Constraining the Kinematics of Coronal Mass Ejections in the Inner Heliosphere with In-Situ Signatures
T. Rollett, C. Möstl, M. Temmer, A. M. Veronig, C. J. Farrugia, H. K. Biernat
aa r X i v : . [ a s t r o - ph . S R ] F e b Solar PhysicsDOI: 10.1007/ ••••• - ••• - ••• - •••• - • Constraining the Kinematics of Coronal MassEjections in the Inner Heliosphere with
In-Situ
Signatures
T. Rollett , · C. M¨ostl , · M. Temmer , · A.M. Veronig · C.J. Farrugia · H.K. Biernat , · c (cid:13) Springer ••••
Abstract
We present a new approach to combine remote observations and in-situ data by STEREO/HI and
Wind , respectively, to derive the kinematicsand propagation directions of interplanetary coronal mass ejections (ICMEs).We use two methods, Fixed- φ (F φ ) and Harmonic Mean (HM), to convertICME elongations into distance, and constrain the ICME direction such thatthe ICME distance-time and velocity-time profiles are most consistent with in-situ measurements of the arrival time and velocity. The derived velocity-timefunctions from the Sun to 1 AU for the three events under study (1 – 6 June2008, 13 – 18 February 2009, 3 – 5 April 2010) do not show strong differencesfor the two extreme geometrical assumptions of a wide ICME with a circularfront (HM) or an ICME of small spatial extent in the ecliptic (F φ ). Due to thegeometrical assumptions, HM delivers the propagation direction further awayfrom the observing spacecraft with a mean difference of ≈ ◦ .
1. Introduction
Coronal mass ejections (CMEs) are manifestations of the most powerful erup-tions on the Sun and are expulsions of a huge amount of plasma and theembedded magnetic field. Their velocities range between a few 100 km s − up tomore than 3000 km s − . The frequency of occurrence correlates with the solarcycle, and faster and more powerful events are more common during the solarmaximum phase. They can have wide latitudinal and longitudinal extents andtheir typical masses are of the order of ≈ − kg ( cf. Gosling et al. , 1974; Institute of Physics, University of Graz, A-8010, Austriaemail: [email protected] Space Research Institute, Austrian Academy of Sciences,Graz A-8042, Austria Space Science Center and Department of Physics,University of New Hampshire, Durham, New Hampshire,USA
SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 1 . Rollett et al.
Hundhausen, 1997). CMEs propagating from the Sun through the interplanetaryspace are called interplanetary CMEs (ICMEs).Before 2006 it was not possible to directly link CMEs and their properties asmeasured in-situ . A milestone in the investigation of CMEs is the NASA
SolarTErrestrial RElations Observatory (STEREO: Kaiser et al. , 2008) mission withits twin satellites STEREO-AHEAD (A) and STEREO-BEHIND (B). STEREO-A is leading the Earth in its orbit around the Sun and STEREO-B is following.The
Heliospheric Imagers (HI1 and HI2: Eyles et al. , 2009) are part of the
Sun-Earth Connection Coronal and Heliospheric Investigation instrument suite(SECCHI: Howard et al. , 2008; Harrison et al. , 2009) onboard the two STEREOspacecraft and they enable us for the first time to observe solar transient eventsfrom two vantage points from outside the Sun-Earth line. Such observationsconstitute a unique way of investigating the behavior of ICMEs all the way fromthe Sun to Earth. In addition, the possibility to study solar minimum events is abig advantage because it is necessary to do case studies of CMEs showing simpleand well-defined remote as well as in-situ signatures.There are different methods that can be used to infer the direction of prop-agation of an ICME. Some methods use single spacecraft observations, e.g. theFixed- φ fitting method (Sheeley et al. , 1999; Rouillard et al. , 2008) or the Har-monic Mean fitting procedure (Lugaz, 2010; M¨ostl et al. , 2011) while others usedata from both spacecraft, e.g. the triangulation method by Liu et al. (2010a),extended to circular fronts by Lugaz et al. (2010).The aim of this work is to analyze the kinematics and propagation directions ofa set of CMEs up to a distance of 1 AU. For this we developed a method based ona combination of remote and in-situ measurements. We constrain measurementsfrom time-elongation plots (Jmaps), produced out of the white-light HI1/HI2images along the ecliptic plane, with the in-situ measured arrival time and arrivalvelocity. The best matches deliver propagation directions and velocity profilesbased on the geometric assumptions we use, for either very wide or narrow ICMEfronts. This should serve as a basis to develop adequate methods to predict thearrival times of Earth-directed CMEs.
