THERMODYNAMICS OF THE SOLAR CORONA AND EVOLUTION OF THE SOLAR MAGNETIC FIELD AS INFERRED FROM THE TOTAL SOLAR ECLIPSE OBSERVATIONS OF 2010 JULY 11

The broadband white light image of the corona, processed with the ACHF, is shown as a negative in Figure 2. Such a display reveals the details of coronal structures better than the positive image, which is available in the online version. The moon inset shows the earthshine acquired through a combination of the different exposure times used to produce this white light image (as described earlier in Section 3). The position of the Moon corresponds to 157 s after C₂, past the midway point of totality; hence, it is almost centered on the solar disk.

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The most striking features in this image are the preponderance of sharply defined ray-like structures filling the corona and expanding away from the Sun, and of arch-like structures of different scales surrounding the Sun with the exception of the polar regions. These features are labeled in Figure 3 for ease of reference. Also labeled in Figure 3 are other unusual features which are described in detail below.

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In the polar regions, rays with very sharp edges and a range of brightnesses, commonly referred to as polar plumes, expand outward to the edge of the field of view. In addition to these plumes, there is a remarkable feature, labeled E, appearing like a shadow, centered almost dead north. It is most likely a projection of the bulge of a streamer along the line of sight. One can readily see that this could be the case from considering the streamer at the northwest, with its stalk labeled SS. Its northernmost boundary, labeled SB, is at position angle P.A. = 340°, measured counterclockwise from 0° north, while the stalk SS extends radially down to P.A. = 300°. If such a streamer were at central meridian at the time of the eclipse, its bulge could readily project up to the height of the observed enhancement E. This will become more evident when we describe the emission from the hotter spectral lines in Section 6.3.

Away from the polar regions, the corona is encircled by a complex of small, seemingly intertwined, loop-like structures, labeled l. At the resolution of this image, the smallest arches are about 1.1 R_☉ in height. The overlay with the Hα emission (Figure 4) shows that prominences lie immediately below them. Overlying these smallest loops is another forest of intricate, and also seemingly intertwined, loops, labeled L, reaching heights of approximately 1.23 R_☉. The largest loops extend out to heliocentric distances of 1.5–1.7 R_☉, with the most evident ones appearing on the northeast. Beyond 1.2 R_☉, the corona becomes dominated by a myriad of converging and diverging open field lines, in what seems to be layers of streamer-like structures populating the line of sight. Some of them have a classically shaped helmet, such as the northeast one. The orientation of others is such that they appear as different projection profiles of their three-dimensional structures onto the plane of the sky, as described earlier in connection with the streamer associated with SS. We also note the presence of rays, such as the one labeled Ray, which do not seem to be associated with any particular large-scale structure, as they seem to criss-cross the corona in arbitrary paths.

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There are also ripples and wave-like structures at the boundary of one streamer, labeled Ripple and WSB, respectively, which are likely the result of the passage of CMEs through the corona prior to the eclipse. This is also the case for the Streak, the Cone, and the Hook, as will be described in more detail later on.

The continuum images, (Z)_C, were processed with both NRGF and ACHF. The comparison between the two is best illustrated in Figure 4 for the same continuum image, which is $(\rm Fe\,\mathsc{xi})_{\rm C}$ in this example. The full suite of NRGF-processed images, with the exception of (H$\alpha \rm)_C$, is given in Figure 5. It is worth commenting first on the main difference between the two processing techniques. The ACHF enhances small structures, namely, the high spatial frequencies. With its equal amplification throughout an image, the comparison between different parts can be readily made. The NRGF method, on the other hand, uses a variable signal amplification which depends on the intensity fall-off with increasing distance, and in latitude within a given radial band. While the amplification can theoretically converge to infinity, in reality the noise stops the amplification at some high level. Consequently, localized enhancements appear visually more amplified in the NRGF- than in the ACHF-processed images.

