in several EUV spectral lines with Hinode/EIS (19 May 2007, 11:41 – 16:35 UT). The loops become less and less contrasted, i.e., fuzzier and fuzzier, at higher and higher temperature. Courtesy of D. Tripathi.

Intensive efforts have been devoted to the analysis of the cool side of the emission measure distribution of hot loops, using data from EUV spectrometers. There is evidence for dynamic structure of active regions with frequent condensations inside (Tripathi et al., 2010) and for steep distributions (Tripathi et al., 2011). Analysis of Hinode and SDO observations were used to reconstruct the emission measure over a broad temperature range (Warren et al., 2011*). Although affected by large uncertainties, it was found that at the apex of high-temperature loops the emission measure distribution has a relatively sharp peak around 4 MK.

3.3.3 Warm loops

The TRACE mission opened new intriguing questions because the data showed new features, e.g., stranded bright structures mostly localized in active regions, name “the moss”, and because the narrow band filters offered some limited thermal diagnostics, but not easy to interpret. Reliable temperatures are in fact found in a very narrow range, and many coronal loops are found to be isothermal in that range.

As mentioned in Section 3.3.2, first loop diagnostics with normal-incidence telescopes were obtained from data collected with NIXT (Peres et al., 1994). The bright spots with Hα counterparts were identified with the footpoints of high pressure loops, invisible with NIXT because not sensitive to plasma hotter than 1 MK. They have been later addressed as the moss in the TRACE images, which undergo the same effect, and their interactions with the underlying chromospheric structures began to be studied (Berger et al., 1999*; Fletcher and De Pontieu, 1999*). Comparison of SoHO/CDS and TRACE observations led to establish that the plasma responsible for the moss emission has a temperature range of about 1 MK and is associated with hot loops at 1 – 2 MK, with a volume filling factor of order 0.1 (Fletcher and De Pontieu, 1999). It was also found that the path along which the emission originates is of order 1000 km long. According to an analytical loop model, a filling factor of about 0.1 is in agreement with the hypothesis of moss emission from the legs of 3 MK loops (Martens et al., 2000). The electron density estimated in specific regions in the active region moss decreases with increasing temperature (Tripathi et al., 2008). The density within the moss region was highest at logT = 5.8– 6.1, with a value around 10 −3 10 cm.

As for temperature diagnostics with narrow band filters, loops soon appeared to be mostly isothermal with ratios of TRACE filters (Lenz et al., 1999*; Aschwanden et al., 2000). Is this a new class of loops? Equivalent SoHO/EIT filter ratios provided analogous results (Aschwanden et al., 1999b). This evidence is intriguing and many investigations have addressed it (see also Section 3.3.2). From the diagnostic perspective, DEM reconstruction along the line of sight from spectral SoHO/CDS data and synthesized EIT count rates led to almost uniform temperatures along the loop, pointing again to an instrumental bias (Schmelz et al., 2001). Simple modeling confirmed that, provided they are flat, i.e., top-hat-shaped, even broad DEMs along the line of sight produce constant TRACE filter ratio values (Weber et al., 2005). On the other hand, the DEM obtained from spectrometers and from multi-wideband imagers data is most probably neither isothermal nor broad and flat, instead peaked with components extending both to low and high temperatures (e.g., Peres et al., 2000*; Reale et al., 2009a). The critical point becomes the DEM width and its range of variation.

Using combinations of data from three filters, instead of two, does not seem to provide more information in the general case for warm loops (Schmelz et al., 2007), but the cross-field thermal structure of a sample of loops was found to be compatible with multithermal plasma with significant emission measure throughout the range 1 – 3 MK (Patsourakos and Klimchuk, 2007*). With a combination of TRACE filter ratios, emission measure loci, and two methods of differential emission measure analysis, a few loops were found either isothermal or multithermal (Schmelz et al., 2009). This might not be a contradiction, in view of the presence of at least three possible conditions of warm loops, as discussed at the end of this section. Along a coronal loop in an active region on the solar limb, while TRACE double filter ratios led to temperatures between 1.0 and 1.3 MK, the emission measure loci from CDS data were consistent with a line-of-sight isothermal structure which increases in temperature from ∼ 1.20 to 1.75 MK along the loop, in contrast with the nearby multithermal background (Noglik et al., 2008*).

