CHARACTERISTICS OF KINEMATICS OF A CORONAL MASS EJECTION DURING THE 2010 AUGUST 1 CME–CME INTERACTION EVENT

On 2010 August 1 a total of five coronal mass ejections (CMEs) could be identified. All CMEs were launched from source regions (SRs) located on the Earth-directed hemisphere of the Sun, which made them potential geoeffective space weather events (for an overview of all these CME events see Harrison et al. 2012). Schrijver & Title (2011) presented a detailed study focusing on the 2010 August 1 CME-associated solar surface activity using observations from the Solar Terrestrial Relations Observatory (STEREO) and the Solar Dynamics Observatory. They showed how complex and widely distributed the magnetic field line connections were over the solar surface that finally caused the initiation and evolution of the observed eruptions. In fact, the eruptions affected half of the solar corona, which makes it necessary to analyze many aspects of these events in detail.

Two of the CME events on 2010 August 1 (named as M- and L-tracks in the overview paper by Harrison et al. 2012) were launched in quick succession from SRs located close together (Harrison et al. 2012). Furthermore, as we shall show, the first event was slower than the second event; hence, the CMEs are expected to interact with each other at a certain distance from the Sun. It has been suggested by Gopalswamy et al. (2001) and Burlaga et al. (2002) that during the interaction process the CMEs may merge and become a single magnetic structure. Using observations from STEREO for the 2007 January 24–25 events, Lugaz et al. (2008) and Webb et al. (2009) reported the overtaking of a slower CME by a faster CME such that the shock wave driven by the faster CME traveled through the slower preceding CME (Lugaz et al. 2009). The studies by Lugaz et al. (2008, 2009) and Webb et al. (2009) revealed that knowing the propagation direction of the potentially interacting CMEs is crucial in order to interpret the observations in a reliable way. Furthermore, enhanced radio emission (Gopalswamy et al. 2001) and highly energetic solar particles have been reported in connection with a CME–CME interaction (e.g., Kahler 1994, 2001; Gopalswamy et al. 2002). Numerical simulations have shown that this is either due to the reconnection processes between the intrinsic magnetic fields of the CMEs, or the additional particle acceleration due to the associated shock wave propagating through the slower CME (e.g., Schmidt & Cargill 2004; Lugaz et al. 2005). All these results provide evidence that the intrinsic magnetic field of a CME, i.e., the assumed flux-rope structure (e.g., Chen 1996; Low 2001, and references therein), plays an important role with respect to its kinematical evolution.

As a CME propagates into interplanetary (IP) space it interacts with the ambient medium and transfers momentum and energy in the form of magnetohydrodynamic (MHD) waves (e.g., Jacques 1977). The interaction of the CME with the solar wind results in the adjustment between the speed of the CME and the solar wind flow. Assuming that the main force that governs the propagation behavior of a CME in IP space is the "aerodynamic" drag force (Cargill et al. 1996; Vršnak 2001; Vršnak & Gopalswamy 2002; Cargill 2004), we may attempt to simulate the kinematical profile of a CME by using the drag-based model (DBM) proposed by Vršnak & Žic (2007), and advanced by Vršnak et al. (2012).

In the following study we focus on two CME events from 2010 August 1 and we investigate if the CMEs may have interacted with each other as they propagated away from the Sun. We use STEREO/SECCHI observations to derive the three-dimensional properties of both CMEs (direction of motion, kinematical profile, width). The derived de-projected kinematical profile is then compared to the results from the DBM. From this we will show that (1) both CMEs head in similar directions as they evolve into IP space, making a CME–CME interaction highly likely; (2) a strong deceleration of the faster CME can be explained by interaction with the slower CME, which can be represented as an ambient medium of higher density and flow speed compared to the unperturbed solar wind; and (3) the interaction between the magnetic structures of the CMEs starts earlier than their leading edges merging in the heliospheric images.

