RHESSI AND SDO/AIA OBSERVATIONS OF THE CHROMOSPHERIC AND CORONAL PLASMA PARAMETERS DURING A SOLAR FLARE

Solar flares are one of the most spectacular solar phenomena and are observed over a wide range of the electromagnetic spectrum from radio frequencies to high-energy gamma-ray emission. These solar explosions are associated with the acceleration of large numbers of energetic electrons, plasma heating, and plasma motions. However, the details of plasma heating and particle acceleration and transport in solar flares are still poorly understood. Over the last decade, spatially resolved hard X-ray (HXR) observations with RHESSI (Lin et al. 2002) have notably enriched our understanding of solar flares. Using these X-ray observations the spatial, angular, and energy characteristics of non-thermal electrons in solar flares have been deduced (see Kontar et al. 2011, as a recent review), which resulted in improved understanding of non-thermal electron evolution (see Holman et al. 2011, as a recent review). The detailed analysis of the footpoint emission, the brightest HXR sources in solar flares, revealed the density structure of the chromosphere (Battaglia & Kontar 2011a, 2011b). At the same time, RHESSI provides diagnostics of thermal plasma in the soft-X-ray- (SXR-) emitting loop. This allows for measuring the temperature, emission measure, and density in the corona, namely, the often observed loop-top coronal SXR sources (e.g., Battaglia et al. 2009; Veronig et al. 2005).

However, RHESSI observations are limited to electrons with plasma temperatures higher than around 8 MK. Since the plasma in a flare is unlikely to be isothermal and the temperature is expected to vary over time and for different flare sources one has to extend the observed temperature range to lower values such as observed in EUV. For example, Hinode spectroscopic studies of hot plasmas provided details of plasma motions (e.g., Warren et al. 2008; Liu et al. 2009; Watanabe et al. 2010) and observations of decaying post-flare loops (e.g., Feldman et al. 1995; Varady et al. 2000) provide estimates of the electron density of the bright regions at the loop tops. Line spectroscopy can provide information on the emission measure at different temperatures (e.g., Graham et al. 2011; Raftery et al. 2009), while Krucker et al. (2011) showed how diffraction patterns in TRACE 171 Å images can be used to make temperature and density estimates. Since its launch in 2010, the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) on the Solar Dynamics Observatory (SDO) has been contributing greatly to our knowledge of the solar flare extreme ultraviolet (EUV) emission via full disk imaging, allowing ready comparison with X-ray observations of flaring events. It covers a temperature range from ∼5000 K to ∼20 MK in nine wavelengths and, even more importantly, provides the spatial resolution allowing to connect the non-thermal and thermal phenomena in solar flares. Combining RHESSI and SDO/AIA observations of flaring loops (complemented by GOES SXR observations) thus allows us to analyze the temperature and density structure from the chromosphere to the corona during a solar flare using two complementary methods.

In this paper we present simultaneous RHESSI, SDO/AIA, and GOES observations taken during the first of three HXR peaks of a limb flare. Fitting RHESSI full Sun spectra with a single temperature model provides the SXR temperature and emission measure while RHESSI images indicate the location of the hot plasma. This is enriched by temperature and emission measure found from GOES, which is most sensitive to temperatures around the RHESSI sensitivity range and down to a few MK. HXR footpoint visibility analysis gives information about the chromospheric density structure while SDO/AIA observations are used for differential emission measure (DEM) analysis along the flaring loop. For the DEM analysis a regularized inversion method, developed by Hannah & Kontar (2012), was used. This allows to make full use of the information contained in the six AIA wavelengths sensitive to coronal temperatures as opposed to using filter ratios or single temperature fits.