Another puzzling issue, certainly linked to the loop isothermal appearance, is that warm loops are often diagnosed to be overdense with respect to the equilibrium values predicted by loop scaling laws (Lenz et al., 1999*; Winebarger et al., 2003a*, Section 4.1.1). To explain both these pieces of evidence, several authors claimed that the loops cannot be at equilibrium and that they must be filamented and cooling from a hotter state, probably continuously subject to heating episodes (nanoflares, Warren et al., 2002*, 2003*, Sections 4.2 and 4.4). Other authors proposed that part of the effect might be due to inaccurate background subtraction (Del Zanna and Mason, 2003).

The Hinode mission has stimulated extensive analyses of warm coronal structures, mostly based on its high quality EIS spectral data. Modeling observations of coronal moss with Hinode/EIS confirmed that the moss intensities predicted by steady, uniformly heated loop models are too intense relative to the observations (Warren et al., 2008b). A nonuniform filling factor is required and must vary inversely with the loop pressure. Observations of active region loops with EIS indicate that isolated coronal loops that are bright in Fe xii generally have very narrow temperature distributions (3 × 105 K), but are not properly isothermal and have a volumetric filling factors of approximately 10% (Warren et al., 2008a*).

In a cooler regime (4.15 < log T < 5.45) observed in coordination by SoHO spectrometers and imagers, STEREO/EUVI, and Hinode/EIS, active region plasma at the limb has been found to cool down from a coronal hole status with temperatures in the 5.6 < logT < 5.9 range (Landi et al., 2009).

A loop reconstruction from STEREO data improves the background subtraction and recovers density and temperature distributions that are able to reproduce the total observed fluxes within 20% (Aschwanden et al., 2009), emission measure distributions not very different from those obtained from spectroscopic observations (Brosius et al., 1996), and is in agreement with other previous studies (Lenz et al., 1999*; Winebarger et al., 2003a*).

Some studies have been devoted specifically to fan loops departing from active regions and observed with Hinode and SDO. It was found that these loops are warm and their temperature distribution is generally narrow (Brooks et al., 2011).

More recently, accurate analysis of warm loops with comparison between EUV spectroscopy and multi-channel imaging with Hinode/EIS and SDO/AIA have put severe warnings on using the latter for DEM reconstruction (Del Zanna et al., 2011). Cool plasma at temperature T < 0.5 MK might contribute considerably to the emission, especially at the loop footpoints, and question, for instance, the interpretation of upflows observed in the 171 Å band as made of million degrees plasma (De Pontieu et al., 2011*). Important results come from observations at very high spatial resolution (0.2 arcsec) with the Hi-C sounding rocket in the EUV 193 Å band. There is evidence of magnetic braiding that indicates the occurrence of magnetic reconnection (Cirtain et al., 2013).

In summary, the current observational framework and loop analysis seems to indicate that for a coherent scenario warm loops are manifestations of at least three different loop conditions: i) in loops consisting of bundles of thin independently-heated strands, few cooling strands of steady hot X-ray loops might be detected as warm overdense loops in the UV band. These warm loops would coexist with hot loops and would show a multithermal emission measure distribution (Patsourakos and Klimchuk, 2007; Warren et al., 2008a; Tripathi et al., 2009*); ii) we might have warm loops as an obvious result of a relatively low average heating input in the loop. These loops would be much less visible in the X-rays and, thus, would not be co-spatial with hot loops, and would also be much less multithermal (Di Giorgio et al., 2003*; Landi and Feldman, 2004*; Aschwanden and Nightingale, 2005; Noglik et al., 2008); iii) warm loops might be globally cooling from a status of hot X-ray loop (Reale and Ciaravella, 2006). These loops would also be overdense and co-spatial with hot loops but with a time shift of the X-ray and UV light curves, i.e., they would be bright in the X-rays before they are in the UV band. Also these loops would have a relatively narrow thermal distribution along the line of sight. There is some indication that there might be fundamental differences in the heating regime and cadence between hot and warm loops (Warren et al., 2010a*).

3.4 Temporal analysis

The solar corona is the site of a variety of transient phenomena. Coronal loops sometimes flare in active regions (see the review by Benz, 2008). However, most coronal loops are well-known to remain in a steady state for most of their life, much longer than the plasma characteristic cooling times (Rosner et al., 1978*, see Section 4.1.1). This is taken as an indication that a heating mechanism must be on and steady long enough to bring the loop to an equilibrium condition, and keep it there for a long time. Nevertheless, the emission of coronal loops is found to vary significantly on various timescales, and the temporal analyses of coronal loop data have been used to obtain different kinds of information, and as a help to characterize the dynamics and heating mechanisms. The time variability of loop emission is generally not trivial to interpret. The problem is that the emission is very sensitive to density and less to temperature. Therefore, variations are not direct signatures of heating episodes, not even of local compressions, because the plasma is free to flow along the magnetic field lines. Variations must therefore be explained in the light of the evolution of the whole loop. This typically needs accurate modeling, or, at least, care must be paid to many relevant and concurrent effects.