For the CME–CME interaction study we analyze white-light images from the STEREO (STEREO-A and STEREO-B) SECCHI instrument suite (Howard et al. 2008). SECCHI consists of two coronagraphs, COR1 and COR2, covering a plane-of-sky (POS) distance range up to ∼15 R_☉, and the heliospheric imagers (HIs), HI1 and HI2, for distances > 15 R_☉. This instrument combination allows us to track CME/ICME events in the inner heliosphere from ∼2 R_☉ to beyond 1 AU. For context information on the low-coronal conditions close to the solar surface, we use data from the SECCHI Extreme Ultraviolet Imager (EUVI; Wuelser et al. 2004).

Due to an observational gap, STEREO-B data are not available from ∼10:00 UT on 2010 August 1 until 04:00 UT on 2010 August 2. For that reason, techniques based on stereoscopic data are used close to the Sun but not for studying the entire propagation path up to 1 AU.

The first CME (hereinafter CME1) was launched from the Sun on 2010 August 1 at ∼2:55 UT with a de-projected mean speed of ∼700 km s⁻¹ in the COR1 and COR2 fields of view (FOVs). STEREO-A EUVI images (Figure 1, top right) show an off-limb dimming region, representing the low-coronal signatures of CME1. From the solar surface signatures we also derive the location of SR for both CMEs as given in Table 1 (cf. Cremades & Bothmer 2004). As can be seen from Figure 2, the CME feature can be seamlessly tracked as it propagates into the coronagraph FoV from which it can be further followed into the HI1 FoV. The CME was associated with a prominence eruption followed by a GOES B4.5 class flare in a small active region (NOAA 11094; cf. Schrijver & Title 2011) located at E14/N14 (if not stated otherwise all locations are heliographic coordinates given in degrees with respect to Earth).

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The second CME (hereinafter CME2) was associated with a long-duration flare classified as GOES C3.8 and was launched from AR 11092 located at about E35/N20. The flare started at ∼7:24 UT, lasted until 10:25 UT and had its maximum intensity at 08:56 UT (for more details on the flare and associated filament eruption see Liu et al. 2010a; Schrijver & Title 2011). CME2 was a fast event with a de-projected mean speed of ∼1200 km s⁻¹ in the COR1 and COR2 FoVs. Clear low-coronal signatures of CME2 are seen in STEREO-A EUVI at ∼7:45 UT (see bottom right panel of Figure 1). CME2 can be seamlessly tracked from EUVI to COR1 (Figure 2) where it shows a very distinct leading edge and is associated with a remote streamer deflection, probably related to a shock front (cf. Liu et al. 2009; Gopalswamy et al. 2009; Ontiveros & Vourlidas 2009).

The in situ signature of the leading edge of CME2 was an IP shock and its high-density sheath region recorded at 1 AU on 2010 August 3 17:05 UT (cf. Harrison et al. 2012) by Wind/SWE/MFI (Ogilvie et al. 1995; Lepping et al. 1995). The arrival time of the shock and proton bulk speed following its arrival are used to further constrain the kinematical profile of CME2 (see Section 3.1.4). The solar wind speed diagnosed in situ near Earth was around 400 km s⁻¹ prior to the arrival of the shock associated with CME2 on 2010 August 3. The solar wind speed measured in the sheath region of CME2 increased to 600 km s⁻¹ (see Figure 14 in Harrison et al. 2012). A detailed study focusing on the in situ signatures of these events is given by Möstl et al. (2012). The readers are also directed to Liu et al. (2012) for connections between imaging observations and in situ signatures with respect to the CME–CME interaction.

CME2 was associated with a type II radio burst showing distinct morphological changes at ∼09:50 UT on 2010 August 1. Emission at the fundamental frequency divided into two branches of different frequency drifts, implying the simultaneous existence of radio emission sites moving with different speeds. More details on the radio signatures associated with the 2010 August 1 events are given by Martinez Oliveros et al. (2012).

