The kinematics of coronal mass ejections using multiscale methods

1.7 MB·English

by  Jason P. Byrne

Astronomy&Astrophysicsmanuscriptno.9811Byrn c ESO2009
(cid:13)
January22,2009
The kinematics of coronal mass ejections using multiscale
methods
J.P.Byrne1,P.T.Gallagher1,R.T.J.McAteer1,andC.A.Young2
9 1 AstrophysicsResearchGroup,SchoolofPhysics,TrinityCollegeDublin,Dublin2,Ireland.
0 e-mail:[email protected]
0 2 ADNETSystemsInc.,NASAGoddardSpaceFlightCenter,Greenbelt,MD20771,USA.
2

n
Received19March2008;accepted16December2008
a
J
ABSTRACT
2
2
Aims.Thediffusemorphologyandtransientnatureofcoronalmassejections(CMEs)makethemdifficulttoidentifyandtrackusing

traditionalimageprocessingtechniques.WeapplymultiscalemethodstoenhancethevisibilityofthefaintCMEfront.Thisenables
]
anellipsecharacterisationtoobjectivelystudythechangingmorphologyandkinematicsofasampleofeventsimagedbytheLarge
R
AngleSpectrometricCoronagraph(LASCO)onboardtheSolarandHeliosphericObservatory(SOHO)andtheSunEarthConnection
S
CoronalandHeliosphericInvestigation(SECCHI)onboardtheSolarTerrestrialRelationsObservatory(STEREO).Theaccuracyof
h. thesemethodsallowsustotesttheCMEsfornon-constantaccelerationandexpansion.
p Methods.We exploit the multiscale nature of CMEs to extract structure with a multiscale decomposition, akin to a Canny edge
- detector.Spatio-temporalfilteringhighlightstheCMEfrontasitpropagatesintime.Weapplyanellipseparameterisationofthefront
o toextractthekinematics(height,velocity,acceleration)andchangingmorphology(width,orientation).
r Results.Thekinematic evolution of the CMEsdiscussed inthispaper have been shown todiffer fromexisting catalogues. These
t
s catalogues are based upon running-difference techniques that can lead to over-estimating CME heights. Our resulting kinematic
a curvesarenotwell-fittedwiththeconstant accelerationmodel. Itisshownthatsomeeventshavehighaccelerationbelow 5R .
[ Furthermore,wefindthattheCMEangularwidthsmeasuredbythesecataloguesareover-estimated,andindeedforsomeeve∼ntso⊙ur

analysisshowsnon-constantCMEexpansionacrosstheplane-of-sky.
1
v Keywords.Sun:coronalmassejections(CMEs)–Sun:activity–Techniques:imageprocessing–Methods:dataanalysis.
2
9
3
1. Introduction kinematics of an erupting flux-rope can be described using a
3
force-balance equation, which includes gas pressure, gravity
.
1 Coronal mass ejections (CMEs) are large-scale eruptions of and the Lorentz force (Krall&Chen 2005; Chenetal. 2006;
0 plasma and magnetic field with energies up to, and be- Manchester2007).Analternativetothisisthemagneticbreak-
9 yond, 1032 ergs. The mass of particles expelled in a CME outmodelinwhichtheCMEeruptionistriggeredbyreconnec-
0 can amount to 1015 g, typically traveling from the Sun tion between the overlying field and a neighbouring flux sys-
:
v at velocities of hundreds up to several thousand kilome- tem (Antiochosetal. 1999; Lynchetal. 2004; MacNeiceetal.
i ters per second (Goslingetal. 1976; Hundhausenetal. 1994; 2004). The increased rate of outward expansion drives a faster
X
Gopalswamyetal. 2001; Gallagheretal. 2003). They can lead rateofbreakoutreconnectionyieldingthepositivefeedbackre-
ar tosignificantgeomagneticdisturbancesonEarthandmayhave quiredforan explosiveeruption.The modelsare dependenton
negative impacts upon space-borne instruments susceptible to geometricalpropertiesoftheCME,suchasitswidthandradius,
high levels of radiation when outside the protection of Earth’s andtheyaredesignedtogiveanindicationoftheprocessesthat
magnetosphere. While they have been investigated by remote driveCMEkinematics.Thusitisimportanttodevelopmethods
sensingand in situ measurementsformorethan 30years,their oflocalisingtheCMEfrontandcharacterisingitintheobserved
kinematicandmorphologicalevolutionthroughthecoronaand datawithhighaccuracyformodelcomparisons.
interplanetaryspaceisstillnotcompletelyunderstood.
To date, most CME kinematics are derived from running-
It is well known that CMEs are associated with filament difference images whereby each image is subtracted from the
eruptions and solar flares (Zhang&Wang 2002; Moonetal.
nextinordertohighlightregionsofchangingintensity.Oncethe
2004)butthedrivermechanismremainselusive.Severaltheoret-
CME is identified, either manually through point-and-clickes-
icalmodelsaredescribedbyKralletal. (2001) withinthe con-
timates, or by a form of image thresholdingand segmentation,
textofthemagneticflux-ropemodelofChen(1996).Thesein-
height-time plots are produced and the velocity and accelera-
cludefluxinjection,magnetictwisting,magneticenergyrelease
tion of each event determined. CMEs are often thought of as
andhotplasmainjection.Thethree-dimensionalmagneticflux-
beingeithergradualorimpulsivedependingonboththeirerup-
ropemodel,inwhichaconvergingflowtowardtheneutralline tion mechanism (e.g. prominence lift off or flare driven) and
results in reconnection beneath the flux-rope (Forbes&Priest
their speed (Sheeleyetal. 1999; Moonetal. 2002). The faster
1995; Amarietal. 2003; Linetal. 2007), assumes that the
eventstendtohaveanaveragenegativeaccelerationattributedto
aerodynamicdragofthesolarwind(Cargill2004;Vrsˇnaketal.