Another important issue is the band in which we observe. The EUV bands of the normal-incidence telescopes are quite narrow. Observations are then more sensitive to variations because cooling or heating plasma is seen to turn on and off rapidly as it crosses the band sensitivity. On the other hand, telescopes in the X-ray band detect hotter plasma which is expected to be more sensitive to heating and therefore to vary more promptly, but the bandwidths are large and do not take as much advantage of the temperature sensitivity as the narrow bands. Finally, spectroscopic observations are, in principle, very sensitive to temperature variations, because they observe single lines, but their time cadence is typically low and able to follow variations only on large timescales. Time analysis studies can be classified to address two main classes of phenomena: temporal variability of steady structures and single transient events, such as flare-like brightenings.

In spite of limited time coverage, the instrument S-054 on-board Skylab already allowed for early studies of variability of hot X-ray loops. Measured decay times showed evidence of continued evaporation of coronal plasma in slowly-decaying structures (Krieger, 1978). found timescales of moderate variability was found on the timescale of a few hours over a substantial steadiness for observations of active region loops in 2 MK lines such as Fe xv and Si xii (Sheeley Jr, 1980; Habbal et al., 1985). Continuous microflare activity (26 28 10 – 10 erg) has been extensively detected in hard X-ray band (20 keV) with non-thermal power-law spectra (Lin et al., 1984). Substantial (but non-flaring) temporal variability was found in active region loops observed with SMM in a few relatively hot X-ray lines (∼ 5 MK) on timescales of some minutes (Haisch et al., 1988). Cooler loops (< 1 MK Foukal, 1976*, see Section 3.5) were found to be more variable and dynamic (e.g., Kopp et al., 1985).

The high time coverage and resolution of Yohkoh triggered studies of brightenings on short timescales. The study of the interaction of differently bright hot loops showed, for instance, that X-ray bright points often involve loops considerably larger than the bright points themselves, and that they vary on timescales from minutes to hours (Strong et al., 1992). The analysis of a large set (142) of macroscopic transient X-ray brightenings indicated that they derive from the interaction of multiple loops at their footpoints (Shimizu et al., 1994). Some other more specific loop variations, e.g., the shrinkage of large-scale non-flare loops were also observed, and interpreted not as an apparent motion, but as a real contraction of coronal loops that brighten and then gradually cool down (Wang et al., 1997). Fine-scale motions and brightness variations of the emission were found on timescales of 1 minute or less, often with dark jets of chromospheric plasma seen in the wings of Hα, and probably associated with the fine structure and dynamics of the upper transition region (Berger et al., 1999).

Loop variability was specifically studied in several UV spectral lines observed with SoHO/CDS for about 3 hours by Di Giorgio et al. (2003*). In the hottest lines, within the limited time resolution of about 10 min, a few brightenings of a hot loop (∼ 2 MK) were detected but they are minor perturbations over a steadily high emission level. A cool loop (log T ∼ 5.3) was confirmed to be a transient structure living a few hours, and confining substantial flows (Section 3.5).

Variability analyses were conducted also on warm loops present in TRACE data. The brightening of a single coronal loop was analyzed in detail in an observation of more than 2 hours with a cadence of about 30 s (Reale et al., 2000a*). The loop brightens from the footpoints to the top, allowing for detailed hydrodynamic modeling (Reale et al., 2000b*, see also Section 4.4). Active region transient events, i.e., short-lived brightenings in small-scale loops, detected over a neutral line in a region of emerging flux were interpreted as reconnection events associated with flux emergence (Seaton et al., 2001). Apparent shrinking and expansion of brightening warm loops suggested heating and cooling of different concentric strands, leading to coronal rain visible in the Hα line (Shimojo et al., 2002, see also Section 3.2.2). Plasma condensations in hot and warm loops were detected also in the analysis of line intensity and velocity in temporal series data from SoHO/CDS (O’Shea et al., 2007). Antiochos et al. (2003*) found no significant variability of the moss regions observed with TRACE. This has been taken as part of the evidence toward steady coronal heating in active region cores (Warren et al., 2010b*, see Section 4.4).

