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Typical Profiles and Distributions of Plasma and Magnetic Field Parameters in Magnetic Clouds at 1 AU L. Rodriguez1, J. J. Masías-Meza2, S. Dasso3,4, P. Démoulin5, A. N. Zhukov1,6, A. Gulisano2,3,7, M. Mierla1,8, E. Kilpua9, M. West1, D. Lacatus8,10, A. Paraschiv8,10, M. Janvier11

1 SIDC, Royal Observatory of Belgium, STCE, Brussels, Belgium

2 Departamento de Física (FCEN-UBA-IFIBA), Buenos Aires, Argentina

3 Instituto de Astronomía y Física del Espacio (UBA-CONICET), Buenos Aires, Argentina

4Departamento de Ciencias de la Atmósfera y los Océanos and Departamento de Física (FCEN-UBA), Buenos Aires, Argentina

5 Observatoire de Paris, LESIA, UMR 8109 (CNRS), F-92195 Meudon Principal Cedex, France

6 Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia

7 Instituto Antártico Argentino, Buenos Aires, Argentina

8 Institute of Geodynamics of the Romanian Academy, Jean-Louis Calderon 19-21, 020032 Bucharest-37, Romania

9 Department of Physics, Division of Geophysics and Astronomy, University of Helsinki, Helsinki, Finland

10 School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia

11 Institut d'Astrophysique Spatiale, UMR8617, Univ. Paris-Sud-CNRS, Université Paris-Saclay, Batiment 121, 91405 Orsay Cedex, France

Abstract

Magneticclouds(MCs)areasubsetofinterplanetarycoronalmassejections(ICMEs).Theyareimportantduetotheirsimpleinternalmagneticfieldconfiguration,whichresemblesamagneticfluxrope,andbecausetheyrepresentoneofthemostgeoeffectivetypesofsolartransients. In this study, we analyze their internal structure using a superposed epochmethodon63eventsobservedatL1byACE,between1998and2006.Inthisway,weobtainanaverageprofileforeachplasmaandmagneticfieldparameterateachpointofthecloud.Furthermore, we take a fixed time window upstream and downstream from the MC, inorder to sample also the regions preceding the cloud and the wake trailing it. We thenperform a detailed analysis of the internal characteristics of the clouds, and theirsurroundingsolarwindenvironments.Wefindthattheparametersstudiedarecompatiblewithlog-normaldistributionfunctions.Theplasmabetaandtheleveloffluctuationsinthemagneticfieldvectorarethebestparameterstodefinetheboundariesofclouds.Wefindthatinonethirdoftheevents,thereisapeakinplasmadensityclosetothetrailingedgeof

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thefluxropes.Weprovideseveralpossibleexplanationsforthisresultandinvestigateifthedensitypeak isofa solarorigin (e.g.eruptingprominencematerial)or formedduring themagnetic cloud travel from the Sun to 1 AU. The most plausible explanation is thecompressionduetoafastovertakingflow,comingfromacoronalholelocatedtotheeastofthesolarsourceregionofthemagneticcloud.

1. Introduction

CoronalMassEjections(CMEs)arelarge-scalesolareruptiveevents,inwhichlargeamountsofplasmacarryingmagneticfluxandhelicity(seee.g.Démoulinetal.,2015,andreferencestherein)areexpelledintotheinterplanetaryspace.Whensampledinsitubyaspacecraftinthe interplanetarymedium, theyarecalled InterplanetaryCMEs (ICMEs).Magnetic clouds(MCs)arean importantsubsetof ICMEs,whichexhibitaparticular internalmagnetic fieldconfiguration resembling that of a flux rope. This is characterized by enhancedmagneticfield intensity, smooth rotation of its magnetic field vector and low temperature (e.g.Burlaga,1991).