Sendoffprintrequeststo:J.P.Byrne 2004). It was also shown by Gallagheretal. (2003) and Zhang
2 J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods
(2005)thatCMEsmayundergoanearlyimpulsiveacceleration
phasebelow 2R .
∼ ⊙
Current methods of CME detection have their limitations,
mostly since these diffuse objects have been difficult to iden-
tify using traditional image processing techniques. These diffi-
culties arise from the transient nature of the CMEs, the scat-
tering effects and non-linear intensity profile of the surround-
ing corona, and the interference of cosmic rays and solar en-
ergetic particles (SEPs) appearing as noise on the coronagraph
detectors. Observations made by the Solar and Heliospheric
Observatory’s(SOHO)LargeAngleSpectrometricCoronagraph
(LASCO) arecompiledintoa CME catalogatthe Coordinated
Data Analysis Workshop (CDAW; Yashiroetal. 2004) which Fig.1.Raw(left)andpre-processedimage(right)ofaCMEob-
operates by tracking the CME in LASCO/C2 and C3 running servedbyLASCOon2004April1.Thepre-processingincludes
differenceimagestoproduceheight-timeplotsofeachevent.It medianfiltering,backgroundsubtractionandoccultermasking.
is a wholly manualprocedureand is subject to user bias in in-
terpreting the data. The Computer Aided CME Tracking rou- 2. Observations&DataAnalysis
tine (CACTus; Robbrecht&Berghmans 2004) is based upon
LASCO/C2 and C3 runningdifferenceimages. Theimagesare In this paper a sample of CMEs observed by SOHO/LASCO
unwrappedintopolarcoordinatesandangularslicesarestacked and STEREO/SECCHI are studied, namely the gradual events
together in a time-height plot. CMEs thus appear as ridges in of 2000 January 2, 2000 April 18, 2001 April 23, 2004 April
these plots, detectedbya HoughTransform.The natureofthis 1, 2007 October 8 and 2007 November 16, and the impulsive
detection constrains the CMEs to have constant velocity and eventsof2000April23and2002April21.
zeroacceleration.The Solar EruptiveEventDetection Systems The LASCO/C2 and /C3 coronagraphs (Brueckneretal.
(SEEDS;Olmedoetal.2008)isanautomaticdetectionbasedon 1995) onboard SOHO give a nested field-of-view extending
LASCO/C2runningdifferenceimagesunwrappedintopolarco- from approximately 2.2 – 30 R . The COR1/2 coronagraphs
ordinates.Thealgorithmusesaformofthresholdsegmentation of the SECCHI suite (Howarde⊙tal. 2000) onboard STEREO
toapproximatetheshapeoftheCMEleadingedge,andautomat- image the corona from 1.4 – 15 R . The image quality of the
icallydeterminestheheight,velocityandaccelerationprofiles. coronagraphobservationscanbe di⊙minishedformanyreasons,
including instrumental effects (e.g. scattered light), noise from
Inthisworkweapplyanewmultiscalemethodofanalysing cosmic rays and SEPs, or data dropouts. In order to minimise
CMEs. The use of multiscale methods in astrophysics have theseeffects,weusethefollowingstandardpreprocessingmeth-
proveneffectiveatdenoisingspectraandimages(Murtaghetal. ods. Firstly the imagesare normalizedwith regardto exposure
1995;Fligge&Solanki1997),analysingsolaractiveregionevo- times in order to correct for temporal variations in the image
lution(Hewettetal.2008),andenhancingsolarcoronalimages statistics. Secondly a median filter is applied to remove pixel
(Stenborg&Cobelli 2003; Stenborgetal. 2008). Multiscale noise,replacinghotpixelswithamedianvalueofthesurround-
analysis has the benefit of working on independent images ingpixelintensities.Finallywe performa backgroundsubtrac-
without any need for differencing. A particular application of tion, obtained from the minimum of the daily median images
multiscaledecompositions,implementedbyYoung&Gallagher across a time span of a month, and remove the occulting disc
(2008), uses high and low pass filters convolved with the im- withazeromask.Thesestepsleadtoaclearimprovementinthe
agedatatoexploitthemultiscalenatureoftheCME.Thishigh- imagequalityforCMEstudy(Fig.1),afterwhichweapplyour
lights its intensity against the background corona as it propa- methodsofmultiscaleanalysis.
gatesthroughthefield-of-view,whileneglectingsmallscalefea- Inrecentyearstheuseofwaveletshasbeenincreasinglyevi-
tures(essentiallydenoisingthedata).Young&Gallagher(2008) dentinimageprocessingofsolarstructures(Stenborg&Cobelli
also describe the use of nonmaxima suppression to trace the 2003;Stenborgetal.2008;Young&Gallagher2008).Herewe
edges in the CME images, and they show the power of multi- illustrate briefly the formalism of the 1D wavelet transform,
scalemethodsoverpreviousedgedetectorssuchasRobertsand and discuss how this is extended to 2D. (For a more detailed
Sobel.WiththesemethodsfordefiningthefrontoftheCMEwe discussion on wavelet transforms the reader is directed to e.g.
can characterise its morphology (width, orientation) and kine- Burrusetal.(1998)andLin&Liu(2004).)Theremainderofthe
matics(position,velocity,acceleration)incoronagraphimages. sectionoutlinesourmethodsofusingthemultiscaleanalysisto
Following previous discussions on the errors in CME heights definetheCMEfrontforcharacterisation.