2. Data
The
Heliospheric Imagers (HI: Eyles et al. , 2009) onboard STEREO for the firsttime give us the possibility to perform remote sensing in white-light betweenthe Sun and the Earth from outside the Sun-Earth line. Because of their wideobservation angles (HI1: 4 − ◦ , HI2: 18 . − . ◦ ) and scattering effects, theinterpretation of these images is challenging ( e.g. Vourlidas and Howard, 2006;Kahler and Webb, 2007; Howard and Tappin, 2009). To derive the kinematics ofICME fronts on their way through the inner heliosphere we used remote observa-tions of both HI instruments on STEREO-A as well as the in-situ proton densityand velocity delivered by the
Wind spacecraft near Earth (SWE: Ogilvie et al. ,1995) and STEREO-B (PLASTIC: Galvin et al. , 2008).In this study, we discuss three CME-ICME events observed end-to-end fromthe Sun to 1 AU, covering a wide range of CME initial conditions and param-
SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 2 ters. The first event of 2 – 6 June 2008 is an example of a very slow streamer-blowout type CME with a small longitudinal angular width (M¨ostl et al. , 2009;Robbrecht, Patsourakos, and Vourlidas, 2009; Lynch et al. , 2010; Wood, Howard, and Socker,2010). The CME of 13 – 18 February 2009 originated from a bipolar active regionand was associated with an EUV wave (Kienreich, Temmer, and Veronig, 2009;Patsourakos and Vourlidas, 2009). It was slow as well but reached its propaga-tion velocity of about 350 km s − very close to the Sun (Miklenic et al. , 2011).The event is expected to have a wider extent in the ecliptic because of a loweraxis inclination (M¨ostl et al. , 2011). The third event of 3 – 5 April 2010 was thefirst fast and geoeffective ICME of Solar Cycle 24 (M¨ostl et al. , 2010; Liu et al. ,2011; Wood et al. , 2011) and led to a damage of the Galaxy 15 satellite ingeosynchronous orbit and to what has been called a perfect substorm.
3. Methods
For the interpretation of HI images it is necessary to consider scattering effects.ICMEs are detected as the photospheric light scattered off free electrons inthe CME body, called Thomson scattering ( e.g.
Billings, 1966; Hundhausen,1993). The scattered light has its maximum when the line of sight (LoS) isperpendicular to the line between the Sun and the scattering particle. That isthe reason light that we see in the white-light images originates on a spherewith the Sun-observer line as its diameter, also called the Thomson-surface (TS:Vourlidas and Howard, 2006). When leaving the TS the intensity of the scatteredlight decreases ( e.g.
Morrill et al. , 2009). Brightness distribution and morphologyare different depending on the ICME axial orientation (Cremades and Bothmer,2004). Thomson scattering influences the geometrical derivations of the followingtechniques.Signatures of ICMEs are measured within time-elongation plots (Jmaps: Sheeley et al. ,1999; Davies et al. , 2009) which are produced out of stripes along the eclipticplane extracted from heliospheric images. These stripes are rotated and alignednext to each other with the time increasing in the x- and the elongation in the y- direction. When an ICME feature is measured within a Jmap the distancefrom Sun-centre is denoted in elongation, i.e. in angular degrees. To use themeasurements for further analysis we are interested in the ICME kinematicsexpressed in radial distance, and thus the measured elongation has to be con-verted. These calculations are limited because of the supposed shape of theICME front, which cannot be determined by using remote sensing from onlyone vantage point. These methods and techniques are reviewed and discussedin Liu et al. (2010b). In the following calculations we converted the elongationangle into radial distance by using two methods that make different geometricalassumptions for the shape of the ICME front: Fixed- φ and Harmonic Mean.3.1. Fixed- φ MethodThe simplest way to convert elongation into distance is the Point P (PP) method(Howard et al. , 2006). It assumes a CME as a circle all the way around the Sun.
SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 3 . Rollett et al. R H M R F Φ o R PP Figure 1.
