Relationship between three-dimensional velocity of filament eruptions and CME association
Daikichi Seki, Kenichi Otsuji, Takako T. Ishii, Ayumi Asai, Kiyoshi Ichimoto
EEarth, Planets and Space manuscript No. (will be inserted by the editor)
Relationship between three-dimensional velocity offilament eruptions and CME association
Daikichi Seki · Kenichi Otsuji · Takako T. Ishii · Ayumi Asai · Kiyoshi Ichimoto
Received: date / Accepted: date
Abstract
It is widely recognised that filament disappearances or eruptions arefrequently associated with Coronal Mass Ejections (CMEs). Since CMEs are amajor source of disturbances of the space environment surrounding the Earth, itis important to investigate these associations in detail for the better prediction ofCME occurrence. However, the proportion of filament disappearances associatedwith CMEs is under debate. The estimates range from ∼
10% to ∼
90% and couldbe affected by the manners to select the events. In this study, we aim to revealwhat parameters control the association between filament eruptions and CMEs. Weanalysed the relationships between CME associations and the physical parametersof filaments including their length, maximum ascending velocity, and direction oferuptions using 28 events of filament eruptions observed in H α . We found that theproduct of the maximum radial velocity and the filament length is well correlatedwith the CME occurrence. If the product is larger than 8.0 × km s − , thefilament will become a CME with a probability of 93%, and if the product issmaller than this value, it will not become a CME with a probability of 100%. Wesuggest a kinetic-energy threshold above which filament eruptions are associatedwith CMEs. Our findings also suggest the importance of measuring the velocityvector of filament eruption in three-dimensional space for the better prediction ofCME occurrence. D. SekiGraduate School of Advanced Integrated Studies in Human Survivability, Kyoto University,Sakyo, Kyoto 606-8306, JapanAstronomical Observatory, Kyoto University, Yamashina, Kyoto 607-8471, JapanDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA, United KingdomCentre for the Study of Existential Risk, University of Cambridge, 16 Mill Lane, CambridgeCB2 1SB, United KingdomE-mail: [email protected]. OtsujiSpace Environment Laboratory, Applied Electromagnetic Research Institute, National Insti-tute of Information and Communications Technology, Koganei, Tokyo 184-8795, JapanT. T. Ishii, A. Asai, and K. IchimotoAstronomical Observatory, Kyoto University, Sakyo, Kyoto 606-8502, Japan a r X i v : . [ a s t r o - ph . S R ] F e b Daikichi Seki et al.
Filaments are regions of dense cool plasma floating in the corona that are supportedby magnetic fields. They are observed in absorption as dark features on the solardisk in H α (6562.8 ˚A) and in emission as prominences above the solar limb. At theend of its life, a filament disappears by slow fading or exhibits a transient eruption.Before it disappears or erupts, small-scale blobs observed in H α in a filament oftenshow a larger standard deviation of the line-of-sight (LOS) velocity[26,25]. Duringeruption phase, the entire body of a filament ascends at a velocity of 100–1000 kms − [22].Filament eruptions are often associated with coronal mass ejections (CMEs),which are observed by coronagraphs such as the Large Angle and SpectrometricCoronagraph (LASCO) [4]. Some CMEs exhibit a three-part structure [13] con-sisting of a leading edge, faint coronal cavity, and dense core. Others exhibit morecomplex forms, appearing as narrow jets or global eruptions, which are called haloCMEs [28]. The core of a CME is believed to originate from the filament mass ifthe CME is associated with a filament eruption. Because the Sun is concealed byan occulting disk in coronagraph observations of CMEs, it is difficult to observethe early evolution of CMEs. Investigations of the evolution of filament eruptionsand their association with CMEs are expected to clarify the early evolution ofCMEs.CMEs often produce severe geomagnetic storms, which expose the Earth to apotential risk of adverse socioeconomic impacts such as a widespread blackout[3].A CME associated with a polar crown filament eruption reportedly caused a severegeomagnetic disturbance (Dst ∼ −
200 nT) three days after the eruption[16,17].Therefore, to mitigate the socioeconomic impacts of geomagnetic disturbances, itis essential to predict the occurrence of CMEs and their arrival to the Earth. Andto reveal the relationship between CMEs and the eruption or disappearance offilaments is important for the better prediction.However, the reported proportion of filament disappearances or eruptions thatare associated with CMEs ranges from ∼
