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.
Moderate diagnostic power is allowed by imaging instruments, by means of multifilter observations. Filter ratio maps 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
where is the particle density and the plasma volume. The ratio of the emission in two different filters is then independent of the density, and only a function of the temperature:
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 non-linear 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 sense, 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. This problem can be important especially when the distribution of the emission measure along the line of sight is not simple and highly non-linear (e.g., Reale et al., 2009b). 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 which alter the filter ratio values. The task of subtracting this “background emission” from the measured emission is non-trivial and can affect seriously 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, 2001; Reale, 2002b). 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., 2008a; 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., 2008a; Terzo and Reale, 2010).
More accurate diagnostics, although with less time and space resolution, is 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). 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.
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 (Jordan et al., 1987) 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. 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.
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 devote attention to the comparison between hot and warm 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, 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 quiescent and active region coronal loops were conducted on Yohkoh observations (Porter and Klimchuk, 1995) using the filter ratio method. For this sample of loops, selected to be steady and isolated, the lengths were measured with assumptions on the loop geometry and ranged in a decade between 5 × 109 < 2L < 5 × 1010 cm. The temperature measurements were averaged over about half of the loops and also ranged in a decade (2 < T < 30 MK), with a mean of about 6 MK. Therefore, it appears as a sample of particularly hot loops, although the uncertainties in the hot tail of the distribution are very large, probably due to the flat dependence of the temperature on the filter ratio at high temperature. Pressures were derived from the equation of state, after derivation of the density, from the emission measure and from the volume inferred from the length and assumptions on the loop aspect. They ranged in two decades (0.1 < p < 20 dyne cm–2). Overall, it was shown that the temperature and length of this sample of hot loops are uncorrelated, that pressure varies inversely with length (as overall expected for a thermally homogeneous sample from loop scaling laws, see Section 4.1.1), although with a large spread. Such distributions were used as constraints on the loop heating through the derivation of the dependence of the magnetic field intensity on the loop length (Klimchuk and Porter, 1995). They also led to accurate analysis of data uncertainties (Klimchuk and Gary, 1995). Another systematic analysis was made on a sample of about 30 bright steady Yohkoh loops located in active regions (Kano and Tsuneta, 1995). The temperatures were measured after averaging several images and taking the value at the loop top. While this analysis confirmed some of the correlations found in Porter and Klimchuk (1995), it found a correlation between the loop length and the temperature, and showed deviations from RTV scaling laws (Section 4.1.1). It cannot be excluded that correlations between parameters depend on the loop sample, as a single scaling law links three parameters. Yohkoh/SXT loops hotter than 3 MK were found also in another study, the hottest ones with shorter lifetimes (less than few hours), and often exhibiting cusps (Yoshida and Tsuneta, 1996).
A big effort has recently been devoted to the possible detection of hot plasma outside of evident flares. This would be a conclusive evidence of nanoflaring activity in coronal loop (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). Evidence of emission from hot lines has been found also in other Hinode/EIS observations, and in particular from the analysis of the emission from the Ca xvii at 192.858 Å, formed near a temperature of 6 × 106 K, which has been found in several parts of active regions (Ko et al., 2009). Using Fe lines, Young et al. (2009) has shown very accurate density measurements ( 5%) across an active region, with values in the range . A smaller density range (from 108.5 to 109.5 cm–3 has been found by Watanabe et al. (2009) using the Fe xiii line group, although one pair has been found to reach the high density limit. Density sensitive lines have been used to measure the filling factor of coronal structures. Dere (2008, 2009) has used spectra and images obtained with EIS and comparison with TRACE to determine the volumetric filling factor of bright points. The emission measure and bright point widths have been compared with the electron densities and with TRACE data. 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.
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). This kind of temperature diagnostics is supported by the evidence of warm structures bright in the TRACE images. Observations including flare filters show evidence of a hot component in active regions outside of flares (Schmelz et al., 2009b) and data in the medium thickness filters appear to constrain better this component of hot plasma as widespread, although minor, and peaking around , with a tail above 10 MK (Reale et al., 2009b). This may support the hypothesis that active regions are heated impulsively. Evidence of a persistent although small hot plasma component outside of flare is shown also by RHESSI data (McTiernan, 2009), and the comparison between RHESSI and XRT data seem to support this scenario in a consistent way (Reale et al., 2009a). The topic of coronal active region heating is debated. Evidence interpreted in the direction of more gradual heating has been obtained by Warren et al. (2010) (see Section 4.4).
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 H 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 109 cm) have a good general morphological correspondence, while larger scale NIXT loops ( 1010 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. Information about the loop filling factor was derived also from the analysis of simultaneous SoHO and Yohkoh observations of a small solar active region, suggesting 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).
Some similarity between loops observed in the TRACE EUV band and Yohkoh X-ray band was found out of the core of 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.
The thermal distribution across the loop structures, i.e., along the line of sight, can be investigated with the analysis of observations in several spectral lines, as obtained, for instance, with the SoHO/CDS. Information on the validity of the data analysis and of the loop diagnostics can be obtained from the comparison with simultaneous and co-spatial data from imaging instruments.