We consider a well-observed limb flare that happened on 2011 February 24 with three HXR peaks between 07:29 and 07:33 UT. This GOES M3.5 class flare has one well-defined footpoint during the first HXR peak, the height structure of which was analyzed in some detail by Battaglia & Kontar (2011b). The flare has demonstrated white-light (WL) emission and is also associated with a large filament eruption.³

In the present study we focus on the time of the first HXR peak, around 07:30 UT, because of substantial saturation of AIA images at later times. The spatial structure of the flare as observed by both RHESSI above ∼6 keV and AIA in the 94 Å, 193 Å, 335 Å, and Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) WL 6173 Å continuum channels is shown in Figure 1. The analysis is focused on four physically distinct regions of interest, namely, the coronal source, two parts of the flaring magnetic loop, and the HXR footpoint. Rectangles in Figure 1 show the corresponding regions selected for the analysis.

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2.1. Alignment between AIA Images and RHESSI

2.2. AIA Emission Measures and Temperatures Using Regularized Inversion

Full Sun AIA level 1 images were prepped to level 1.5 and normalized by exposure time (see Lemen et al. 2012, and online documentation linked therein). Using only AIA wavelength channels with unsaturated images sensitive to coronal temperatures we find the line-of-sight DEM from AIA data using the method of regularized inversion (Hannah & Kontar 2012). The method allows to reconstruct the DEM, ξ(T), for a selected area or individual pixel,

$$\begin{equation} \xi (T)=n^2\frac{dl}{dT} \, (\mbox{cm}^{-5}\,\mbox{K}^{-1}), \end{equation} \tag{ 1 }$$

where n is the plasma density, T is the temperature, and l is the distance along the line of sight.

Using a set of different wavelength values from a pixel or a region in AIA maps, the method returns a regularized DEM as a function of T. This allows unambiguous determination of the contribution of different temperatures to the total emission measure as opposed to RHESSI, where the spectrum is often consistent with different combinations of EM/T (e.g., Prato et al. 2006). Due to high photon flux during flares, images in some of the wavelengths tend to be saturated during the main phase of the flare so that not all AIA wavelength channels can be used to find the DEM during the peak of the flare. In the present flare the image in the 131 Å wavelength channel was saturated for most of the flaring loop region, while the 193 Å image saturated near the top of the coronal source. This is illustrated in Figure 2 showing the AIA image profiles along the x-direction averaged over 6'' in the y-direction. This one-dimensional cut across the images (Figure 1) includes the flaring footpoints, the legs of the magnetic loop, and the coronal source.

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Therefore, for the subsequent DEM analysis, we use images at 94, 171, 335, 193, and 211 Å for the EUV loop and HXR footpoint regions, omitting 193 Å for the region at the loop top where the image in this wavelength was saturated. We discuss the consequences of this omission in Section 3.1.1. For the inversion we use zeroth-order regularization in a range of temperatures log₁₀T = 5.7 to log₁₀T = 7.5 with 16 temperature bins. This corresponds to ΔlogT = 0.11 in temperature space. The latest version of the AIA response function (including the new CHIANTI fix ⁵) was used.

We focus the analysis of emission measure, temperature, and density on a few selected, physically meaningful regions.

• 1.  
  Coronal source, corresponding to the bright SXR source at the top of the loop (region 1 in Figure 1).
• 2.  
  EUV loop. Two regions are selected at the southern loop leg between the SXR coronal source and the footpoints (regions 2 and 3).
• 3.  
  Footpoint region. This region is near the origin of the HXR and WL emission but also contains some hot plasma observed in EUV (region 4 in Figure 1).

For each of the selected regions we find the total DEM from the region near the first HXR peak of the flare in EUV images taken around 07:30:10 UT. Figure 3 shows the DEM divided by the number of pixels in the area as a function of temperature from each of the four selected regions. The DEM from all of the regions suggests the presence of two temperature components, a low temperature component around 2 MK, and a high temperature component around/above 8 MK. There are several possible reasons for this bi-model distribution: (a) line-of-sight effect: the low temperature component may not originate from the flaring loop itself, but from higher layers of the atmosphere, (b) true multi-temperature structure of the flaring site, and (c) artifacts related to the SDO/AIA response calibration or the assumed theoretical spectral calculations. To test for (a) we calculated the DEM for the same four regions in images taken around 15 minutes, 10 minutes, 5 minutes, 2 minutes, and 1 minute before the analyzed flare time interval (Figure 4). The time evolution for all four flare regions suggests that the low temperature component is always present, while the high temperature component increases in intensity by more than one order of magnitude during the rise phase of the flare.

