FIRST MEASUREMENTS OF THE MASS OF CORONAL MASS EJECTIONS FROM THE EUV DIMMING OBSERVED WITH STEREO EUVI A+B SPACECRAFT

We start with the eight CME events analyzed in Colaninno & Vourlidas (2009), which have been detected with the STEREO/A and B spacecraft, once they entered the r>4 R_☉ field of view of the COR2 coronagraphs. We detect CME-associated EUV dimmings with the EUVI telescopes in six out of these eight CME events defined by COR2, preceding the detection in COR2 by several hours. The events 4 and 5 did not exhibit an associated dimming that could reliably be detected by EUVI, and thus are dropped from further analysis. We analyze EUVI data in time intervals of 3–5 hr before appearance in the COR2 instrument. The analyzed EUVI time intervals, the starting times of EUV dimming observed with EUVI, the flare starting times observed with GOES and RHESSI, the initiation times extrapolated from linear height-time plots of COR2, and the CME appearance times in both COR2/A and B fields are listed in Table 1. The two STEREO spacecraft had separation angles in the range of α_sep ≈ 41°–50° during the time period of the 8 selected events between 2007 December and 2008 April.

Table 1. Observational Parameters of Eight Analyzed Flare/CME Events

Events	1	2	3	6	7	8
Date	2007 Dec 4	2007 Dec 31	2008 Jan 2	2008 Mar 25	2008 Apr 5	2008 Apr 26
GOES flare class	...	C8.3	C1	M1.7	A5	B6
NOAA active region	10975 (?)	10980	10980	10989	10987	AR/no number
STEREO separation	4116	4397	4407	4717	4783	4951
EUVI analyzed interval	03:00–07:00	00:00–04:00	06:00–11:00	18:00–20:30	15:00–17:00	12:00–15:00
EUVI/A/195 start time	03:23	00:23	08:04	18:38	15:31	12:41
EUVI/B/195 start time	03:24	00:38	07:26	18:27	15:22	12:58
GOES start time	...	00:37	06:05	18:26	15:30	13:58
RHESSI start time	...	00:01	...	18:44	15:37	13:29
CME initiation COR2/A	04:24	00:19	09:38	18:19	15:31	13:25
CME initiation COR2/B	04:14	00:14	09:12	18:33	15:32	13:31
Appearance COR2/A+B	07:08	01:22	10:22	19:22	16:22	15:07
COR2–EUVI/A/195 delay	+4.3 hr	+0.7 hr	+3.9 hr	+0.8 hr	+1.0 hr	+2.5 hr
Longitude l (NOAA,AR)	115° (?)	−90°	−71°	−81°	116°	...
Longitude l (COR2,mass)	68°	−100°	−64°	−78°	117°	−48°
Longitude l (COR2,model)	68°	−95°	−56°	−83°	116°	−21°
Longitude l (EUVI,stereo)	...	...	−64° ± 4°	...	...	−7° ± 2°
Longitude l (EUVI,model)	100° ± 2°	−94°	−72° ± 6°	−85° ± 1°	107° ± 1°	−9° ± 4°
Latitude b (EUVI,stereo)	...	...	−14° ± 2°	...	...	15° ± 2°
Latitude b (EUVI,model)	−13°	−13° ± 2°	−8° ± 3°	−13° ± 3°	−7° ± 1°	10° ± 2°
Altitude h (EUVI,stereo)	...	...	10 ± 3 Mm	...	...	65 ± 56 Mm
Altitude h (EUVI,limb)	23 ± 1 Mm	48 ± 27 Mm	...	43 ± 1 Mm	60 ± 10 Mm	...

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Because the selection of CME events was done with COR2 at a (projected) distance of more than 4 solar radii away from the Sun, the localization of corresponding EUV dimming events down in the lower corona at altitudes of ≲0.1 solar radius is not always unambiguous, in particular when multiple CMEs or flares are fired in rapid succession. Moreover, the visible area on the Sun is different for each STEREO spacecraft and from Earth (or the Earth-orbiting spacecraft RHESSI and GOES).

The first localization method with COR2 is based on the ratio of CME masses determined from the total brightness images of COR2/A and B, which yields the direction and improved mass of CMEs as described in Colaninno & Vourlidas (2009). The so-obtained longitudinal directions (see Table 1 in Colaninno & Vourlidas 2009) are listed in our Table 1 (COR2,mass). A second method based on COR2 data was carried out by forward modeling of a flux-rope model by Thernisien et al. (2009), which yields longitudinal directions that are also quoted in Table 1 of Colaninno & Vourlidas (2009) and listed in our Table 1 (COR2,model). Note that both methods determine the longitudinal direction 4 solar radii away from the Sun and thus do not necessarily need to coincide with the heliographic longitude of the source region.

Determining the CME source location with EUVI data can be accomplished by measuring the centroid position of the strongest EUV dimming in EUVI/A and B. If the source location is visible by both spacecraft, confined to the range of ≈±70 longitude from central meridian, we can use a stereoscopic 3D reconstruction method. This is only feasible for events 3 and 8. For these events, we determine the source locations with stereoscopic triangulation of the EUV dimming centroids (for a description of the method see Figure 4 in Aschwanden et al. 2008 and Figure 5 in Aschwanden 2009). All other events are partially occulted for at least one of the STEREO spacecraft, and thus stereoscopic triangulation is not a reliable method, because the centroid of CME dimming is shifted to higher altitudes above the occulting edge. In those cases, it is more reliable to use only the position measurement from the spacecraft that observes the source closer to disk center, and to assume a height corresponding to a half thermal density scale height for the centroid of the dimming region, Events 1, 2, 6, and 7 occur near the limb, and we can measure the altitude of the centroid of EUV dimming directly, which indeed cover a similar altitude range of h(EUVI, limb) ≈ 20–60 Mm (see Table 1). Correcting for this EUV altitude, we determine the heliographic longitudes of the events 1, 2, 6, and 7. The obtained longitudes l (EUVI,model) and latitudes b (EUVI,model) (see Table 1) agree with the CME directions derived from COR2 or with the active region positions (NOAA AR) (see Table 1) within a few degrees, which corroborates the correct association of EUVI dimmings with COR2 detections of CMEs.