(e.g. Wenetal. 2007), multiscale methods allows us to deter-
mine the kinematics to a high degree of accuracy in order to
2.1.MultiscaleFiltering
confidentlycompareourresultstotheory.Whilethesemethods
are not currently automated, they have great potential for such The continuous wavelet transform (CWT) of a signal f(x)
animplementationwhichtheauthorsintendtopursue. L2(R) with respect to the mother wavelet ψ(x) L2(R) is de∈-
∈
finedby:
InSect.2wediscusscurrentimagepre-processingmethods
fromthecoronagraphsonboardtheSOHO(Domingo1997)and W(a,b) = ∞ f(x)ψ (x)dx (1)
STEREO (Kaiseretal. 2008) spacecraft.We outlinethe imple- Z a,b
mentation of multiscale methods and ellipse fitting to charac- −∞
whereψ (x)isaspatiallylocalisedfunctiongivenby:
terise the CME front. In Sect. 3 we present a sample of CME a,b
eventsanalysedbythesemethods,andSect.4isadiscussionof 1 x b
ψ (x) = ψ( − ) (2)
thesefirstresultsandconclusions. a,b √a a
J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods 3
l
ψ(x) = √2 g φ(2x s) (4)
s
X −
s=0
where h and g are constants called the low-pass and high-pass
filter coefficients respectively. Unlike the CWT, the DWT de-
composesasignalintoasetofwaveletcomponentswithdyadic
scaling,i.e.thescaleincreasesinpowersof2(21,22,etc).Inthis
way,the computationaltime requiredto performthe decompo-
sitionisdrasticallyreduced.
Weexploreamethodofmultiscaledecompositionbymeans
of the DWT in 2D throughthe use of low and highpass filters
usingadiscreteapproximationofaGaussianθanditsderivative
ψrespectively.Sinceθ(x,y)isseparablewecanwrite:
∂θ(x)
ψ (x,y) = θ(y) (5)
x ∂x
∂θ(y)
ψ (x,y) = θ(x) . (6)
y ∂y
Successiveconvolutionsofanimagewiththefiltersproducesthe
scales of decomposition,with the high-pass filtering providing
thewavelettransformofimageI(x,y)ineachdirection:
W I = W I(x,y) = ψ (x,y) I(x,y) (7)
x x x
Fig.2. Top left, the horizontal,and top right, the vertical coef- ∗
ficients from the high-pass filtering at scale 3. Bottom left, the W I = W I(x,y) = ψ (x,y) I(x,y). (8)
y y y
correspondingmagnitude(edge strength)and bottom right, the ∗
angleinformation(0–360◦)takenfromthegradientspace,for AkintoaCannyedgedetector(Young&Gallagher2008),these
aCMEobservedinLASCO/C2on2004April1. horizontalandverticalwaveletcoefficientsarecombinedtoform
thegradientspaceΓforeachscale:
Γ(x,y) = W I, W I . (9)
x y
h i
The gradient information has an angular component α and a
magnitude(edgestrength)M:
α(x,y) = tan 1 W I/W I (10)
− y x
(cid:16) (cid:17)
M(x,y) = (W I)2+(W I)2. (11)
x y
q
Theresultanthorizontalandverticaldetailcoefficients,andthe
magnitudeandangularinformationareillustratedinFig.2.
(a) 00:40UT (b) 01:00UT Overlayinga meshofvectorarrowsonthedatashowshow
themagnitudeandangularinformationillustratetheprogression
Fig.3. The vectors plotted represent the magnitude and angle of the CME. Each vector is rooted on a pixel in the gradient
determinedfromthegradientspaceofthehigh-passfilteringat space,andhasalengthcorrespondingtothemagnitudeM with
scale 3. The CME of 2004 April 1 shown here is highlighted ananglefromthenormalα(Fig.3).Byutilisingalltheinforma-
veryeffectivelybythismethod. tion gainedfromthe convolutionson the data arrayit becomes
possibletothresholdouttheCMEwithaviewtocharacterising
itsprogressionthroughspace.
The magnitude information was found to have the highest
anda,b L2(R)correspondtothescaling(dilation)andshifting signal-to-noiseratioatthethirdscaleofthedecomposition.This
∈
(translation)ofψ(x).NotethattheCWTspectrumobtainedhas scale is very effective at smoothing unwantedartefacts such as
norestrictionastohowmanyscalesareused,norofthespacing cosmic rays which the median filter may have missed. The an-
betweenthescales. gular component α of the gradient specifies a direction which
On the other hand, the discrete wavelet transform (DWT) pointsacrossthegreatestintensitychangeinthedata(anedge).
consists of a scaling function φ(x) and corresponding wavelet Athresholdisspecifiedwithregardtothisgradientdirectionin
ψ(x) with finite support[0,l](l being a positive number)given ordertochainpixelsalongmaxima,highlightingtheedgesinthe
by: image.Aspatio-temporalthresholdisimplementedwithregard
to changesof magnitudein orderto highlightmovingfeatures.