3.1. Observations and Reconstruction Methods

3.2. Simulation of Kinematics of CME2 Using the DBM

The DBM (Vršnak et al. 2012) is based on the assumption that the kinematical profile of a CME in IP space is mainly controlled by drag force (Cargill et al. 1996; Vršnak 2001; Vršnak & Gopalswamy 2002; Cargill 2004; Vršnak & Žic 2007). The drag force can be expressed in its simplest form as

$$\begin{eqnarray*} &&F_{D}=\gamma (v-w)|v-w|, \end{eqnarray*}$$

with w the solar wind speed and v the CME speed. The drag parameter γ is defined as

$$\begin{eqnarray*} &&\gamma =C_{d} \frac{A_{\rm CME}\rho _{\rm sw}}{m_{\rm CME}}, \end{eqnarray*}$$

where C_d is the drag coefficient, A_CME is the cross-sectional area of the CME, ρ_sw is the density of the solar wind, and m_CME is the mass of the CME (cf. Cargill 2004). C_d is a dimensionless number, typically of order of unity (see Batchelor 1967). Working on this assumption, we calculate the kinematical profile of CME2 and compare it with the kinematical profile derived from observations.

As input parameters, DBM requires the launch time t₀ and speed of the CME v₀ at a certain distance from the Sun R₀, the asymptotic solar wind speed w at 1 AU as well as γ. From white-light observations, we derive t₀, v₀, and R₀, while w is taken directly from Wind data. For γ we obtain the parameters A_CME and m_CME from stereoscopic reconstruction methods, and ρ_sw is calculated using the empirical formula developed by Leblanc et al. (1998) depending only on the radial distance from the Sun. Assuming that a CME expands in a self-similar manner and that the density falls off as distance squared, γ can be kept constant for the distance range from Sun to Earth. For a detailed description of the DBM we refer to Vršnak et al. (2012). The DBM is available for public usage through a Web interface under http://oh.geof.unizg.hr/CADBM/cadbm.php.

Figure 3 shows base difference images and J-maps for HI1-A data from which we observe that the signatures of the leading edge of CME1 and CME2 merged somewhere between 14:00 and 16:00 UT, corresponding to a distance of ∼38 ± 5 R_☉. After the interaction, no identifiable signatures of CME1 were observed, i.e., CME1 was "lost" in the white-light signature of CME2.

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Figure 4 shows the simulated flux-rope model (see Section 3.1.1) overlaid on white-light COR1 (for CME1) and COR2 (for CME2) images. Applying this model, we derive the radial back-projection of the CME apex onto the solar surface, which represents the launch site of the CME (CME1: E20/N09; CME2: E28/N20), the tilt angle relative to the solar equator (CME1: 39°; CME2: 47°), the face-on width (CME1: ∼68°; CME2: ∼100°), and the edge-on width (CME1: ∼23°; CME2: ∼52°). Typical uncertainties lie in the range of ±10° and depend on the identified boundaries of the CME.

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The top panel of Figure 5 shows how the Billings (1966) equations are used to obtain a reconstructed point within a CME relative to the spacecraft POS (see Section 3.1.6). The bottom panels show two possible reconstructed CMEs for each event based on STEREO-A percent polarization measurements, one ahead of the spacecraft POS, and one behind the POS. The correct reconstruction, which can be deduced by utilizing in addition STEREO-B percent polarization measurements, is the colored reddish-orange one traveling eastward of the Sun–Earth line (i.e., ahead of the spacecraft POS). What can be seen immediately is that both CMEs have a similar trajectory, and that CME2 is significantly larger than CME1.

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Table 1 gives a summary of results for the direction of motion and speed of CME1 and CME2, respectively, derived from using the different methods described in Section 3.1. We find that both ejecta propagate in similar directions which makes an interaction between both CMEs within the FoV of HI1-A highly likely. Due to the unknown geometry of the CMEs we are not able to determine which method delivers the most reliable result. Taking the average of all methods used, we derive for CME1 the direction E16° ± 7° which is close to its SR located at E14 (cf. Figure 1). For CME2 we derive the average longitude of E23° ± 15°. A large deviation from its associated SR (E35) is obtained for CME2 from the remote sensing and in situ (R+IS) method. This gives an average direction of E13 (E12 if we match the derivative of the converted elongation with the speed of the sheath region and E14 if we match the averaged arrival time of the sheath region at the Wind spacecraft). Inspecting the direction of motion for CME2 derived from other methods (forward modeling, polarimetric localization, HM) we obtain ∼E30–E35 which would be more consistent with the location of the SR.