Comparison between Point P, Fixed- φ , and Harmonic Mean methods. The grayline shows the line of sight, angle ǫ is the measured elongation, d o is the Sun-observer distance, φ is the propagation direction relative to d o . For the same value of φ , Fixed- φ gives a largerdistance than HM. In contrast to PP the Fixed- φ method (F φ : Sheeley et al. , 1999; Kahler and Webb,2007) assumes a radial propagation of a single plasma element along a straightline (see Figure 1), i.e. a constant propagation direction. This is an importantdifference to other methods ( e.g. the triangulation technique by Liu et al. , 2010a)that make geometrical assumptions of a point wise extent of the CME as well butuse two different vantage points (STEREO-A and STEREO-B) and are thereforeable to determine the direction for each point along the track. This approachconverts the measured elongation angle into radial distance from the Sun for agiven propagation direction of the ICME: R F φ ( t ) = d o sin ǫ ( t )sin( ǫ ( t ) + φ ) , (1)where R F φ ( t ) is the calculated distance, d o is the Sun-observer distance, ǫ ( t ) themeasured elongation angle and φ the derived propagation direction, measuredaway from the observer, with positive values corresponding to solar West.3.2. Harmonic Mean MethodFor wide CMEs, the Harmonic Mean method (HM: Howard and Tappin, 2009;Lugaz, Vourlidas, and Roussev, 2009) may be more appropriate than F φ . It as-sumes that the measured part is not a single particle but a sphere (or a circle inthe ecliptic plane) connected to the Sun at all times. As shown in Figure 1, itfurther assumes that the observer always looks along the tangent to this circle.The resulting equation can be understood as the harmonic mean of the PP andF φ methods: SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 4 igure 2.
Resulting radial distance as function of time for five different propagation directionsfor the F φ (upper panel) and the HM (lower panel) methods. The angle is the propagationdirection relative to the observer — negative means eastward. The solid horizontal line marksthe location of the spacecraft providing the in-situ measurements and the vertical solid lineindicates the arrival time of the ICME at the in-situ spacecraft. R HM ( t ) = 2 d o sin ǫ ( t )1 + sin( ǫ ( t ) + φ ) , (2)where R HM ( t ) is the calculated distance, d o is the Sun-observer distance, ǫ ( t )the measured elongation angle, and φ the derived propagation direction. Thiswas introduced by Lugaz, Vourlidas, and Roussev (2009) who found that CMEvelocities at large elongation angles in a simulation were reproduced better withthe HM method, and were over- and underestimated by the Fixed-Φ and Point Pmethods, respectively. SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 5 . Rollett et al.
In-Situ
SignalsWe have developed a new technique, based on the two conversion methods, byadding two boundary conditions: first, the arrival time [ t a ] of the ICME frontat the in-situ spacecraft and second, the in-situ measured velocity [ V i ]. As anillustration, Figure 2 shows the resulting distance-time profiles of the 1 – 6 June2008 event calculated with different propagation angles (Top: F φ , Bottom: HM).The cross is the measured arrival time of the ICME front at the location of the in-situ spacecraft. For estimating the most reliable propagation angle [ φ ] the measured elongationvalue at the in-situ arrival time of the ICME [ ǫ t a ] is converted with F φ intoa distance, R F φ,t a ( φ ), by using different angles ( φ ∈ [0 ◦ , ◦ ]). R F φ,t a ( φ ) issubtracted from the distance between the Sun and the in-situ spacecraft [ d i ]:∆ d F φ ( φ ) = R F φ,t a ( φ ) − d i . (3)The angle which minimizes ∆ d F φ ( φ ), which we call φ dF φ , is the resulting direc-tion from the constraint with the arrival time.To do the same calculation for HM we have to consider the particular, circulargeometry of the front. To this end one cannot use the whole diameter of the circle[ R HM ], but rather the distance between the Sun and the point of intersectionof the HM circle with the line connecting the Sun and the in-situ spacecraft, asillustrated in Figure 3. We call this distance R HMi,t a ( φ ), and it is calculated by R HMi,t a ( φ ) = R HM,t a ( φ ) cos δ, (4)where δ is the angle between d i and R HM . Similar to above, we calculate:∆ d HMi ( φ ) = R HMi,t a ( φ ) − d i , (5)where ∆ d HMi ( φ ) is the resulting difference and R HMi,t a ( φ ) the result of HMalong d i . The propagation direction [ φ dHM ] corresponding to the minimum of∆ d HMi ( φ ), is again the outcome of the technique. We applied the same minimization method as described before by subtractingthe in-situ measured velocity [ V i ] from the calculated velocity converted fromthe measured elongation value at t a , V F φ,t a ( φ ∈ [0 ◦ , ◦ ]):∆ V F φ ( φ ) = V F φ,t a ( φ ) − V i , (6)where ∆ V F φ ( φ ) is the calculated difference, V F φ,t a ( φ ) the derived velocity atarrival time, and V i is the in-situ measured velocity of the ICME front. SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 6 δ in situObserver Figure 3.