Itworksbycreatinga specific detectionmaskwhichis usedto
l
φ(x) = √2 h φ(2x s) (3) pullouttheedgesalongtheCMEfront.IncasesoffaintCMEs
s
X − or strong streamer deflections the filter is presently limited by
s=0
4 J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods
working on only one scale, meaning current analysis involves
a user removing/includingcertain edges that the algorithm has
ρ
mistakenly retained/discarded. Future work on more than one
scale may help alleviate this issue, since the additive angular
distributionalongaCMEfrontissignificantlylargerthanalong
ω′
a streamer when considered throughmultiple scales. Including
ω
thiscaveatwillbetterenablethealgorithmtoautomaticallyde-
γ
termine the CME edges, leading to a near real-timecharacteri-
sationandkinematicanalysis.
a b
2.2.CharacterisingtheCMEFront
UsingamodelsuchasanellipsetocharacterisetheCMEfront
across a sequence of images, has the benefit of providing the
kinematicsandmorphologyofamovingand/orexpandingstruc-
ture. The ellipse’s multiple parameters, namely its changeable
axes lengths and tilts, is adequate for approximating the vary- Fig.4. Ellipse inclined at angle γ, with semimajor axis a,
ing curved structures of CMEs. Chenetal. (1997) suggest an semiminor axis b, and radial line ρ inclined at angle ω to the
ellipsetobethetwo-dimensionalprojectionofafluxrope,and semimajoraxis.
Krall&St.Cyr (2006) use ellipses to parameterise CMEs and
exploretheirgeometricalproperties.Wefitellipsestothepoints
determinedtobealongtheCMEfrontbyconsideringaradialfan space.Atscale3ofthedecompositionthesmoothingfilteris23
fromSuncentreacrossthedefinededges.Thismeansthereare pixelswide,whichweuseasourerrorestimateinedgeposition.
morepointsalongthefrontthanontheflanksoftheCMEforin- Thiserroris inputto the ellipse fitting algorithmforweighting
clusioninthefit,andtheedgesneverdoublebackonthemselves the ellipse parameters, and a final error output is produced for
incaseswheretheCME’sinternalstructuremightbeotherwise eachellipsefit.Inthecaseofafadingleadingedgethereduced
included.Akinematicanalysisprovidesheight,velocityandac- amountof points along the front will increase the error on our
celerationprofiles;whiletheellipse’schangingmorphologypro- analysis. The finalerrorsare displayed in the height-timeplots
videsthe inclination angleand angularwidth. Measuringthese oftheCMEs, andareusedinthevelocityandaccelerationcal-
propertiesinthe observeddata isvitallyimportantforaccurate culations. The derivative is a 3-point Lagrangianinterpolation,
comparisonwiththeoreticalmodels. sothereisanenhancementoferrorattheedgesofthedatasets.
The implementation of the ellipse fitting routine is based Theerrorsontheheightsareusedtoconstrainthebestfitto
uponaninitialguessofellipsecentreastheaverageofthepoints aconstantaccelerationmodeloftheform:
specifiedalongthefront.Theellipse equation(inpolarcoordi-
h(t) = a t2+v t+h (14)
nates)isdefinedas: 0 0 0
wheretistimeanda ,v andh aretheacceleration,initialve-
ρ2cos2ω ρ2sin2ω 0 0 0
+ = 1 (12) locityandinitialheightrespectively.Thisprovidesalinearfitto
a2 b2
thederivedvelocitypointsandaconstantfittotheacceleration.
wherea andb are the lengthsofthe semimajorandsemiminor Animportantpointtonoteisthesmalltimeerror(takentobe
axes respectively,so allowing for an inclinationangle γ on the theimageexposuretimeofthecoronagraphdata)sincetheanal-
ellipsegives: ysis is performed upon the observed data frames individually.
Previous methodsof temporal-differencingwould increase this
a2b2 timeerror.Withthesemoreaccuratemeasurementswearebet-
ρ2 = (13)
(a2+b2) (a2 b2)cos(2ω 2γ) terabletodeterminethevelocityandaccelerationerrors,leading
2 − −2 ′− toimprovedconstraintsuponthedataandprovidinggreatercon-
whereω = ω+γ,asillustratedinFig.4.Thisgivesafirstap- fidenceincomparingtotheoreticalmodels.
′
proximationwhichcanthenbeusedtoiterativelyfloattheellipse
parameters until a Levenberg-Marquardtleast-squares minimi-
3. Results
sationisreached.
CMEheightmeasurementsaretakenastheheightofthefur- Thissectionoutlineseventswhichhavebeenanalyzedusingour
thestpointontheellipsefromSuncentre.Theangularwidthis multiscale methods.We use data fromthe LASCO/C2 and C3,
taken as the cone angle of the ellipse from Sun centre, and the andSECCHI/COR1andCOR2instruments,andpreprocessthe
tilt of the ellipse is given by the calculated angle γ. Note that imagesasdiscussedinSect.2.Theellipsefittingalgorithmap-
incaseswherethecodeproducesanextremelylargeandoblate plied to each event gives consistent heights of the CME front
ellipse with one apex approximatingthe CME front, the width measured from Sun centre to the maximum height on the el-
and tilt information is deemed redundant. Hence the resulting lipse,andtheseleadtovelocityandaccelerationprofilesofour
analysisofsomeeventscanhavelessdatapointsincludedinthe events. The ellipse fitting also providesthe angularwidths and
widthandtiltplotsthanintheheight-timeplots. orientations,asshownbelow.Thevelocity,accelerationandan-
gularwidth resultsof eachmethodare highlightedin Tables1,
2 and 3. In each instance we includethe valuesfromCACTus,
2.3.ErrorAnalysis&ModelFitting
CDAW and SEEDS, noting that CACTus lists a median speed
ThefrontoftheCMEisdeterminedthroughthemultiscalede- of the CME; CDAW provide the speed at the final height and
compositionandconsequentrenderingofagradientmagnitude fromthevelocityprofileweinferthespeedattheinitialheight;
J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods 5
andthe SEEDSdetectionappliesonlyto the LASCO/C2 field-
of-viewbutdoesn’tcurrentlyprovideavelocityrangeorprofile.