10% to ∼ α data observed by the Solar Dynamics Doppler Imager(SDDI)[12] on the Solar Magnetic Activity Research Telescope (SMART)[27] atHida Observatory, Kyoto University, and found that 50% of them were associatedwith CMEs. [18] studied 904 filament and prominence eruptions observed in HeII (304 ˚A) by the Atmospheric Imaging Assembly (AIA)[15] and found that 73%of them were associated with CMEs. In contrast, [1] automatically classified 7332filament/prominence eruptions reported by the National Centers for Environmen-tal Information as events associated or not associated with CMEs and found thatonly 17% of them were associated with CMEs. (For a more detailed summary ofprevious studies on the filament–CME association, see Table 1 in [1]). It is sup- posed that the discrepancy among these results could depend on how to select theevents.In this study, we aim to reveal what parameters control the association be-tween the filament eruptions and CMEs. We investigate the relationships between ftp://ftp.ngdc.noaa.gov/STP/SOLAR DATA/SOLAR FILAMENTS/ accessed in 2008D velocity of filament eruptions & CME association 3 physical parameters that characterise filament eruptions, i.e., the length, velocityduring eruption, and direction of eruption, and the CME association. Several stud-ies have shown that these parameters are well correlated with the CME associationof filament eruptions[24,8,19]. [8] studied 54 prominence eruptions observed abovethe limb in H α . They defined “eruptive prominences” as those in which all or partof the material escaped from the solar gravitational field and “active prominences”as those in which none of the material appeared to escape. They found that erup-tive prominences clearly had a larger apparent velocity (the velocity projected onthe plane of the sky) above 1.10 solar radii than active prominences did and thateruptive prominences were more strongly associated with CMEs (94%) than activeones (46%). Our previous study[24] found that filament eruptions are more likelyto be associated with CMEs if the filament length exceeds 150 Mm, the maximumradial velocity exceeds 140 km s − , or their direction is inclined by less than 48deg with respect to the solar normal. Thus, in the present study, we focus on thesethree parameters of filament eruptions and investigate how the association ratevaries with respect to them. Note that, in contrast to our previous work that weinvestigated the tendency of CME association with respect to individual physicalparameters, the present study aims to improve the predictability of CME associa-tion by combining those parameters. In Section 2, we provide a description of thedata we utilised. In the succeeding section, the results will be provided, followedby summary and discussion. We selected events from the SMART/SDDI Filament Disappearance Catalogue (hereafter, the catalogue)[24]. The unique advantage of the SDDI is its wide wave-length coverage, which makes it possible to determine the LOS velocity of eruptingfilaments up to 400 km s − . The catalogue lists 43 filament/prominence disap-pearances observed by SDDI from 2016 May 1 to 2019 June 18, in which fila-ments/prominences totally disappeared at the H α line centre. We selected 28 ofthese events that had a credibility value of 2 or 3 for CME association in thecatalogue (description of “credibility” will be provided later). That is, we usedonly events whose CME association or non-association is fairly clear. Note thatsome of the events were excluded from our analysis, even though their credibilitywas 2 or 3, because (1) terrestrial clouds covered the target filaments, and it wasimpossible to estimate their precise LOS velocities (No.001, 007, 018, 021, 022,035, and 043), or (2) the length of the target filament could not be measured dueto the lack of observation (No.029). Most of the selected events (26 of 28) are fila-ment eruptions, and two events (on May 24 and June 20 in 2016) are prominenceeruptions observed on the solar limb. Hereafter, we refer to these 28 events simplyas filament eruptions.The credibility value indicates how credible the CME association of an event is. We made a movie containing solar full-disk images of each event in the H α line centre or in 304˚A and LASCO C2 running difference images. While watchingeach movie, we examined the directional and temporal association of each filamenteruption with the CME and assigned a credibility value based on our judgement. The actual movies used for examination can be accessed at the catalogue webpage(click the credibility column). Our judgement is based on (1) ∆T , which is thedifference