Illustration showing the calculation of the distance [∆ d ] from the Sun to the pointof the circular CME front in the direction of the in-situ observing spacecraft. The gray lineshows the line of sight, angle ǫ is the measured elongation, d o is the Sun-observer distance, φ is the propagation direction relative to d o , R HM is the distance of the CME apex from theSun, R HMi is the distance of the CME front in direction of the in-situ spacecraft from theSun, and δ is the angle between R HM and R HMi . The same method can be applied by using HM. The velocity V HMi wascalculated on the basis of R HMi , thus in the direction of the in-situ spacecraft,which for HM does not necessarily have to be the apex of the ICME front, butcan, in principle, be also any point along the circle. We define∆ V HMi ( φ ) = V HMi,t a ( φ ) − V i , (7)where ∆ V HMi ( φ ) is the calculated difference and V HMi,t a ( φ ) the derived velocityat arrival time. The angle belonging to the minimum difference [ φ V F Φ or φ V HM ]is the direction resulting from the constraint with the velocity at arrival time.Liu et al. (2010b) pointed out that there is an ambiguity for possible propagationdirections for HM. Because of mathematical reasons there are two minima withinthe range of φ ∈ [0 ◦ , ◦ ]. Since we get two minima for both constraints (∆ d ,∆ V ) we choose the value where both minima show the best agreement witheach other; in our cases, it seems the smaller value. The conversion using thenext minimum would yield a large distance of the CME apex, which may not bepossible given the observed CME size from two vantage points (Figure 4).The directions from the arrival time and velocity constraints will not beidentical. To combine the resulting propagation directions for each method, wedefine SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 7 . Rollett et al.
Figure 4.
Two possible solutions for HM. The green arrow shows the direction of the ICMEapex resulting from the first minimum and the green circle shows the ICME front (CME 1) forthis direction at arrival time. The red arrow indicates the direction derived from the secondminimum of ∆ V for the ICME event of June 2008. The apex of this ICME (CME 2) would be ≈ . in-situ spacecraft. φ F φ = ( φ dF φ + φ V F φ ) / φ HM = ( φ dHM + φ V HM ) / φ HM is the propagation direction of the ICME apexfor the HM method. However, all kinematics are calculated for the part of thecircle which hit the in-situ spacecraft and not for the apex.The distance-time profile for the defined mean propagation angle was fittedby using a cubic spline, from which we derived the velocity profile via numericaldifferentiation. All errors result from the manual tracking of the ICME front only.To be able to do an error estimation, every feature was measured five times. Theresulting standard deviation also yields a reliable error for the numerical velocityderivation using three-point, Lagrangian interpolation. We also indicate an errorfor the propagation direction for both methods. SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 8 . Results
Three different ICMEs were investigated to cover a range from slow to fast CMEinitial speeds. One event was slow and narrow (June 2008), the second was alsoslow but had a wide longitudinal extent (February 2009), and the third ICME(April 2010) was a fast and geoeffective event.4.1. 02 – 06 June 2008 ICMEThe leading edge of this ICME was seen on 2 June 2008 09:00 UT in the HI1field of view (FoV) and on 3 June 2008 12:00 UT in the HI2 FoV of STEREO-A. This CME had no obvious signatures of magnetic reconnection on the Sun(Robbrecht, Patsourakos, and Vourlidas, 2009). A magnetic cloud was detectedbetween 6 June 2008 ≈
22 UT and 7 June 2008 ≈
12 UT at STEREO-B(M¨ostl et al. , 2009; Lynch et al. , 2010; Wood, Howard, and Socker, 2010). Theseparation between both STEREO spacecraft was 53 . ◦ at that time. Figure 5shows the proton density (STEREO-B, PLASTIC) and the Jmap (STEREO-A,HI1/2) with two clear traces of the event. The first one is the leading edge andthe second one is the core of the ICME. Both Jmap-tracks match with the in-situ arrival times (sudden increase of the proton density at STEREO-B) as indicatedwith the vertical red lines. Its in-situ signature as well as the heliospheric imagesboth reveal a pronounced three-part structure, with the density enhancementsbracketing the magnetic flux rope (M¨ostl et al. , 2009; Lynch et al. , 2010).To obtain the propagation direction and the velocity only the first track, i.e. the ICME leading edge, was investigated. Figure 6 shows the calculation of theminima of the differences between the converted distance at in-situ arrival timeand the distance between Sun and in-situ spacecraft ( φ dF φ and φ dHM ) as wellas for the differences between the derived velocity at arrival time and the in-situ measured arrival velocity [ φ V F φ and φ V HM ]. F φ (top panel) yields as a meandirection E24 ± ◦ (relative to the Sun-Earth line) and HM (bottom panel) resultsin E51 ± ◦ .Figure 7 shows the kinematics of this event derived from F φ using the ob-tained propagation angle. The upper panel displays the result of the conversionfrom elongation into solar radii and the link to the arrival time at the in-situ spacecraft. The standard deviation lies between 0.5 R ⊙ (HI1) and 1.6 R ⊙ (HI2).The middle panel shows the direct derivation of the measurements (crosses) andthe derivative of the spline fit. The kinematics using F φ ( φ F φ = E24 ± ◦ ) yielda continuous acceleration from ≈
330 to ≈
440 km s − and a mean velocityof 389 ±
48 km s − . The velocity at arrival at STEREO-B derived from F φ is 432 ±
61 km s − . F φ results in a typical late acceleration at ≈ et al. (2009). The new method using in-situ data as constraints diminishesthis effect. The same approach but for HM is shown in Figure 8. The errors ofthe measurements are between 0.4 R ⊙ (HI1) and 1.2 R ⊙ (HI2). Kinematicsusing HM ( φ HM = E51 ± ◦ ) deliver a mean velocity of 395 ±
35 km s − . TheCME shows a strong acceleration from ≈
280 to ≈
440 km s − up to a distance SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 9 . Rollett et al.