NotealsothattheCMEsof2007October8and2007November
16areanalysedin SECCHI imagesbyCACTusandourmulti-
scalemethods(markedbyasterisksintheTables),whileCDAW
andSEEDScurrentlyonlyprovideLASCO analysis.Itisclear
thatmanyoftheCACTus,CDAWandSEEDSresultslieoutside
theresultsanderrorrangesofouranalysis.
Table1.SummaryofCMEvelocitiesasmeasuredbyCACTus,
CDAW,SEEDSandmultiscalemethods.
Date CACTus CDAW SEEDS Multiscale
kms 1
−
2000Jan02 512 370–794 396 396–725
2000Apr18 463 410–923 339 324–1049
2000Apr23 1041 1490–898 595 1131–1083
2001Apr23 459 540–519 501 581–466
2002Apr21 1103 2400–2388 702 2195–2412
2004Apr01 487 300–613 319 415–570
2007Oct08 235* 85–331 103 71–330*
2007Nov16 337* 210–437 154 131–483*
*analysisofSECCHIdataratherthanLASCO.
Fig.6.Kinematicandmorphologicalprofilesfortheellipsefitto
Table 2. Summary of CME accelerations as measured by the multiscale edge detection of the 2000 January 2 CME ob-
CACTus,CDAW,SEEDSandmultiscalemethods. served by LASCO/C2 and C3. The plots from top to bottom
are height, velocity angular width, and ellipse tilt. The CDAW
Date CACTus CDAW SEEDS Multiscale heightsare over-plottedwith a dashedline. The heightand ve-
ms−2 locityfitsarebasedupontheconstantaccelerationmodel.
2000Jan02 0 21.3 5.8 14.7 3.6
− ±
2000Apr18 0 23.1 17.5 32.3 3.5
±
2000Apr23 0 48.5 8.9 4.8 20.6
− − − ±
2001Apr23 0 0.7 1.4 4.8 4.1
2002Apr21 0 −1.4 −33.5 3−2.5 ±26.6 3.1.ArcadeEruption:2000January2
− ±
2004Apr01 0 7.1 12.9 4.4 2.0
2007Oct08 0* 3.4 2.4 5.7 ±0.9* ThisCME wasfirstobservedinthesouth-westat06:06UTon
2007Nov16 0* 4.9 11.0 13.7± 1.7* 2000January2andappearstobeafar-sideeventassociatedwith
± anarcadeeruptionconsistingofoneormorebrightloops.
*analysisofSECCHIdataratherthanLASCO.
The height-time plot has a trend not unlike that of CDAW
(overplottedintopFig.6withadashedline).Howevertheoffset
oftheCDAWheights-whichputsthemoutsideourerrorbounds
-maybeduetohowthedifferenceimagesarescaledfordisplay.
This is a problem multiscale methods avoid. From Fig. 6, the
Table 3. Summary of CME angular widths as measured by velocity-fitwasfoundtobeincreasingfrom396to725kms−1,
CACTus,CDAW,SEEDSandmultiscalemethods. givinganaccelerationof14.7 3.6ms−2.Theellipsefitspans
±
approximately50–70 ofthefield-of-viewintheinnerportion
◦
Date CACTus CDAW SEEDS Multiscale ofC2,andexpandstoover95◦ inC3.Thisexpansionmaysim-
ply be attributed to the inclusion of one or more loops in the
degrees
2000Jan02 160 107 96 50–95 ellipsefitasthearcadetraversestheLASCO/C2andC3fields-
2000Apr18 106 105 108 68–110 of-view. The orientation of the ellipse as a function of time is
2000Apr23 352 360 130 96–130 showninbottomFig.6.Itcanbeseenthattheorientationangle
2001Apr23 124 91 74 55–60 ofthe CMEincreasestoapproximately100 beforedecreasing
◦
2002Apr21 352 360 186 53–65 toward60 .
◦
2004Apr01 66 79 58 44–38
Theconstantaccelerationmodelisnotasufficientfittothe
2007Oct08 52* 82 59 23–60*
datainthisevent.Thekinematicsproducedfromthemultiscale
2007Nov16 68* 78 54 40–55*
edgedetectionwouldbebetterfitwithanon-linearvelocityand
*analysisofSECCHIdataratherthanLASCO. anon-constantacceleration.ThiswouldshowtheCMEtohave
aperiodofdecreasingaccelerationintheC2field-of-view,lev-
elingofftozeroinC3(ifnotdeceleratingfurther).
6 J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods
Fig.5.Asampleofellipsefitstothemultiscaleedgedetectionoftheeventsstudied.Foreacheventtheupperandlowerimageshow
LASCO/C2and/C3(exceptforthe2007eventswhichshowSECCHI/COR1and/COR2).
J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods 7
Fig.7.SameasFig.6butforthegradualCMEof2000April18. Fig.8.SameasFig.6butfortheimpulsiveCMEof2000April
23.
3.2.Gradual/ExpandingCME:2000April18
ThisCMEwasfirstobservedoffthesouthlimbat16:06UTon 3.4.FaintCME:2001April23
2000April18andexhibitsafluxropetypestructure.