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In the comparison of Figure 4, both images have the same scale, with the ACHF shown as a negative image, as in Figure 2. The circular grid corresponds to the position of the underlying solar disk relative to the Moon at that moment of totality. It is not always at the same location since the optimal frames chosen within each bandpass, when the impact of clouds was minimal, did not necessarily correspond to the same exposure times. Although the spatial resolution of the continuum images is 65 compared to the 1'' in the white light image of Figure 2, most of the details found in Figure 2 are visible here. Since the NRGF amplifies low contrast and faint signals far from the Sun, the visual impression of coronal structures is somewhat different when compared to ACHF. For example, the large-scale structures are more evident with the NRGF, while the details of the polar regions are lost in that image. The sharp streamer stalk, SS, is very well defined in both images, so are the Streak, the outlines of the Cone, delineated by dashed lines, and the Hook. The details of the small-scale loops seen in Figure 2 are reduced in the lower resolution ACHF image and absent in the NRGF one. However, some of them appear as dark "cavities" in the latter image, as is often the case in most low-resolution white light images.

To establish the origin of the small-scale loops associated with dark cavities, we consider next the emission from prominences as seen in Hα, shown as an inset in Figure 4. The inset is a composite of two different observing times: C₂ + 23 s with an exposure time of 0.26 s and C₂ + 185 s with an exposure time of 1.05 s. In Figure 4(b), these prominences are shown in red overlaid on the white light corona. The prominence at the southwest, at P.A. = 250°, is the largest one as it protrudes above the edge of the Moon in Figure 2 at that time of totality. This composite shows how the intricate small-scale loop-like structures directly overlay prominences. Comparison with the NRGF-processed image (a) further shows how all the prominences lie at the base of the large-scale structure, or bulges, of streamers. We also note that the strong Hα emission from the prominences, coupled with the varying sky conditions, limited the choice of useable Hα exposure times to 0.26 and 1.05 s. With these exposure times the only detected Hα emission was from prominences. Therefore, we cannot conclude from these observations whether other traces of Hα emission were present in the corona.

The full suite of continuum images shown in Figure 5 was also very useful for testing the quality of the optical systems and for gauging the impact of the observing conditions on the different wavelengths, if any. When taking into account the detector response of both Atik (Figure 1) and PIXIS cameras as a function of wavelength, the transmission curves of the filters, and the approximately blackbody curve of the photospheric radiation, the intensities in all these white light images were found to be comparable. In particular the sharp streamer stalk, SS, the Streak, the outlines of the Cone, delineated by dashed lines in $(\rm Ni\,\mathsc{xv})_{\rm C}$, and the Hook readily stood out in all images with the exception of $(\rm Fe\,\mathsc{ix})_{\rm C}$ and $(\rm Fe\,\mathsc{xiii})_{\rm C}$. These exceptions are attributed to the impact of the sky conditions, which was strongest at the (Fe ix)_C wavelength, as is evident from the much higher noise level beyond 2 R_☉ in comparison with the other continuum images, and to the very low detector response at $(\rm Fe\,\mathsc{xiii})_{\rm C}$ (see Figure 1).

Finally we point out that the $(\rm Fe\,\mathsc{ix})_{\rm C}$ image, centered at 434.8 nm, was such that it captured some Hγ emission at 434.0 nm at the 10% level within its bandpass. Consequently, emission from the cool prominences appeared in that bandpass. The subtraction process of offline from online images then led to negative values at those locations, seen as black in the Fe ix image of Figure 6, which will be described next.

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The suite of selected spectral lines covered the temperature range from 4 × 10⁵ K to 3 × 10⁶ K, as demonstrated by the ionization equilibrium curves shown in the lower panel of Figure 1. Since the peaks of their ionization curves are well separated, this choice provided a relatively clear identification of the underlying electron temperature in the observed emission without having to recur to any modeling, or differential emission calculations, such as is the case for most current space-borne EUV observations (e.g., EIT, STEREO, and SDO). For example, any structure observed only in Ni xv would have a temperature at its peak ionization fraction, T_max = 2.5 × 10⁶ K, but not more than 3 × 10⁶ K. Beyond that temperature, the ionization fraction of Ni xv drops to less than 10% of its peak. At T_max(Fe xiv) emission from both Fe xiii and Ni xv should be present. At T_max(Fe xiii), emission from Fe xiv could be present but not from Ni xv. Moving to lower temperatures, at T_max(Fe xi), the ionization fraction of Fe x and Fe xiii is down by almost a factor of two, hence it would be possible to see structures in Fe xi only, if the electron temperature were so narrowly distributed. On the other hand at T_max(Fe x), Fe xi should be detected, while Fe ix, whose ionization fraction is down by more than a factor of two, would be much weaker. At T_max(Fe ix) emission from that spectral line only would be visible.