The classical three-part structure of a CME (bright front, dark cavity, and dense core) isusuallyalsointerpretedintermsofamagneticfluxropepropagatinginthecorona(seee.g.Illing andHundhausen, 1986; Vourlidas et al., 2013). The bright front corresponds to theplasmapile-upinfrontofthefluxrope,thecavityrepresentsthebulkofthefluxrope,andthedensecoreistheeruptingprominencethatislocatedinthebottom(concave-out)partsof the flux rope field lines. As coronagraphic white-light observations of CMEs are onlysensitivetothecoronalelectrondensity(weighteddependingonthedistancewithrespectto the plane of the sky, see e.g. Billings, 1966), a possible method to identify thecorrespondencebetweenCMEandICMEstructuresistheinvestigationofdensitystructuresinsitu.However, it isverydifficultto identifythecorrespondingthree-partmorphology inICMEsdetected insitu(e.g.Kilpuaetal.,2013a).ForfastICMEs,oneusuallydetectsafastforwardshockdrivenbythemagneticcloud,anddenseplasmainthesheathbetweentheshockandthecloudwhichiscausedbytheplasmapile-up.AlinkbetweenCMEsandICMEscanbeestablishedusingheliosphericimagingthatcantrackCMEdensitystructuresallthewayfromthesolarcoronato1AU(Howardetal.,2008;Davisetal.,2009),orbycombiningobservationswithmodelling (Rodriguez et al., 2011).Möstl et al. (2009) investigated twoCME-ICMEpairsandfoundthattheCMEbrightfrontcorrespondstothepost-shocksheathinfrontofthecloud,andthedenseCMEcorecorrespondstothedensityenhancementinthe trailingpartof themagneticcloud.However, theCME-drivenshockwaveobserved incoronagraph images (see e.g. Ontiveros and Vourlidas, 2009) travels ahead of the classicbrightfrontalstructure(Vourlidasetal.,2013).Thustwodensestructurescorrespondingtotheshockandtothebrightfrontareexpectedtobeobservedaheadofthemagneticcloud,which isnotthecase.Similarly,adensestructureatthetrailingendof interplanetaryflux

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ropes is notdetected systematically. Leppinget al. (2003) studied19MCsobserved from1995 to 1998 and createdprofiles of theplasmaandmagnetic field parameters in them.Theyfoundadensity increasetowardstheendof thecloud inhalfof thecases (seetheirFigures3and4).Lynchetal.(2003)presentedastudyof56MCsobservedbetween1998and 2001. They divided their observations into fast and slow clouds, which exhibiteddifferent plasma characteristics and composition, but the trailing density peakswere notobservedineitherpopulation.Unusualchargestates(e.g.He+ions)areusuallyinterpretedastracesofthecoldprominenceplasma(Schwennetal.,1980;Leprietal.,2010).However,ionswith unusual charge states are very rarely identified in situ, soerupting prominenceplasma is typicallynot found in ICMEobservations (e.g. Leprietal.,2014). Ingeneral, thecorrespondence between the coronal and interplanetary structures in CME-ICME eventsremainsunclear.

Theprimarymotivationofthecurrentworkistoconstructthetypicalprofilesofthemainplasma and magnetic field properties within magnetic clouds and in their immediatesurroundings,usingalargesampleofeventsobservedindifferentphasesofthesolarcycle.AsstatedbyKilpuaetal.(2013b),definingmagneticcloudboundariesisoftenverydifficultand such generic profiles can be very valuable in providing context for interpretingindividualobservationsandingeneralforstudyingtheinternalstructureofmagneticclouds.

In particular, we focus on the plasma density profile within those clouds, for which weobserveadensitypeakneartheirtrailingedge.Theinformationprovidedbytheseprofilesisimportant forunderstanding theeffect that an increase indensitymayhaveon the solarwind-magnetosphere coupling efficiency (both when connected to southward andnorthwardIMF).Densityinthesolarwindcorrelateswiththedensityoftheplasmasheetinthe Earth’s magnetotail (e.g. Borovsky et al., 1998), which is the primary source of thestorm-timeringcurrent(e.g.Wangetal.,2008).DuringperiodswithanorthwardIMF,highdensitymayleadtotheformationofasuper-denseplasmasheet,whichlatercanincreasetheringcurrent(e.g.Lavraudetal.,2005).Forexample,theMCthatarrivedattheEarthonJanuary10,1997(Burlagaetal.,1998)containedahigh-densitypeak in its tail that ledtosignificantgeomagneticeffectsandseverelydamagedtheU.S.Telstar401satellite(Reevesetal.,1998).Forthatcase,thepeakindensitywasrelatedtoprominencematerial,whichisoneof thepossibleexplanations for thepeaksobserved in thepresentstudy.The trailingdensitypeakcouldalsoresultfromthedynamicsoftheMCtransportfromtheSuntotheEarth,forexamplecompressioncausedbyatrailingfastsolarwindstream,whichcouldinturnleadtoincreasedgeoeffectiveness(FenrichandLuhmann,1998;Kilpuaetal.,2012a).Inthiswork,wepresentandanalyseseveralpossibleexplanationsforsuchpeaksobservedinthetailsofMCs.