Figure 6 shows speed and radial distance profiles for the leading edge of CME2 that have been derived from elongation measurements from COR1/COR2/HI1/HI2 ecliptic observations from STEREO-A using directions E13 and E30. The speed profile is derived by performing numerical differentiation of the distance–time data applying three-point Lagrangian interpolation. The error bars in the speed profile represent uncertainties in the measurements of the leading edge of CME2 and are calculated as the standard deviation of the derivative from errors in the distance–time data. As can be seen, starting at a distance of ∼20 R_☉ a clear deviation especially in the distance profile is obtained, revealing that E30 would not fit the boundary conditions at 1 AU. For that reason we chose to use the direction E13 for conversion and to compare with the results from the drag model. We note that this might give hints toward some longitudinal deflection of CME2, which is also found by Liu et al. (2012). However, we cannot rule out artifacts in the direction finding due to the geometrical assumptions underlying the different methods.

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Inspection of the speed profile of CME2 as given in the top panel of Figure 6 reveals that there were two distinctly different stages in the deceleration of CME2. The first one, characterized by a rapid deceleration of a ≈−40 m s⁻², lasted from ∼10 UT until ∼14 UT. After that deceleration decreased to a ≈ −2 m s⁻². In Figure 7 we show the de-projected radial distance profile of CME1 (results taken from the geometric triangulation method; see Liu et al. 2012) extrapolated using a polynomial fit of second order until the time of interaction with CME2. Although the exact time depends on the direction of motion used for converting elongation into radial distance the interaction takes place between approximately 13:30 UT and 15:30 UT. From this we are able to attribute the first deceleration stage to the interaction of CME2 with CME1, whereas in the second stage the deceleration is due solely to the interaction of the merged structure with the ambient solar wind. The kinematical profile shows that the rapid deceleration stage actually begins a few hours before the leading edges of CME1 and CME2 merged in the white-light data (∼10 UT), which can be attributed to a finite thickness of CME1.

From the results presented in Table 1, CME1 has a mean speed of ∼700 km s⁻¹ within the FoV of COR2 and a total ("true") mass of ∼6–8 × 10¹⁵ g; in contrast CME2 is a much faster event with a mean speed of ∼1200 km s⁻¹ within the FoV of COR2 and has a total mass of ∼2–3 × 10¹⁶ g.

Figure 8 shows the speed–distance, speed–time, and distance–time profiles of the leading edge of CME2 as derived from COR1/COR2/HI1/HI2 ecliptic observations from STEREO-A. The conversion to radial distance uses the result from the remote sensing and in situ method with E13 as ecliptic longitude. The speed profile and error bars are derived in the same way as given for Figure 6. The middle and bottom panels of Figure 8 show the speed–time and distance–time curves of CME2 overlaid with the results from the DBM simulating two different scenarios of CME evolution.

For calculating the kinematical profile of CME2 from the DBM we use C_d = 1 fixed over the Sun–Earth distance range, and constrain the other parameters by observations (see also Figure 9). The asymptotic solar wind speed w at 1 AU before the arrival of CME2 was measured by Wind as ∼400 km s⁻¹ (see Harrison et al. 2012; Liu et al. 2012). There is no indication from in situ data that CME2 crossed a high-speed solar wind stream during its propagation from Sun to Earth, which would result in a strong variation of the background solar wind speed w (see also Temmer et al. 2011). From the observational results of CME2 we derive t₀ to be 2010 August 1 10:19 UT and v₀ = 1400 km s⁻¹ at R₀ = 15 R_☉. We first calculate the kinematical profile DBM1 assuming that CME2 moves in unperturbed solar wind conditions from Sun to Earth. The parameter γ is kept constant over the Sun–Earth distance range and chosen to be γ = 0.25 × 10⁻⁷ km⁻¹, representing a CME which moves in an unperturbed environment of lower density and lower speed than the CME itself (see also the parameter study by Cargill 2004). As can be seen, the results from DBM1 based on such an assumption do not match the observational results. In another approach we calculate DBM2 using the same values for t₀, v₀, and R₀ but changing w and γ at a distance of 35 R_☉, which is the distance at which the interaction of the two CMEs is likely to be finished. With this we simulate a scenario in which a CME moves up to 35 R_☉ in an ambient flow that is of higher speed and density than the unperturbed environment. Beyond 35 R_☉, CME1 and CME2 move as single structure in an ambient flow of speed and density comparable to an unperturbed solar wind, having the cross section of CME2 and the combined mass of CME1 and CME2. In order to match the observational results, for radial distances ⩽ 35 R_☉ we used γ₁ = 1.65 × 10⁻⁷ km⁻¹ and w₁ = 600 km s⁻¹, and for radial distances > 35 R_☉ we used γ₂ = 0.2 × 10⁻⁷ km⁻¹ and w₂ = 400 km s⁻¹ (cf. Figure 9).