To expose the temperature in the large-scale and small-scale density structures, the eclipse spectral line images were processed with both NRGF (Figure 6) and with ACHF (Figure 7). As in the comparison of the continuum images, here too the two processing approaches yield different features. Since the NRGF reveals faint features at large radial distances, secondary ghost images created by internal reflections in the optics in some filters, despite the care taken to tilt the filters, appeared enhanced relative to the background in NRGF but were absent in the ACHF. This was the case for the Fe xi online image, the Ni xv online image, the Fe xiii offline image, and consequently the Fe xiii line image when the offline was subtracted from the online image. However, since these ghost images have less than 0.1% of the intensity of the primary image, and since their position is known, their potential effect and corresponding uncertainty can be calculated so as not to interfere with the coronal line emission diagnostics.

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Inspection of both Figures 6 and 7 shows that the strongest and most radially extended emission appears in Fe x, Fe xi, and Fe xiv, while the Fe ix, Fe xiii, and Ni xv images show the weakest and least extended emission. Furthermore, the small- and large-scale structures are not the same in the different spectral lines. There is also a distinct demarcation in the appearance of the corona between the cooler lines of Fe ix, Fe x, and Fe xi formed below 1.2 × 10⁶ K, and the lines formed above 1.8 × 10⁶ K, namely, Fe xiii, Fe xiv, and Ni xv. This demarcation is especially striking in the large-scale structures of the NRGF-processed images. We consider next the weaker emission, and then proceed to a discussion of the temperatures associated with the stronger emission.

The observed weakness of the Fe ix emission can be attributed, in part, to its particular transition mechanism. While all other emission lines are caused by magnetic dipole transitions to the ground state of their respective ion, the Fe ix emission is a metastable magnetic dipole transition between two high lying states (3p⁵3d¹D₂ to 3p⁵3d³F₂) of Fe^{8 +}. Therefore, there is essentially no radiative excitation of this line, as radiative excitation out of the ground state would require significant incident intensity at 21.9 nm. Furthermore, the branching fraction into Fe ix 436 nm from the upper level is only 22%, as this forbidden transition competes with other forbidden transitions from the same upper level to ground and various lower lying excited states. Consequently, the population of the upper ¹D₂ state is diminished and emission from this spectral line is expected to be weak. Another factor potentially contributing to this weakness is the paucity of coronal density structures at the peak of the ionization fraction of Fe^{8 +} around 6 × 10⁵ K.

Despite its weakness, the striking characteristic of the Fe ix NRGF-processed images is the presence of very sharply delineated structures extending out to at least 2 R_☉. One example is the appearance of "negative" (black) emission at the location of some prominences, for example at P.A. = 75°, 120°, 250°. Although caused by emission from Hγ in the bandpass of the offline filter, thus becoming negative when subtracted from the online as noted earlier, the resulting sharply delineated prominences prove that the quality of the optical system was excellent and that the alignment of the offline and online Fe ix images was such that the fine structures are indeed real. Most striking among these features are the fine details of the southeast streamer, the Streak, and the northern boundary of the northwest streamer with its stalk, labeled SB and SS, respectively, in Figure 3. The Hook is very faint but sharply delineated. There is also one dim low-lying loop at the base of this streamer, appearing as an absorption feature. A dashed line has been drawn over the Streak, and another one as a curve below outlining one boundary of the southwest streamer. The relevance of the cone-shaped region defined by these two curves, and labeled Cone in Figure 3, will become more apparent in Section 6.4 when we consider the passage of a CME in that location prior to the eclipse observations. Although polar plumes appear clearly in the south, but less so in the north, their structures are not as sharply delineated as the other structures described above. The impression from the corresponding ACHF-processed image is that the emission is more diffuse and fills the corona when compared to the NRGF-image. In both images, however, no Fe ix emission appears in the Cone. Based on these two differently processed Fe ix images, it is clear that some coronal emission does indeed exist in the temperature range where Fe ix can be ionized. A tighter constraint on the temperature range of the Fe ix observed structures can be set once we consider emission from Fe x, as will be discussed in the following section.

