THE NATURE OF CME-FLARE-ASSOCIATED CORONAL DIMMING

The eruptive event takes place near the disk center. It produces a C-5.7 flare. According to the GOES catalog,⁴ the soft X-ray (1–8 Å) emission of the flare starts to rise at 11:23 UT, peaks at 11:50 UT, and lasts until 12:18 UT. The flare is well observed by SDO/AIA. Figure 1 gives an overview of the flare in nine UV/EUV wavelengths. Each image is taken at the peak time of the total emission in the given bandpass. The flare is a very typical two-ribbon flare, with brightening of the two ribbons visible in multiple passbands. The ribbon brightening quickly spreads from southwest to northeast along the magnetic polarity inversion line (PIL), and then expands outward away from the PIL. Such a time sequence of ribbon brightening is displayed in Figure 3, superimposed on a longitudinal magnetogram obtained by SDO/HMI before the flare onset. Subsequently, post-flare loops are clearly seen in the EUV channels. The light curves observed by AIA for the flaring region are displayed in the top panel in Figure 4. The figure shows that UV and EUV emissions at the flare ribbons, particularly in the 1600 and 304 Å bands, start to rise at around 11:10 UT, 10 minutes before the rise of the GOES SXR emission. In the plots, the vertical dashed lines indicate the start of the flare ribbon brightening, as well as the start and peak times of the soft X-ray emission observed in GOES, respectively.

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According to the standard flare model (Carmichael 1964; Sturrock 1966; Hirayama 1974; Kopp & Pneuman 1976), the expansion of flare ribbons indicates a progressive reconnection that continuously forms flare loops. From the flare ribbon evolution, we can measure the reconnection rate by summing up the magnetic flux in newly brightened UV pixels (Fletcher & Hudson 2001; Qiu et al. 2002, 2004; Saba et al. 2006; Qiu et al. 2010). An automated procedure has been developed to identify flaring pixels and minimize measurement uncertainties caused by fluctuations in photometry calibration and by non-flaring signatures (Qiu et al. 2010). We use the SDO/HMI LOS magnetogram combined with the SDO/AIA 1600 Å images of flare ribbon evolution (see Figure 3) to derive the magnetic reconnection flux and magnetic reconnection rate, which are displayed in the middle and bottom panels of Figure 4, respectively. The calculation is made between 11:00:00 UT and 13:20:00 UT. In this flare the uncertainty in reconnection flux measurement is about 40%, mostly caused by the imbalance between the measured positive and negative fluxes, although the two fluxes well track each other during the flare evolution. At 11:10 UT when ribbon brightening starts, the reconnection flux starts to rise, and the total reconnection flux is measured to be 1.8 × 10²¹ Mx. The reconnection rate is the time derivative of the reconnection flux, which amounts to 1.5 × 10¹⁸ Mx s⁻¹ at around 11:30 UT.

The associated CME is a partial halo CME observed by LASCO with an average speed of 736 km s⁻¹ in the LASCO C2 and C3 field of view, according to the LASCO CME catalog by the Coordinated Data Analysis Workshops (CDAW)⁵ CME catalog (Gopalswamy et al. 2009). The CME event, particularly in its early stage, is best observed by the STEREO instruments from the limb. Figure 2 shows the CME evolution observed by EUVI, COR1, and COR2 on board STEREO. The CME is first seen at 11:06:25 UT as a faint loop structure in the running difference images at 195 Å by EUVI-B, and expands afterwards. The bright CME front is clearly seen in COR1 at 11:30:55 UT. Five minutes later, a bright core beneath the front also appears in the COR1 field of view. These structures can also be identified in COR2 images from 12:24:55 UT.