Section 2 reports the data and theMCs used in this study. In Section 3we describe thesuperposedepochanalysisandthemethodsusedtoobtainthetypicalMCprofilesat1AU.Section 4 presents the analysis of the results and describes the observations of plasma

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densityenhancementsinthetrailingpartoftheMCs,whichareinvestigatedinmoredetailinSection5.Finally,Section6providesasummaryandconclusionsofourwork.

2. DataandEventSelection

In this study, theMCsare taken from the listof “Near-Earth InterplanetaryCoronalMassEjections Since January 1996”, compiled by I. Richardson and H. Cane (R&C list hereon)available at http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm (RichardsonandCane,2010).WeusedatafromtheACEspacecraftformagneticfieldandplasmadatawith 64-second cadence and the plasma composition data for oxygen charge states(O+7/O+6)takenwith1-hourcadence.ACEwaslaunchedonAugust25,1997andiscurrentlyoperatingclosetotheLagrangianpointL1oftheSun-Earthsystem.TheR&ClistseparatestheMCs into three categories according to the quality ofMC (thisMC flag is located incolumn“L” in thecatalogue).A flagof2 indicatesaclearMC,a ‘1’ signalsadoubtfulMCidentification and a ‘0’ denotes that aMC is not detected within the ICME. Only clearlyidentifiedMCs (i.e. thosewith a quality flag ‘2’) are used in thiswork.Our list of eventsstarts in February 1998 (with the start of availability of ACE plasma data) and finishes inDecember 2006 (last events with detailedMC information in the R&C list). Our final listcontainsatotalof63MCs.

Inordertofindthesolarcounterpartofthemagneticclouds(i.e.CMEs)weuseddatafromtheLargeAngleSpectroscopicCoronagraph(LASCO,seeBrueckneretal.,1995)onboardtheSOlar and Heliospheric Observatory (SOHO) spacecraft. The C2 and C3 coronagraphs ofLASCOrecordthebrightnessofthewhite-lightcoronafrom2.2to6solarradii(Rs)andfrom3.7to32Rs,respectively.Toidentifytheon-discsignaturesofCMEsweusedthedatafromthe Extreme-ultraviolet Imaging Telescope (EIT, see Delaboudinière et al., 1995) onboardSOHO and/or Hα ground based observations (taken fromftp://ftp.bbso.njit.edu/pub/archive/ that contains Hα observations from Big Bear SolarObservatory, Kanzelhoehe Solar Observatory and Yunnan Astronomical Observatory). EITobservesthesolaratmosphereupto1.5Rs,inatemperaturerangefrom6x104to3x106Katfourdifferentwavelengths:30.4nm,17.1nm,19.5nmand28.4nm.Hα imagesdetecttheemissionof thecoolerchromosphereataround6000K,whereeruptingfilamentscanbeidentified.AnexampleCMEisshowninFigure1,withtheeruptionfromsourceregionNOAA AR 9866 visible in EIT (left panel) and the corresponding CME on LASCO C2 (rightpanel).

3. SuperposedEpochMethod

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Inthisstudy,theMCsareanalysedbymeansofasuperposedepochanalysis.Thismethodisused tocreateanaverageprofileof theMCplasmaandmagnetic fieldcharacteristics.Toperformthisanalysis,werequireeachmagneticcloudtoberecordedwithanequalnumberofdatapoints.This isnormallynotthecase,sinceeachcloudhasadifferentduration.Toremedythis,wedetermineagridof50equallyspacedbins insideeachMC.Allvaliddatapoints are averagedwithin each bin to build the average profile. If there is no data in acertainbinwindow,foracertainevent,thiseventisthennotcountedinthisbin.Moreover,ifanoriginaltimeserieshasdatagapsinmorethan20%oftheMCstructure,wediscarditfromtheaverageprofile.

ThenextstepconsistsinaveragingcorrespondingdatapointsoverallMCs,sodatapoints1fromeachmagneticcloudwillbeaveraged,followedbydatapoints2,andsoon.Wetakethemeanandthemedianvalueateachpointtakingintoaccountthenumberofeventsthatcontributeinthatbin.Weincludethemedianasitislessaffectedbyextremevaluesinthedistribution. Inthismanner,anaverageprofileofall theMCscanbecreated,whereeachpoint has associated standard deviations for the distribution, the mean and the medianvalue. This procedure is done for the magnetic field intensity, solar wind speed, protontemperature, proton number density, plasma beta, oxygen charge state ratio (O+7/O+6),alpha-to-protonratio,andthemagneticfieldvectorvariance.