We consider next the Fe xiii emission. The low count rates, which resulted in a higher additive noise and a lower image quality, are a direct consequence of the 100 times weaker response of the detector at 1074.7 nm compared to its response at 530.3 nm, as noted earlier when discussing the corresponding continuum images. Although the scattering radiation from the photosphere at 1074.7 nm is 3× weaker than at 530.3 nm (see Table 1), the radiative scattering cross section is more than an order of magnitude larger than at 530.3 nm, so that visually the coverage of this emission is nearly as extended as Fe xiv and seemingly comparable to Fe xiv, albeit with lesser well-defined details. We note that the ionization fraction of Fe xiii is equal to that of Fe xi at T = 1.35 × 10⁶ K and to Fe xiv at 1.9 × 10⁶ K. It is therefore likely that the observed Fe xiii emission, despite the low detector response and the lower scattering radiation from the photosphere at that wavelength, is a reflection of the presence of coronal structures at the peak ionization temperature of Fe xiii.

The other observed weak emission in the corona is from Ni xv. This is evident in both NRGF- and ACHF-processed images. In comparison with Fe ix, the emission appears much more diffuse but has an equally limited radial extent. The weaker observed Ni xv emission is likely due to a factor of 20 lower Ni abundance compared to Fe. Although the detector response (see Figure 1) at 670.2 nm is 25% lower than at 530.3 nm, the range of exposure times should have been sufficient to unveil this emission to large distances if it were present. Indeed, the corresponding continuum emission (Ni xv)_C is indistinguishable from (Fe xiv)_C (see Figure 5). From the ionization fraction curves shown in Figure 1, it is clear that Ni xv emission should be present whenever Fe xiv emission is detected. Since no Ni xv emission was observed without an Fe xiv counterpart, we conclude that the overall weakness of the Ni xv emission most likely reflects the absence of coronal structures at electron temperatures T_e > T_max(Ni xv). The low Ni abundance compared to Fe is another potential contributing factor.

The details of the most prominent and puzzling coronal structures labeled in Figure 3 are best described in the strongest emission of Fe x, Fe xi, and Fe xiv, in both the NRGF- and ACHF-processed images. Based on their ionization fraction curves, one would expect the emission from Fe x and Fe xi to be very similar to, but not necessarily the same as, Fe xiv.

Features, labeled l, refer to low-lying loops at the base of streamers best seen in the white light image of Figure 2. A large number of them stands out on the east limb in both Fe x and Fe xi in Figure 6, overlying cavities centered at P.A. = 75°, 105°, 125°, and 145°. The latter is very prominent in Fe ix. In contrast, the loops at 35°, 145°, and 315° are dominated by hotter material.

Large-scale loops, like the one labeled L in Figure 3, dominate the streamer centered at P.A. = 35° in the NRGF-processed Fe xiii and Fe xiv images of Figure 6. They are faint in the Ni xv image. Their edges are visible in Fe x and Fe xi, mostly in the ACHF-processed images.

The thinly defined structure labeled Hook in Figure 3 is prominent in Fe x and more so in Fe xi. It appears as a complex structure connected to the solar surface in both NRGF- and ACHF-processed images. The fainter structures between the Hook and the solar surface appear more like a void in the NRGF-processed Fe xiii, Fe xiv, and Ni xv images. But their ACHF counterparts show intricate features, implying that hotter structures are present, albeit rather faint when compared to their immediate surrounding.

Twisted structures, such as the Ripple, pervade the NRGF-processed Fe x and Fe xi images. The wavy streamer boundary, labeled WSB in Figure 3, is another example of a ripple effect. As will be discussed later in Section 6.4, ripples are most likely the byproduct of the passage of CMEs through the corona and are best seen in emission around 10⁶ K.