To measure the height of the CME, we track the position of the leading edge of the CME along a guide line, indicated in the figure, in the direction of its ejection. The CME leading edge is best visible in the running difference images by EUVI, COR1, and COR2. This position is tracked manually several times. The mean and standard deviation of these measurements are presented in the figure as the CME height and its uncertainty, respectively. The middle panel of Figure 4 shows the measured height (starting from the solar center) of the CME front together with the reconnection flux measured from the flare ribbon evolution. We derive the CME velocity using a linear fit to every four consecutive points, in order to reduce large fluctuations in the original measurements. The uncertainty indicated in the velocity plot is the standard deviation of this linear fit. The plot shows that the CME starts moving slowly at a speed below 100 km s⁻¹ when the flare UV emission starts, and then speeds up in the next 10 minutes. It achieves the maximum velocity of about 1000 km s⁻¹ around the time of the GOES soft X-ray emission peak, when the increase of the reconnection flux starts to slow down substantially. The CME then moves at a relatively constant speed of about 700 km s⁻¹ for the next few hours. The CME velocity profile shows a temporal correlation with the reconnection flux as well as the GOES soft X-ray light curve during the rise phase, consistent with previous observations of the timing relationship between fast CMEs and flares (Zhang et al. 2001; Qiu et al. 2004; Patsourakos et al. 2010, 2013; Cheng et al. 2014). The CME acceleration is also estimated and compared with the magnetic reconnection rate. The bottom panel of Figure 4 shows that these two quantities exhibit similar evolution trends. The CME acceleration peaks around 11:30 UT with a peak value of 0.4 km s⁻², and diminishes after 12:00 UT, when flare reconnection has also stopped. At these times when acceleration/reconnection starts (11:10 UT), peaks (11:30 UT), and stops (12:00 UT), the front of the CME is at 0.2, 1, and 3 solar radii above the surface, respectively.

In summary, these observations show the following stages of the CME and flare evolution:

• 11:10 start of flare ribbon emission, CME motion, and reconnection;
• 11:20 start of SXR rise, significant CME acceleration, and fast reconnection;
• 11:30 peak of CME acceleration and reconnection rate;
• 12:00 peak of SXR emission and CME velocity, and reconnection diminished.

In the standard flare-CME model, energy stored in the magnetic field is released by magnetic reconnection to heat flare plasmas, as well as to accelerate the CME. The observed coincidence between the CME evolution and magnetic reconnection, within the uncertainty of a few minutes, suggests that acceleration of the CME is related to the reconnection process.

3.2.1. Temporal and Spatial Evolution

Coronal dimming is often observed to accompany CMEs. In this event, dimming signatures are observed in AIA images of several EUV bands, most prominently 171, 193, 211, and 335 bands, suggesting that the characteristic temperature of the dimming areas ranges between 1 and 3 MK. By checking the full disk images, the most significant dimming occurs near the flare region. No other obvious dimming is detected during that time.

In the middle panel of Figure 4, we plot the 171 and 193 light curves produced from pixels exhibiting dimming. The pre-dimming counts level in these pixels is within ${I}_{q}\pm \sigma$, Iq and σ being the median counts and standard deviation, respectively, of a control region free of coronal loops, and EUV counts in these pixels keep decreasing continuously for a few minutes. In this way, we exclude apparent dimming signatures due to removal or motion of overlying coronal loops during the eruption (Qiu et al. 2007; Hock et al. 2010, 2012; Harra et al. 2011). The plots show that coronal dimming evolves along with the flare reconnection and CME eruption. EUV emission in the 193 passband starts to decrease quickly at 11:15 UT, 5 minutes after the start of the flare reconnection and CME takeoff, whereas dimming in the 171 band starts about 5 minutes later. The maximum dimming occurs around the peak time of the GOES SXR emission as well as the CME velocity, and then the EUV emission in these dimming regions starts to rise as post-flare loops form in these regions.

To study the evolution of dimming and its relation to the eruptive flare, Figure 5 gives an overview of the flare region in three different passbands by AIA in 171, 131, and 304 Å at several critical times during the flare/CME evolution. The dimming pixels selected above mostly locate in EUV moss areas adjacent to the flare ribbons. One dimming region is found at the left end of the flare ribbon in the positive magnetic fields. Dimming also occurs at the right end of the conjugate flare ribbon in the negative magnetic fields. These two regions are indicated by the rectangular boxes in Figure 5, as well as in the magnetogram in Figure 3. We also find a band of dimming region along the flare ribbon in the positive magnetic fields, indicated by the long parallelogram in Figure 3. These regions are denoted as "LF" (left foot), "RF" (right foot), and "RB" (ribbon) in the figures as well as the following text. Dimming is also visible along the other ribbon in the negative magnetic fields, but not as outstanding and widespread as in the RB region, perhaps because of projection effects given the disk position of the active region. Seen in the leftmost panels of Figure 5, before the flare, these regions are characterized by EUV moss structures at the base of the corona, and are mostly free from overlying coronal loops. After the eruption, the moss structure in some areas is removed, causing coronal dimming seen in a few EUV bands including the 304 Å band observing the transition region, as shown in the rightmost panels of the figure.