The analysis of temporal series from various missions has been used to investigate the possible presence of continuous impulsive heating by nanoflares. The temporal evolution of hot coronal loops was studied in data taken with GOES Solar X-ray Imager (SXI), an instrument with moderate spatial resolution and spectral band similar to Yohkoh/SXT (López Fuentes et al., 2007). The durations and characteristic timescales of the emission rise, steady and decay phases were found to be much longer than the cooling time and indicate that the loop-averaged heating rate increases slowly, reaches a maintenance level, and then decreases slowly (Figure 9*), not in contradiction with the early results of Skylab (Section 2). This slow evolution is taken as an indication of a single heating mechanism operating for the entire lifetime of the loop. If so, the timescale of the loop-averaged heating rate might be roughly proportional to the timescale of the observed intensity variations.

View Image
Figure 9: X-ray light curve observed with the SXI telescope on board GOES. The loop lifetime is much longer than the characteristic cooling times. Courtesy of J. A. Klimchuk and M. C. López Fuentes).

Joint TRACE and SoHO/CDS observations allowed to study temperature as a function of time in active region loops (Cirtain et al., 2007). In many locations along the loops, the emission measure loci were found consistent with an isothermal structure, but the results also indicated significant changes in the loop temperature (between 1 and 2 MK) over the 6 hr observing period. This was interpreted as one more indication of multistranded loops, substructured below the resolution of the imager and of the spectrometer. Further support to fine structuring comes from the analysis of the auto-correlation functions in SXT and TRACE loop observations (Sakamoto et al., 2008*). The duration of the intensity fluctuations for the hot SXT loops was found to be relatively short because of the significant photon noise, but that for the warm TRACE loops agrees well with the characteristic cooling timescale, thus supporting a continuous heating by impulsive nanoflares. The energy of nanoflares is estimated to be 1025 erg for SXT loops and 1023 erg for TRACE loops, and their occurrence rate about 0.4 and 30 nanoflares s–1, respectively.

Time series have been studied also on data taken with the Hinode mission. Hinode’s Solar Optical Telescope (SOT) magnetograms and high-cadence EIS spectral data were used to distinguish hot, relatively steadily emitting warm coronal loops from isolated transient brightenings and to find that they are both associated with highly dynamic magnetic flux regions. Brightenings were confirmed in regions of flux collision and cancellation, while warm loops are generally rooted in magnetic field regions that are locally unipolar with unmixed flux (Brooks et al., 2008). It was suggested that the type of heating (transient vs. steady) is related to the structure of the magnetic field, and that the heating in transient events may be fundamentally different from that in warm coronal loops.

More recently, light curves in individual pixels have been investigated in the X-ray band to search for significant variability connected to variable heating. Although some pulses are detected, most of the emission in active region cores and loops has been found to be steady on the timescale of hours with fluctuations on the order of 15% and with no correlation between warm and hot emission (Warren et al., 2010b*, 2011). Improving on previous studies (Sakamoto et al., 2008*), high cadence observations with the Hinode/XRT have revealed that the distributions of intensity fluctuations have small but significant and systematic asymmetries. Part of this asymmetry has been explained through a tendency for exponentially decreasing intensity, i.e., the plasma has been cooling for most of the time (Terzo et al., 2011).

Loop light curves have been systematically analysed also in the EUV band. A systematic tendency has been found to have ordered time lags from channels sensitive to emission from hotter plasma to cooler plasma, that is also evidence for dominant cooling (Viall and Klimchuk, 2011, 2012). Light curves in the EUV band have been analysed also with a different approach: they have been compared to simulated ones obtained from sequences of random pulses with power-law distribution (Tajfirouze and Safari, 2012*). Artificial neural network (ANN) was used for the comparison and it was found many that light curves are matched by those generated from events power-laws with a steep index (≥ 2). While studying the long-term evolution of active regions on the large scale, it was found that active regions show less and less variability as they age (Ugarte-Urra and Warren, 2012), thus suggesting a qualitative change of heating frequency with time. At the other extreme of the smallest scales, the Hi-C observations show in some moss regions variability on timescales down to ∼ 15 s, that may indicate the presence of heating pulses of comparable duration.