Regarding the association of the CME source regions with NOAA active regions (NOAA ARs), we identified NOAA-numbered active regions without ambiguity in four events (2, 3, 6, 7), and with a spotless active region that is not numbered by NOAA, but clearly visible in EUV in one other case (8). The remaining case 1 is unclear. There is no active region visible on the disk, and we detect EUV dimming above the limb. If this CME event originates in AR 10975, its position would be l = 120° west seen from Earth, or l_A = 100° west for STEREO/A, and thus occulted for both STEREO/A and B. The COR2 methods infer a position of l = 68° west on the disk, so this case is ambiguous.

One of our goals is to determine the mass of CMEs, which requires electron density measurements in the EUV dimming region as well as in the coronal background, because both densities contribute to EUV emission along any given line of sight and thus need carefully to be modeled in a self-consistent way. A standard method to model the gravitational stratification of the background corona is the multi-hydrostatic model (e.g., see Section 3.3 in Aschwanden 2004), where the EUV emission measure EM(h, T) at altitude h (in the plane of sky perpendicular to the line of sight) and temperature T can be expressed in terms of a (temperature-dependent) base density n_e(h₀, T) and an equivalent column depth z_eq(h, T),

$$\begin{equation} EM(h,T)=\int _{-\infty }^{\infty } n_e^2(h,z,T) dz = n_e^2(h_0,T) \ z_{\rm eq}(h, T). \end{equation} \tag{ 2 }$$

The equivalent column depth z_eq(h, T) can be computed by integrating the exponential barometric density model along the line of sight z,

$$\begin{equation} z_{\rm eq}(h,T)=\int _{z_1}^{z_2} \exp { \left(-{ [\sqrt{(R_\odot +h)^2+z^2}-R_{\odot }] \over \lambda _T} \right)} \ dz, \end{equation} \tag{ 3 }$$

where the integration limits are ±∞ above the limb (h ⩾ 0), or bound by the intersection of the line of sight with the visible solar surface for positions inside the solar disk (−R_☉ ⩽ h ⩽ 0). Approximating the stratified atmosphere with a constant density n₀ over a height range of one thermal scale height λ_T (see Figure 2, bottom panel), the equivalent column depth z_eq(h, T) can be derived from the relations sin(l₀) = (r/R_☉), cos(l₀) = (z/R_☉), sin(l₁) = (r/[R_☉ + λ_T]), cos(l₁) = (z₁/[R_☉ + λ_T]), and z_eq = (z₁ − z₀) (on the disk), or z_eq = 2z₁ (above the limb), respectively,

$$\begin{equation} z_{\rm eq}(h,T) = \left\lbrace \begin{array}{@{}ll} \sqrt{(R_\odot +\lambda _T)^2-r^2}-\sqrt{R_\odot ^2-r^2} & {\rm for}\ z < R_{\odot } \\ 2 \sqrt{(R_\odot +\lambda _T)^2-r^2} & {\rm for}\ z \ge R_{\odot }. \end{array} \right. \end{equation} \tag{ 4 }$$

Using this relation for the column depth, we can then determine the average coronal background density n_B for every pixel with altitude h or the radial distance r = R_☉ + h from the Sun center, for an EUV filter sensitive at a mean temperature of T (using Equation (2)),

$$\begin{equation} n_B = \sqrt{ {EM(h,\; T) \over z_{\rm eq}(h,T) }} = \sqrt{ {I(h,T) \over z_{\rm eq}(h,T)\ R(T) } {10^{44}\ {\rm cm}^{-3} \over \Delta x^2} }, \end{equation} \tag{ 5 }$$

where I(h, T) (in units of DN s⁻¹) is the observed EUV intensity, R(T) represents the average response function of the EUV filter, and Δx² is the pixel area. The peak response functions of EUVI/A are R₁₇₁ = 3632, R₁₉₅ = 1444, R₂₈₄ = 158 DN s⁻¹ (for an emission measure EM = 10⁴⁴ cm⁻³ pixel⁻¹), at peak temperatures of T=0.90, 1.39, and 1.74 MK, respectively, while the average responses are a factor of R_avg/R_peak ≈ 0.73 lower, if the average of the response function is taken over the FWHM. The response functions for EUVI/B are very similar (Wuelser et al. 2004). The density value n_B corresponds to the average density in the approximation of a constant electron density extending over one vertical density scale height (Figure 2, bottom panel), or to the coronal base density in an exponential barometric model (because the mean of an exponential function is exactly the e-folding value of the exponential function).

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We list the so-obtained coronal background densities measured for all eight events for each of the three EUV wavelength filters (171, 195, 284 Å) and for both spacecraft EUVI/A and B in Table 2. Although they sample the corona at different places, on the disk, at the limb and above the limb, though mostly in equatorial latitudes, they come out very similar, with an average and standard deviation of 〈n_B〉 = (3.3 ± 0.6) × 10⁸ cm⁻³. Sorting the densities for each wavelength range, we find

$$\begin{equation} \begin{array}{l} n_B=(3.8\pm 0.5) \times 10^8\ {\rm cm}^{-3}\ (171\ {\rm \AA}) \\ n_B=(2.7\pm 0.3) \times 10^8\ {\rm cm}^{-3}\ (195\ {\rm \AA}) \\ n_B=(3.3\pm 0.3) \times 10^8\ {\rm cm}^{-3}\ (284\ {\rm \AA}) \\ n_B=(3.3\pm 0.6) \times 10^8\ {\rm cm}^{-3}\ (171+195+284\ {\rm \AA}). \end{array} \end{equation} \tag{ 6 }$$

Note that the column depth varies from about z_eq(h = −R_☉, T = 1.0 MK) ≈0.03 R_☉ at the disk center to z_eq(h = 0, T = 1.0 MK) ≈0.3 R_☉ at the limb, and doubles about for T = 2.0 MK (see Figure 2 top panel). Thus, the intensity, which is proportional to the column depth, varies by a factor of ≳20, while the deconvolved density varies less than a factor of 0.2, which corroborates the robustness of our coronal background deconvolution model.