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The second possibility (b) can be tested by analyzing the pixel-by-pixel DEM parallel as well as perpendicular to the magnetic loop. Such analysis suggests that the intensity of the low temperature component is constant both in parallel and perpendicular direction to the magnetic field, while the intensity of the high temperature component in the parallel direction in, e.g., the coronal source region decreases by a factor of three at larger heights consistent with reduced flare emission above the top of the coronal source. This is supported by images in 193 Å that show faint loop structures which are probably not associated with the flare. Thus, it is unlikely that the low temperature component is due to flaring emission but it can be explained as line-of-sight effect. In other words, the high temperature component dominates the actual flare emission and this component is what we focus on.

From the DEM curve in Figure 3 we can then calculate the total emission measure per area. Here we define the total emission measure as the DEM integrated over the main (hot) flare temperature component from T_min = 2.5–3 MK to T_max = 32 MK (see Figure 3):

$$\begin{equation} \frac{{\rm EM}}{A}=\int _{T_{{\rm min}}}^{T_{{\rm max}}} \xi (T) {dT}, \end{equation} \tag{ 2 }$$

where A is the area of the analyzed region A = (0.6 × 7.25 × 10⁷)² × N_pixel cm² with N_pixel being the pixel number over which the flux was averaged. For comparison with RHESSI and GOES we define a peak, or main, temperature as the first moment of the DEM curve between T_min and T_max:

$$\begin{equation} \langle T\rangle =\frac{\int _{T_{{\rm min}}}^{T_{{\rm max}}}\xi (T)\times TdT}{\int _{T_{{\rm min}}}^{T_{{\rm max}}}\xi (T)dT}, \end{equation} \tag{ 3 }$$

and the second moment gives an uncertainty range of possible temperatures. All temperatures are given in the form 〈T〉 = 〈T〉  ±  ΔT, where 〈T〉 is the temperature found from Equation (3) and ΔT is the half-width of the second moment. In the next sections we discuss the results for each of the four regions individually. Table 1 summarizes the temperature and emission measure values.

3.1. Soft X-Ray Coronal Source

The SXR emission originated from higher altitude than the EUV loop as seen in 94 Å, but coincided with the 193 Å emission. The SXR thermal parameters (temperature and emission measure) of the coronal source were found by fitting the full Sun RHESSI spectrum which is dominated by the coronal source emission at low energies. A thermal component plus a single power-law thick target component with a low energy cutoff were fitted over a time interval of 07:30:00–07:30:40 UT (same time interval as RHESSI imaging). Fits for two different values of the low energy cutoff resulted in comparable goodness of fit, thus we cite the two resulting values of the temperature and emission measure, which also gives a confidence interval for these parameters. The temperature resulted in T_RHESSI = 18.5  ±  1.5 MK and the emission measure EM_RHESSI = (9.4 ± 3.4) × 10⁴⁷ cm⁻³, respectively. For comparison with AIA emission measures, the emission measure per unit area ${\rm EM}_{{\it RHESSI}_A}$ is used. Here we assume that the RHESSI emission originated from an area the size of the 50% contours in a CLEAN image (8.5 × 10¹⁷ cm², CLEAN beam corrected), therefore ${\rm EM}_{{\it RHESSI}_A}=(1.1\pm 0.4)\times 10^{30}\,\mathrm{cm^{-5}}$. Another method is to use filter ratios from the GOES satellites (White et al. 2005), where we assume the same area as for RHESSI. This results in an emission measure per area of ${\rm EM}_{{\it GOES}_A}\sim 3.1\times 10^{30}\,\mathrm{cm^{-5}}$ at a temperature of 14 MK. The EUV emission measure and temperatures were found as described above and amount to 6.8 ± 1.3 MK and EM_A = (5.8 ± 1.1) × 10²⁸ cm⁻⁵.