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. From the analysis of a single loop observed on the solar limb with SoHO/CDS, Schmelz et al. (2001) found 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 loop is inconsistent with isothermal plasma both across and along the loop. A whole line of works started from this study 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, 2002; Schmelz et al., 2003). Similar results but different conclusions were reached by Landi and Landini (2004); Landi and Feldman (2004) who analyzed a loop observed with SoHO and, finding it nearly isothermal, considered this evidence as real and invoked a non-constant cross-section to explain it. 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 diagnostics with narrow band instruments is a delicate issue.
An interesting debate has 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 which 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. Del Zanna and Mason (2003) found a loop detected with TRACE to be isothermal (with temperatures below 1 MK) along the line of sight from diagnostics of spectral lines obtained with SoHO/CDS. Schmelz et al. (2005) analyzed another loop on the limb observed with SoHO/CDS, with a DEM reconstruction and a careful analysis of background subtraction, and found a multi-thermal distribution across the loop. From the comparison with the isothermal structure of hot loops derived from CDS data (Di Giorgio et al., 2003; Landi and Landini, 2004), they concluded that there may be two different classes of loops, multi-thermal and isothermal, which they found to be confirmed by a systematic inspection of the CDS atlas (Figure 7).
Multiband observations allow to obtain even more information and constraints. Reale and Ciaravella (2006) analyzed a well-defined loop system detected 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 (). The data analysis supported a coherent scenario across the different bands and instruments, indicating a globally cooling loop and the presence of thermal structuring. The study overall indicated that the loop analysis can be easily affected by a variety of instrumental biases and uncertainties, for instance due to gross 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).
Specific analyses of SoHO spectrometric data have continued to contribute much to the study of the loop thermal structure up to recently. A Differential Emission Measure (DEM) analysis of coronal loops using a forward-folding technique on SoHO/CDS data has shown different results for two loops, one to be isothermal and the other to have a broad DEM (Schmelz et al., 2007b). Landi and Feldman (2008) have analyzed an extensive active region spectrum observed by the SUMER instrument on board SOHO and found that the plasma is made of three distinct isothermal components, whose physical properties are similar to coronal hole, quiet-Sun, and active region plasmas.
Hinode/EIS observations of active region loops certify that structures which are clearly discernible 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).
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 which evolve mostly in the temperature range 0.4 – 1.3 MK.
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 H 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. Interactions of moss with underlying chromospheric structures were first described by Berger et al. (1999a). 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).
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, Schmelz et al. (2001) reconstructed DEM distributions along the line of sight from spectral SoHO/CDS data and synthesized EIT count rates from them, which led to almost uniform temperatures along the loop, pointing again to an instrumental bias. Weber et al. (2005) 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. However, we learn from DEM studies made both with spectrometers and from multi-wideband imagers that the DEM of coronal loops 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., 2009b). The critical point becomes the DEM width and its range of variation.
Later, Schmelz et al. (2007a) found that even TRACE triple-filter data cannot, in general, constrain the temperature distribution for plasma in warm loops. On the other hand, Patsourakos and Klimchuk (2007) studied the cross-field thermal structure of a sample of coronal loops from triple-filter TRACE observations, and found that the observations are compatible with multithermal plasma with significant emission measure throughout the range 1 – 3 MK. Schmelz et al. (2009a) used TRACE filter ratios, emission measure loci, and two methods of differential emission measure analysis to examine the temperature structure of three different loops. In agreement with previous studies, they found both isothermal and multithermal cases. This might not be a contradiction, in the view of the presence of at least three possible conditions of warm loops, as discussed at the end of this section. Noglik et al. (2008) compared TRACE to CDS data to measure the temperature along a coronal loop in an active region on the solar limb. Their double filter ratio temperature analysis technique led to temperatures between 1.0 and 1.3 MK. Emission measure loci from CDS lines 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.
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 is stimulating new 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).
Schmelz et al. (2008) studied temperatures of loops identified in a TRACE image in three density-sensitive line ratios. While emission measure loci plots indicated that the loop plasma is not isothermal, a more detailed differential emission measure analysis showed that two broad components can reproduce the background-subtracted intensities. They proposed that the two-component DEM distribution represents two ensembles of strands, one for each of the loops seen in the TRACE image.
Density diagnostics through density-sensitive line ratio also led to measure directly density values, for instance in active regions (e.g., Doschek et al., 2007b). Tripathi et al. (2008) found that the hot core of the active region is densest with values as high as 1010.5 cm–3. The electron density estimated in specific regions in the active region moss decreases with increasing temperature. The density within the moss region was highest at , with a value around 1010 cm–3.
In a cooler regime () 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 range (Landi et al., 2009).
The loop reconstruction analysis described in Aschwanden et al. (2009) was used mainly for density and temperature modeling of the warm loops of an active region observed with STEREO. The rendering reduces the problem of background subtraction. Although based on simple model assumptions, the derived density and temperature distributions are able to reproduce the total observed fluxes within 20%. The modeling extrapolates results quite outside of the range of sensitivity of the STEREO EUV filters, anyhow finding emission measure distributions not very different from those obtained from spectroscopic observations (Brosius et al., 1996) and deviations from hydrostatic values in agreement with other previous studies (Lenz et al., 1999; Winebarger et al., 2003a).
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 cospatial with hot loops, and would also be much less multithermal (Di Giorgio et al., 2003; Landi and Landini, 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 cospatial 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.
Living Rev. Solar Phys. 7, (2010), 5
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