We attempt a mass determination of a CME by measuring the local EUV brightness decrease at the launch site of the CME. Since the mass is essentially proportional to the average proton density and volume, i.e.,

$$\begin{equation} m_{\rm CME} = m_p n_e V_{\rm CME}, \end{equation} \tag{ 7 }$$

where the proton density n_p is generally set equal to the electron density n_e in the so-called coronal approximation of a fully ionized plasma, i.e., n_e ≈ n_p, we have to model the volume V_CME of a CME and the average density n_e at the same time. Our concept is to estimate the volume of the initial CME from the volume of the EUV dimming region, V_D ≈ V_CME(t = t₁), where a deficit of mass occurs after the CME takes off (at t>t₁). We parameterize the pre-CME volume, which is identical with the post-CME dimming volume, by a cylindrical geometry with vertical axis, where the circular footpoint area is A_D = (π/4)w²_D, with w_D = R_☉Δφ_D being the diameter, Δφ_D the angular extent of the dimming region (i.e., CME) at the solar surface, while the vertical extent is approximated by one density scale height λ_T:

$$\begin{equation} V_D = A_D \lambda _T = {\pi \over 4} w_D^2 \lambda _T = {\pi \over 4}\;R_{\odot }^2 \Delta \varphi _D^2 \lambda _T, \end{equation} \tag{ 8 }$$

where the hydrostatic scale height λ_T depends on the electron temperature T_e as

$$\begin{equation} \lambda _T = {2 k_{\rm B} T_e \over \mu m_{\rm H} g_{\odot }} \approx 47 \ \left({T_e \over 1\ {\rm MK}} \right) \ {\rm (Mm)}, \end{equation} \tag{ 9 }$$

with k_B being the Boltzmann constant, m_H the hydrogen mass, and μ ≈ 1.27 the mean molecular weight for a H:He=1:10 atmosphere. Thus, the observables we need to measure is the angular extent Δφ_D of the EUV dimming region and the decrease of the electron density n_e(t) in the dimming region, compared with the pre-CME background density.

The footpoint area A_D of the EUV dimming region is modeled with a circular geometry (on the solar surface), which generally appears as an elliptical shape in projection (in the image plane) and degenerates to a curved line segment at the limb. The unforeshortened angular extent φ_D of the dimming area has to be measured in the azimuthal direction, which corresponds to the major axis in the elliptical projection (Figure 3). The positions and angular extents of the detected EUV dimming regions measured this way are shown in Figure 4. The typical width of dimming regions is Δφ_D = 17° ± 5° (Table 2), corresponding to w_D = R_☉Δφ_D ≈ 200 ± 50 Mm (between 1/5 and 1/3 solar radius).

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The technical procedure and related difficulties to measure the azimuthal width of EUV dimming regions are illustrated in Figure 5. Generally, the EUV dimming occurs in an active region where the average local density or EUV intensity I(r, φ) is enhanced above the surrounding coronal background I_B, which we model by fitting a Gaussian function (with Gaussian width σ_A at time t₁) before the dimming onset,

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$$\begin{equation} I(r_0, \varphi, t_1) = I_B(r_0) + I_{A}(r_0) \exp {\left[{-}{(\varphi - \varphi _0)^2 \over 2 \sigma _{A}^2}\right] }, \end{equation} \tag{ 10 }$$

with r₀ being the radial distance of the centroid of an active region from the Sun center, as depicted in Figure 5 (top left panel and insert below). After the launch of a CME, a large fraction of the active region exhibits EUV dimming, but there occur also new postflare loops that are very bright in EUV (Figure 5, top right panel), which cannot easily be eliminated in difference images (Figure 5, bottom left panel). Our strategy is to reconstruct a lower envelope to the azimuthal flux profile of the difference image before (at time t₁) and after (at time t₂) the CME launch

$$\begin{equation} I_{\rm dim}(r, \varphi, t_2) = I(r, \varphi, t_2)-I(r, \varphi,t_1). \end{equation} \tag{ 11 }$$

Note that the background flux I_B(r) drops out in the difference profile I_dim(r, φ, t). We reconstruct a lower envelope in the azimuthal direction at the dimmest position in the difference images, in order to filter out the bright EUV emission of postflare loops, as the simulated example demonstrates (dashed curve in Figure 5 bottom left). The dimming profile I_dim(φ, t₂) at time t₂ is reconstructed by fitting a Gaussian function through the dimmest point in a smoothed difference image I_dim(r, φ, t₂), which is a function that has only two free parameters (I_D and σ_D at time t₂),

$$\begin{equation} I_{\rm dim}(\varphi) = -I_D \exp {\left[-{(\varphi - \varphi _0)^2 \over 2 \sigma _D^2}\right] }, \end{equation} \tag{ 12 }$$

as illustrated in Figure 5 (bottom right panel and insert below). We correct also for the spatial offset between the brightest pre-CME location and the dimmest post-CME position according to the two-dimensional (2D) brightness distribution I(r, φ) defined in Equation (10). We find that the full width of the EUV dimming region is nearly identical to the full width of the active region (i.e., σ_D ≈ σ_A) in cases without interfering postflare loops, and thus we can use it also as a robust measure of the width of the EUV dimming region, rather than fitting the ragged dimming profile I_dim(φ) that is often contaminated by bright flare loops. Otherwise, the width σ_D of the dimming region would be significantly underestimated when bright postflare loops are present. This procedure efficiently filters out the contaminating EUV-bright flare and postflare loops, as long there exist still some dark locations in the dimming region that are not outshone by flare loops. A physical limit for the maximum dimming flux is the maximum pre-CME EUV brightness, i.e., I_D ⩽ (I_A + I_B) (see also definitions of I_A, I_B, and I_D in profiles shown in Figure 5).