Structures in the polar regions are seen in the NRGF-processed images only in Fe ix and Fe x, and only in the south pole, but they are prominent in Fe ix, Fe x, and Fe xi in both polar regions in the ACHF-processed images (Figure 7). Curiously, some Fe xiv emission appears between P.A. = 350° and 360°. As discussed earlier, upon closer examination of the details of the fine scale structures in white light (Figure 2) it becomes evident that this emission is due to the bulge of a streamer in the foreground or background, or along the line of sight. Such a bulge would have a shape very similar to the streamers adjacent to the polar coronal hole but seen in projection from 90° away from the central meridian in the plane of this image. This is also the case for the south polar region with faint rays appearing in Fe xiv.

The Streak, which appeared as a remarkably sharp boundary in the white light image of Figure 2 extending outward from P.A. = 240°, is delineated by a dashed line in both the NRGF and the ACHF images, defined by the Fe ix emission. The Streak also shows up as a very sharp boundary in Fe xiii, Fe xiv, and Ni xv, but, curiously, is extremely faint in Fe x and is absent in Fe xi. Another boundary, delineated by a dashed line south of it, also determined from the Fe ix emission, and present in the white light and continuum images, originated at almost the same latitude at the Sun. These two dashed lines form the Cone. The Streak is likely to represent a very thin sheet with a two-temperature structure: very cold (Fe ix) on one side, and very hot (Fe xiii, Fe xiv, and Ni xv) on the other.

To further proceed with the identification of coronal structures with well-defined electron temperatures, overlays of the strongest emission lines from the ACHF-processed images are shown in Figure 8. Fe x is shown in red and Fe xiv in green, following the true colors of these spectral lines. Fe xi is shown in cyan. The overlay of Fe x and Fe xi, two lines which are very close in their peak formation temperature, is shown in Figure 8(a). Since the images do not have an absolute calibration, neutral gray is chosen as a reference ratio of equal Fe x and Fe xi average intensities. Fe x and Fe xiv, which vary by a factor of two in their peak ionization temperature, are shown in Figure 8(b). When Fe x is dominant the color is red, while the dominance of Fe xi appears as cyan. The same amount of Fe x and Fe xiv yields yellow, which represents a reference ratio between the intensities of these two lines. When Fe x is dominant, the color is red. The dominance of Fe xiv appears as green.

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Although the peak ionization temperatures of Fe x and Fe xi are very close (see Figure 1), the overlay of Figure 8(a) shows a clear distinction in the emission from these two lines. The poles are dominated by Fe x emission, while the rest of the open field lines in the corona are biased toward Fe xi. On the other hand, the overlay of Figure 8(b) yields a clear view of the demarcation in temperatures between open and closed magnetic structures in the corona. The large-scale loops are dominated by hot plasma (Fe xiv), while the expanding open structures are dominated by cool plasma (Fe x). These observations confirm the earlier results of Habbal et al. (2010c) who showed that the base of streamers are the hottest plasmas in the corona, forming shrouds around prominences, while the ubiquitous open field lines are dominated by emission from the cooler lines. The overlay of Fe x and Fe xiv emission in Figure 8(b) also makes it very clear that emission from plumes in the south polar region is dominated by Fe x emission with faint Fe xiv emission interspersed with it. In the north polar region there is marked diffuse Fe xiv emission overlying the streamlined Fe x plumes. These eclipse observations thus provide uncontroversial evidence for the occasional contamination of the polar regions by hot material along the line of sight. Hence they resolve a long-standing dilemma associated with the occasional appearance of Fe xiv emission in coronagraph observations over the poles, and provide conclusive evidence supporting Esser et al.'s (1995) statement that "... much of the temperature variations seen in the coronal holes are due to contributions along the line of sight [from the background]" (p. 19836).

Finally, we note that the Cone and the Streak clearly stand out as sharp boundaries in Figure 8(b), but are totally absent in Figure 8(a). Another example of a sharp boundary is the Ripple in Figure 8(b) clearly delineating the transition between the cool Fe x emission in the south pole and the neighboring streamer. It is not apparent as such in Figure 8(a).