Figure 5.
In-situ measured proton density from STEREO-B (top). The first red line fromthe left marks the time of the ICME arriving at STEREO-B and others delimit two strongpeaks in the proton density. The lower panel shows the Jmap produced from remote sensingdata of heliospheric images of STEREO-A with overplotted measurement points (red crosses).The white horizontal line indicates the position of STEREO-B. of about 100 solar radii followed by a slight deceleration to a final velocity of422 ±
44 km s − , consistent with the in-situ measured velocity at STEREO-Bof 403 km s − .4.2. 13 – 18 February 2009 ICMEThe ICME arrived on 13 February 2009 11:00 UT in the HI1 FoV of STEREO-A and became visible in HI2 on 14 February 2009 04:00 UT. This CME wasassociated with a flare and an EUV wave (Kienreich, Temmer, and Veronig,2009) occurring at the limb as seen by STEREO-A, since the separation of theSTEREO satellites was 91 ◦ at that time. Compared to the June 2008 event there SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 10 ixed - Φ
Φd = -56° (E27°)FΦΦ = -50° (E21°)VFΦ
Φ ΦF = -53° (E24°)Harmonic Mean
Φ = -86° (E57°)dHMΦ = -74° (E45°)VHM
ΦHM = -80° (E51°)
Propagation Direction at Arrival Time [°]
Angle calculation June 2008
Figure 6.
Propagation directions for Fixed- φ (top panel) and Harmonic Mean (bottom panel).The black crosses show the differences between the calculated distance at arrival time and thedistance of the in-situ spacecraft from Sun-centre for different propagation angles. The redasterisks indicate the same approach but for the difference of the calculated velocity and the in-situ measured velocity at arrival time. is no characteristic three-part structure — neither in the heliospheric images norin the in-situ data. STEREO-B measured an increase of the proton density thatwas followed by a large-scale magnetic flux rope (M¨ostl et al. , 2011).Figure 9 shows the proton density measured by STEREO-B and the Jmapfrom STEREO-A. The ICME track became faint rather quickly, as expected fora limb CME (Morrill et al. , 2009). Comparing the track in the Jmap and theproton density in Figure 9 shows that the ICME seems to arrive earlier at theelongation of STEREO-B than it was measured in-situ .Figure 10 illustrates the calculation of the propagation directions ( φ F φ =E36 ± ◦ , φ HM = E61 ± ◦ ). Again, HM gives a direction further away from theobserver. The upper panel in Figure 11 shows the result of the conversion fromelongation into radial distance [F φ ] and the linkage with the in-situ arrival time.The standard deviation of both conversion methods is between 0.5 R ⊙ (HI1)and 1 R ⊙ (HI2). Kinematics using F φ yield a mean velocity of 310 ±
29 km s − .The velocity profile shows a nearly constant speed up to a distance of ≈ ⊙ followed by an acceleration from ≈
280 km s − to a velocity at arrival time SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 11 . Rollett et al.
ST BST B - Φ Φ FΦ = - ° ( )53 E24° Figure 7.
Top: Resulting distance-time profile for F φ . The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontalline shows the arrival time of the ICME at STEREO-B. Middle: The solid curve shows thederivation of the fit, which is done to determine the velocities of this event. The gray areaindicates the standard deviation of the measurements. The horizontal line indicates the in-situ measured velocity at STEREO-B. Bottom: Residuals of the fit and the direct measurements. of 416 ±
35 km s − . Again F φ shows an apparent acceleration close to 1 AU.The mean velocity derived of HM is 325 ±
28 km s − and the impact velocityis 398 ±
34 km s − , whereas the in-situ measured impact velocity of the ICMEat STEREO-B is ≈
362 km s − (see Figure 12). There seems to be an upwardkink in the track in the Jmap at about 35 ◦ elongation that is also visible in thederived kinematics as an acceleration.4.3. 03 – 05 April 2010 ICMECompared to the previous mentioned events this CME was relatively fast forsolar minimum. The ICME arrives in the HI1 FoV of STEREO-A on 3 April 2010 SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 12
T BST B Φ HM = - 80° (E51°) Figure 8.