An example of an EUV dimming measurement is shown in Figures 6 and 7. A time sequence of analyzed EUV difference images is shown in Figure 6, for event 2. The initial image of the pre-CME flux at 195 Å is shown in Figure 7 (top left panel), with the azimuthal flux profile of the active region fitted by a Gaussian (Equation (10)), yielding the flux values I_A, I_B, and width σ_A (second left panel). The final difference image (Equation (11)) is shown in Figure 7 (middle left panel), with the lower envelope fitted by a Gaussian function with the same width σ_D = σ_A (Figure 7, bottom left panel). The profile of the dimming flux at a central position of the dimming region is indicated with a hatched area (Figures 7–9), which also contains contamination (of the dimming flux) from bright postflare loop EUV emission. The evolution of the dimming flux is also shown for all 24 images separately (Figure 7, middle column), or as a function of time, I_d(t) (Figure 7 top right). We see that the final dimming flux q_D(t) = I_d(t)/(I_A + I_B) approaches a value of q_D ≈ 0.63, so the EUV brightness drops by more than half of the initial pre-CME brightness in the active region. The corresponding plots of the same event for both spacecraft and all wavelengths shown in Figure 8 exhibit little flare contamination for spacecraft EUVI/A 171 and 195 Å, for which the primary flare emission was occulted, but much stronger contamination for EUVI/B, for which the postflare loops were visible on the disk. In Figure 9, we show the corresponding plots for all other analyzed CME events (1, 3, 6, 7, and 8) in the same format as shown for event 2 in Figure 8, for the EUVI/A spacecraft and the 195 Å wavelength. A sensitive test of the robustness of our dimming reconstruction technique will be the comparison of obtained CME masses presented in the following.

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In summary, we developed a robust algorithm that measures the EUV peak flux I_A, coronal background I_B, and geometric width σ_A of the pre-CME active region at time t₁, as well as the EUV flux I_D (with width σ_D ≈ σ_A) of the dimming region at times after the EUV dimming starts (when the CME takes off). The values of the fluxes I_A, I_B, I_D, dimming ratios q_D = I_D/(I_A + I_B) ⩽ 1 are listed in Table 2 for each of the six detected events, both EUVI/A and B spacecraft, and all three wavelengths (171, 195, and 284 Å). These observables will be the basis for the calculation of the CME masses described in the next section.

We determine now the electron density n_e and CME mass in the EUV dimming region, based on the observables of I_A, I_B, and I_D, with the dimming region defined by the geometry of a 2D Gaussian function with Gaussian width σ_D (Figure 5). The FWHM of the Gaussian flux distribution is defined by $\mbox{FWHM} = 2 \sqrt{(2 \ln 2)} \sigma _D \approx 2.35 \sigma _D$. In addition, since the EUV flux I(φ) is proportional to the squared electron density, i.e., I ∝ n²_e (e.g., Equation (2)), the FWHM of the density distribution is another factor $\sqrt{2}$ larger, so the relevant full width of the CME mass is

$$\begin{equation} w_D = R_{\odot } \Delta \varphi _D = 2 \sqrt{(4 \ln 2)} \ \sigma _D \approx 3.33 \ \sigma _D. \end{equation} \tag{ 13 }$$

This yields the volume of the dimming region V_D or the CME volume V_CME before CME launch according to Equation (8). In order to obtain the CME mass m_CME (Equation (7)), we need to determine the electron density n_e in the active region that covers the EUV dimming volume V_D.

The total EUV flux of an active region is composed of (1) the emission measure of the active region (with density n_A) and (2) the emission measure of the coronal foreground and background along the same line of sight (with density n_B). Usually the background density n_B is measured from the background level outside of the active region and the background-subtracted excess flux I_A of the active region is dependent on the background density n_B as

$$\begin{equation} n_A= \sqrt{ n_B^2 + {I_A \over \Delta z R_T } {10^{44}\ {\rm cm}^{-3} \over \Delta x^2} }, \end{equation} \tag{ 14 }$$

where Δz is the column depth of the active region, Δx² is the pixel area, and R_T is the instrumental response function per pixel area.

For the determination of the average dimming mass in the same volume of the active region, we can now use the proportionality of the dimming flux (or the emission measure) to the square of the electron density, as it generally holds for optically thin EUV emission,

$$\begin{equation} {n_d(t) \over n_A} = \sqrt{ {I_d(t) \over I_A }}, \end{equation} \tag{ 15 }$$

to obtain the mass loss m_d(t) associated with the EUV dimming. Note that the initial density associated with EUV dimming is zero before CME launch, i.e., n_d(t = t₀) = 0 and I_d(t = t₀) = 0, while the dimming-associated density n_d(t = t₂) = n_D approaches the maximum value at the end of the dimming, when the dimming function approaches the value I_d(t) = I_D. The mass loss m_d(t) that makes up the CME mass can then be expressed as a function of time t and depends on the observables I_d(t), I_A, n_A, and w_D ≈ w_A only

$$\begin{equation} m_d(t,T) = m_p n_d(t) V_D = m_p n_A \sqrt{ {I_d(t) \over I_A} } \ {\pi \over 4} w_D^2 \lambda _T. \end{equation} \tag{ 16 }$$