To establish the origin of the Hook, the Streak, and the Cone, we consider next the SOHO/EIT Fe x 17.1 nm emission and the SOHO/LASCO-C2 white light coronagraph observations preceding and coinciding closely with the time of the eclipse observations, shown in Figure 9.

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The sequence of three EIT images, given in the top panels, shows two erupting prominences. The largest of the two, shown encircled, is at the southeast limb centered at P.A. = 110°. It had practically disappeared from the EIT field of view by 07:19 UT on July 11. On the southwest limb, shown by the arrow on the disk, another much smaller prominence had also disappeared by that time. A time sequence of LASCO/C2 images, with four images given in the lower panels, the last of which being a composite of EIT and the Fe x eclipse image, shows that there were two CMEs accompanying the disappearance of these prominences. The encircled one was less dramatic than the one on the southwest which led to a spectacular cone-shaped CME.

The Hook observed throughout the eclipse starting at 18:47 UT was most prominent in Fe x and Fe xi. Its position angle and its shape strongly suggest that it is the leading edge of the encircled very large prominence at the east limb. The Fe xi image indicates that it remained attached to the solar surface with intricate structures appearing between the leading edge (the Hook) and the solar surface. From the time difference between its disappearance at 07:19 UT on July 11 in the EIT field of view, and its observed height in the eclipse images, an average rising speed of 15 km s⁻¹ can be inferred. The unique contribution of these eclipse observations is that a temperature of about 10⁶ K can be assigned to its leading edge and to the intricate underlying threads extending down to the solar surface, since best seen in Fe x and Fe xi.

The evolution of the cone-shaped CME is shown in the LASCO/C2 frames preceding and almost coinciding with the end of the eclipse. This CME has two very distinct sharp boundaries (see also movie available in the online version). The composite of EIT and Fe x eclipse image (panel g) shows that the Streak which is dark in Fe x coincides remarkably well with its northern edge. Its lower boundary also has a counterpart in the Fe ix eclipse image, albeit not as striking as the streak in white light and the other lines, and would not have been necessarily singled out. These two boundaries converge through a sharp C-shaped curve that intercepts the solar disk at P.A. = 230°, which is the position angle of the east-limb prominence seen in the EIT image above. Interestingly this cone-shaped enclosure is best seen in the NRGF-processed Fe ix and Ni xv image, with the streak bright in Fe ix only (see Figure 6).

These two examples provide the best evidence for the impact of eruptive prominences and CMEs on the density structures in the inner corona, i.e., 1–3 R_☉, a region that is not imaged by any other instrument. What these observations also yield is a temperature marker for the sharp boundaries that they create. Although prominences are the coolest material in the corona, surrounded by the hottest loops there, these observations indicate that their temperature signature changes dramatically as they expand through the corona: the temperature of the leading edge of the prominence reaches 10⁶ K, while the bulk of the volume of the CME associated with the prominence eruption consists of a complex of coronal material with a mixture of hot and cool material. The example of the cone, however, yields an original example of a cool void (around 10⁶ K) created by the passage of the CME, with a very thin boundary in the form of a two-temperature sheath, as determined from the Fe ix and Fe xiv emissions.

The availability of observations of the Fe x 17.4 nm line by the Proba2/SWAP instrument during the eclipse provided an ideal tool for illustrating the importance of the radiative component in the coronal forbidden lines by comparing emission from this EUV line with its Fe x 637.4 nm counterpart. The invaluable importance of this comparison is twofold: (1) it offers a direct comparison between the behavior of a collisionally excited spectral line (17.4 nm) and one (637.4 nm) where radiative excitation dominates collisional excitation beyond a given heliocentric distance and (2) it provides a test for the accuracy with which the acquisition, calibration, alignment, and composing of the online and offline eclipse images were executed.

