CME observation

On 12 December 2008, an erupting prominence was observed by STEREO while the spacecraft was in near quadrature at 86.7° separation (Fig. 1a). The eruption were visible at 50–55° north from 03:00 UT in SECCHI/Extreme Ultraviolet Imager (EUVI) images, obtained in the 304 Å passband, in the northeast from the perspective of STEREO-(A)head and off the northwest limb from STEREO-(B)ehind. The prominence is considered to be the inner material of the CME, which was first observed in COR1-B at 05:35 UT (Fig. 1b). For our analysis, we use the two coronagraphs (COR1/2) and the inner HI1 (Fig. 1c). We characterize the propagation of the CME across the plane of sky by fitting an ellipse to the front of the CME in each image38 (Supplementary Movie 1). This ellipse fitting is applied to the leading edges of the CME but equal weight is given to the CME flank edges as they enter the field of view of each instrument. The 3D reconstruction is then performed using a method of elliptical tie pointing within epipolar planes containing the two STEREO spacecraft, illustrated in Figure 2 (see Methods section).

Figure 1: Composite of STEREO-A and B images from the SECCHI instruments of the CME of 12 December 2008. (a) Indicates the STEREO spacecraft locations, separated by an angle of 86.7° at the time of the event. (b) Shows the prominence eruption observed in EUVI-B off the northwest limb from approximately 03:00 UT, which is considered to be the inner material of the CME. The multiscale edge detection and corresponding ellipse characterization are overplotted in COR1. (c) Shows that the CME is Earth-directed, being observed off the east limb in STEREO-A and off the west limb in STEREO-B. Full size image

Figure 2: Epipolar geometry used to constrain the reconstruction of the CME front. The reconstruction is performed using an elliptical tie-pointing technique within epipolar planes containing the two STEREO spacecraft27. For example, one of any number of planes will intersect the ellipse characterization of the CME at two points in each image from STEREO-A and B. (a) Illustrates how the resulting four sight lines intersect in 3D space to define a quadrilateral that constrains the CME front in that plane56,57. Inscribing an ellipse within the quadrilateral such that it is tangent to each sight line58,59 provides a slice through the CME that matches the observations from each spacecraft. (b) Illustrates how a full reconstruction is achieved by stacking multiple ellipses from the epipolar slices. As the positions and curvatures of these inscribed ellipses are constrained by the characterized curvature of the CME fronts in the stereoscopic image pair, the modelled CME front is considered to be an optimum reconstruction of the true CME front. (c) Illustrates how this is repeated for every frame of the eruption to build the reconstruction as a function of time and view the changes to the CME front as it propagates in 3D. Although the ellipse characterization applies to both the leading edges and, when observable, the flanks of the CME, only the outermost part of the reconstructed front is shown here for clarity, and illustrated in Supplementary Movie 2. Full size image

Non-radial CME motion

It is immediately evident from the reconstruction in Figure 2c (and Supplementary Movie 2) that the CME propagates non-radially away from the Sun. The CME flanks change from an initial latitude span of 16–46° to finally span approximately ± 30° of the ecliptic (Fig. 3b). The mean declination, θ, of the CME is well fitted by a power law of the form as a result of this non-radial propagation. Tie pointing the prominence apex and fitting a power law to its declination angle result in , implying a source latitude of in agreement with EUVI observations. Previous statistics on CME position angles have shown that, during solar minimum, they tend to be offset closer to the equator as compared with those of the associated prominence eruption39. The non-radial motion we quantify here may be evidence of the drawn-out magnetic dipole field of the Sun, an effect predicted at solar minimum because of the influence of solar wind pressure40,41. Other possible influences include changes to the internal current of the magnetic flux rope11, or the orientation of the magnetic flux rope with respect to the background field10, whereby magnetic pressure can function asymmetrically to deflect the flux rope poleward or equatorward depending on the field configurations.

Figure 3: Kinematics and morphology of the 3D reconstruction of the CME front of 12 December 2008. (a) Shows the velocity of the middle of the CME front with the corresponding drag model and, inset, the early acceleration peak. Measurement uncertainties are indicated by one standard deviation error bars. (b) Shows the declinations from the ecliptic (0°) of an angular spread across the front between the CME flanks, with a power-law fit indicative of non-radial propagation. It should be noted that the positions of the flanks are subject to large scatter: as the CME enters each field of view, the location of a tangent to its flanks is prone to moving back along the reconstruction in cases in which the epipolar slices completely constrain the flanks. Hence the 'Midtop/Midbottom of Front' measurements better convey the southward-dominated expansion. (c) Shows the angular width of the CME with a power-law expansion. For each instrument, the first three points of angular width measurement were removed as the CME was still predominantly obscured by each instrument's occulter. Full size image

