Desaturated EUV Flare Ribbons in an X-class Flare

As this is the first time that have we derived the DEM from desaturated AIA fluxes, we simplify the task by only analyzing a single time during the impulsive phase of the flare with images taken between 22:18:36 and 22:18:48 UT. Relative to the main hard X-ray emission that starts at 22:18:05 UT and has at least five peaks until 22:19:00 UT followed by a decay of about a 30 s duration, the selected AIA images represent a time in the middle of the impulsive phase after electron precipitation has occurred for about 30 s (see Figure 2, top). To avoid potential uncertainties in the detailed shape of the reconstructed flare ribbons, we only derived DEM distribution from the total flux from each ribbon. The more challenging task of looking into details of the flare ribbon morphology and time evolution is left until the successful completion of the feature-averaged, single time step analysis presented here (see also discussion on timescales at the end of Section 2.5).

We use the regularized inversion code from Hannah & Kontar (2012) to derive separate DEM distributions for the northern and southern ribbons (Figure 3). To test the robustness of the code and test the possible influence of systematic errors of the desaturation code, we rerun the code with randomly added uncertainties of up to 20%. We note that the 20% uncertainty assumed here is a conservative assumption, as it is well above the 5% accuracy of the desaturation algorithm estimated by Torre et al. (2015). The results appear to be consistent showing a peak EM around 9 × 10⁶ K with a steep decline in EM at higher temperatures. At lower energies the EM is significantly reduced, by a factor of 20 around 2 × 10⁶ K, for example. There is a dip in the distribution around 4 × 10⁶ K, but it is unclear if the dip is a real feature or if it is due to the rather weak diagnostic ability of AIA at these temperatures (see Lemen et al. 2012, Figure 13). As the uncertainties are largest for those temperatures, the gap remains questionable. The derived peak temperature and peak DEM value agrees well with the full-disk DEM derived from SDO/EUV Variability Experiment (EVE) data for the same event (Kennedy et al. 2013, Figure 3(d)). There is also a hotter component in DEM derived from EVE data peaking between 20 and 25 × 10⁶ K, which we attribute to the coronal emissions seen in hard X-rays and in Fe xxiv (see discussion in Section 2.4).

Zoom In Zoom Out Reset image size

Ignoring the potential gap around 4 × 10⁶ K, the derived temperature distribution of the flare ribbons of this X-class flare looks similar to the DEM from a range of B class flares from Graham et al. (2013), except that the EM values are much higher. Graham et al. (2013) had peak temperatures around 8 × 10⁶ K and DEM values from 10²⁸–10²⁹ cm⁻⁵; here we report ∼9 × 10⁶ K and 2 × 10³¹ cm⁻⁵, respectively. Hence, the EM per area is enhanced roughly proportional to the difference in GOES class between the events considered, but the ribbon temperature is in the same range. This comparison indicates that the enhanced EUV flux in this X-class flare is due to a larger EM, i.e., due to an enhanced density and/or an enlarged volume of the flare ribbons. To estimate the density of the hot ribbon, we first sum the DEM over the hot component giving 1.9 and 2.5 × 10⁴⁸ cm⁻³ for the northern and southern ribbon, respectively. The volume estimates are not well constrained by observations mainly because of the unknown radial extent of the flare ribbons in the EUV range, but also because of the ribbon width. Therefore, we use three different assumptions to estimate the ribbon volume and this consequently results in a range of densities. The ribbon length is 7'' for all assumptions. As a lower value for the ribbon thickness, we use a very narrow and thin ribbon of 0.3'', while for a large volume we assume a width of 1'' and a radial extend of 2''. To get a middle range for volume estimate, we use an equal width and radial extent of 1''. With these three assumptions, we get a middle value for the density of 9 × 10¹¹ cm⁻³, and extreme values of 6 × 10¹¹ cm⁻³ and 3 × 10¹² cm⁻³, respectively. The densities derived here are above the values from the statistical study of soft X-ray flare ribbons by Mrozek & Tomczak (2004), which revealed densities up to 6 × 10¹¹ cm⁻³ with most values below 2 × 10¹¹ cm⁻³. However, the areas used for deriving their densities were taken from 10% contours of the soft X-ray images with a pixel size of 2.45'' and an FWHM angular resolution of 3.7''. Hence, an unresolved ribbon width results in a 10% width of around 8''. Assuming such a wide ribbon, the event discussed here would have a density within the statistical spread of the study of Mrozek & Tomczak (2004). Considering that more recent observations revealed narrow ribbon structures (e.g., Dennis & Pernak 2009), the volume estimates used in Mrozek & Tomczak (2004) are therefore upper limits, and densities are accordingly lower limits.