Top: Resulting distance-time profile for HM. The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontalline shows the arrival time of the ICME at STEREO-B. Middle: The solid curve shows thederivation of the fit, which is done to determine the velocities of this event. The gray areaindicates the standard deviation of the measurements. The horizontal line indicates the in-situ measured velocity at STEREO-B. Bottom: Residuals of the fit and the direct measurements.
Wind , situated atthe L1 point sunward of the Earth (M¨ostl et al. , 2010). The separation betweenSTEREO-A and
Wind was 67.4 ◦ at that time. It was a geoeffective ICME andcaused a moderate geomagnetic storm with a minimum of the Dst index about −
72 nT and maximum Kp of 8 (M¨ostl et al. , 2010; Wood et al. , 2011).Figure 13 shows the proton density at
Wind and the Jmap of HI1A andHI2A of the event. The track of the ICME fits well with the sharp increase inproton density. As illustrated in Figure 14 the two conversion methods yield apropagation direction of φ F φ = W3 ± ◦ and φ HM = E25 ± ◦ , respectively.The measurement errors for F φ are 1.3 R ⊙ (HI1) and 1.5 R ⊙ (HI2), for HM1 R ⊙ (HI1) and 1.3 R ⊙ (HI2). Kinematics from F φ result in a mean velocity SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 13 . Rollett et al.
Figure 9.
In-situ measured proton density from STEREO-B (top). The first red line fromthe left marks the time of the ICME arriving at STEREO-B and others delimit two strongpeaks in the proton density. The lower panel shows the Jmap produced from remote sensingdata of heliospheric images of STEREO-A with overplotted measurement points (red crosses).The white horizontal line indicates the position of STEREO-B. of 829 ±
122 km s − and an impact velocity of 825 ±
129 km s − (Figure 15),kinematics from HM yield a mean velocity of 854 ±
100 km s − and at arrival at Wind a velocity of 813 ±
106 km s − (Figure 16). The average speed of the ICMEsheath region between the shock and the magnetic cloud as measured in-situ by Wind , was ≈
720 km s − . Both methods slightly overestimate the impact velocityby about 100 km s − . In this case, differences in the velocity-time profiles aremore pronounced: F φ shows a nearly constant velocity between 800 and 900km s − while HM delivers an acceleration up to ≈
100 solar radii to about 1000km s − followed by a deceleration to 800 km s − . Since the irregularity in thevelocity profile happens in the transition region between the fields of view of HI1and HI2 it could also be related to the different sensitivities of the cameras. The SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 14 ropagation Direction at Arrival Time [°]
Angle calculation February 2009
Harmonic Mean
Φ = -108° (E64°)dHMΦ = -102° (E58°)VHM
ΦHM = -105° (E61°) Fixed - Φ
Φ = -84° (E40°)dFΦΦ = -76° (E32°)VFΦ
Φ = -80° (E36°)FΦ
Figure 10.
Propagation directions for Fixed- φ (top panel) and Harmonic Mean (bottompanel). The black crosses show the differences between the calculated distance at arrival timeand the distance of the in-situ spacecraft from Sun-centre for different propagation angles.The red asterisks indicate the same approach but for the difference of the calculated velocityand the in-situ measured velocity at arrival time. signal of HI1 turns faint rather quickly at larger elongations while HI2 seems tooverexpose at lower elongations what yields to a discontinuity of the front andmakes the tracking of the leading edge difficult. These circumstances could be apossible reason for the untypical shape of the velocity evolution.Table 1 lists the results of the three events for the two conversion methods,F φ and HM, and the relevant in-situ measurements.
5. Discussion and Conclusions
The purpose of our study was to introduce a new technique, pointed out byM¨ostl et al. (2009, 2010), to additionally use the constraints imposed by in-situ measurements to derive ICME kinematics end-to-end from the Sun to 1 AU.This method uses single-spacecraft heliospheric-imager data together with single-spacecraft in-situ data and assumes a constant propagation direction.
SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 15 . Rollett et al.
ST BST B - Φ Φ FΦ = - ° ( )80 E36° Figure 11.