Finally,weselectaregioninfrontoftheMCwiththesamedurationastheMCandaregionwith the double duration after the MC rear boundary. This choice was made to givesufficient time for the parameters to recover background solar wind levels. The regionaheadoftheMCwillinsomecasesincludepassageoftheshockandhenceconsistofboththe sheathandupstreamambient solarwind. TheMCboundaries correspond to the firstandlastpointoftheMC.Alltheregionsarere-sampledwiththesamefactor, inthisway,weresampledeachcloudto50points,plus50pointsbeforeand100pointsaftertheevent(200pointsintotal).ThesheathsoftheeventsanalysedinthisstudyaretreatedindetailbyMasias-Mezaetal.(2016).

4. AnalysisoftheResults

4.1MagneticFieldandPlasmaProfiles

Severalcharacteristicsofmagneticcloudsandtheirenvironmentcanbededucedfromtheresultof thesuperposedepochanalysis.Figure2showstheprofilesofmagnetic fieldandplasmaparametersinandaroundselectedeventscreatedusingtheproceduredescribedinSection3.Eachplotwascreatedbyapplyingthesuperposedepochmethodto63MCs.MCperiodsaremarkedbytheblueareas.Errorbars(ingrey)representthestandarddeviationsofthemean(blackcurve),andtheredcurveisthemedian.

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Firstly,themagneticfieldmagnitudeisfoundtopeakinsidethecloud,reachingvaluestwiceaslargeasthosefoundintheambientsolarwind(ascanbeseenfrompanel(a)ofFigure2).Also,thepeakisasymmetrictowardstheleadingedge.TheexpansionoftheMCistypicallynotenoughtoexplain thisasymmetry (seeDémoulinetal.,2008,andtheirFigure3),butthis could be a consequence of the combined intrinsic spatial asymmetrywithin the fluxrope,anditsinteractionwiththesurroundingsolarwind(withahighertotalpressureintheregionprecedingthefluxrope).

Next,theprotondensity(panel(d))andtemperature(panel(c))peakbeforethearrivalofthe flux ropeand represent a clear signatureof the compressedpile-upplasma region infrontofthefluxrope.TheprotontemperaturethendecreasesandreachesaminimumintheMCregion,whichisalsoaconsequenceoftheinternalexpansion(Goslingetal.,1973;RichardsonandCane,1995).AsmentionedinSection1,theprotondensitypeakobservedclose to the flux rope leading edge probably corresponds to the bright front of theassociatedCMEobservedbycoronagraphs.Thenegativeslopeof thespeedprofile (panel(b))marksthetypicalexpansionofmagneticclouds(e.g.KleinandBurlaga,1982;Gulisanoetal.,2010).Theplasmabeta(panel (e)) is lowwithintheclouds,meaningthatthesearemagneticallydominatedstructures.

Theprofiles of temperature, density, plasmabeta and the variationof themagnetic fieldvector (panel (c), (d) and (h)) as well as O+7/O+6 (panel (f)) relative abundances haverelatively flatprofileswithin the superposedMC (i.e. therearenobigvariations fromtheleadingedgetothetrailingpartof thecloud).Protondensityandplasmabeta (panels (d)and(e))havetheirminimumintheleadingpartofthecloud,whilethetemperaturereachesitsminimumtowardstheendofthecloud(butindeedthedifferencesarenotlargewithinthecloud).

ThevariationofthemagneticfieldunitvectorisdenotedinFigure2(panel(h))asrmsBoB(meaningtheRMSofBoveritsmagnitude),withitsmagnitudebeingtheroot-mean-square (RMS) value of the magnetic field vector over a 64 seconds window, normalized to themagnitudeoftheaveragemagneticfieldintensityinthesamewindow(Equations1and2).