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To analyze the temporal and spatial pattern of dimming evolution we sample pixels in these regions by generating stack plots of EUV emissions in a few passbands along a few slices across these regions. These slices are marked in Figure 5. The left and middle panels in Figure 6 show the stack plots of EUV counts along slices AB and CD, which are placed along and across the dimming band RB next to the flare ribbon, respectively. The right panel shows the stack plots along slices EF and GH, which sample the two dimming regions at the ends of the conjugate ribbons. From top to bottom, the plots are generated for the AIA 131, 335, 193, 171, and 304 Å passbands, sampling plasma emission at different temperatures. Each stack plot is normalized to the EUV counts at 10:00:12 UT. The two vertical dashed lines indicate the times at 11:10 UT and 11:30 UT, respectively, when CME acceleration and flare reconnection start and peak.

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Seen in these plots, dimming is observed in multiple EUV bands including the EUV 304 Å band. In most dimming pixels, significant dimming starts after the flare/CME onset (11:10 UT) in the 335 and 304 passbands, and even later in other wavelengths. In a few locations, gradual dimming appears to occur before 10:30 UT. The middle panel of Figure 6 sampling the evolution across the flare ribbon along slice CD also shows apparent spreading of dimming away from the PIL, followed by spreading of ribbon brightening. For example, seen in the 193 Å passband, between 11:25 and 11:35 UT, the dimming front along the ribbon spreads away from the PIL at the speed of about 10 km s⁻¹. On the other hand, the right panel shows that dimming along the EF and GH slices across the LF and RF regions also spreads out, but these pixels are not brightened later on.

The temporal and spatial evolution of dimming in multiple wavelengths suggests that dimming in these regions is not caused by thermal dimming or disruption of pre-flare active region loops (Hock et al. 2010; Harra et al. 2011), neither do they appear to be obscured by absorptive materials. Most likely, dimming is caused by density decrease due to expansion of corona structures anchored at these locations. Specifically, the LF and RF regions at the two ends of the flare ribbons locate at oppositely curved magnetic elbows that loop out on opposite ends of the neutral line (Sterling & Hudson 1997; Moore et al. 2001), and likely map the footpoints of the erupting CME, similar to the event reported by Webb et al. (2000). On the other hand, the narrow band of dimming along the outer edges of flare ribbons is brightened afterwards. The morphology evolution at these locations much resembles the scenario depicted by Forbes & Lin (2000), Švestka (1996), and Moore et al. (2001), where the erupting flux rope stretches the overlying coronal arcade, causing dimming at the feet of the arcade; the stretched field lines then reconnect and form closed loops, and therefore these locations are brightened due to heating along closed loops. Note that at these locations, reconnection as inferred from the ribbon brightening starts after the dimming; yet in other regions, such as in the inner part of the flare ribbons, reconnection takes place much earlier, and dimming is not observed in some of these regions. As a result, the global signature of significant dimming appears to occur after the onset of reconnection.

3.2.2. Coronal Dimming versus CME Evolution

To further examine the timing of coronal dimming with respect to the CME eruption, we analyze the EUV light curves of the three regions, with a focus on the 193, 171, and 304 passbands that observe the base of the corona. The AIA response functions for the 193 and 171 bandpasses each have a dominant single peak at temperatures below 10 MK (Boerner et al. 2012), so observations in these passbands provide a more reliable estimate of the characteristic temperature of the dimming plasma. Light curves of the 211 passband are very similar to those at the 193 passband and are therefore not presented. Emission in the 304 Å passband includes a large contribution of the He ii 304 Å line that forms in the transition region or upper chromosphere at a characteristic temperature of about 0.1 MK. Traditionally, dimming is not often studied in this wavelength, but we present observations in this wavelength as a reference. Observations show that dimming is also visible in the 304 band, likely caused by the diminished transition-region emission due to decreased coronal pressure along expanding field lines anchored at these locations.