It is straightforward to derive the column density N_EUV within the hot EUV source, and then the largest energy (in keV) of nonrelativistic electrons that completely stop within the EUV source can be estimated by (e.g., Emslie 1978):

$$\begin{eqnarray}&&{E}_{\mathrm{stop}}({N}_{\mathrm{EUV}})\approx \sqrt{{N}_{\mathrm{EUV}}/1.5\times {10}^{17}\,{\mathrm{cm}}^{-2}}.\end{eqnarray} \tag{ 1 }$$

For the different selected volumes, the values of E_stop vary only slightly between 21 and 24 keV. Hence, electrons below these values seem to be able to stop within the EUV source, while higher energy electrons actually fly through the EUV source and precipitate toward deeper layers in the chromosphere, at least in the simplest propagation model. For electron transport in more complex models (such as collisional pitch angle scattering, mirroring, etc.), higher energy electrons could potentially also stop within the EUV source.

From the derived DEM, we calculate the expected GOES flux for each temperature bin (Figure 3, center column). The peak in the GOES flux distribution is slightly shifted in temperature to 10 × 10⁶ K compared to the DEM temperature peak, but the bins with large DEM clearly produce the largest contribution. In total for both ribbons, we estimate a GOES flux in the low channel corresponding to a C5 GOES level. This is about 10% of the actual observed GOES flux at that time in the low-energy channel. Due to the low peak temperature of the flare ribbon DEM, the high-energy channel only increases by 1.5%. These estimates show that the flare ribbon can contribute to the GOES soft X-ray flux, in particular early in the impulsive phase, even though at a moderate level.

While the DEM distribution can be directly obtained from observations, the energy content as a function of temperature is the physically more relevant distribution. We estimate the thermal energy content using the standard formula (e.g., Hannah et al. 2011) assuming the same radial extent of the ribbon for all temperatures and neglecting radiative and conducting losses:

$$\begin{eqnarray}&&{E}_{\mathrm{th}}(T)\approx 3{kT}\sqrt{\mathrm{EM}(T)V(T)}=3{kT}\sqrt{\mathrm{EM}(T)A(T)h(T)},\end{eqnarray} \tag{ 2 }$$

where T is the temperature, k the Boltzmann constant, EM(T) is in units of (cm⁻³), and V(T), A(T), and h(T) are the volume, area, and thickness of the ribbon, respectively. Assuming the same volume for all temperatures, the thermal energy distribution shows that most of the energy is around the peak temperature of the emission measure with a steep decline to a lower temperature. For the total EM of the hot component (see Table 1), using Equation (1), we get a total thermal energy content of 5.4 × 10²⁸ erg assuming a volume of 7'' × 1'' × 1'' for each ribbon.

The weakness of the above simple estimation of the thermal energy content is in the assumption of an equal volume for all temperatures. The temperature structure in the chromosphere is likely layered with an increasing temperature with altitude. For such a thickness distribution, the thermal energy distribution has a different shape as shown in Figure 3. As the layers at lower temperatures are expected to be thinner compared to the layers at high temperatures, the distribution of the thermal energy content would undergo an even steeper decline with decreasing temperatures than those shown in Figure 3. On the other hand, the hottest temperature could have larger radial extends h, in particular if "evaporation" of chromospheric plasma occurs and the high-temperature plasma is distributed over a large radial distance. In such a case, the peak temperature in the thermal energy content could be at a higher temperature as shown in Figure 3. As an example, we approximate how much thicker the 20 × 10⁶ K plasma source needs to be compared to the 9 × 10⁶ K layer so that the 20 × 10⁶ K plasma has the same energy content as the plasma at the peak temperature of around ∼9 × 10⁶ K. From Equation (2), we can see that the thermal energy scales linearly with temperature and it depends on the square root of DEM(T) × h(T). The derived DEM is about 15 times smaller at 20 × 10⁶ K compared to the peak value (see Figure 3). Hence, to make the 20 × 10⁶ K thermal energy content as high as the peak value in Figure 3 (i.e., a flat distribution), the spatial extent at 20 × 10⁶ K would need to be about four times larger than at the peak temperature (∼9 × 10⁶ K). Such a value is potentially plausible in an evaporation scenario. In any case, it shows that the peak temperature in the DEM does not necessarily imply that the thermal energy content distribution peaks around the same temperature. It highlights that the unknown distribution of the altitude of heated plasma significantly limits our diagnostic capabilities for flare ribbons.