Shown in Figure 10 is the SWAP Fe x 17.4 nm image (a), the Fe x 637.4 nm eclipse image (b), and a composite of the solar disk imaged in 17.4 nm with the corona in 637.4 nm (c). Here, the brightness of the 637.4 nm coronal image was calibrated against the innermost corona in 17.4 nm, thus rendering the transition between the two images invisible. This would not have been possible had there been an inherent difference between the two. To illustrate the point, all three images are shown without any structure enhancement. Images in panels (a) and (b) are displayed in a logarithm brightness scale, while panel (c) is displayed in a brightness scale with increased contrast in the dark part of the image. The similarity between the two images close to the Sun becomes even more remarkable with the realization that they were taken with two different instruments, under different observing conditions with one from space and the other from the ground. The extent of the 637.4 nm in the corona, compared to the extent of the 17.4 nm, is striking. Most noticeable is the fact that the Hook, which is so prominent in 637.4 nm, is very weak in 17.4 nm.

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A close-up of the details of the northwest quadrant of the corona is shown in Figure 11. The first two images are the same 17.4 nm SWAP image, with the solar disk covered by a black disk in the middle panel. The right image is the 637.4 nm emission. In the middle and right panels, the 17.4 and 637.4 nm images are indistinguishable. The only exception is the marked radial extent of the 637.4 nm image further out in the corona compared to 17.4 nm, especially in the polar region. This comparison is a classic illustration of the difference between the dominance of radiative excitation, such as in Fe x 637.4 nm, with only collisional excitation, such as in Fe x 17.4 nm.

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Another visualization of the effect of radiative excitation by photospheric radiation for the Fe x 637.4 nm is shown in Figure 12. This color overlay of the two lines, in the quadrant shown in Figure 11, shows red for Fe x 17.4 nm and cyan for Fe x 637.4 nm. We note that the vastly different average lifetimes of their excited state are 5.56 × 10⁻¹² s and 1.44 × 10⁻² s, respectively. Because of the use of complementary colors, neutral gray represents a 1:1 ratio. The cross indicates the position where the ratio was defined as 1:1. This location was chosen in a dense coronal region where the collisional excitation (which is the only excitation process for 17.4 nm) is dominant for 637.4 nm. Note that the actual ratio (in photons) of the 637.4 nm to 17.4 nm line intensities under these conditions is 0.82 (CHIANTI version 6.0). The colors thus reflect the relative ratios between the intensities of these two lines. The appearance of blue indicates where the radiative component of 637.4 nm dominates over the collisionaly excited emission from 17.4 nm line.

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Another byproduct of this comparison is how fast collisional effects decrease with radial distance in different coronal structures. The 637.4 nm emission (blue) dominates in the polar region very close to the coronal base and along the boundary of the adjacent streamer beyond 1.1 R_☉. This implies that the density gradient is very steep there leading to a sharp drop in the 17.4 nm intensity, while the radiative component of 637.4 nm secures a detectable emission. On the other hand, in the densest part of the streamer, the 17.4 nm emission extends further away from the Sun than in the poles, a reflection of the shallower gradient of the density there compared to that in the polar region.

To summarize, the advent of contemporaneous observations in two Fe x lines, namely, 637.4 nm and 17.4 nm, yielded a unique opportunity to compare the behavior of a collisionally excited spectral line (17.4 nm) and one (637.4 nm) where radiative excitation is significant. The strong, often indistinguishable, similarity between the 17.4 and 637.4 images in the densest coronal structures lends very strong support to the reliability with which the acquisition, calibration, and alignment of the online and offline eclipse images were executed. The extent of the 637.4 nm emission beyond emission from the 17.4 nm line yields a direct proof for the unequivocal advantage of the coronal forbidden lines for exploring the radial extent of structures in the inner corona.

The comparison between the forbidden Fe x line and its ultraviolet counterpart, described above, could in principle be used to identify the radial distance where the transition from a collision dominated excitation to a collisionless one occurs, i.e., when the radiative component takes over. Such a transition is important for establishing the distance beyond which the frequency of charge exchanges in the corona drops significantly, thus leading to the so-called freezing-in distance of the charge states (see Hundhausen 1968).

As illustrated above, such a comparison existed only for the Fe x line. However, we show next how this identification can be made for all the observed forbidden lines by taking the ratio of the spectral line intensity to the intensity of the corresponding continuum. This approach was first demonstrated by Habbal et al. (2007a).