In the top row of Figure 7, we plot light curves of the total EUV counts from all pixels in the LF (left), RF (middle), and RB (right) regions, respectively. Each light curve is normalized to the pre-eruption counts at 10:00 UT. In the second row, the inverse of the same light curves are presented, in order to compare with the CME height profile overplotted in symbols. In these light curves, the 171 total counts appear to be rising (brightening) rather than decreasing (dimming), partly because not all pixels in the regions are dimming. We select pixels that show evidently and continuously decreased counts, or dimming, in each bandpass during the eruption, and compare their light curves with the CME height profile. We also find that, in the 171 passband, a significant number of selected dimming pixels in all three regions exhibit a brief brightening before dimming. This will be discussed later. Light curves from two groups of dimming pixels are presented in the following four rows of the figure.

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In the third and fourth rows we show light curves of the total counts of the first group of pixels that exhibit dimming in both the 193 and 171 bandpasses without brightening before dimming. In the bottom two rows we plot light curves of the second group of pixels with dimming in both bandpasses but also significant brightening in the 171 passband before dimming. All these light curves show a rapid decrease of EUV counts in the 193 and 171 bands at or after the onset of fast CME acceleration at around 11:10 UT. Dimming well tracks the CME height for about 20 minutes, and the slope of the dimming growth, namely the rate of the counts decrease, particularly in the 193 bandpass, is comparable with the growth rate of the CME height. When the two groups of the dimming light curves are compared it appears that the dimming slope of the 193 light curve in the second group, which show significant brightening in the 171 band before dimming, is slightly larger than in the first group. Finally, in some regions and at some wavelengths, gradual dimming starts earlier, well before 11:00 UT, consistent with the stack plots in Figure 6.

If coronal dimming results from the decreased density in expanding coronal structures, the dimming light curve at a given location is related to the height of the structure anchored at that location. It is not possible to identify expanding coronal structures anchored at different locations or pixels of dimming; however, we may use the measured CME height as a common reference to examine the growth of dimming in various places. For this purpose we make a routine to select and fit the dimming light curve in each of the three bandpasses (193, 171, and 304) in each dimming pixel as related to the CME height by the following function

$$\begin{eqnarray}&&{\rm{ln}}\left(\displaystyle \frac{{I}_{0}}{I}\right)\sim \alpha {\rm{ln}}\left(\displaystyle \frac{H}{{H}_{0}}\right)\end{eqnarray} \tag{ 1 }$$

where I refers to the EUV counts in a given pixel observed by AIA, and H is the CME height above the solar surface measured in STEREO observations. I₀ and H₀ are values at 11:06 UT when the CME is first visible in STEREO observations. The fitting parameter, α, gives the slope, or the growth rate, of dimming relative to the growth of the CME height, both of which are interpolated to a grid of 1 minute time cadence. For each pixel, fitting is performed in the time range when EUV counts monotonically decreases (i.e., dimming). The period of pre-dimming brightening is excluded from fitting, and obviously the gradual dimming period before the CME is visible is also excluded. In some pixels, post-eruption dimming apparently evolves in two stages, with a rapid first-stage dimming followed by a gradual dimming. In this case, fitting is performed in two stages, and we use α from the first stage.