Note that this expression contains only the CME mass detected with a particular EUV filter (with temperature T), while the total CME mass needs to be synthesized from multiple temperature filters. The so-determined electron densities n_A of the active region (pre-CME) volumes and dimming masses m_D(t = t₂, T) are listed in Table 2 for each event, spacecraft, and EUV filter temperature T ≈ 1.0, 1.5, 2.0 MK separately. The active region densities have a mean of n_A = (5.0 ±  3.8) × 10⁸ cm⁻³ (per filter) and are only slightly higher than the average densities of the coronal background, i.e., n_B = (3.3 ± 0.6) × 10⁸ cm⁻³. For the dimming masses, we find an average of m_D ≈ (1.5 ± 1.1) × 10¹⁵ g per EUV filter (see averages at bottom of Table 2).

In Figure 10, we plot the dimming masses m_D(t = t₂, T) that have been detected at the end time (t = t₂) of the analyzed time interval in each of the three EUV filters, which have the following FWHM temperature ranges: T₁₇₁ = 0.51–1.25 MK for the 171 Å filter, T₁₉₅ = 1.05–1.90 MK for the 195 Å filter, and T₂₈₄ = 1.54–2.87 MK for the 284 Å filter. Since the three temperature ranges are slightly overlapping, we have to normalize the dimming masses by the temperature interval ΔT in each filter in order to obtain a differential emission measure-type mass distribution Δm_D(t, T_F)/ΔT_F. We fit then a Gaussian curve that has the same integrated mass in each filter temperature range and integrate the differential mass distribution to obtain the total mass of the dimming volume or CME

$$\begin{eqnarray} m_{\rm CME}(t=t_2) &=& \int _{T_1}^{T_2}\left({dm_D(t,T) \over dT}\right) dT\nonumber\\ &=& \int _{T_1}^{T_2} {\Delta m_{D} \over \Delta T_{F}}\,\exp {\left(-{(T-T_{0})^2 \over 2 \sigma _T^2}\right)} dT, \end{eqnarray} \tag{ 17 }$$

where T₁ = 0.51 MK and T₂ = 2.87 MK are the lower and upper bounds of all three EUVI filters combined together. Note that the peak temperature of the Gaussian fit is typically around T₀ ≈ 1.5 MK, which proves that most of the CME mass is detected in the 195 Å filter, where also CME-associated EIT waves are best visible. The numerical values of the so-obtained CME masses m_CME are listed in Figure 10 and in Table 3, for both EUVI/A and B spacecraft separately. The values from spacecraft A and B are consistent with an average ratio of m_A/m_B ≈ (1.3 ± 0.6).

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In Figure 11, we compare our results of the CME masses measured from EUVI with those of COR2, given in Colaninno & Vourlidas (2009). The diamonds mark the improved CME masses derived from the mass ratio of COR2/A and B, while the horizontal bars indicate the mass difference measured between COR2/A and B. For the determination of CME masses with EUVI it is not clear a priori how the results from EUVI/A and B should be weighted. On one side, we expect that the less occulted spacecraft has a fuller view on the CME and thus sees the EUV dimming more completely, but on the other side slight occultation helps to block out the unwanted contaminating bright EUV emission from flare loops, which makes the reconstruction of the EUV dimming volume less contaminated and more reliable. We thus give equal weight to both spacecraft and average the CME masses measured by A and B, indicating the difference measured with A and B with the vertical error bars in Figure 11. The COR2 and EUVI measurements correlate well, with a mean and standard deviation of m_EUVI/m_COR2 = 1.1 ± 0.3, so they agree typically within ±30%.

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For events 4 and 5, we detect no reliable EUV dimming, which could be because of either complete occultation or absence of dimming. The EUV dimming levels we measured for these two events are comparable with CME-unrelated dimmings, such as cooling of bright points or time variability of other small-scale sources. We also performed a null test by running our automated EUV dimming code at a random location near the solar north pole (where no CME is expected) and measured a residual mass equivalent of m_res ≈ 0.6 × 10¹⁵ g (event 0 in Figure 11 bottom left). Thus, we consider this limit of ≲10¹⁵ g as an empirical confusion limit for CME detection on the disk with our automated code. Above the limb, where chromospheric EUV emission is absent, our method can detect much fainter dimming levels.

The differences in CME masses determined from EUVI/A and B can arise from a number of model assumptions, such as the cylindrical 3D geometry, the circular footpoint area, the hydrostatic scale height, the temperature derivation from the peak of the EUV response function, but also from perspective effects from different spacecraft viewing angles, such as different degrees of occultation of dimming regions as well as postflare loops. While it is difficult (and probably unreliable) to quantify uncertainties for each model parameter formally, the obtained difference in the final result of CME masses between EUVI/A and B provides a reliable (empirical) error for a single-spacecraft measurement, which constitutes a smaller absolute error for the combined two-spacecraft measurement.

We show the time evolution of the EUV dimming 1 − I_d(t)/(I_A + I_B) in Figure 12, normalized by maximum pre-CME flux (I_A + I_B). In order to characterize the dimming time, we fit a semi-Gaussian curve to the time evolution, with I_D representing the maximum dimming flux I_D = I_d(t ≫ t₀),

$$\begin{equation} I_d(t) \approx \left\lbrace \begin{array}{@{}ll} 0& {\rm for}\ t < t_1 \\ I_D \ \left[ 1 - \exp {\left(-{(t-t_0)^2 \over 2 t_D^2}\right)} \right] \ & {\rm for}\ t \ge t_0 \\ I_D& {\rm for}\ t \gg t_0, \end{array} \right. \, \end{equation} \tag{ 18 }$$

which yields an objective measure of the dimming starting time t₀ (within the definitions of our model), the EUV dimming timescale t_D (when the dimming flux drops from unity to the level of exp(−1) ≈ 0.61), and the final dimming level I_D. The statistics of all dimming times yield a mean and standard deviation of t_D = 1.3 ± 1.4 hr (see bottom of Table 2). The dimming starting times often agree for both spacecraft within a fraction of the dimming time t_D.