In this section we derive from RHESSI hard X-ray observations the parameters of the hot coronal loop as well as for the nonthermal component to compare with the values derived for the ribbons. We use standard RHESSI imaging and spectroscopy techniques to derive the temperature, density, and thermal energy content of the main thermal flare loop using the time range over which the AIA images used in the DEM analysis are taken. The RHESSI spectral observations show the typical thermal and nonthermal components, with the thermal component being larger below 22 keV (Figure 4).

Zoom In Zoom Out Reset image size

2.4.1. Thermal

2.4.2. Nonthermal

In this section, the radiative and conductive losses of the flare ribbons are approximated and then compared to the energy input by nonthermal electrons as derived from the hard X-ray spectral observations.

To estimate the radiative losses of the hot (>×10⁶ K) ribbons we use the radiative emissivity curve η (i.e., total radiated power per unit of EM as a function of temperature for an optically thin plasma such as given in Figure 1 of Landi & Landini 1999):

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{rad}}=\eta ({T}_{\mathrm{hot}}){\mathrm{EM}}_{\mathrm{hot}},\end{eqnarray} \tag{ 3 }$$

where T_hot and EM_hot are the temperature and EM of the hot ribbon, respectively. With the values of temperature and EM derived in the previous sections (see Table 1), we get radiative losses of a few times 10²⁶ erg s⁻¹. As the EM of the colder plasma is declining faster than the radiative emissivity curve increases (see Figures 2 and 1 of Landi & Landini 1999), the radiative losses of the lower temperature EUV ribbon are smaller and they are not considered in our simple approximation. In any case, radiative losses of the hot ribbons are more than two orders of magnitude below the energy input for nonthermal electrons as derived above. Compared to the derived thermal energy content of the flare ribbon of 5.4 × 10²⁸ erg, radiative cooling alone would take minutes to cool the flare ribbons after the energy input by flare-electron stop.

For the derived temperature and density of the flare ribbon, classic Spitzer conductivity is a valid approximation (see Figure 6 of Battaglia et al. 2009):

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{cond}}={\kappa }_{0}{T}^{5/2}\displaystyle \frac{{dT}}{{dz}}A\approx {\kappa }_{0}{T}^{5/2}\displaystyle \frac{T}{{L}_{z}}A,\end{eqnarray} \tag{ 4 }$$

where κ₀ = 10⁶ erg s⁻¹ cm⁻¹ K^7/2, L_z is the temperature scale length, and A is the total ribbon area. For T ∼ 9 × 10⁶ K, L_z  = 1'', and A = 7.4 × 10¹⁶ cm², we get a conductive loss rate of 2.2 × 10²⁷ erg s⁻¹. For shorter temperature scale lengths, the loss rate could be even larger. In any case, for all reasonable cases of L_z  = 1'' conductive losses dominate over radiative losses, as is generally the case for flare ribbons (e.g., Fletcher et al. 2013; Simões et al. 2015). Integrated over the duration of the EUV emission, roughly 25 s from the start of the impulsive phase, conductive losses become of the same order of magnitude as the estimated thermal energy content. Hence, it is in principle not justified to neglect conductive losses when approximating the total thermal energy by simply taking the instantaneous thermal energy content (Equation (1)). Compared to the energy input by nonthermal electrons, however, conductive losses are about ∼30 times smaller than the energy input by electrons above 20 keV. Hence, as a rough approximation, conductive losses can be neglected for this event during the time of the main hard X-ray emission.

We finish this section by briefly discussing the timescales of the cooling of the flare ribbons and the required time resolution to properly measure ribbon cooling timescales. After the energy input by flare-accelerated electrons stops, conductive losses are able to cool the EUV ribbons rather efficiently with significant cooling on the timescale of the AIA image cadence of 12 s. The duration of the energy input by flare-accelerated electrons at a fixed location is limited not only by the duration of electron acceleration, but also because of the ribbon motion (e.g., Yang et al. 2009). As newly reconnected field lines make the flare ribbons move apart, the maximum duration of electron precipitation at a fixed location can be estimated from the ribbon width and the apparent ribbon velocity. For a ribbon width of 1'' and for a typical ribbon velocity of 30 km s⁻¹, we get energy input at a fixed ribbon location of the duration of 24 s. This demonstrates the need for high time cadence EUV imaging observations below the available 12 s cadence provided by SDO/AIA. High cadence IR observations of flare ribbon heating and cooling reveals impulsive heating on a ∼4 s timescale, and exponential decay time of ∼10 s for a single event with well-separated individual hard X-ray peaks (Penn et al. 2016). Hence, a cadence of a few seconds is a minimum requirement to study heating and cooling of flare ribbons.