3.1.1. Saturation and High Temperature Wavelength Channels

The 193 Å and 131 Å images were saturated near the SXR coronal source and across the whole loop, respectively, which is why they cannot be used to find the DEM in some regions. However, the images suggest that the 193 Å emission was cospatial with the RHESSI coronal source. Since the 193 Å response has a peak at around 16 MK (Lemen et al. 2012), which is close to the observed RHESSI temperature, it is likely that the two images show the same emission at similar temperature. Thus, by omitting the 193 Å and 131 Å wavelength channels in the DEM calculation, most high temperature emission will be missed. To estimate the effect on the DEM we calculated DEMs by including 193 Å and 131 Å and compared the resulting DEM and total emission measure per area. Figure 5 shows this comparison in the case of exclusion of 193 Å, 131 Å individually and both at a time. When these wavelength channels are included the emphasis is on the high temperature emission, the temperature range extends to the upper limit in the DEM reconstruction (32 MK) and the emission measure per area is found as EM_A = (4.2 ± 1.1) × 10²⁹ cm⁻⁵ which is seven times higher than when these wavelength channels are not used but is still 2.6 times smaller than the RHESSI emission measure (compare Table 1). However, the data values from the 193 Å and 131 Å images are lower limits due to the saturation. This points out the effect of omitting the high temperature response wavelength channels and the obtained coronal source emission measure has to be viewed as a lower limit. Furthermore, the temperature sensitivity range of AIA has to be considered as additional limiting factor. Temperatures around 20 MK are at the upper limit of the AIA sensitivity (the high temperature response of 193 Å peaks at 16 MK). Therefore, if the bulk of the plasma is at such high temperatures it is likely that the DEM analysis will result in a smaller emission measure due to lack of sensitivity, even if all coronal wavelength channels are used.

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3.2. EUV Loop

3.3. Footpoint

3.4. Comparison of Thermal Parameters and Density

In this section we compare the thermal parameters found from EUV data with the RHESSI observations, as well as with GOES measurements, and we also determine the densities. In a next step, every radial (x)-coordinate is mapped to a height above the photosphere, using the reference coordinate that represents the photospheric height found from visibility analysis of RHESSI footpoints as described in Battaglia & Kontar (2011a, 2011b), where we found a reference position of r₀ = 9294 ± 03.

Similar to previous results (e.g., Battaglia et al. 2005; Hannah et al. 2008) the RHESSI temperature is highest, while the GOES emission measure is higher but at a temperature a few MK lower than the RHESSI temperature. The EUV emission measures per area from all four regions of interest are up to two orders of magnitude smaller than the RHESSI and GOES emission measure. This can be explained by a number of reasons. The RHESSI and GOES emission measures are calculated for the full Sun, though in the case of a flare this emission originates predominantly from the flaring site. To compare the emission measure per area with the value from AIA, we assume that the bulk of the RHESSI and GOES emission originates from within an area corresponding to the 50% contours in a RHESSI 6–12 keV image. We can calculate the AIA emission measure of the coronal source for the same area to find EM = (1.2  ±  0.3) × 10²⁹ cm⁻⁵. This is a factor of two larger than the emission measure from region 1, but still almost one order of magnitude smaller than the RHESSI emission measure. The main reason, as illustrated in Section 3.1.1, is that emission at highest temperatures is missed by omitting the highest temperature response wavelengths 193 and 131 Å. This is likely worsened by the fact that the temperature at this stage of the flare is higher than the range to which AIA is most sensitive, even if the high temperature response was included, thus the emission measure is smaller.