The average dimming level at the end of the analyzed time interval is q_D = 1 − I(t₂)/(I_A + I_B) = 0.47 ± 0.37, so the brightness dropped to a factor of ≈1/2, which corresponds to a density drop of $\approx 1/\sqrt{2} \approx 0.7$ (Equation (15)). We have to be aware, however, that this refers to the pre-CME brightness level of the active region. Since the pre-CME EUV emission of an active region has an average excess brightness of I_A ≈ 200 ± 210 DN s⁻¹, which is comparable with the average background level I_B ≈ 170 ± 160 DN s⁻¹ (see bottom of Table 2), a dimming fraction of 50% in I_D/(I_A + I_B) essentially eliminates all the excess emission of an active region. This is particularly true for limb events, which are most of the events (except event 8). This is a surprising new fact that has not been appreciated or quantitatively measured before. In other words, virtually all plasmas in an active region are evacuated away from the Sun, except for new flare loops that are created after the launch of the CME and gradually fill in the new vacuum. Consequently, we would expect completely dark dimming regions for a CME launch at the disk center, if the CME evacuation channel is aligned with the line of sight. However, inspecting Figures 12 and 2, we find no clear trend whether the final dimming level or dimming time depends on the viewing angle (different spacecraft), wavelength, or location (different events).

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The CME mass m_d(t) scales proportionally to the dimming-associated density (Equation (16)), which allows us to quantify the time evolution of the mass loss m_d(t) as a function of time. We show this observed mass loss evolution in Figure 13 for the major five events from spacecraft EUVI/A, 171 Å (which has the highest cadence), scaled to the total mass loss detected in all EUV filters). According to the semi-Gaussian fit of the dimming function I_d(t) (Equation (18)) and the mass–density relationship (Equation (16)), we can express the mass loss with the analytical approximation,

$$\begin{equation} m_d(t) \approx m_{\rm CME} \left[ 1 - \exp {\left(-{(t-t_0)^2 \over 2 t_D^2}\right)} \right]^{1/2}. \end{equation} \tag{ 19 }$$

The slopes of the mass loss function dm_d(t)/dt (see Figure 13) vary more than an order of magnitude between different CMEs. The CME with the fastest mass loss is associated with the largest flare (6, GOES M1.7 class, 2008 March 25), but the mass loss rate does not correlate with the flare magnitude for the other events.

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The time evolution of the dimming mass m_d(t) is monotonically increasing as more CME mass leaves the corona. This is the consequence of the adiabatic expansion of the CME bubble, which is a dynamically expanding magnetic field structure that confines the enclosed plasma. We can therefore relate the density evolution n(t) = n₀ − n_d(t) in the expanding volume V_D(T) (of the dimming region) to the pre-CME density n₀ and volume V₀ according to mass conservation inside the CME bubble,

$$\begin{equation} m_{\rm CME} = m_p n_0 V_0 = m_p [n_0-n_d(t)] V_D(t), \, \end{equation} \tag{ 20 }$$

which implies a reciprocal relationship between density and volume. For the geometry of the CME bubble, we might use a 3D shape that expands in a self-similar way, so that the volume scales with the third power of its vertical extent h(t), which can be the geometry of a spherical bubble, an ice cone, or a flux rope,

$$\begin{equation} V_D(t) = V_0 \left({h(t) \over h_0}\right)^3. \end{equation} \tag{ 21 }$$

The self-similar expansion yields the following time evolution for the expanding height h(t) (using Equations (20) and (21)):

$$\begin{equation} h(t) = h_0 \left({V_D(t) \over V_0} \right)^{1/3} = h_0 \left({n_0 \over n_0-n_d(t)} \right)^{1/3}. \end{equation} \tag{ 22 }$$

Since the electron density scales with the square root of the intensity for optically thin EUV emission (Equation (15)), we expect the following evolution as a function of time (using the approximation of Equation (18)),

$$\begin{equation} h(t)=h_0 \left({I_D \over I_D-I_d(t)} \right)^{1/6} \approx h_0 \left(\exp { \left[{(t-t_0)^2 \over 12 t_D^2}\right]} \right). \end{equation} \tag{ 23 }$$

From this model, we can also characterize the CME front speed v(t):

$$\begin{equation} v(t) = {dh(t) \over dt} \approx {h_0 (t-t_0) \over 6 \ t_D^2} \exp { \left[{(t-t_0)^2 \over 12 t_D^2}\right]}. \end{equation} \tag{ 24 }$$

Based on the expression of Equation (23), we can predict the time delay Δt_COR2 between the CME arrival at COR2 and the CME launch time t₀ at EUVI,

$$\begin{equation} \Delta t_{\rm COR2} = t_D \sqrt{ 12 \ \ln {\left({h_{\rm COR2} \over h_0}\right)}}, \end{equation} \tag{ 25 }$$

where the radial distance is h_COR2 ≈ 4 solar radii (for a launch site near the disk center, or h_COR2 ≈ 3 solar radii for a launch near the limb), and the initial height is the mean height in a gravitationally stratified atmosphere, i.e., a thermal scale height, h₀ ≈ λ_T.