3.5 Flows and waves

Diagnosing the presence of significant flows in coronal loops is not an easy task. Apparently moving brightness variations may not be a conclusive evidence of plasma motion, since the same effect may be produced by the propagation of thermal fronts or waves. Conclusive evidence of plasma motion comes from measurements of Doppler shifts in relevant spectral lines. However, the detection of significant Doppler shifts requires several conditions to be fulfilled at the same time, e.g., significant component along the line of sight, amount of moving plasma larger than amount of static plasma, plasma motion comparable to typical line broadening effects.

In general, we can distinguish two main classes of mass bulk motions inside coronal loops: siphon flows, due to a pressure difference between the footpoints, and loop filling or draining, due to transient heating and subsequent cooling, respectively. Some other evidence of bulk motions, such as systematic redshifts in UV lines, has been difficult to interpret.

Siphon flows have been mainly invoked to explain motions in cool loops. The existence of cold loops has been known for a long time (Foukal, 1976, see Section 2) and SoHO has collected high-quality data showing the presence of dynamic cool loops (Brekke et al., 1997*). A well-identified detection was found in SoHO/SUMER data, i.e., a small loop showing a supersonic siphon-like flow (Teriaca et al., 2004) and in SoHO/CDS data (Di Giorgio et al., 2003*).

Redshifts in transition region UV lines have been extensively observed on the solar disk (e.g., Doschek et al., 1976; Gebbie et al., 1981; Dere, 1982; Feldman et al., 1982; Klimchuk, 1987; Rottman et al., 1990; Brekke, 1993; Peter, 1999). Some mechanisms have been proposed to explain these redshifts: downward propagating acoustic waves (Hansteen, 1993*), downdrafts driven by radiatively-cooling condensations in the solar transition region (Reale et al., 1996*, 1997b*), nanoflares (Teriaca et al., 1999*); the scenario is improving with the better and better definition of the observational framework. Downflows are systematically confirmed in lines at transition region temperatures (≤ 0.5 MK) from a few km s–1 (Feldman et al., 2011) to a few tens km s–1 (Chen and Ding, 2010*; Ugarte-Urra and Warren, 2011*). Moderate downflows have been detected at the boundary of active regions (Boutry et al., 2012). Redshifts between 5 and 15 km s–1 have been measured accurately from SoHO/SUMER data in three active regions with little spatial and temporal correlation (Winebarger et al., 2013).

Blueshifts in the transition region are also studied but not necessarily associated with coronal loops (e.g., Dere et al., 1986). More localized and transient episodes of high velocity outflows, named explosive events, have been observed in the transition lines such as C iv, formed at 100 000 K (e.g., Dere et al., 1989; Chae et al., 1998b; Winebarger et al., 1999, 2002b,a). However, there are indications that such EUV explosive events are not directly relevant in heating the corona, are characteristic of structures not obviously connected with the upper corona, and have a chromospheric origin (Teriaca et al., 2002). Moderate outflows at about 1 MK or more have been found from combined SoHO/SUMER and Hinode/EIS observations of the quiet Sun around disk center (Dadashi et al., 2011*).

Doppler shifts have been extensively studied as a function of temperature across the transition region. Figure 10* shows a summary of the results updated to 2011.

View Image
Figure 10: Average Doppler shift in the quiet Sun at disk center of various TR and coronal ions measured from SUMER and EIS spectra. Positive/negative values indicate red- (downflows) / blue- (upflows) shifts. Solid and dashed lines respectively represent polynomial fittings. Image reproduced with permission from Dadashi et al. (2011), copyright by ESO.

Redshifts increasing up to ∼ 10 km s–1 at 5 ∼ 2 × 10 K and then decreasing with increasing temperature have been found from SUMER and EIS spectra in the quiet Sun and explained by the dominance of emission from plasma flowing downward from the upper hot region to the lower cool region along flux tubes with varying cross section (a factor about 30, Chae et al., 1998c, see also Section 3.1). The redshift peak increases to 15 km s–1 in an active region at temperature of 5 10 K, while the redshifts were found to turn into blueshifts at temperatures above 5 × 105 K (Teriaca et al., 1999*). The trend from redshift to blueshift also applies to active region moss, but the transition from red to blue appears to occur at a higher temperature in the moss (∼ 1 MK versus 0.5 MK in the quiet Sun) (Dadashi et al., 2012*; Tripathi et al., 2012b).