between the time when a CME was first observed in LASCO and thetime of total disappearance of the filament in H α centre (same as FD end timein the catalogue), and (2) ∆φ , which is the difference between the position angleof the filament and the central position angle of the CME. Table 1 describes howwe determined the credibility 2 or 3 of the CME association on the basis of ∆T and ∆φ . The credibility 1 was labeled to events which were difficult to determineone-to-one correspondence. More specifically, we labeled the credibility 1 (1) iftwo filaments disappeared within one hour, the difference between their ∆φ ’s waswithin 15 deg, and they were diagnosed as being associated with the same CME,or (2) if there were flares located within 30 deg from the central position angleof the CME and within a few hours prior to CME occurrence. For example, theevents No.002 and No.003 in the catalogue were categorised as the credibility of 1because two filaments disappeared within one hour, and it was ambiguous which ofthese events was actually associated with one CME. Another example is No.012,in which a CME could be attributable to a C-class flare occurred in an activeregion rather than to the filament eruption of the interest, and thus we concludedthe credibility of this event as 1. Table 1
Criteria for determining the credibility of a CME association on the basis of ∆T and ∆φ . The units of ∆T and ∆φ are hour and deg, respectively. ∆T < < ∆T < < ∆T < < ∆T∆φ <
30 with CME with CME without CME without CMEcredibility 3 credibility 2 credibility 2 credibility 330 < ∆φ <
70 with CME with CME without CME without CMEcredibility 2 credibility 2 credibility 2 credibility 370 < ∆φ <
100 without CME without CME without CME without CMEcredibility 2 credibility 2 credibility 2 credibility 3100 < ∆φ without CME without CME without CME without CMEcredibility 3 credibility 3 credibility 3 credibility 3Table 2 shows the selected 28 events with their CME associations and physicalparameters.
D velocity of filament eruptions & CME association 5
Table 2
Filament eruptions used in this study. Data are taken from the SMART/SDDI Filament DisappearanceCatalogue[24]. date & time CME Cred. a V r max V r fin V pos b V max L Θ c (UT) (km s − ) (km s − ) (km s − ) (km s − ) (Mm) (deg)2016-05-24 01:00 Yes 3 134 36.4 134 175 137 11.82016-06-01 21:00 Yes 3 173 50.8 189 226 151 25.72016-06-20 05:30 Yes 3 215 41.3 223 224 63.6 16.62016-07-07 07:19 Yes 3 359 189 272 365 35.6 9.672016-07-19 05:30 No 3 30.8 − − − − − − − − − − a The credibility of the association between a CME and a filament eruption. 3 > >
1. Events witha credibility of 1 are excluded from this study. b The apparent velocity of a filament. It is defined as (cid:113) V x + V y , where V x and V y are the east–westand south–north velocities projected on the plane of the sky, respectively. c The inclination angle of a filament eruption with respect to the solar normal.‘Date & time’ is the start time of a filament eruption and is defined as the first observation of a dark feature in H α − V r max , V r fin , V pos , and V max are determined as follows. We manuallytracked and measured the position and LOS velocity of a blob at the apex of thefilament that was present until its total disappearance in H α . Then, we constructed Daikichi Seki et al. its three-dimensional velocity as a function of time. V r max is the maximum radial(or ascending) velocity during the eruption, whilst V max is the maximum mag-nitude of three-dimensional velocity. V pos is equal to (cid:112) V x + V x , where V x and V y are the velocities of the filament in the east–west and south–north directionson the plane of the sky, at the time of V r max , respectively. V r fin is the radialvelocity at the last observation of a filament in H α . L is the length of a filamentmeasured at the same time as ‘date & time’. The projection effect is correctedaccording to the location of the filament on the solar disk. Θ is the inclinationangle between the direction of the filament velocity at the time of V r max and thesolar normal (see Figure B on the catalogue webpage). For further details of howthese values were determined, see our previous paper[24]. Figure 1 displays the CME associations according to L (vertical axis) and V r max (top left), V max (top right), or V pos (bottom left) on a logarithmic scale. Here,the length and velocities are normalised by L = 100 Mm and V = 100 km s − ,respectively. We can see the tendency that the longer and faster filaments are morelikely to be associated with CMEs. The solid lines in the panels are drawn by thefollowing relationships; (cid:18) V r max V (cid:19) × (cid:18) LL (cid:19) . = 0 .