ThisCME wasfirstobservedinthesouth-westat12:39UTon
Theheight-timeplotforthiseventhasatrendsimilartothat
2001April23andexhibitssomedegreeofstreamerdeflection.
of CDAW (overplotted in top Fig. 7 with a dashed line). The
Theheight-timeplothasasimilartrendtoCDAW(overplot-
velocity-fitwasfoundtobelinearlyincreasingfrom324toover
tedintopFig.9withadashedline).Thevelocity-fitwasfound
1000 km s 1, giving an acceleration of 32.3 3.5 m s 2. The
− ± − tobelinearlydecreasingfrom581to466kms 1,givingadecel-
ellipsefitspansfrom68 ofthefield-of-viewintheinnerportion −
◦ erationof 4.8 4.1ms 2.Theellipsefitspansapproximately
ofC2,toapproximately110◦inC3.Theorientationoftheellipse 55– 60 o−fthe±field-of-v−iewthroughouttheevent,andthe ori-
asafunctionoftimeisshowntoincreasefromjustabove0 to ◦
◦ entationoftheellipseasafunctionoftimeisshowntodecrease
over60 inFig.7.
◦ fromapproximately50 toalmost0 (seeFig.9).
ThisCMEisfittedwellwiththeconstantaccelerationmodel ◦ ◦
ThisCMEisfittedwellwiththeconstantaccelerationmodel.
but shows an increasing angular width implying expansion
acrossthefield-of-view.
3.5.FastCME:2002April21
3.3.ImpulsiveCME:2000April23
ThisCMEwasfirstobservedinthewestfrom01:27UTon2002
ThisimpulsiveCMEwasfirstobservedinthewestat12:54UT April21.
on2000April23andexhibitsstrongstreamerdeflection. Theheight-timeplotfollowsasimilartrendtothatofCDAW
Theheight-timeplotderivedusingourmethodshasa trend (overplottedin topFig. 10 with a dashedline). Thevelocity-fit
which diverges from that of CDAW (overplotted in top Fig. 8 wasfoundtobelinearlyincreasingfrom2195to2412kms−1,
withadashedline).Thevelocity-fitwasfoundtobelinearlyde- givinga constantaccelerationfit of 32.5 26.6 m s−2. The el-
±
creasingfrom1131to1083kms−1,givingaconstantdecelera- lipse fit spans 53◦ in C2, and shows an likely increasing trend
tionof 4.8 20.6ms−2.TheCMEispresentforoneframein to65◦ inC3.Theorientationoftheellipseasafunctionoftime
C2with−ane±llipsefitspanning96◦,increasingtoapproximately isshowntoscatterabout115◦ thoughitdropstoapproximately
120–130◦intheC3field-of-view,andtheorientationoftheel- 81◦inthefinalC3image.
lipseasafunctionoftimeisshowntorisefrom71 to95 then The kinematics of this event are not modeled satisfactorily
◦ ◦
fallto64 (seebottomFig.8). bytheconstantaccelerationmodel,sincethefitsdonotliewithin
◦
Thiseventismodeledsatisfactorilywithaconstantdeceler- all error bars. The argument for a non-linear velocity profile,
ation. However, due to the impulsive nature of the CME there withapossibleearlydecreasingacceleration,isjustifiedforthis
are onlya few framesavailablefor analysis,makingit difficult event,althoughtheinstrumentcadencelimitsthedatasetavail-
toconstrainthekinematics. ableforinterpretation.ThepreviousanalysisofGallagheretal.
8 J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods
Fig.9.SameasFig.6butforthefaintCMEof2001April23. Fig.10.SameasFig.6butforthefastCMEof2002April21.
spacecraftseparationsincreaseovertime.OnthisdateSTEREO-
(2003) resulted in a velocity of 2500 km s 1 past 3.4 R
whichisconsistentwithourresult∼spast 6R −inFig.∼10. ⊙ Bwasatanangularseparationof16.5◦fromEarth.
The height-time plot for this event is shown in Fig. 12.
∼ ⊙
The velocity-fitwas foundto be linearlyincreasing from 71 to
330 km s 1, givingan acceleration of 5.7 0.9 m s 2. The el-
3.6.Flux-Rope/SlowCME:2004April1 − ± −
lipsefitinCOR1spansapproximately23 steppinguptoascat-
◦
This CME was first observed in the north-east from approxi- ter about 40 – 50 which rises slightly to 50 – 60 in COR2.
◦ ◦
mately 23:00 UT on 2004 April 1, is in the field-of-view for The orientationof the ellipse as a functionof time is shown to
over9hours,andexhibitsabrightloopfront,cavityandtwisted increasefrom55–110 thenjumpstoanapproximatelysteady
◦
core. scatterabout180–190 .
◦
Theheight-timeplotfollowsasimilartrendtothatofCDAW ThisCMEisfittedwellwiththeconstantaccelerationmodel.
(overplottedin topFig. 11 with a dashedline). Thevelocity-fit
wasfoundtobelinearlyincreasingfrom415to570kms 1,giv-
− 3.8.STEREO-AEvent:2007November16
ingan accelerationof 4.4 2.0m s 2. Note also thatthe kine-
−
±
matics of this event exhibitnon-linearstructure clearly seen in This CME was first observed in the west from approximately
the velocity and acceleration profiles. The ellipse fit spans ap- 08:26 UT on 2007 November 16, and is best viewed from the
proximately44 in C2, stepping downto approximately38 in STEREO-A spacecraft.On this date STEREO-A was atan an-
◦ ◦
C3.Theorientationoftheellipseasafunctionoftimeisshown gularseparationof20.3 fromEarth.