Regarding the spatial localization of the flows, a complex scenario of Doppler flows was found in active region loops observed by Hinode EIS (Del Zanna, 2008, Figure 11*). Persistent redshifts, stronger in cooler lines (about 5 – 10 km s–1 in Fe xii and 20 – 30 km s–1 in Fe viii), were confirmed in most loop structures. Persistent blueshifts, stronger in the hotter lines (typically 5 – 20 km s–1 in Fe xii and 10 – 30 km s–1 in Fe xv), were present in areas of weak emission, in a sharp boundary between the low-lying “hot” 3 MK loops and the higher “warm” 1 MK loops.

An active region was comprised of red-shifted emissions (downflows) in the core and blue-shifted emissions (upflows) at the boundary (Tripathi et al., 2009*). No strong flows were found in an active region core in the Hinode/EIS Fe xii 195 Å line (Brooks and Warren, 2009). In the core of moss regions SUMER and EIS data show some blueshifts of a few km s–1 at low coronal temperatures, decreasing at higher temperatures (Dadashi et al., 2012). Specific studies of coronal loops in an active region show mostly blue-shifted emission at coronal temperatures, with speed of about 20 km s–1 at the footpoints (Tripathi et al., 2012a).

View Image
Figure 11: Monochromatic (negative) images and dopplergrams km s–1) of an active region (NOAA 10926) observed with Hinode/EIS in Fe viii, Fe xii, Fe xv lines. Courtesy of G. Del Zanna.

Non-thermal velocities in the transition region and corona of the quiet Sun were measured from the widths of SoHO/SUMER UV lines (Chae et al., 1998a). They were found to increase with temperature from values smaller than 10 km s–1 at temperatures < 2 × 104 K, to a peak value of 30 km s–1 around 3 × 105, and then to increase with temperature, to about 20 km s–1 at coronal temperatures. Since the motions are small-scale and isotropic they were interpreted in terms of MHD turbulence. Non-thermal velocities were studied also in solar active regions on Hinode/EIS spectra (Doschek et al., 2007). The largest widths seem to be located more in relatively faint zones, some of which also show Doppler outflows.

Coronal plasma motions near footpoints of active region loops showed a strong correlation between Doppler velocity and non-thermal velocity (Hara et al., 2008). Significant deviations from a single Gaussian profile were found in the blue wing of the line profiles for the upflows. These may suggest that there are unresolved high-speed upflows.

EUV spectra of coronal loops above active regions show also clear evidence of stronger dynamical activity. In the O v 629 Å line, formed at 240 000 K, line-of-sight velocities greater than 50 km s–1 have been measured with the shift extending over a large fraction of a loop (Brekke et al., 1997). Active region loops appear to be extremely time variable and dynamic at transition region temperatures, with large Doppler shifts (Brekke, 1999). The birth, evolution and cooling of one of such transient cool loops was directly observed with the SoHO/CDS, and a blue-shifted upflow was measured all along the loop, probably a one-direction siphon flow (Di Giorgio et al., 2003, see also Section 3.5). Line-of-sight flows of up to 40 km s–1 were measured along warm and apparently static active region loops in co-aligned TRACE and the SoHO/SUMER observations (Winebarger et al., 2002c*). Apparent motions were also detected in other TRACE images (Winebarger et al., 2001*). Strong localized outflows (∼ 50 km s–1) in a widespread downflow region were clearly visible in Doppler-shifts maps obtained with EIS (Doschek et al., 2008). The outflows might be tracers of long loops and/or open magnetic fields. High-speed outflows at about 1 MK or more have been found in microflares (Chen and Ding, 2010), and transient ones at the boundary of active region cores on the timescale of minutes in time sequences of EIS spectra (Ugarte-Urra and Warren, 2011). Studies on the temperature structure and chemical composition of the plasma producing the faint blue wings at about 100 km s–1 have shown a peaks at coronal temperatures above 1 MK and coronal FIP bias values (Brooks and Warren, 2012). Cool plasma flowing in multi-threaded coronal loops were detected in high resolution Hinode SOT observations with speeds in the range 74 – 123 km s–1 (Ofman and Wang, 2008*). In addition to flows, the loops exhibited transverse oscillations. Even stronger upflows, more typical of flare chromospheric evaporation (e.g., Antonucci et al., 1982), have also been detected during some small transient brightenings in the X-ray band (Hinode/XRT), with speeds up to 500 km s–1 (Nitta et al., 2012).