In order to reproduce the CME–CME interaction in DBM2 we used values that give γ₁/γ₂ = 8.25. According to the CME–CME interaction scenario as described above we may express γ₁ = (A_CME2ρ_CME1)/(m_CME2) and γ₂ = (A_CME2ρ_sw)/(m_CME1 + m_CME2) from which we obtain

$$\begin{eqnarray*} &&\frac{\gamma _{1}}{\gamma _{2}}=\frac{\rho _{\rm CME1} (m_{\rm CME1}+m_{\rm CME2})}{\rho _{\rm sw} m_{\rm CME2}}. \end{eqnarray*}$$

We now compare ρ_CME1 and ρ_sw at a distance of 35 R_☉. Assuming a cone model (e.g., Michalek 2006), we calculate the volume of CME1 using the derived width of ∼68°. Using the total mass of CME1 of ∼6–8 × 10¹⁵ g implies ρ_CME1 ∼ 1.0 × 10⁻²¹ g cm⁻³. Applying the model by Leblanc et al. (1998) for the solar wind density we obtain ρ_sw ∼ 4.5 × 10⁻²² g cm⁻³ (cf. Vršnak et al. 2010). This gives us ρ_CME1 ≈ 2 ρ_sw. From total mass calculations we obtain m_CME2 ≈ 3 m_CME1. Beyond ∼10 R_☉ the mass is assumed to remain constant (Colaninno & Vourlidas 2009) from which we suppose that the ratio between the masses is constant. We note that this is a simplistic assumption since Lugaz et al. (2005) have shown from simulations that the mass of a CME might increase up to a distance of 1 AU. From this we derive γ₁/γ₂  ∼ 3, which shows that there is discrepancy to the model results. We may speculate that, besides the aerodynamic drag effect, magnetic forces (i.e., magnetic tension and magnetic pressure gradients raised due to the interaction) significantly contributed to the enhanced deceleration of CME2.

Applying currently available models and reconstruction techniques for observations of the CME events from 2010 August 1 we are able to analyze a CME–CME interaction process quantitatively. Keeping in mind that the three-dimensional reconstruction techniques are only approximate and the kinematic results may vary greatly (see, e.g., Lugaz et al. 2010), we use several (independent) methods. The results derived for the three-dimensional propagation directions are in agreement and provide evidence that a full interaction takes place between two consecutively launched CMEs. From observations we derive that the faster CME (CME2) is about three times more massive and ∼30% larger in volume than the slower preceding CME (CME1). The white-light signatures of the CMEs obtained from heliospheric imagery show that CME1 seems to be "lost" within the structure of CME2 since there are no features that can be attributed to CME1 after interaction (see also Harrison et al. 2012). What we observe in white light as the leading edge of CME2 after merging with CME1 most probably includes the mass of CME1. Whether the magnetic features really merge, i.e., reconnect, or whether CME1 stays as a magnetic entity that is compressed and pushed forward by CME2, is not possible to derive from remote sensing data. In situ data give more information on this aspect and are discussed in detail by Liu et al. (2012). The results by these authors show that the multi-point in situ observations are consistent with compression of CME1 rather than its disintegration.