𝑟𝑚𝑠𝐵𝑜𝐵 𝑡 = 𝑟𝑚𝑠(𝑩 𝑡 )/𝐵(𝑡) (1)

𝑟𝑚𝑠 𝑩 𝑡 = 𝐵, − 𝐵, ./,01 (2)

This normalization is important because the absolute RMS is highly correlated to themagnitudeoftheaveragevector,andweareinterestedinseeingtheintrinsicmagneticfieldvariability along these structures. Themagnetic fieldwithin theMC is found to vary verysmoothly,anditsnormalizedvariation,rmsBoB,isafactorof3smallerthanintheambientsolarwind.Wealsonotetheverynarrowstandarddeviationsfromthemeanvalue,andthesimilaritiesbetweenthemeanandmedianvalues,hintingatamoresymmetricdistributioncomparedtotheotherparameters.Asaconsequence,themagneticfieldvariationcanbe

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considered as a very robust parameter forMC identification. Furthermore, togetherwiththeplasmabeta,thevariationofthemagneticfieldunitvectorclearlymarkstheboundariesoftheclouds.Thisconfirmspreviousstudies(e.g.Burlagaetal.,1981;Gosling,1990).Thesefeatures have an additional importance as the identification of the MC boundaries is adifficult issue(e.g.Dassoetal.,2006)andthesetwoparameterscanbeveryhelpfulwhendefining the limits between MCs and the surrounding solar wind. Our result is also inagreementwith thework by Kilpua et al. (2013a), who showed that ultra-low-frequencyfluctuationsinthemagneticfieldcomponentsdecreasedramaticallyattheICMEedges.Ourquantityprovidesausefulquantitativebackgroundtomeasurethe levelof fluctuations inMCs.

4.2 CompositionProfiles

Thealpha-to-protonratioprofileisfoundtopeaktowardstheendoftheMCs(panel(g)ofFigure2),andtakeslongertorecovertoitsambientsolarwindvaluesafterthecloudshavepassed,whichisincontrasttotheratewithwhichtheratiorisesinfrontoftheclouds.Thisbehavior was also observed by Richardson and Cane (2004), who suggested that anenhancedalpha-to-proton ratio is the resultofheliumgravitational settling. Ina separatestudy,Manchesteretal.(2014)simulatedaveryfastCMEand,duetoitsdeceleration,theyfoundthattheprominencematerialmovedtowardsthefrontoftheICME.Incontrast,theaveragealpha-to-protonratiofoundhereincreasestowardstheendofthecloud.Thiscouldbeaconsequenceofareverseprocess:mostMCsinthisstudyareslow,andthenamuchweaker deceleration is experienced in the interplanetarymediumwhile the gravitationalsettlingwouldoccurwhen they are accelerated in the corona. So theheavier ionswouldhavemoreinertiaandthetendencytoaccumulateattherear,assuggestedbyRichardsonandCane(2004).

Therelativeionizationstatesofsolarwindionsbecomeconstant,i.e.they“freeze-in”,atafew solar radii from the Sun (Hundhausen, 1968). Hence, at greater distances, themeasurementofthechargestatescanbeusedasaproxyfor inferringconditionsclosetothe Sun, thus providing a link between interplanetary and conditions at a few solar radiifromtheSun.Furthermore,chargestatesaretheparametersleastaffectedbypropagationeffects,becausetheyarefrozen-in,incontrasttodensityandtemperatureforexample,thatmaybesignificantlyaffectedbycompressionandexpansionoftheMC.TheO+7/O+6showninFigure2(panel(f))isclearlyincreasedwithintheMC,indicatinghightemperaturesinthesourceregionoftheCME(Henkeetal.,1998;Rodriguezetal.,2004,Songetal.2015).Thisparameterprovidesaverygoodsignatureforidentifyingmagneticcloudmaterial(seealsoFigure8ofRichardsonandCane,2004).