80 (1) (cid:18) V max V (cid:19) × (cid:18) LL (cid:19) . = 1 . (cid:18) V pos V (cid:19) × (cid:18) LL (cid:19) . = 0 .
85 (3)They were determined by using the algorithm of Linear Support Vector Classifi-cation implemented in LIBLINEAR[6] (for further explanation of the algorithm,see Appendix and [6]). In the top left panel ( V r max ), 27 events out of 28 (96%)were correctly classified into the two groups of filament eruptions with (open cir-cles) and without (crosses) CMEs, whilst in the other cases, 21 (for V max ) and25 ( V pos ) events were correctly separated. If we make a separation so that thenumber of correctly classified events can be maximised, 27 ( V r max ), 24 ( V max ),and 26 ( V pos ) events will be correctly classified (the separations not shown in thefigure). Thus, a better prediction of the CME association could be obtained byusing V r max rather than using V max or V pos at least with our limited number ofthe events, 28. This result suggests the advantage of measuring the radial veloc-ity of filament eruptions. It also suggests that measuring both the velocity andthe length of filaments should contribute to the better prediction of CME occur-rence. The three-dimensional velocity observation provides a better capability forpredicting the occurrence of CMEs, whilst the H α imaging observations without Doppler measurements ( V pos ) can still contribute to it.Figure 2 displays histograms of events with (grey) and without (black) CMEswith respect to the left-hand sides (LHS) of Equation (1)–(3). These histogramsalso demonstrate that the CME association is better identified when V r max isused than when V max or V pos is used. In the top left panel, we see a clear bimodal D velocity of filament eruptions & CME association 7 log ( V r _ max / V ) l o g ( L / L ) log ( V max / V ) l o g ( L / L ) log ( V pos / V ) l o g ( L / L ) Fig. 1
Plots of filament eruptions according to V r max (top left), V max (top right), or V pos (bottom left) and filament length, L , on a common logarithmic scale. V and L correspond tothe typical velocity (100 km s − ) and typical length (100 Mm) of filaments, respectively. Opencircles and crosses represent events with and without CMEs, respectively. The solid lines aredescribed in the text. distribution, which is less clear in the other cases. To confirm the bimodalityquantitatively, we introduced a statistic, D-value, which is defined as D ≡ | µ − µ | σ , (4)where µ and µ are the averages of the two normal distributions fitted to theevents with and without CMEs, and σ is equivalent to σ = (cid:115) σ + σ , (5)where σ and σ are their standard deviations. The D-value represents the distancebetween the means of two normal distributions relative to their standard devia-tions. These distributions can be regarded as being separated if the D-value is Daikichi Seki et al. log {( V r _ max V ) × ( LL ) } o f e v e n t s log {( V max V ) × ( LL ) } o f e v e n t s log {( V pos V ) × ( LL ) } o f e v e n t s Fig. 2
Histograms of the LHS of Equation (1)–(3) on a common logarithmic scale. The darkand light grey bars correspond to the events without and with CMEs, respectively. The barsare stacked. The size of a bin is 0.33 larger than 2 [2,20,5]. The means and standard deviations of two normal distribu-tions (with and without CMEs) for each case of Equation (1)–(3) are summarisedin Table 3 together with the D-values. We obtained D values of 2.3, 1.8, and 1.7for V r max , V max , and V pos , respectively. Only V r max exhibits the D-value largerthan 2. The better bimodality when V r max is used is confirmed quantitatively. D velocity of filament eruptions & CME association 9
100 0 100 200 300 400 500 V r _ fin [km s ] L [ M m ]
100 0 100 200 300 400 500 V r _ fin [km s ] l o g { ( V r _ m a x V ) × ( L L ) . } Fig. 3
Plot of filament eruptions according to V r fin and L (left) or common log of theproduct of normalised V r max and normalised L to the power of 0.92 (right). Open circles andcrosses have the same meaning as in Figure 1. Grey area corresponds to negative V r fin . Table 3