As discussed in Section 2.4.1, the best chance of simultaneously observing the thermal emissions from the ribbons and the loop is in the soft X-ray range. Figure 4 shows the extrapolation of the X-ray spectrum of the ribbon and loop thermal emissions down to 1 keV. While it is very challenging to simultaneously observe both thermal components in the hard X-ray range, it becomes easier at soft X-ray wavelengths as the difference in flux levels are becoming smaller. This can be seen in the derived GOES fluxes where the ribbons are about 10% in the low GOES channel signal, but down to 1.5% in the high channel (see Table 1). For soft X-ray filter observations the intensities of loop and footpoint sources can even be similar. For SOL2011-09-06, Hinode/XRT (Golub et al. 2007) provides a "Be-thin" filter image taken during the same time interval as the AIA images used in the derivation of the DEM shown in Figure 3. Using the derived EM and temperature pairs from AIA and RHESSI, we estimate a ratio of the ribbon to loop thermal component in the Be-thin image of 1.1 (for the XRT response function see Figure 7 in Golub et al. 2007). Despite the very low exposure time, the Be-thin image is unfortunately saturated (Figure 5). Nevertheless, the saturation signatures suggest emissions from the two flare ribbons as well as from the loop, as expected from our simple considerations given above. The only other soft X-ray images available for this time range are from the GOES Solar X-Ray Imager (SXI; Hill et al. 2005), but the image with the best temporal match is taken ∼20 s later when the GOES emission is already increased by more than a factor of 2. This SXI image is taken with the "Be 50 μm" (i.e., a thick Be filter), where low temperature emission is slightly more suppressed relative to high temperatures than for the Be-thin filter used by XRT. The expected ratio of the ribbon to loop thermal component is therefore about 0.5 (for response curves see Figure 11 of Pizzo et al. 2005). The SXI observations show indeed the coronal loop as the stronger source, but this could also be due to the later time of the SXI image when the thermal loop is much brighter as indicated by GOES and RHESSI. In summary, the available soft X-ray observations provide an unfortunately limited additional diagnostic power for this event.

Zoom In Zoom Out Reset image size

The next step in our AIA flare ribbon study will be to look at other events to corroborate that the DEM generally peaks around 10 × 10⁶ K for all flares. Furthermore, the diagnostics of the AIA diffraction patterns are not limited to reconstructing the saturated images as used in this paper, but the wavelength dependence of the diffraction acts as a spectrometer. The diffraction patterns show a convolution of the source shape and the source spectrum within the EUV passband. The high-order patterns can therefore be used to extract spectral information of the saturated sources (e.g., Krucker et al. 2011b). Such analyses are planned to be carry out for AIA data as well, but the topic is proving to be challenging (Raftery et al. 2011).

Soft X-ray and spectral EUV observations from HINODE are excellent diagnostics to better limit the steep decline of the high-temperature component in flare ribbon DEM distributions. Saturation of these instruments during the biggest flare in combination with the slit position being located on the flare ribbons, however, makes such observations rather rare. The heavily underused HINODE/EIS slot images (Harra et al. 2020) are a further excellent diagnostic source that should be added to improve our understanding of flare ribbon temperature distributions. Optical observations should be used in the future to constrain the coolest heated layers within the flare ribbons, in particular with the Daniel K. Inouye Solar Telescope (e.g., Tritschler et al. 2016).

To detect flare ribbons in hard X-rays is very challenging for indirect imaging such as RHESSI or the Spectrometer Telescope for Imaging X-rays onboard the Solar Orbiter (Krucker et al. 2020). The sensitivity and imaging dynamic range of these instruments is insufficient, in particular when attenuators are inserted during large flares. For the discussed X-class flare, the thermal emission from the flare ribbon is expected to be even lower than the extrapolated nonthermal emission for energies down to 7 keV. Hence, in hard X-rays, the low-energy tail of the nonthermal emission appears to be easier to detect than the thermal emission from the ribbons. For future observations with hard X-ray focusing optics (e.g., Krucker et al. 2014) with a much improved dynamic range in imaging and enhanced sensitivity, we will be able to detect X-rays from ribbons both in the thermal and nonthermal range providing direct diagnostics of both components.

Finally, we encourage modelers to use the derived parameters of energy input by electron beams from this flare, and see which conditions can reproduce the parameters for the flare ribbons.