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Both the charge states and the alpha-to-proton values take longer to reach backgroundsolarwind levels following theMCcompared to the rateof their increasebefore theMC(panels(f)and(g)ofFigure2).Thiscouldbeanindicationofthepresenceofalongwakeorbackregionfollowingmagneticclouds,i.e.aregiontrailingthecloudwheremagneticcloudandambientsolarwindplasmasmix.Incontrast,theplasmaandmagneticfieldparameters(panels(b),(c),(d)and(h))donotshowaclearICME-relatedsignatureinthisbackregion,consistentwith theanalysis in Section5ofRichardsonandCane (2010). Theplasmabeta(panel (e)) is larger thanunity, and the density (panel (d)) has nominal solarwind values(apartfromapeakattheMCrear,seebelow).Alsotheleveloffluctuationsofthemagneticfieldvector(panel(h))increasessignificantlyaftertheMCwithatransitionregionwhereitgoes back to solar wind conditions. The magnetic field intensity and the temperature(panels (a) and (c))have themostprogressive transition from theMC to the typical solarwind conditions. All these features could be the consequence of the formation of a backregioninmagneticclouds,duetoreconnectionofthefluxropewiththesurroundingsolarwind (seeDassoetal., 2006,2007;Ruffenachetal., 2015).Thisback region isa remnantpart of the flux rope after its reconnectionwith the solarwind fields at the front of themagnetic cloud.Theoriginal composition is stillpresent in this region.There,O+7/O+6andalpha-to-protonratiosare larger than theambientsolarwindvalues (panels (f)and (g)offigure2).Thefluxropeplasmagetsmixedwiththesolarwindplasma,asaconsequenceofreconnection (the collision time is long, so ions can travel along field lines). Themixing isexpectedtoincreasewithtime(fromthereconnectiontime),soindeedtheplasmafurtherawayfromtheMCrearboundary,thatreconnectedearlier, isexpectedtobemoremixedwiththesolarwind,asobservedinFigure2.

Inconclusion,theO+7/O+6andalpha-to-protonratiosareimportantparameters,notonlyfordefiningthefluxropeextentasobservedat1AU,butalsoforcharacterizingitwhenitwasmuchclosertotheSun,beforereconnectionwiththesolarwindfieldstarted.Stilltherearboundary of this extended flux rope is not well defined (no sharp transition). Theinterplanetarymagnetic fieldmagnitudehas a similar property (i.e. it decreases graduallyaftertheMCrearendtoreachquietsolarwindvalues),butwithaslightlyshortertailthanbothO+7/O+6andalpha-to-protonratio.

4.3 DistributionFunctionsofPlasmaandMagneticFieldParameters

In general there is a noticeable difference between mean and median values in theparameter profiles shown in Figure 2, and these differences are not the same inside andoutsidetheMC.This indicatesanon-symmetricdistributionfunctionfortheseparameterswithinMCs. One exception is seen in the panel of rmsBoB, the similarities between themean and median values hint at a more symmetric distribution compared to the otherparameters. As can be seen in the other panels, the mean values are higher than the

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mediansandthusthedistributionsareskewedtovalueslargerthanthemeanvalues.ThisisinagreementwithresultsofGuoetal.(2010)andMitsakouandMoussas(2014),whofoundsimilar results related to ICMEmean values. In their work it was shown how such ICMEparameter distributions could be approximated by log-normal distribution functions.Burlaga et al. (1979, 1998) have found log normal distributions in solarwind plasma andmagnetic field. In order to assess whether log-normal distributions are also found inmagneticclouds,wegeneratedhistogramsofeachoftheparametersanalyzed,insideMCs,andfittedthemwiththelognormalfunctionasdescribedbyEquation3:

𝑓 𝑥, 𝜇, 𝜎 = 178 .9

𝑒;(<= 7 ;>)? .8? (3)

whereµandσarethemeanandstandarddeviationofthenatural logarithmofvariablexrespectively.

Theanalysisiscarriedoutover16pointsaroundthecenterofeachcloud(33%ofthepointsineachMC).Thenumberofpointswaschosenasacompromiseinordertoproperlysamplethecharacteristicsandhomogeneouspropertiesofthecenterofthecloud,whileavoidingmixing the fluctuations of a global trend with boundary contamination. The observeddistributionsarebinnedinordertoresolvethemainpeakandtheshapeofthedistributionbelow and above the peak in a comparable manner. The bin number is limited to haveenoughcasesineachbinaroundthemaximum(typicallyabove40).Withtheseconstraintswetrytooptimizetherepresentationoftheobserveddistributions.TheresultsareshowninFigure3.Log-normal fitsare included inthefigure,withthecorrespondingparameters.Themedianvalue is indicatedasaverticaldashed line,andaredband isshownbetweenthepercentiles(50-33/2=33.5%)and(50+33/2=66.5%).The33%waschosenafteraniterativeprocesstorepresentcorrectlythecoreofthedistribution.

We find thatallquantitieshavedistributionsclose to the fitted lognormal functions,withthevelocitybeingthequantitythatleastresemblesthefittedlognormalfunction.InTable1,wecompare themeanandmedianvalueswith thoseobtainedbyMitsakouandMoussas(2014) in a similar studyof ICMES. Themeanmagnetic field inMCs is larger than that inICMEs,as itcanbeexpectedwhencrossinga fluxrope.TheaverageMCplasmabetaandtemperature are lower than in ICMEs, also expected results as a consequence of thepresenceofafluxropeinMCs.