Top: Resulting distance-time profile for F φ . The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontalline shows the arrival time of the ICME at STEREO-B. Middle: The solid curve shows thederivation of the fit, which is done to determine the velocities of this event. The gray areaindicates the standard deviation of the measurements. The horizontal line indicates the in-situ measured velocity at STEREO-B. Bottom: Residuals of the fit and the direct measurements. Kinematics covering measurements in the HI1 and HI2 FoV were analyzedfor three well-observed CMEs on their way from Sun to 1 AU. Images fromthe
Heliospheric Imagers onboard the NASA STEREO mission were used toproduce time-elongation plots (Jmaps) from which the ICME measurements werederived. The measured elongation angles were converted into radial distances(in units of solar radii) by using two methods — Fixed- φ (F φ ) and HarmonicMean (HM) — which approximate the ICME front as a point (F φ ) or a circle(HM). By combining remote sensing with in-situ measurements it was possibleto calculate the propagation directions as well as the kinematics of the eventswithin the geometrical assumptions of the conversion methods. We constrained SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 16
T BST B Φ HM = - ° ( )105 E61° Figure 12.
Top: Resulting distance-time profile for HM. The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontalline shows the arrival time of the ICME at STEREO-B. Middle: The solid curve shows thederivation of the fit, which is done to determine the velocities of this event. The gray areaindicates the standard deviation of the measurements. The horizontal line indicates the in-situ measured velocity at STEREO-B. Bottom: Residuals of the fit and the direct measurements. the ICME direction in such a way that the ICME distance-time and velocity-time profiles are most consistent with in-situ measurements of the arrival timeand the velocity on arrival. In Temmer et al. (2011) the velocity profiles of thesame three events were compared to the ambient solar wind, modeled by theENLIL 3D MHD model (Odstrcil, 2003).The ICME of 02 – 06 June 2008 was clearly identified in the Jmap. It was aslow event ( ≈
390 km s − ) that was embedded in the solar wind. It propagatedtoward STEREO-B, where clear signatures of a magnetic flux rope could be iden-tified in-situ . The F φ method reveals a propagation direction toward STEREO-B( φ F φ = E24 ± ◦ ), while the HM method assumes a wider longitudinal extent SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 17 . Rollett et al.
Figure 13.
In-situ measured proton density from
Wind (top). The first red line from theleft marks the time of the ICME arriving at
Wind and others delimit two strong peaks inthe proton density. The lower panel shows the Jmap produced from remote sensing data ofheliospheric images of STEREO-A with overplotted measurement points (red crosses). Thewhite horizontal line indicates the position of
Wind . which may be improbable for this ICME event ( φ HM = E51 ± ◦ ), because theextent in the ecliptic should be around 25 degrees (Wood, Howard, and Socker,2010). The method of Wood, Howard, and Socker (2010), where synthetic im-ages of a tube-like CME are adjusted to fit the CME’s appearance in theSTEREO/HI images, yields a direction in longitude of E34 ◦ , and various di-rections derived by M¨ostl et al. (2009) range from E24 ◦ to E45 ◦ , all consistentwith the directions derived in this paper.The event of 13 – 18 February 2009 was a slow event too ( ≈
320 km s − ). Itsparameters were measured in-situ by STEREO-B but do not show a clear three-part structure as for the June 2008 event. This CME originated from the limband seems to have a wider longitudinal extension in the ecliptic and thereforewas difficult to investigate since it dimmed rather quickly in the Jmap because SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 18 ropagation Direction at Arrival Time [°]
Angle calculation April 2010
Fixed - Φ
Φ = -68° (E1°)dFΦΦ = -60° (W7°)VFΦ
Φ = -64° (W3°)FΦHarmonic Mean
Φ = -102° (E35°)dHMΦ = -82° (E15°)VHM
ΦHM = -92° (E25°)
Figure 14.
Propagation directions for Fixed- φ (top panel) and Harmonic Mean (bottompanel). The black crosses show the differences between the calculated distance at arrival timeand the distance of the in-situ spacecraft from Sun-centre for different propagation angles.The red asterisks indicate the same approach but for the difference of the calculated velocityand the in-situ measured velocity at arrival time. it left the TS early. The results of the used methods differ again by about 25degrees ( φ F φ =E36 ± ◦ , φ HM =E61 ± ◦ ) and agree with the directions derivedby M¨ostl et al. (2011) who found E35 ◦ (F φ fitting) and E63 ◦ (HM fitting),respectively. The kinematics of both conversion methods are consistent withthe in-situ measured velocity.The event of 03 – 05 April 2010 is an outstanding event for this solar minimum.In contrast to the other two events it was relatively fast ( ≈
835 km s − ). Thederived propagation directions range from φ F φ = W3 ± ◦ to φ HM = E25 ± ◦ from Earth. Here, M¨ostl et al. (2010) found a direction of longitude W0 ± ◦ using various methods (triangulation, Fixed- φ fitting, and forward modeling),and Wood et al. (2011) find a direction of W2 ◦ , which makes our Fixed- φ resultmore consistent with the others quoted in the literature. The velocity profileshows a different evolution for both methods. While F φ results in a nearlyconstant velocity between ≈
750 and 850 km s − , HM shows an acceleration upto ≈
100 R ⊙ followed by a slight deceleration. The event seems to be decelerated SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 19 . Rollett et al. - Φ Φ FΦ = - ° ( )64 W3° WindWind
Figure 15.