◦
tojumpdownfromapproximately130 inC2toapproximately Theheight-timeplotforthiseventisshowninFig.13.The
◦
70–80 inC3. velocity-fit was found to be linearly increasing from 131 to
◦
This event shows unexpected structure in the velocity and 483 km s−1, giving an acceleration of 13.7 1.7 m s−2. The
±
accelerationprofileswhichindicatesacomplexeruptionnotsat- ellipse fit in COR1 spans approximately 40 – 50◦ stepping up
isfactorilymodeledwithconstantacceleration. slightlytoascatterabout45–55 inCOR2.Theorientationof
◦
theellipseasafunctionoftimeisshowntostartat153 andend
◦
at120 withthemidpointsscatteredabout170 .
◦ ◦
3.7.STEREO-BEvent:2007October8 ThisCMEisfittedwellwiththeconstantaccelerationmodel.
This CME was first observed in the west from approximately
12:00 UT on 2007 October 8, and is best viewed from the
4. Discussion&Conclusions
STEREO-B spacecraft. It is noted that the kinematics as mea-
sured by SOHO and STEREO will be different due to projec- Avarietyoftheoreticalmodelshavebeenproposedtodescribe
tioneffects(Vrsˇnaketal.2007).Itisintendedthattheseeffects CMEs, especially their early propagationphase. Observational
bemeasuredandcorrectedforinfuturework,especiallyasthe studies,suchasthoseoutlinedabove,arenecessarytodetermine
J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods 9
Fig.11.SameasFig.6butfortheslowCMEof2004April1. Fig.13.SameasFig.12butfortheCMEof2007November16.
CMEcharacteristics.Wearguethattheresultsofpreviousmeth-
odsarelimitedinthisregardduemainlytolargekinematicerrors
which fail to constrain a model, an artefact of CME detection
based upon either running- (or fixed-) difference techniques or
otheroperations.Currentmethodsfiteitheralinearmodeltothe
height-timecurve,implyingconstantvelocityandzeroacceler-
ation(e.g.CACTus)orasecondorderpolynomial,producinga
linearvelocityandconstantacceleration(e.g.CDAW,SEEDS).
The implementation of a multiscale decomposition provides a
timeerroronthescale ofseconds(theexposuretime ofthein-
strument)andaresultingheighterrorontheorderofafewpix-
els.Theheight-timeerrorisusedtodeterminetheerrorsofthe
velocityandaccelerationprofilesoftheCMEs.Itwasshownthat
forcertaineventstheresultsofCACTus,CDAWandSEEDScan
differsignificantlyfromourmethods,asillustratedintheTables
ofSect.3.
Our results clearly confirm that the constant acceleration
modelmaynotalwaysbeappropriate.The2000January2 and
2002 April 21 CMEs are good examples of the possible non-
linearvelocityprofileandconsequentnon-constantacceleration
profile (see Fig. 6 and Fig. 10). Indeed these eventsare shown
to havea decreasingacceleration,possiblyto zeroor below,as
the CMEs traverse the field-of-view. Simulations of the break-
out model outlined in Lynchetal. (2004) resulted in constant
acceleration fits which do not agree with these observations. It
maybefurthernotedthattheeventsof2001April23and2004
April1showapossibledecreasingaccelerationphaseearlyon,
thoughwithinerrorsthiscannotbecertain(seebottomFig.9and
Fig.12.SameasFig.6butfortheCMEof2007October8ob-
Fig. 11). Furthermore,the structureseen in someeventswould
servedbySECCHI/COR1andCOR2.ForthisreasonCDAWis
indicate thatthe CME doesnotprogresssmoothly.The veloci-
notoverplotted.
tiesofthe2004April1CMEinFig.11andthe2007November
16 CME in Fig. 13 show non-smooth profiles and may imply
10 J.P.Byrneetal.:ThekinematicsofCMEsusingmultiscalemethods
aformofburstyreconnectionorotherstaggeredenergyrelease Chen,J.,Howard,R.A.,Brueckner,G.E.,etal.1997,AstrophysicalJournal,
driving the CME. Other profiles such as Fig. 6 and to a lesser 490,L191
extent Figs. 9 and 10 may show a stepwise pattern, indicative Chen, J., Marque´, C., Vourlidas, A., Krall, J., & Schuck, P. W. 2006,
AstrophysicalJournal,649,452
of separate regimes of CME progression. None of the current
Domingo,V.1997,Adv.SpaceRes.,20,581
CME models indicate a form of non-smooth progression, al- Fligge, M. & Solanki, S. K. 1997, Astronomy & Astrophysics Supplement
thoughthe flux-ropemodeldoesdescribe an earlyacceleration Series,124,579
regimegivinganon-linearvelocitytotheeruption(seeFig.11.5 Forbes,T.G.&Priest,E.R.1995,AstrophysicalJournal,446,377
Gallagher,P.T.,Lawrence,G.R.,&Dennis,B.R.2003,AstrophysicalJournal,
inPriest&Forbes2000).
588,L53
Itmaybeconcludedthattheangularwidthsoftheeventsare
Gopalswamy,N.,Yashiro,S.,Kaiser,M.L.,Howard,R.A.,&Bougeret,J.-L.