The CME–CME interaction is associated with transfer of momentum between the ejecta (Farrugia & Berdichevsky 2004) and this might be compared to simplified scenarios of one-dimensional elastic and inelastic collision (cf. Lugaz et al. 2009). At the time of interaction at about 10 UT, the speed of CME1 is ∼600 km s⁻¹ and CME2 ∼ 1400 km s⁻¹, and the total mass of CME2 is derived to be ∼3 times higher than for CME1. Assuming a full interaction in the form of a perfectly inelastic collision, we would expect CME2 to move with a speed of ∼1200 km s⁻¹. Assuming an elastic collision, CME1 would experience an acceleration, reaching a speed of ∼1800 km s⁻¹. From observations, we derive a speed for the leading edge of the merged structure at about 15 UT of ∼800 km s⁻¹ that makes both scenarios unlikely. As derived from the polarimetric localization method and the forward modeling (cf. Figures 4 and 5), CME2 is significantly larger than CME1, from which it is not hard to imagine that CME1 will be "lost" within CME2. However, given the differences in size as well as mass, it is hard to imagine how the interaction between the two CMEs could result in substantial deceleration of CME2. Nevertheless, we must not forget that we are dealing with magnetic structures. As reported for the early kinematical evolution of CMEs, the interaction with strong overlying coronal magnetic fields may cause enhanced deceleration (e.g., Temmer et al. 2008, 2010).

By applying the DBM proposed by Vršnak & Žic (2007) and advanced by Vršnak et al. (2012), we are able to simulate the kinematical profile of CME2. The observational results can be reproduced by varying γ values and ambient flow speeds in the drag formula at a radial distance from the Sun of ∼35 R_☉ (the distance at which the interaction process is likely to be finished). This can be interpreted in such a way that CME1 represents an MHD obstacle for CME2, which leads to increased deceleration. In other words, CME2 propagates into a medium of denser plasma, higher flow speed, and stronger magnetic field than the unperturbed solar wind. After the interaction process the merged entity, i.e., CME2, carries the sum of masses of CME1 and CME2 and moves on as a single structure through an ambient flow of speed and density typical for quiet solar wind conditions.

Inspecting the kinematical profile of CME2 we derive that the strong deceleration starts a few hours before the merging of the white-light leading edge signatures of the CMEs (10 UT versus ∼14 UT). This can be interpreted as an interaction between their magnetic structures, i.e., by a finite thickness of CME1. As shown at the end of Section 4, observations favor a scenario in which magnetic forces, induced during the CME–CME interaction, may play a substantial role in decelerating CME2. We speculate that the increase in magnetic tension and pressure when CME2 bends and compresses the magnetic field lines of CME1 increases the efficiency of drag. We would like to note that the interaction lasted for about ∼4–5 hr, which is probably too short for the total reconnection of the magnetic flux in CME1. This might support the results by Liu et al. (2012) who suggest that CME1 and CME2 most probably remain as two independent magnetic structures.

A metric type II burst emitted from two radio sources moving with different speeds is recorded at 09:50–10:15 UT, which is indicative of an interaction process (Gopalswamy et al. 2001, 2002). This supports the conclusion that the start of the interaction process is represented in the kinematical profile of CME2 by the strong deceleration observed around 10 UT. A detailed study for the 2010 August 1 events with respect to radio observations is given by Martinez Oliveros et al. (2012).

CME–CME interaction processes are still not well understood, mostly due to the lack of appropriate observational data to give information on the three-dimensional characteristics of CMEs. Interaction processes between ejecta are also important with respect to forecasting the arrival times of Earth-directed CME events and their enhanced geoeffectiveness (e.g., Burlaga et al. 1987). As has been shown in the present study, the kinematical profile of a CME can be significantly changed due to the interaction with a preceding slower CME. Especially in times of enhanced solar activity, CMEs cannot be treated as isolated events. Analytical models in combination with unprecedented observations and three-dimensional reconstruction techniques are powerful tools which give us deeper insight and help us to better understand the evolution of CME events in IP space.

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We thank Tim Howard for constructive discussions and an anonymous referee for helpful comments. M.T. greatly acknowledges the Austrian Science Fund (FWF): FWF V195-N16. The present work has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 218816 (SOTERIA) and No. 263252 (COMESEP). B.B. was funded by the Austrian Space Applications Programme (ASAP-7 project No. 828271 3D-POC). This research was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. C.A. de Koning was supported by NASA TR&T grant NNX09AJ84G.