The measured dimming times t_D are listed for each event, spacecraft, and wavelength in Table 2. Inspecting the values of t_D and the fitted curves in Figure 12, we notice some discrepancies between the values obtained from different spacecraft, which ideally should be similar. There are several reasons for inconsistencies that affect the results differently for the two spacecraft views: (1) bright EUV emission from postflare loops can significantly hamper the reconstruction of the EUV dimming curve, which tends to lead to overestimates of the dimming time; (2) occulted emission underestimates the dimming mass; or (3) vertical gradients in the CME mass loss leads to stronger dimming for hotter plasma (with larger density scale heights), etc. These effects need to be investigated in more detail and will be pursued in a future study. At present, we recommend to use the shortest dimming time among the values determined from different views (spacecraft) and wavelengths for each event.

As an example, we test event 6, the CME event of 2008 March 25, 18:40 UT, which shows a well-defined self-similar expansion of a spherical bubble and has been analyzed in various studies (e.g., Aschwanden 2009; Zhang 2008). From our semi-Gaussian fits to the EUV dimming profiles, we found dimming times of t_D = 0.11 hr for EUVI/A 195 Å (discarding the shorter dimming time of t_D = 0.05 hr obtained in 171 Å because of partial occultation for EUVI/A), and the same value t_D = 0.11 hr for EUVI/B 171 Å (which is the shortest among the different wavelengths). Using this dimming time values and the exponential height-time model (Equation (23)), we predict time delays of Δt = 0.70 ± 0.02 hr (after a start time of 18:38 UT in EUVI/A and 18:27 UT in EUVI/B) for the arrival at COR2 after a travel distance of 3 solar radii (Figure 14). COR2 reports an earliest detection of the CME in both COR2/A+B at 19:22 UT, which corresponds to a delay of Δt = 0.82 ± 0.09 hr, which is consistent within ≈10%. Alternatively, the self-similar expansion of the CME bubble was measured by fitting a spherical geometry to the periphery of the CME bubble and fitted with a quadratic height dependence (Aschwanden 2009),

$$\begin{equation} h(t) = h_0 + v_0 (t-t_0) + \case{1}{ 2} a (t-t_0)^2 \end{equation} \tag{ 26 }$$

with best-fit values of h₀ ≈ 40 Mm, v₀ ≈ 0, and a ≈ 0.4 km s⁻¹. We plot this height-time fit in Figure 14 also, which yields a prediction of a time delay of Δt = 0.89 hr at COR2, which is also consistent with the COR2 detection time within ≈10%. Comparing the two methods, we notice a different functional dependence, which implies that the approximations must break down at some distance. The EUV dimming could only be constrained in the lowest altitudes in the corona, while the spherical expansion can be detected out to the edge of the EUV field of view (1.6 solar radii) and further (using the lateral expansion). We envision therefore that a combined measurement method for the EUV dimming and CME expansion could lead to a more self-consistent model and provides the missing link between the CME origin in the lower corona and CME propagation in the heliosphere as observed by coronagraphs (which have to block out the lower corona with an occulting disk).

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This is one of the first systematic studies that quantitatively compares CME observations in EUV and white light. There are a number of fundamental differences between the two wavelengths. First, white-light observations record photospheric photons that get scattered in the corona and heliosphere (i.e., Thomson scattering), and thus is sensitive to all electrons independent of their temperature. Emission in EUV wavelengths, in contrast, is mostly produced by thermal bremsstrahlung (free–free emission) of energized electrons with ambient ions, as well as by line emission from free-bound transitions, excitations, and ionizations of atoms. Since EUV filters have a narrow-band response function, each filter is sensitive to a particular temperature range. For the three coronal EUV filters of STEREO/EUVI, this temperature range is approximately T ≈ 0.5–2.9 MK, which covers the bulk (i.e., the peak of the distribution) of the coronal mass in active regions, the quiet Sun, and coronal holes, and thus we expect that they also catch the bulk of the low coronal component of CME masses. Therefore, this comparison of CME masses derived from EUV versus white light represents an important test whether this assumption is true. We find indeed a very good correspondence between the two methods here, with a ratio of m_EUVI/m_COR2 = 1.1 ± 0.3, which corroborates the self-consistency of both methods. It is conceivable that we do not recover identical masses with both methods, if for instance CMEs contain a significant fraction of cold chromospheric mass (i.e., prominences), or if some CME mass that gets expelled from the lower corona would fall back at altitudes r < 4 solar radii before it is detected with COR2. Such coronal inflows in the trailing wakes of CMEs were indeed detected before (e.g., Wang et al. 1999; Sheeley & Wang 2002), but apparently they do not carry a significant mass fraction of the CME.

The limited temperature range of EUV filters apparently does not truncate the measured CME masses, although we are only sensitive in the temperature range of T ≈ 0.5–2.9 MK. Our three-point CME mass distribution (Figure 10) indeed suggests that the peak of the CME mass distribution occurs around T ≈ 1.5 MK, which renders the 195 Å wavelength filter to the most important sensor of CME masses. It was already noticed before that EIT waves, which are a side product of CMEs, were seen with the best contrast in the 195 Å filter (e.g., Wills-Davey & Thompson 1999; Delannee 2000). Our analysis adds the same preference for the 195 Å filter in observing and detecting EUV dimming and associated CMEs.

Interesting consequences arise also from the non-cospatiality of the detection of EUV dimming and associated CMEs in the lower corona (≲0.1 solar radius) and the white-light coronagraph detection with COR2 (at ⩾4 solar radii). Since we expect that most of the CME mass should propagate outward, and therefore will show up after some time in the coronagraphs, we should expect that every EUV dimming event should lead to a CME detection with COR2, unless they fall below the sensitivity threshold. Currently, we find a lower mass limit of m_CME ≈ 1.0 × 10¹⁵ g from the detection of EUV dimming, while detections of lower values appear to be related to cooling bright points or cooling loop structures, rather than leaving CMEs. Vice versa, we do not expect a dimming signal in EUV for every COR2 detection of a CME, because some of the CMEs may originate high in the corona where the EUV intensity is very low or they might originate on the backside of the Sun, where EUV emission is obscured or occulted (near the limb), unless the STEREO spacecraft cover some fraction of the Sun's backside. For our observation period, the two STEREO spacecraft cover already approximately a quarter of the Sun's backside, and thus we expect an EUVI detection rate of five out of eight, as indeed observed. Although the COR2 observations suggest that all eight selected CMEs originate on the frontside of the Sun or near the limb, four cases are partially occulted for at least one of the spacecraft, while one of the localization is dubious, suggesting a high altitude origin for the CME. In any case, the complementarity of EUVI and COR2 observations provides important information on the source region of CMEs.