Simply stated, the collisional component depends on the product of the electron, n_e, and ion, n_i, densities, i.e., proportional to n_en_i, while the radiative component is proportional to n_i only. On the other hand the white light is directly proportional to the electron density n_e. By taking the ratio of the spectral line to the continuum, the dominance of the collisional component translates into a term that is proportional to the ion density, and hence drops very sharply with distance. When the radiative component is dominant, the ratio of spectral line intensity to white light is proportional to the ratio of the ion to electron density. If the two have the same gradient, then the ratio should be flat. Any difference in gradients should be manifested as either an increasing or a decreasing ratio with distance depending on whether the ion density lags behind the electron density in its decrease with distance or decreases faster.

Four examples of such ratios are shown in Figure 13 for different structures in the corona. The background image is the negative of $(\rm Fe\,\mathsc{xi})_{\rm C}$ processed with the ACHF. The concentric circles at intervals of 0.25 R_☉ merely serve as a guide. The four black lines on the inner white disk give the position angles at which the intensities were measured along radial traces. P.A. = 392 goes through the northeast streamer. P.A. = 1812 passes through the Hook. The trace at P.A. = 1812 passes through the south pole and the trace at P.A. = 3567 extends outward in the north pole intercepting the enhancement E detected in Fe xiv. The corresponding plots of line to continuum intensity ratios are shown in the four panels labeled with their respective P.A. values, and plotted out to 2.6 R_☉, the edge of the field of view of the image shown above. The ratios were calculated for the strongest observed spectral lines: Fe x (red), Fe xi (cyan), and Fe xiv (green).

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The scan through the center of the northeast streamer (P.A. = 392) provides clear evidence for the transition from collision to radiative dominance for the Fe x and Fe xi lines, which occurs around 1.25 R_☉. Beyond this distance the ratio flattens. Note that the Fe x signal becomes noisy past 2 R_☉, while the Fe xi line remains very strong. For Fe xiv, this transition is clearly complete by 2 R_☉, past a small bump between r = 1.5 and 1.75 R_☉. In referring to the third concentric circle in the image above, this bump coincides with the top of the bulge of the streamer, often referred to as the cusp. This bump is an indication of a localized enhancement in the Fe^{13 +} ion density relative to the electron density, very likely associated with the trapping of these heavy ions in the underlying closed magnetic structures.

The second example at P.A. = 1071 is a scan through the Hook that coincides with the top of an eruptive prominence. As noted earlier, the Hook was visible only in Fe x and Fe xi. This is evident here from the bump that appears between 1.5 and 2 R_☉. In this example too, the transition occurs around 1.25 R_☉ for both spectral lines. The Fe xiv ratio, on the other hand, shows a very different behavior, with two small and consecutive bumps, the first starting at the inner boundary and ending at 1.25 R_☉, and the second following immediately, and ending at 1.65 R_☉. Going back to the fine details of Figure 2, it is clear that these two bumps correspond to the intersection with underlying complex arch-like structures close to the Sun.

The third example over the south pole, P.A. = 1812, shows a transition at 1.5 R_☉ for Fe x and Fe xi. The Fe xiv ratio increases steadily close to the Sun, but then flattens around 1.3 R_☉. It is not clear if this is a consequence of hot material intercepting the line of sight either in front or behind the plane of the sky.

The fourth and final example is from the north pole at P.A. = 3567. The transition for Fe x and Fe xi occurs at 1.5 R_☉, the same location as for the south pole. Fe xiv, however, shows a bump a little before 1.25 R_☉ and expands to 1.5 R_☉. This is further supporting evidence for the slight enhancement, E, seen in the white light emission (see Figure 3), and correspondingly in Fe xiv as described earlier. Such an enhancement in the Fe xiv intensity was attributed to the interception of the bulge of a streamer along the line of sight, which is quantitatively supported here by the ratio plots.

In summary, the transition from the collisional to the radiative component seems to occur consistently for Fe x and Fe xi at the same radial distance around 1.25 R_☉. Such a transition in the hotter line of Fe xiv is harder to determine as reliably, since it is often unavoidably contaminated by closed magnetic structures along the line of sight below 1.75 R_☉ in the examples of this eclipse.