Figure 8 shows the statistics of the fitting parameter, α, for a few thousand dimming pixels in the three regions. The fitted slope mostly ranges between 0.4 and 1.2, although different regions show small variations. Goodness of fit is measured by ${\chi }^{2}$, and we accept fitting results with ${\chi }^{2}\leqslant 2$. The uncertainty in the fitting parameter, α, is about 0.2. For the LF region (left panel), about 75% of pixels show dimming in 193 Å, 25% of pixels show dimming in 171 Å, and 20% of pixels show dimming in 304 Å, the median of the dimming slope (α) being 0.45, 0.36, and 0.39, respectively. For the RF region (middle panel), about 85%, 36%, and 39% of pixels show dimming in 193 Å, 171 Å, and 304 Å, the median of the slope being 0.5, 0.4, and 0.3 for the three passbands. For the RB region along the flare ribbon (right panel), 73%, 39%, 36% of pixels show dimming in 193, 171, and 304 Å, and the median slope is 0.7, 0.5, and 0.3 for the three bands. Pixels with a larger slope usually exhibit stronger maximum dimming (i.e., lower counts). We also find that the dimming slope in the second group of pixels, which exhibit pre-dimming brightening, is statistically larger than in the first group.

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We further study the spatial distribution of the fitted dimming slope by mapping α in Figure 9. Different colors indicate different α values, which are indicated in the figure. The fitted results for the three wavelengths (193, 171, and 304 Å) are displayed in the figure. We find more dimming pixels in 193 Å than in the other two wavelengths. A large percentage of pixels have a dimming slope between 0.4 and 1.2. A very small number of pixels have $\alpha \geqslant 1.6$. Generally, the slope in most pixels is less than 1.2, both in footpoint regions and along the flare ribbon. Interestingly, the map shows a certain pattern of the slope distribution, which is most evident in the 193 band. The right and left footpoint regions each exhibit a core of a large slope (i.e., deep dimming) shown in cyan and green colors, surrounded by outer layers in yellow and then red, indicating the dimming slope successively decreasing outward. The RB area also shows a regular pattern: from right to left as approaching the left foot along the ribbon, the slope becomes larger, from red (α = 0–0.4) to green (α = 0.8–1.2). Such a spatial pattern is also seen in the other two bandpasses, but it is not as prominent as in the 193 band.

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In summary, we find that the dimming slope mostly ranges between 0.4 and 1.2, and its spatial distribution exhibits deep dimming cores, most evident in the 193 band, around the regions which probably map the CME feet. These results will be discussed in the following section in the context of the CME expansion process.

The fact that dimming curves well track the CME time height profile may indicate that dimming is related to the expansion of the CME. As the coronal structure expands, density decreases, so the emission measure along the line of sight decreases to produce diminished EUV emission. In the following, we test a few CME expansion models to investigate whether these models can explain the observed dimming signatures.

The AIA observed EUV emission in terms of data counts in a given pixel can be approximated by

$$\begin{eqnarray}&&I\approx {n}^{2}R(T)L,\end{eqnarray} \tag{ 2 }$$

where L is the length along the line of sight, n and T are the mean electron density and temperature along L, and R(T) is the temperature response function of the AIA filter.

If the CME expansion is one-dimensional, for mass conservation, the plasma density inside the expanding coronal structure decreases linearly with the increasing L, namely $n\propto {L}^{-1}$. If we assume $L\sim H$, H being the CME height, for an isothermal model where plasma temperature, T, is constant, the observed EUV counts variation is related to the CME height by

$$\begin{eqnarray}&&\displaystyle \frac{I}{{I}_{0}}=\displaystyle \frac{{n}^{2}R(T)H}{{n}_{0}^{2}R(T){H}_{0}}=\displaystyle \frac{{H}_{0}}{H},\end{eqnarray} \tag{ 3 }$$

where n₀, H₀, and I₀ are the initial values at 11:06 UT, when CME is first visible in the STEREO field of view. The CME height, H, is measured above the solar surface.

If the expansion is self-similar, the plasma density decreases with the increasing L by the relation $n\propto {L}^{-3}$. Again, assuming that $L\sim H$, in an isothermal model, we arrive at

$$\begin{eqnarray}&&\displaystyle \frac{I}{{I}_{0}}={\left(\displaystyle \frac{{H}_{0}}{H}\right)}^{5}.\end{eqnarray} \tag{ 4 }$$