In a next step we compare the densities found from the different methods. An estimate for the density of the coronal source in SXR can be found by measuring the area A_cs of the coronal source in CLEAN or Pixon images and using $n_{{\rm cs}}=\sqrt{{\rm EM}_{{\rm cs}}/V_{{\rm cs}}}$, where the volume is estimated to be V_cs = A^3/2_cs. In this case, using 50% contours in a CLEAN image at 6–12 keV and accounting for the CLEAN beam, we get a volume of 7.9 × 10²⁶ cm³ and thus a density of n_cs = (3.4 ± 0.6) × 10¹⁰ cm⁻³. In the case of AIA observations the density is given as the square root of the emission measure per area divided by the distance along the line of sight. For the line-of-sight component the observed portion of the loop is assumed to be "cylindrical." We use the size of the HXR footpoint to estimate the loop diameter and approximate the line-of-sight distance to 5'' = 3.6 Mm for regions 2–4. The coronal source (region 1) appears extended compared with the loop, therefore a value of 9 Mm is used for the line-of-sight distance. It is often not possible to determine the thermal parameters of the footpoints, even in imaging spectroscopy (Battaglia & Benz 2006; Hudson et al. 1994; McTiernan et al. 1993), either because of the dominance of the coronal source and the dynamic range of RHESSI, or because the plasma is at temperatures to which RHESSI is not sensitive. However, using RHESSI visibility analysis it is possible to determine the chromospheric density near the footpoints by fitting an exponential density model to the energy-dependent positions of the footpoints (Battaglia & Kontar 2011b; Kontar et al. 2010, 2008). Figure 6 gives an overview of the densities as a function of height. The densities in regions 2–4 are all around 2 × 10¹⁰ cm⁻³. A similar density is found using the SXR RHESSI data. This is consistent with previous densities found from RHESSI thermal analysis and indicates a constant density along the loop. For these calculations a filling factor of one was assumed. It cannot be excluded that the filling factor is smaller. However, recent analysis of several flare loops suggests a value that is generally close to one (Guo et al. 2012a, 2012b). Even a filling factor as low as 0.1 would lead to a density only three times higher which is still feasible for a flaring loop.

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Since the density found from HXR observations is the neutral plasma density, and AIA observes hot, ionized plasma, combining these observations gives a complete picture of the density in the solar atmosphere during a flare. The combined observations represent a steeply decreasing density from the photosphere to a height of about 4''–5'' with a flatter decrease or near constant value at larger heights, similar to models such as from Vernazza et al. (1981) and Avrett & Loeser (2008). The Avrett & Loeser (2008) quiet-Sun model is shown in Figure 6 along with a double-exponential density model with two scale heights (220 km at small heights, 17,000 km at larger heights) that follows the observed pattern. The AIA-determined density of region 1 is lower by about a factor of four compared with RHESSI because of the small emission measure.

Table 1. Temperatures, Emission Measures, and Densities Found by the Different Methods

Instrument/Region	T	EM/Area	ne
	(MK)	(cm−5)	(cm−3)
RHESSI/coronal source	18.5 ± 1.5	(1.1 ± 0.4) × 1030	(3.4 ± 0.6) × 1010
AIA/Region 1	6.8 ± 1.3	(5.8 ± 1.1) × 1028	(8.0 ± 0.8) × 109
AIA/Region 1 (incl. 193 Å)	11.6 ± 3.9	(2.7 ± 0.9) × 1029	(1.7 ± 1.0) × 1010
AIA/Region 1 (incl. 131 Å)	12.4 ± 3.0	(3.2 ± 0.8) × 1029	(1.9 ± 0.9) × 1010
AIA/Region 1 (incl. 131 and 193 Å)	13.6 ± 4.0	(4.2 ± 1.1) × 1029	(2.2 ± 1.0) × 1010
AIA/Region 2	7.5 ± 2.7	(1.2 ± 0.3) × 1029	(1.8 ± 0.2) × 1010
AIA/Region 3	7.4 ± 2.2	(2.1 ± 0.6) × 1029	(1.5 ± 0.2) × 1010
AIA/Region 4	8.7 ± 2.0	(2.1 ± 0.8) × 1029	(2.4 ± 0.5) × 1010
GOES/coronal source	14	3.1 × 1030