Summary statistics of the fitted normal distributions andthe corresponding D values. with CMEs without CMEs µ σ µ σ DV r max (Eq. (1)) 0.28 0.23 -1.0 0.76 2.3 V max (Eq. (2)) 0.46 0.28 -0.20 0.44 1.8 V pos (Eq. (3)) 0.29 0.29 -0.81 0.88 1.7Figure 3 shows the CME association with respect to the radial velocity of thelast observation ( V r fin ) and L (left panel) or a common log of the LHS of Equation(1) (right panel) for each filament eruption. Open circles and crosses denote eventswith and without CMEs, respectively. Most of the filament eruptions (80%) withnegative V r fin (grey area), i.e., events in which the filaments fall back to the Sun,were not associated with CMEs. In addition, 77% of the filament eruptions withpositive V r fin and L larger than 70 Mm were associated with CMEs. Note thatthe filaments with the smaller (larger) value of the LHS of Equation (1) similarlytend to have smaller (larger) V r fin (see the right panel).From Figure 3, we can also recognise that there are exceptional events thatwere associated with CMEs despite their negative V r fin ’s ( − − and − − ). We speculate that the blobs which escaped the solar gravity anderupted into the interplanetary space became invisible in H α , and we tracked apart of the filament that fell back to the solar surface. Figure 4 shows the CME association according to the LHS of Equation (1)(vertical axis) and Θ , the inclination angle (angle from the solar normal) of thevelocities (horizontal axis). We found that 82% of the filament eruptions withdirections that were inclined by more than 45 deg from the solar normal were notassociated with CMEs, and 71% of those with their Θ ’s smaller than 45 deg were [str] l o g { ( V r _ m a x V ) × ( L L ) . }
15 30 45 60 75 90 [deg]
Fig. 4
Plot of filament eruptions according to Θ (inclination angle in steradians and degrees)and a common log of the LHS of Equation (1). The symbols have the same meaning as inFigure 1. associated with CMEs. Thus, the inclination angle of eruptions will provide a cluefor forecasting the CME occurrence. Note that the LHS of Equation (1) of thefilament eruptions with their Θ ’s larger than 45 deg seldom exceeds − Θ ’s smaller than 45 deg, while only 36% of the non-associated oneshave Θ smaller than 45 deg. These results are consistent with the work of [9],in which they defined two types of prominence eruptions, radial and transverseevents, according to the eruptive motion of the prominence observed on the solarlimb. In their statistical study, they found that 94% of the prominence eruptionsassociated with CMEs were radial events (86% in our study) and that 76% of thetransverse events were not associated with CMEs (82% in our study).Figure 5 shows the linear speed of the CMEs in the SOHO/LASCO CMECatalog[29] against V r max . The CME speed is expected to be larger than the ve- locity of the associated filament eruption[9]. The black line indicates equal speeds.All the data points but one ( V r max = 359 km s − ) are above or close to the blackline, as expected. However, since there is a large scatter in the ratio of CME linearspeed to V r max , it is difficult to predict CME linear speeds from the maximumradial velocity. D velocity of filament eruptions & CME association 11 V r _ max [km s ] C M E li n e a r s p ee d [ k m s ] Fig. 5
Plot of filament eruptions according to V r max and CME linear speed. The black linecorresponds to equal speeds. In this study, we investigated the relationships between the physical parametersof filament eruptions (three-dimensional velocity, filament length, and direction oferuption) and their CME associations using 28 events observed by SDDI at HidaObservatory. We found that the filament eruptions are well separated into twogroups of events, one with and the other without CMEs, according to the productof the normalised maximum ascending velocity ( V r max /V ) and the normalisedfilament length ( L/L ) to the power of 0.96, and that among the filament eruptionswith (cid:16) V r max V (cid:17) × (cid:16) LL (cid:17) . > .