The first measurements of the CME masses using EUV observations of coronal dimmings were reported by Harrison & Lyons (2000). A small CME observed with LASCO in white light with a mass of m_CME = (5 ± 1) × 10¹³ g was spectroscopically observed with SOHO/CDS also. The authors determined from the Si X 356 Å/347 Å ratio a density of n_e = 10⁹ cm⁻³ in the center of the dimming region. From a rough estimate of the projected dimming area in Mg IX 368 Å, the authors arrive at a mass estimate of m_CME = 3.3 × 10¹³ g, which amounts to 70% of the white-light estimate. Comparing with our method presented here, the EUV-based mass estimate could further be improved by quantifying the unprojected CME footpoint area and the vertical density scale height to obtain a more accurate estimate of the 3D dimming volume (Equation (8)), as well as modeling of the fore/background density along a line of sight (Equation (5)) in order to obtain an uncontaminated density in the dimming region.

In a follow-up study by Harrison et al. (2003), a total of five CME events were analyzed based on LASCO and SOHO/CDS observations, including the event analyzed in Harrison & Lyons (2000). The CME was determined from the EUV dimming within a box that encompasses the darkest dimming area, using two different methods to extrapolate the mass loss over a comprehensive temperature range: (a) using a canonical DEM curve for active regions specified in Raymond & Doyle (1981), and (b) the density derived from the Si X 356 Å/347 Å line ratio. The CME masses derived from white light and EUV have ratios of m_CME/m_EUV = 1.2, 0.3, 4.7, 0.01, 0.7 with the DEM method, and m_CME/m_EUV = 0.4, 0.07, 1.0, 0.004, 0.3 with the line-ratio method. The biggest discrepancy was found for the fourth event, where we suspect that the dimming volume was largely overestimated according to the box chosen in their Figure 7. If the box is overestimated by a factor of L = 2, the resulting volume and CME mass would be overestimated by a factor of V ≈ L³ = 8. Also the contamination from postflare loops, which causes bright EUV emission in the EUV dimming region, may enter large uncertainties in electron densities derived from line ratios averaged over a box that contains both dimming and flare loop emission. Three-dimensional volume modeling of the EUV dimming region and elimination of flare loops are thus essential for improving the accuracy of CME mass estimates based on EUV dimming. In our study, we modeled these effects in detail and arrived at much smaller differences between white light and EUV masses, i.e., m_COR2/m_EUVI = 1.1 ± 0.3. In addition, we benefit from the redundancy of dual stereoscopic imaging observations here, while the observations of Harrison et al. (2003) were based on a spectroscopic single-spacecraft instrument.

A CME mass based on EUV dimming was also derived in Zhukov & Auchere (2004), who got a fair agreement with the white-light CME mass. The authors measure the area A of the dimming region and assume a volume of V = Aλ_T extending over a thermal scale height, similar to our method (Equation (8)). The authors perform some DEM modeling based on three EIT filters (similar to our method), but the three-filter EIT data set was taken three hours before the CME event, while all our three-filter EUVI data sets are strictly simultaneous with the CME and dimming events (thanks to the higher cadence of multi-filter observations of STEREO/EUVI).

Throughout this paper, we made the tacit assumption that a detected EUV dimming is identical to the coronal mass loss of a CME, and vice versa we expect that every detected CME should also cause an EUV dimming, unless the CME originates in the upper corona (where we have little EUV emission because of the gravitational stratification). The latter case, however, would imply very low masses compared with a CME that originates at the base of the corona, i.e., ≈30% at one thermal scale height, or ≈10% at two thermal scale heights. In fact, the detection probability should equally drop for both EUV and white-light coronagraphs with altitude, because the detection threshold scales with the total mass of CMEs in both cases.

A number of studies of coronal dimming as a means for identifying CME source regions have been undertaken, focusing on transient coronal holes caused by filament eruptions (Rust 1983; Watanabe et al. 1992), EUV dimming at CME onsets (Harrison 1997; Aschwanden et al. 1999), soft X-ray dimming after CMEs (Sterling & Hudson 1997), soft X-ray dimming after a prominence eruption (Gopalswamy & Hanaoka 1998), or simultaneous dimming in soft X-rays and EUV during CME launches (Zarro et al. 1999; Harrison & Lyons 2000; Harrison et al. 2003). All these studies support the conclusion that dimmings in the corona (either detected in EUV, soft X-rays, or both) are unmistakable signatures of CME launches, and thus can be used vice versa to identify both phenomena. A statistical study on the simultaneous detection of EUV dimmings and CMEs has recently been performed by Bewsher et al. (2008). This study based on SOHO/CDS and LASCO data confirms a 55% association rate of dimming events with CMEs, and vice versa a 84% association rate of CMEs with dimming events. Some of the non-associated events may be caused by occultation, CME detection sensitivity, or incomplete temperature coverage in EUV and soft X-rays. Their detection rate is consistent with ours, since we detect EUV dimming in six out of the eight cases (75%). Perhaps this CME-dimming association rate will climb up to 100% once the STEREO spacecraft reaches a separation of 180° and cover all equatorial latitudes of the Sun.