Top: Resulting distance-time profile for F φ . The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontal lineshows the arrival time of the ICME at Wind . Middle: The solid curve shows the derivationof the fit, which is done to determine the velocities of this event. The gray area indicates thestandard deviation of the measurements. The horizontal line indicates the in-situ measuredvelocity at
Wind . Bottom: Residuals of the fit and the direct measurements. from the slower ambient solar wind, in which the ICME was embedded ( e.g.
Gopalswamy et al. , 2001).The interpretation of the heliospheric images is rather difficult. Both conver-sion methods (Fixed- φ and Harmonic Mean) are useful to analyze the kine-matics of ICMEs on their way through the heliosphere. How appropriate itis to use one or the other clearly depends on the chosen event. The big ad-vantage of these methods compared to fitting methods such as the Sheeley-Rouillard (Sheeley et al. , 1999; Rouillard et al. , 2008) or the Harmonic Meanfitting method (Lugaz, 2010; M¨ostl et al. , 2011) is that a constant velocityis not assumed. On the other hand they are not useable for forecasting be- SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 20 indWind Φ HM = - 92° ( )E25° Figure 16.
Top: Resulting distance-time profile for HM. The crosses are the converted meanvalues of the direct measurements and the red line is the spline fit. The blue horizontal lineshows the arrival time of the ICME at
Wind . Middle: The solid curve shows the derivationof the fit, which is done to determine the velocities of this event. The gray area indicates thestandard deviation of the measurements. The horizontal line indicates the in-situ measuredvelocity at
Wind . Bottom: Residuals of the fit and the direct measurements. cause remote observations over the whole distance and in-situ measurements at1 AU are used as input to constrain CME kinematics. To assess the validityof the technique, numerical simulations should be used ( e.g.
Odstrcil and Pizzo,2009; Lugaz, Roussev, and Gombosi, 2011), because there the distance-time andvelocity-time functions of the ICME front and its shape are known. Anotherdisadvantage of the method is that for the calculation of the propagation direc-tion only the remotely sensed elongation value at arrival time at 1 AU is usedand constrained with in-situ data. Assuming constant direction, the resultingdirection is then used to convert the whole track of the remotely sensed CME.Using only one spacecraft from one vantage point it is not possible to derive the
SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 21 . Rollett et al.
Table 1.
Summary of the results for all three events. The table lists thepropagation angle, the arrival time, the mean velocity, and the impactvelocity of the ICME for the used methods.02 – 06 June 2008 F φ HM in-situ propagation angle E24 ± ◦ E51 ± ◦ –arrival day – – 06 Jun. 2008arrival time – – 15:35mean velocity [km s − ] 389 ±
48 395 ±
35 –impact velocity [km s − ] 432 ±
61 422 ±
44 40012 – 18 February 2009 F φ HM in-situ propagation angle E36 ± ◦ E61 ± ◦ –arrival day – – 18 Feb. 2010arrival time – – 10:00mean velocity [km s − ] 310 ±
29 325 ±
28 –impact velocity [km s − ] 416 ±
35 398 ±
34 36203 – 05 April 2010 F φ HM in-situ propagation angle W3 ± ◦ E25 ± ◦ –arrival day – – 05 Apr. 2010arrival time – – 07:58mean velocity [km s − ] 829 ±
122 854 ±
100 –impact velocity [km s − ] 825 ±
129 813 ±
106 720 direction of every point along the CME-track in contrast to the triangulationtechnique by (Liu et al. , 2010a).All this is needed as a basis to be able to better forecast the direction andarrival time of coronal mass ejections using empirical or numerical propagationmodels. It will be necessary to investigate a large number of events to reveal theirdifferent kinematics in order to be able to apply the most appropriate method.Furthermore, the geometrical limitations of the F φ (point shaped CME) andHM (circle shaped CME) methods should be adjusted to consider the differentwidths of the CMEs. Acknowledgements
T.R., C.M. and M.T. were supported by the Austrian Science Fund(FWF): [P20145-N16]. The presented work has received funding from the European UnionSeventh Framework Programme (FP7/2007-2013) under grant agreement n ◦ SOLA: Rollett_2011.tex; 18 September 2018; 14:45; p. 22 eferences
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