indicative of whether the CME expands radially or otherwise 2001,JournalofGeophysicsResearch,106,29219
in the plane-of-sky.For the CMEs studied above, the observa- Gosling,J.T.,Hildner,E.,MacQueen,R.M.,etal.1976,SolarPhysics,48,389
tionsof 2000April18,2000April23 and2002April21show Hewett,R.J.,Gallagher,P.T.,McAteer,R.T.J.,etal.2008,SolarPhysics,248,
311
a super-radialexpansion(see Fig.7,Fig. 8andFig. 10).These
Howard,R.A.,Moses,J.D.,&Socker,D.G.2000,ProceedingsoftheSPIE,
eventsalso show high velocities, obtainingtop speeds of up to 4139,259
1000kms 1,over1100kms 1 and2500kms 1 respectively, Hundhausen, A. J.,Stanger, A. L.,& Serbicki, S. A.1994, Proc. 3rd SOHO
− − −
and may therefore indicate a link between the CME expan- Workshop,SP-373,409
Kaiser,M.L.,Kucera,T.A.,Davila,J.M.,etal.2008,SpaceScienceReviews,
sionandspeed.Furthermore,itissuggestedbyKrall&St.Cyr
136,5
(2006) that the flux-rope model can account for different ob-
Krall,J.&Chen,J.2005,AstrophysicalJournal,628,1046
served expansion rates due to the axial versus broadside view Krall, J., Chen, J., Duffin, R. T., Howard, R. A., & Thompson, B. J. 2001,
oftheeruptingfluxsystem. AstrophysicalJournal,562,1045
The observedmorphologyof the ellipse fits may befurther Krall,J.&St.Cyr,O.C.2006,AstrophysicalJournal,652,1740
Krall, J., Yurchyshyn, V. B., Slinker, S., Skoug, R. M., & Chen, J. 2006,
interpretedthroughthetiltanglesplottedinSect.3.Inknowing
AstrophysicalJournal,642,541
the ellipse tilt and the direction of propagation of the CME it Lin,E.&Liu,P.2004,J.App.Math.,2004:5,379
ispossibletodescribethecurvatureofthefront.Fortheevents Lin,J.,Li,J.,Forbes,T.G.,etal.2007,AstrophysicalJournal,658,L123
above,the changingtilt and hence curvatureis possibly signif- Lynch,B.J.,Antiochos,S.K.,MacNeice,P.J.,Zurbuchen,T.H.,&Fisk,L.A.
2004,AstrophysicalJournal,617,589
icant for the 2000 April 18, 2004 April 1 and 2007 October 8
MacNeice,P.,Antiochos,S.K.,Phillips,P.,etal.2004,AstrophysicalJournal,
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614,1028
rope model of Kralletal. (2006) was shown to have a chang- Manchester,W.B.2007,AstrophysicalJournal,666,532
ingorientationofthemagneticaxiswhichresultsinadynamic Moon,Y.-J.,Chae,J.,Choe,G.S.,etal.2004,J.KoreanAstro.Soc.,37,41
radius of curvature of the CME, possibly accounting for these Moon,Y.-J.,Choe,G.S.,Wang,H.,etal.2002,AstrophysicalJournal,581,694
Murtagh, F., Starck, J.-L., & Bijaoui, A. 1995, Astronomy & Astrophysics
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SupplementSeries,112,179
The work outlinedhere is an initialindicationthatthe zero Olmedo, O., Zhang, J., Wechsler, H., Poland, A., & Borne, K. 2008, Solar
and constant acceleration models in CME analysis are not an Physics,248,485
accuraterepresentationofallevents,andtheover-estimatedan- Priest, E. & Forbes, T. 2000, Magnetic Reconnection (Cambridge University
Press,UK)
gularwidthsarenotindicativeofthetrueCMEexpansion.The
Robbrecht,E.&Berghmans,D.2004,Astronomy&Astrophysics,425,1097
ellipse characterisation has provided additional information on
Sheeley,N.R.,Walters,J.H.,Wang,Y.-M.,&Howard,R.A.1999,Journalof
the system through its changing width and orientation which GeophysicsResearch,104,24739
shall be further investigated with the analysis of many more Stenborg,G.&Cobelli,P.J.2003,Astronomy&Astrophysics,398,1185
events. This work will be further explored and developed with Stenborg,G.,Vourlidas,A.,&Howard,R.A.2008,AstrophysicalJournal,674,
1201
STEREOdatawherebythecombinedview-pointscangiveaddi-
Vrsˇnak, B., Ruzˇdjak, D., Sudar, D., & Gopalswamy, N. 2004, Astronomy &
tionalkinematicconstraintsandmayleadtoacorrectionforpro- Astrophysics,423,717
jectioneffectsandpossiblethreedimensionalreconstructions. Vrsˇnak,B.,Sudar,D.,Ruzˇdjak,D.,&Zˇic,T.2007,Astronomy&Astrophysics,
469,339
Acknowledgements. ThisworkissupportedbygrantsfromScienceFoundation Wen,Y.,Maia,D.J.,&Wang,J.2007,AstrophysicalJournal,657,1117
Ireland’s Research Frontiers Programme and NASA’s Living With A Star Yashiro,S.,Gopalswamy,N.,Michalek,G.,etal.2004,JournalofGeophysics
Program. JMA is grateful to the STEREO/COR1 team at NASA/GSFC Research,109:A7
and is currently funded by a Marie Curie Fellowship. We would also Young,C.A.&Gallagher,P.T.2008,SolarPhysics,248,457
like to thank the anonymous referee for their very helpful comments. Zhang,J.2005,Proc.IAU,226,65
SOHO is a project of international collaboration between ESA and NASA. Zhang,J.&Wang,J.2002,AstrophysicalJournal,566,L117
The STEREO/SECCHI project is an international consortium of the Naval
Research Laboratory (USA), Lockheed Martin Solar and Astrophysics Lab
(USA), NASA Goddard Space Flight Center (USA), Rutherford Appleton
Laboratory (UK), University of Birmingham (UK), Max-Planck-Institut fu¨r
Sonnen-systemforschung(Germany),CentreSpatialdeLiege(Belgium),Institut
d’Optique The´orique et Applique´e (France), and Institut d’Astrophysique
Spatiale(France).
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