If on the other hand, the CME structure undergoes adiabatic expansion, then ${{TV}}^{\gamma -1}=\mathrm{const}.$, V being the plasma volume, with $\gamma =\tfrac{5}{3}$. For the one-dimensional expansion $V\propto L\propto {n}^{-1}$. Therefore,

$$\begin{eqnarray}&&T={T}_{0}{\left(\displaystyle \frac{{L}_{0}}{L}\right)}^{2/3},\end{eqnarray} \tag{ 5 }$$

where L0 and T₀ are the initial values at 11:06 UT. With $L\sim H$, the observed EUV counts change as

$$\begin{eqnarray}&&\displaystyle \frac{I}{{I}_{0}}=\displaystyle \frac{R(T)}{R({T}_{0})}\displaystyle \frac{{H}_{0}}{H}.\end{eqnarray} \tag{ 6 }$$

For an adiabatic self-similar expansion, we have

$$\begin{eqnarray}&&T={T}_{0}{\left(\displaystyle \frac{{L}_{0}}{L}\right)}^{2},\end{eqnarray} \tag{ 7 }$$

and

$$\begin{eqnarray}&&\displaystyle \frac{I}{{I}_{0}}=\displaystyle \frac{R(T)}{R({T}_{0})}{\left(\displaystyle \frac{{H}_{0}}{H}\right)}^{5}.\end{eqnarray} \tag{ 8 }$$

With these models, we estimate the observed dimming evolution ($I/{I}_{0}$) as related to the measured height $H/{H}_{0}$ of the CME. First, applying the filter ratio method to AIA data at 171, 193, and 211 Å, we find the plasma temperature ${T}_{0}=1.4$ MK at 11:06 UT, which is a reasonable active region coronal temperature. In the isothermal model, $T={T}_{0}=1.4$ MK. In the adiabatic model, T varies as described by Equations (5) and (7) for the one-dimensional and self-similar expansion, respectively. As the CME propagates, the derived temperature decreases to ${10}^{5.5}$ K or even lower. Then, from Equations (3), (4), (6) and (8), we calculate the EUV light curves $I/{I}_{0}$ as would be observed in the AIA 171 and 193 passbands for the four different CME expansion models. From the analysis above, if the CME expansion is isothermal, the EUV counts monotonically decrease as the CME expands by ${I}_{0}/I\sim {(H/{H}_{0})}^{\alpha }$, and the power index, α, should be one for the one-dimensional expansion or five for the self-similar expansion in both the 193 and 171 bands. On the other hand, if the CME undergoes an adiabatic expansion as density decreases, the plasma temperature also decreases, so the EUV counts variation becomes a bit complicated. The response function for the 193 band peaks at around 1.5 MK, comparable with T₀, so the adiabatic expansion will reduce the observed 193 counts further, more than in the case of isothermal expansion. Therefore, the predicted slope of the 193 dimming is greater than one in the one-dimensional expansion model and greater than five in the self-similar expansion model. In the 171 passband, the filter response function peaks at 0.8 MK, lower than ${T}_{0}=1.4$ MK, hence the predicted light curve for adiabatic expansion models is more complicated.

Figure 10 shows these modeled light curves in the 193 (left) and 171 (right) bands using Equations (3), (4), (6), and (8), in comparison with some observed light curves in the left footpoint region (top), right footpoint region (middle), and ribbon region (bottom). As discussed above, in the 193 band, the predicted light curves with adiabatic expansion models (blue and red) have a larger slope than isothermal expansion models (cyan and green), and in the 173 band, adiabatic expansion produces apparent brightening in the observed light curves, followed by a sharp dimming with a large dimming slope. As shown in the last section, the observed EUV light curves have the dimming slope, α, mostly ranging between 0.4 and 1.2, whereas the predicted EUV light curves should have slopes greater than one. Therefore, dimming in many pixels do not agree with any of the expansion models. In the figure we chose to plot the light curves of the pixels in dimming cores, which have relatively large slopes. For the three selected regions (LF, RF, RB), the 193 counts variation of these pixels most closely follows the 1D isothermal expansion model. In the 171 band, most of these same pixels appear to be brightened first, similar to the 1D adiabatic curve, and then the subsequent dimming curve again mostly resembles the 1D isothermal expansion model.