80, 93% are associated with CMEs, and 100%of filament eruptions with the product < .
80 are not associated with CMEs.The apparent velocity and the length of filaments measured in H α observationcould also provide a good measure for predicting the occurrence of CMEs, though the accuracy of the prediction using the apparent velocity is worse than thatusing the radial velocity. Our results suggest that the three-dimensional velocity,or more specifically the radial velocity derived from it, and the length of theerupting filament are the notable parameters for improving the predictability ofCME association. And thus, we suggests the importance of observations of the three-dimensional velocity of filament eruptions for the prediction of CMEs. Itshould be noted, however, that improvement of statistics, i.e., studies with a largernumber of examples, are strongly required to confirm these results.Here, we propose a possible physical interpretation for the solid line in the topleft panel of Figure 1. This line, which is represented by Equation (1), successfullyseparates events into those with and without CMEs. We assume that (1) the crosssection of filaments, A , follows the relationship of (cid:18) AA (cid:19) = (cid:18) LL (cid:19) , (6)where A is the typical cross section of filaments (100 Mm ), and that (2) theaverage hydrogen density is common among filaments, i.e., 10 cm − , which is atypical value for quiescent prominences [10]. Then, if we regard Equation (1) as (cid:18) V r max V (cid:19) × (cid:18) LL (cid:19) ∼ . , (7)or V r max × L ∼ . × km s − , then its square represents the kinetic energy ofan erupting filament, i.e., × proton mass × density × volume × Vr max = 5.4 × erg. This relationship could be regarded as the kinetic-energy threshold abovewhich filament eruptions are associated with CMEs. Note that if the length of afilament is 100 Mm, the deduced mass gets 1.7 × g. [7] reported the massesof 18 prominences, which ranged from (1.08 ± × to (2.09 ± × g. Our assumed “typical” mass is consistent with the reported values.As mentioned in Section 1, the CME association rates of filament eruptionsreported to date range from ∼
10% to ∼ − ). Therefore, the selected prominences in these studies seem to have a largersize (e.g., larger than 70 Mm, because 75% of the filaments smaller than 70 Mmwere not associated with CMEs according to our result.)The association rate could also depend on whether studies include disk events(filament disappearances) in the records. In contrast to the high association rates(80 to 90%) reported in the studies taking into account only limb events (promi- nence disappearances)[8,9,11], some studies[23,14,24] in which both disk and limbevents were considered manifested the association rate of approximately 40–50%.[23] reported that 39% of filament and prominence eruptions observed in H α wereassociated with CMEs. [14] reported that 56% of filament eruptions were associ-ated with CMEs by automatically detecting filament disappearances in H α . In our D velocity of filament eruptions & CME association 13 study, considering only credible events, we found that 50% of filament eruptionsin H α were associated with CMEs.Additionally, the observational wavelengths at which filaments or prominencesare detected could also affect the association rate. In H α , as mentioned in theprevious paragraph, approximately 40 to 50% of disappearance events were asso-ciated with CMEs. By contrast, [18] used full-disk solar images in the 171, 193,and 304 ˚A AIA passbands and reported an association rate of 72%.The low association rate (17%, [1] ) might be attributable to the fact that theauthors include ejecta such as surges in addition to filament eruptions in theirsample. Among their 7332 events, they introduced 15 “filament types”, includingcoronal rain, sprays, and surges. In our study, we did not refer to these ejecta asfilaments, and we excluded them from our list. Thus, the definition of filaments inthat study was different from ours. Moreover, most of their events ( ∼ ∼
70 Mm (see Figure 8 in [1]). According to our result (see Figure 1or 3), 75% of the eruptions of filaments with lengths smaller than 70 Mm were notassociated with CMEs. Assuming that this relation holds for coronal rain, surges,and sprays, ∼