CME angular width expansion

Over the height range of 2–46 , the CME angular width (Δθ=θ max −θ min ) increases from ∼30° to ∼60° with a power law of the form (Fig. 3c). This angular expansion is evidence of an initial overpressure of the CME relative to the surrounding corona (coincident with its early acceleration inset in Fig. 3a). The expansion then tends to a constant during the later drag phase of CME propagation, as it expands to maintain pressure balance with heliocentric distance. It is theorized that the expansion may be attributed to two types of kinematic evolution, namely, spherical expansion due to simple convection with the ambient solar wind in a diverging geometry, and expansion due to a pressure gradient between the flux rope and solar wind13. It is also noted that the southern portions of the CME manifest the bulk of this expansion below the ecliptic (best observed by comparing the relatively constant 'Midtop of Front' measurements with the more consistently decreasing 'Midbottom of Front' measurements in Fig. 3b). Inspection of a Wang-Sheeley-Arge solar wind model run42 reveals higher speed solar wind flows (∼650 km s−1) emanating from open-field regions at high/low latitudes (approximately 30° north/south of the solar equator). Once the initial prominence/CME eruption occurs and is deflected into a non-radial trajectory, it undergoes asymmetric expansion in the solar wind. It is prevented from expanding upwards into the open-field high-speed stream at higher latitudes, and the high internal pressure of the CME relative to the slower solar wind near the ecliptic accounts for its expansion predominantly to the south. In addition, the northern portions of the CME attain greater distances from the Sun than the southern portions as a result of this propagation in varying solar wind speeds, an effect predicted to occur in previous hydrodynamic models14.

CME drag in the inner heliosphere

Investigating the midpoint kinematics of the CME front, we find that the velocity profile increases from approximately 100 to 300 km s−1 over the first 2–5 , before rising more gradually to a scatter between 400 and 550 km s−1 as it propagates outwards (Fig. 3a). The acceleration peaks at approximately 100 m s−2 at a height of ∼3 , then decreases to scatter about zero. This early phase is generally attributed to the Lorentz force whereby the dominant outward magnetic pressure overcomes the internal and/or external magnetic field tension. The subsequent increase in velocity, at heights above ∼7 for this event, is predicted by theory to result from the effects of drag17, as the CME is influenced by solar wind flows of ∼550 km s−1 emanating from latitudes ≳ ± 5° of the ecliptic (again from inspection of the Wang-Sheeley-Arge model). At large distances from the Sun, during this postulated drag-dominated epoch of CME propagation, the equation of motion can be cast in the following form:

This describes a CME of velocity v cme , mass M cme and cross-sectional area A cme propagating through a solar wind flow of velocity v sw and density ρ sw . The drag coefficient C D is found to be of the order of unity for typical CME geometries18, whereas the density and area are expected to vary as power-law functions of distance r. Thus, we parameterize the density and geometric variation of the CME and solar wind using a power law43 to obtain

where γ describes the drag regime, which can be either viscous (γ=1) or aerodynamic (γ=2), and α and β are constants primarily related to the cross-sectional area of the CME and the density ratio of the solar wind flow to the CME (ρ sw /ρ cme ). The solar wind velocity is estimated from an empirical model44. We determine a theoretical estimate of the CME velocity as a function of distance by numerically integrating Equation (2) using a fourth order Runge–Kutta scheme and fitting the result to the observed velocities from ∼7 to 46 . The initial CME height, CME velocity, asymptotic solar wind speed and α, β and γ are obtained from a bootstrapping procedure that provides a final best fit to the observations and confidence intervals of the parameters (see Methods section). Best-fit values for α and β were found to be ( )×10−5 and , which agree with values found in previous modelling work44. The best-fit value for the exponent of the velocity difference between CME and the solar wind, γ, was found to be , which is clear evidence that aerodynamic drag (γ=2) functions during the propagation of the CME in interplanetary space.

The drag model provides an asymptotic CME velocity of km s−1 when extrapolated to 1 AU, which predicts the CME to arrive ∼1 day before the Advanced Composition Explorer (ACE) or WIND spacecraft detects it at the L1 point. We investigate this discrepancy by using our 3D reconstruction to simulate the continued propagation of the CME from the Alfvén radius (∼21.5 ) to Earth using the ENLIL with Cone Model21 at NASA's Community Coordinated Modeling Center. ENLIL is a time-dependent 3D magnetohydrodynamic code that models CME propagation through interplanetary space. We use the height, velocity and width from our 3D reconstruction as initial conditions for the simulation, and find that the CME is actually slowed to ∼342 km s−1 at 1 AU. This is a result of its interaction with an upstream, slow-speed, solar wind flow at distances beyond 50 . This CME velocity is consistent with in situ measurements of solar wind speed (∼330 km s−1) from the ACE and WIND spacecraft at L1. Tracking the peak density of the CME front from the ENLIL simulation gives an arrival time at L1 of ∼08:09 UT on 16 December 2008. Accounting for the offset in CME front heights between our 3D reconstruction and ENLIL simulation at distances of 21.5 gives an arrival time in the range of 08:09–13:20 UT on 16 December 2008. This prediction interval agrees well with the earliest derived arrival times of the CME front plasma pileup ahead of the magnetic cloud flux rope from the in situ data of both ACE and WIND (Fig. 4) before its subsequent impact on Earth34,36.