Quantity Median Mean Mean(ICME)

B[nT] 13.1 15.1 10.1

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V[km/s] 456 488 467

Np[cm-3] 5.64 7.34 6.8

T[105K] 0.25 0.54 0.76

β 0.22 0.32 0.84

rmsBoB 0.02 0.02 -

O+7/O+6 0.68 0.93 -

nα/np 0.05 0.06 -

Table 1.Median (2nd column) andmean (3rd column) values of the different plasma andmagnetic field parameters within magnetic clouds as calculated in this work. Forcomparison,themeanvaluesforICMEsaregiveninthe4thcolumn(takenfromTable1and2ofMitsakouandMoussas,2014)

5. OriginofDensityPeaksintheTrailingEdgeofMCs

The results of the superposed epoch analysis in Figure 2 indicate that there is anenhancementinprotondensityattherearboundaryoftheMC(panel(d)ofFigure2).Thevelocity panel of Figure 2 (panel (b)) also shows that there is typically a faster streamfollowing theMC (i.e., a clear peak of Vsw at around 1.3 in normalized time). This thenmotivatesthequestions:Istheobservedpeakintheprotondensityprofileaconsequenceof dynamical processes thatoccurredduring theMC transport from the Sun to the Earth(i.e.afastsolarwindstreamthatpushesthefluxropefrombehind)?CanitbegeneratedbyintrinsicprocessesrelatedtotheoriginoftheMCsinthelowcorona(i.e.pre-existingdenseplasma resulting e.g. from prominence material as one can expect from observations ofthree-partCMEs,asshownbyMöstletal.,2009)?

Apartfromcompressionfromahighspeedstream(HSS)andintrinsicprocessesattheSun,flux rope expansion is yet another process that should be taken into account (see e.g.Goslingetal.1998).Thisexpansionwouldneedtobestrongerthantheexpansionrequiredforpressureequilibriumwiththesurroundings(DémoulinandDasso,2009;Gulisanoetal.,2010), so that itwould exert a pressure on the adjacent solarwind, and could thereforeproduce the observed density increase. A priori, we could make a distinction betweenexpansionandcompressionbylookingatthelocationofthedensitypeak:insideoroutside

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thefluxropeboundary.Unfortunately,inpracticeitisnotpossible,becausetheuncertaintyon the boundary location is larger than the precision needed to carry out a consistentanalysis.

One should also consider that a combination of the processes described above could beactingtogetherontheclouds,andmayexplainwhysomecloudsexhibitmultiplepeaks.Weexplorethedifferentexplanationsinthefollowingsubsections.

Followingtheanalysisoftheindividualevents,wefindthatin22outof63casesapeakinprotonnumberdensityisfoundclosetothetrailingedgeofthecloud.Weconsideronlythepeaksappearingwithin30%oftheclouddurationbeforeandaftertherearboundary,andfor which the intensity clearly exceeds that of the variations in the background.Furthermore,forsomeofthese22events,morethanonepeakisfound.InTable2welisteachofthe22eventsthatexhibitpeaksintheprotondensitynearthetrailingedgeoftheMC. These are listed together with one or more possible explanations describing thepresenceofthedensitypeaks.

5.1 IntrinsicProcessesattheSun

WelookedforthelowcoronalcounterpartsofeachoftheobservedMCsinTable2.Totrackan ICME back to the solar disc, we estimated the CME launch time by using the ICMEleading-edgespeedmeasuredbyACE,whichhasbeenproventobeabettermeasurementforestimatingtraveltimesthantheCMEspeedasderivedfromcoronagraphs(Kilpuaetal.,2012b),andconsideringaconstantspeedonthewayfromtheSunto1AU.ToaccountforprobableaccelerationsordecelerationsofCMEsintotheinterplanetaryspace,wesearchedfortheCMEcandidateswithinathree-daytimewindowaroundtheestimatedCMElaunchtime. In order to find the associated CMEs, we used the online LASCO CME catalogue(http://cdaw.gsfc.nasa.gov/CME_list/ , Yashiroet al., 2004) and studieddaily coronagraphmovies aswell as extreme ultravioletmovies from EIT observations. The identified lowercoronal signaturesare listed inTable2 (last twocolumns).For someeventsdatagaps,ormultipleeventsoccurringcloseintimedidnotallowtofindanunambiguouslinkbetweenaMCandaCME.