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From the fitting result we can exclude the self-similar expansion process for this event, if expansion of the coronal structures anchored at the dimming locations can be approximated by, or linearly scaled with, the measured CME height. The core regions of deep dimming exhibit EUV light curves mostly tracking the 1D isothermal expansion model based on the measured CME height. It is not clear whether the observed initial brightening in the 171 band is caused by adiabatic expansion for the initial period, since light curves in the 193 band of the same pixels during that period do not follow the prediction by the adiabatic expansion model.

We can also estimate the mass and kinetic energy of the erupting CME, assuming that dimming is primarily caused by expansion of CME field lines anchored at these dimming locations. From the filter-ratio analysis mentioned above, we get the pre-eruption mean plasma temperature around 1.4 MK. The pre-eruption mean plasma density is estimated by

$$\begin{eqnarray}&&{n}_{0}={\left[\displaystyle \frac{{I}_{0}}{R({T}_{0}){L}_{0}}\right]}^{\tfrac{1}{2}},\end{eqnarray} \tag{ 9 }$$

and the total mass of the CME is

$$\begin{eqnarray}&&m=\sum ({n}_{0}{\rm{\Delta }}{{Sf}}_{1}{L}_{0}),\end{eqnarray} \tag{ 10 }$$

where ${\rm{\Delta }}S$ is the area of a dimming pixel, and f₁ is a scaling factor larger than one, since the half length of the structure is usually a few times the length scale along the line of sight L₀. We may further write ${L}_{0}\approx {f}_{2}{H}_{0}$, with ${f}_{2}\lt 1$, indicating that L₀ is a fraction of the CME height, H₀. Combining the above equations, the CME mass is given as

$$\begin{eqnarray}&&m\approx {\left[\displaystyle \frac{{I}_{0}}{R({T}_{0})}\right]}^{\tfrac{1}{2}}{f}_{1}\sqrt{{f}_{2}{H}_{0}}\sum {\rm{\Delta }}S.\end{eqnarray} \tag{ 11 }$$

The values of f₁ and f₂ greatly depend on the geometry, including the aspect ratio of the CME structure. Since the CME structure before its eruption is hardly visible in the corona, its unknown geometry presents the largest uncertainty in the mass estimate. If the pre-eruption CME structure is approximated by a semi-circular loop with the axis of the loop in a plane perpendicular to the solar surface, and the major radius of the loop, which is the same as H₀ in this geometry, is four times the minor radius of the loop, then ${f}_{2}\approx 0.5$, and ${f}_{1}\approx \pi$. With this geometry, the mean density is estimated to be ∼1.0 $\quad \times \quad {10}^{9}$ cm⁻³. By summing up all the dimming pixels, the total mass loss is $m\approx 1.1\quad \times$ 10¹⁵ g. The derived maximum CME velocity is about 1100 km s⁻¹, yielding the maximum kinetic energy 6.9 × 10³⁰ erg. If we consider that dimming along the other ribbon in the negative field is obscured by projection effects, the mass and kinetic energy could be increased, but by no more than a factor of two. In comparison, the CME mass and kinetic energy are estimated to be $4.3\times {10}^{15}$ g and $1.5\times {10}^{31}$ erg (using the mean speed of 736 km s⁻¹), respectively, with the LASCO white light coronagraph observations (CDAW). An estimate from the dimming analysis appears to set a lower-limit of the CME mass, which is about one-quarter of the estimate from coronagraph observations. Such an estimate is very rough, subject to the uncertainties in f₁ and f₂ because of the unknown CME geometry; it is therefore only appropriate as an order-of-magnitude estimate.

Finally, we measure the magnetic flux encompassed by the dimming regions. In the entire active region, about 4% pixels exhibit dimming in both the 193 and 171 bands with the longitudinal magnetic flux density greater than ±10 G. The sum of the magnetic flux in these pixels amounts to $3.4\times {10}^{20}$ Mx in positive fields and $1.4\times {10}^{20}$ Mx in negative fields. Magnetic field in dimming pixels in the LF and RB regions is predominantly positive, and the field in the RF region is negative. That the negative flux is smaller than the positive flux is due to lacking dimming signatures along the flare ribbon in negative fields, most likely because of a projection effect. The total flux at the feet of the expanding field lines should be closer to the measured positive flux, which is about 20% of the total reconnection flux measured from flare ribbons.