60% (80% × ± ∼ Appendix Linear Support Vector Classification (LSVC)
Linear Support Vector Classification (LSVC), which we utilised to estimate theCME association from the observation of filaments, is one of the popular machine-learning methods for classification. Our goal is to obtain the coefficients of the solidlines in Figure 1, which successfully separate the events associated with CMEs fromthose without CMEs in accordance with the velocity and length of filaments. Theselines can be expressed as w T x = w + w x + w x = 0 , (8)where w = ( w , w , w ) T is a coefficient vector to be optimised, and x = (1 , x , x ) T is a feature vector, which corresponds to the observation. In our case, x is a com- mon log of a normalised velocity ( V r max , V max , or V pos divided by V ), and x isa common log of a normalised length ( L divided by L ).We optimised w by minimising the loss, l , defined as l = 12 w T w + C N (cid:88) i =1 (max(1 − y i w T x i , , (9) X X X X X X x
The schematic view of LSVC in our case. where i and N are the index and the number of our selected events, y i ∈ {− , } isthe label of the CME association for the event i (-1: without CME, 1: with CME), x i = (1 , x i , x i ) T is an actual observed values for the event i , and C is a constant (inour case, set to be 100). The first term in Equation (9) is a penalty term, whichprevents the classifier from overfitting to the sample. As for the second term,intuitively, to minimise it corresponds to (1) maximising the sum of the distancesto the line from the correctly classified “near” data points and, simultaneously, (2)minimising the sum of the distances to the line from the misclassified data points.Here, we describe the meaning of the second term in more detail. Figure 6displays the schematic view of our analysis. Suppose that we aim to divide opencircles and crosses according to two variables, x and x . On the basis of thepresent w , we can calculate d defined as d = 1 (cid:113) w + w , (10) and select the correctly classified “near” data points whose distances to the lineare smaller than d , i.e., the correctly classified data points between the dashedlines in the figure (coloured in red). We also select the misclassified data pointsregardless of their distances to the line (coloured in blue). Then, Equation (9) D velocity of filament eruptions & CME association 15 should be written as l = 12 w T w + Cd { ( d + d + 2 d ) + ( d + d + d ) } . (11)The first parenthesis in Equation (11) corresponds to the sum of the distances tothe solid line from the misclassified events (and d multiplied by the number ofthem). The second parenthesis sums up the distances to the nearest dashed linefrom the correctly classified “near” data points. Finally, by solving the minimisa-tion of l for w , we obtained the well separable lines shown in Figure 1. DeclarationsList of abbreviations–
CME: Coronal Mass Ejection – LASCO: Large Angle and Spectrometric Coronagraph – SMART: Solar Magnetic Activity Research Telescope – SDDI: Solar Dynamics Doppler Imager – AIA: Atmospheric Imaging Assembly – LOS: line-of-sight – LSVC: Linear Support Vector Classification
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Competing interests
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Funding
This work was supported by JSPS KAKENHI grant numbers JP15H05814 (Projectfor Solar-Terrestrial Environment Prediction, PSTEP), JP16H03955, and JP18J23112.D. S. is supported by Research Fellowships for Young Scientists from the JapanSociety for the Promotion of Science.
Authors’ contributions–
Daikichi Seki: statistical analysis, structure and strategy of the paper, andwriting the paper – Otsuji Kenichi: developing an algorithm to deduce three-dimensional velocityof filaments. – Takako T. Ishii: observation and calibration – Ayumi Asai: structure and strategy of the paper – Kiyoshi Ichimoto: structure and strategy of the paper
Acknowledgements
D.S. thanks anonymous reviewers for their precious comments. D.S. also thanksGSAIS Empirical Research Group (GERG) for the discussion to enrich the method-ology. The SOHO/LASCO CME Catalog is generated and maintained at theCDAW Data Center by NASA and The Catholic University of America in co-operation with the Naval Research Laboratory.
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