3.5.1 Chromospheric flows

It has been proposed that an important role in the dynamics and heating of plasma inside coronal loops might be played by upcoming chromospheric flows. Although the discovery is not new (Athay and Holzer, 1982), recently much attention has been devoted to these flows, and in particular to a specific class of finger-like ejections with speeds between 50 and 150 km s–1 and lasting a couple of minutes or less, the so-called type II spicules (De Pontieu et al., 2007a). There is evidence for a spatial and temporal correlation between spicules and faint upflows detected in the EUV band suggesting the possibility that the flows are heated to coronal temperatures when they are injected in coronal loops. The upflows were detected as a blue-shifted excess (wing asymmetry) in an EUV line (Fe xiv). The implication is that spicules may provide a substantial contribution to coronal heating, thus shifting the source of coronal heating down in the chromosphere (De Pontieu et al., 2009) and proposing a new challenge for coronal heating theory. The evidence is debated. Wave-like propagations in coronal EUV images have been also re-interpreted as evidence for repetitive upflows (Tian et al., 2011; Kamio et al., 2011). However, 3D MHD modeling shows that waves and flows may results from the same impulsive events (Ofman et al., 2012*), while flows may be important very low in the corona, the propagating disturbances are dominated by waves at higher altitudes in active region loop (Wang et al., 2013). Coronal counterparts have been directly identified in EUV images (De Pontieu et al., 2011) and also a correspondence between upflows and downflows, the latter at moderate speed (∼ 10 km s–1) and in the cool passbands (McIntosh et al., 2012). These are to be compared with the usual evidence of redshifts in the transition region. In other analyses high speed spicules were not found to have coronal counterparts (Madjarska et al., 2011) and to be a separate population from lower speed spicules (Zhang et al., 2012). It has been estimated that only a small fraction of coronal plasma can be supplied by chromospheric upflows (Klimchuk, 2012*).

3.5.2 Waves observations

Although this review focusses more on the plasma confined in loops, recently considerable efforts have been devoted to models that point to the importance of magnetohydrodynamic waves. The question is again the contribution of the dissipation of wave energy to the heating of the corona, that is not easy to evaluate (Klimchuk, 2006*). The wave propagation is often connected to and needs to be distinguished from the presence of flows. Therefore, we dedicate attention to recent evidences regarding coronal waves and oscillations that involve loops.

Evidence for photospheric Alfvén waves was obtained from magnetic and velocity fluctuations in regions of strong magnetic field (Ulrich, 1996) and from granular motions in the quiet Sun (Muller et al., 1994) with fluxes of the order of 7 −2 −1 10 erg cm s, which might contribute to heating if transmitted efficiently to the corona.

In SoHO/EIT high-cadence 304 Å images, analyzed systematic intensity variations along an off-limb half loop structure were observed to propagate from the top toward the footpoints (De Groof et al., 2004*). These intensity variations are more probably be due to flowing/falling plasma blobs than to slow magneto-acoustic waves (Section 4.4). This evidence has been addressed also by modeling studies (see Section 4.3).

Widespread evidence for outward propagation of Alfvén waves is reported from ground optical polarimetric observations (Tomczyk et al., 2007*), and non-thermal broadening has been shown to correlate (McIntosh and De Pontieu, 2012) with swaying motions detected in the corona from SDO/AIA data (speed of ∼ 20 km s–1 and periods of few minutes) (McIntosh et al., 2011). TRACE EUV observations provided the first evidence of resolved transverse waves in coronal loops (Aschwanden et al., 1999a*; Nakariakov et al., 1999*; Nakariakov and Ofman, 2001). Undamped, or even growing waves were observed by SDO/AIA (Wang et al., 2012*; Nisticò et al., 2013). Transverse waves were detected also in high resolution observations with the HiC in thin loops (≥ 100 km) at low speed amplitude (Morton and McLaughlin, 2013). The contribution of this class of waves is estimated, discussed, and debated although there is still no clear convergence. Other oscillations were observed to propagate along coronal loops at more than 100 km s–1 with periods of a few minutes and interpreted as slow magnetosonic waves (De Moortel et al., 2000), but also as due to faint upflows (De Pontieu and McIntosh, 2010). We mention that also much faster (> 1000 km s–1) propagating oscillations were detected in SDO/AIA observations during eruptive events and interpreted as fast magnetosonic waves (e.g., Liu et al., 2011; Ofman et al., 2011).

  Go to previous page Scroll to top Go to next page