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In this work we present a comprehensive study of the thermal parameters (emission measure, temperature) and the density in four different regions of a flaring loop, using both X-ray as well as EUV data. Detailed temperature, emission measure, and density analysis along the loop near the flare HXR peak indicate that the hottest plasma is found near the coronal loop-top source, in line with previous observations. The EUV observations suggest that the density in the loop legs increases with decreasing height, but the temperature is constant within uncertainties. The footpoint structure is such that the plasma is neutral or partly ionized up to ∼1–2 Mm with a steep, unresolved rise to ∼5 MK 1–2 Mm above the height of the HXR and WL emission.

The DEM in EUV was found using the method of regularized inversion developed by Hannah & Kontar (2012). We show that the method is capable of recovering two temperature components, one at around 2 MK and one at or around 8 MK. The low temperature component around 2 MK is observed in all four regions and is only weakly changing with time, while the intensity of the high temperature component increases by more than one order of magnitude at the time of the flare. Therefore, the low temperature component can be attributed to line-of-sight effect. The existence of this component has to be kept in mind when DEMs are determined by fitting single temperature Gaussians. The results also show the presence of hot (≳ 8 MK) plasma not only in the coronal source but also in the coronal loop legs, and near the footpoints of the loop. As the flare progresses, the high temperature emission starts to increase from around 07: 15 UT with the emission finally saturating the "hottest" wavelength channels around 07: 30 UT near the first HXR peak. This rise is first seen in the coronal source and then propagates downward to the footpoints. This is consistent with the start of the flare and initial heating taking place in the corona. Note also that the loop-top emission in the SDO/AIA image in 193 Å is cospatial with RHESSI coronal loops, while the other "hot" wavelength channel 94 Å is not. The loops visible in 94 Å are around 5'' lower than the 193 Å loop structure. While the brightest SXR feature seen by RHESSI in 10–15 keV is undoubtedly the coronal source, the brightest 193 Å source is in fact the region to the north of the flare located near x = −925'', y = 285''. This is intriguing since the emission seems to be part of the active region and as such contains a significant fraction of the thermal energy. However, this region is not associated with either RHESSI source at any stage of the flare.

The saturation in the "hottest" wavelength channels 193 Å and 131 Å disallows the study of the hottest plasma and limits the temperature range of which plasma can be analyzed. Comparison of the total AIA emission measure with RHESSI and GOES emission measures suggests that the EUV emission is up to more than one order of magnitude smaller than the X-ray emission measure. This can be partly attributed to omitting the highest temperature wavelength channels in the analysis due to saturation, and it emphasizes the importance of using all six "coronal" wavelength channels for the DEM reconstruction. An additional likely cause it that the bulk of the plasma is at a temperature higher than the main sensitivity range of AIA. Cooler events (i.e., with a RHESSI temperature closer to 10 MK) are probably better suited for more detailed comparative studies. In addition, in weaker events the likelihood for AIA saturation is reduced.

Combined RHESSI/SDO-AIA studies allow to investigate in detail a broad temperature range from 1–2 MK up to ∼20 MK. Moreover, the use of DEM analysis helps to quantify the temperature, emission, and density structure in the flaring loop and fills the gap between the coronal source and footpoints that are observed in SXR and HXR.

Financial support by an STFC UK rolling grant, the Leverhulme Trust, and by the European Commission through HESPE (FP7-SPACE-2010-263086) and the "Radiosun" (PEOPLE-2011-IRSES-295272) Networks is gratefully acknowledged. M.B. was supported by a travel grant from the Swiss Society for Astronomy and Astrophysics (SSAA). We thank Iain Hannah and Säm Krucker for helpful discussions and James Lemen for useful comments.