Apossiblecauseof thedensitypeak in theMCtail isanassociatederuptive filament. Ifafilament eruption was observed in EIT (19.5 or/and 30.4 nm) observations within a fewhoursintervalbeforethefirstappearanceoftheCMEinLASCOC2fieldofview,orifintheHαseriesofimageswecouldseeafilamentwhichwasclearlygoneaftertheCMEerupted,we consider it tobeassociatedwith theMCobservations.Nevertheless,weencounteredseveraldifficulties in identifying theassociatederuptive filaments:1)Asall theCMEshadtheirsourceregionsclosetothecentreofthesolardisc(andnotonthelimb),theerupting

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filamentwasoftendifficulttoidentifywithinthebrightsurroundingsolarfeaturesintheEIT19.5nmdata;2)ThetemporalcadenceofEIT30.4nmandHα imageswasgenerallyverylow,andtheeruptingfilamentcouldthenbeeasilymissed,orinsomecasesitwasnotclearifthefilamenthadreallyeruptedorjustdisappearedfromthebandpass(forexampleduetoheating).OutoftheeventspresentingaprotondensitypeakneartheMCtrailingedge,only four could be unambiguously linked to a filament eruption at the Sun (indicated by“FIL”inthelastcolumnofTable2).Hence,forthemajorityofthecases,thedensitypeakscanhardlybeexplainedbythepresenceofthefilamentmaterial.ThisisinagreementwiththeresultsbyLeprietal.(2010),whoshowedthatprominencematerial isnormallyfoundonly inaveryfewICMEsobservedat1AU.Furthermore,Howard(2015)showedthattheprominencemasscanbeseentodisappearprogressivelyinheliosphericimagerdatawhilepropagatingawayfromtheSun(seeFigure7inthepaperbyHoward,2015).Thismightbedue to the prominence material mixing with the surrounding solar wind, leaving littleprominenceplasmatobedetectedat1AU.

Itshouldbenotedthatevenwithoutthepresenceofassociatedprominencematerial,thedensityenhancementcouldstillbeanintrinsicpartoftheMCcreatedinthelowcorona.Forexample, dense loops encircling the erupting flux rope can become a part of it afterreconnection (vanBallegooijenandMartens,1989;Aulanieretal.,2010). Thecrossingofsmall-scale flux tubes with different densities within a single MC could be a plausibleexplanation.Withthetotalpressurebalancemaintained,adensitypeak isexpectedtobeassociatedwith a decrease of themagnetic fieldmagnitude (unless the plasma pressureremainsthesamedueto lowertemperature).Magneticfluxtubeswithanorigindifferentthanthatoftheirenvironment(e.g.high-densityreconnectedloops,seeDereetal.1999)orthe post-eruptive reconnection outflow proposed by Riley et al. (2002), could partiallyexplainthedensitypeaksinmorethanahalfoftheevents inTable2(14casesoutof22,indicatedby“I”incolumn6ofTable2).Weusedthesimultaneousincreaseofdensityanddecreaseofmagneticfieldmagnitudeasthecriteriontomarkthedensitypeakasintrinsic(I) in Table 2. An example of such an event is shown in the left panels of Figure 4,corresponding to aMC from6November 2000. The density peaks right after the trailingedgeof theMC, at the same time that themagnetic field intensitydrops.As seen in thesolarwindspeedpanel,thereisnoHSStrailingtheMC.Furthermoretherearethreeevents(1999/02/18, 2000/02/12, 2006/08/30) where only an intrinsic explanation could explainthedensitypeaks,astheseMCswereneitherfollowedbyahigh-speedstreamnordidtheyshowastrongexpansion.

5.2 CompressionbyanOvertakingHigh-SpeedStream

Thedynamicpressureexertedonamagnetic cloudbyaHSSovertaking it couldgeneratethe compressionnecessary toproduceapeak inprotondensity.Byvisualexaminationof

13

theeventsitwasfoundthat17casesofthetotal22showingreardensitypeakshavesuchaHSStrailingthem.Figure4(rightpanel)showsanexampleofaMCfrom22July2004withadensity peak just before its trailing edge followed by a HSS, which is clear from thecomparisonofthesolarwindspeedattherearboundaryoftheMCwiththespeedofthesolarwindtrailingit.Table2(lastcolumn)indicatesthatoutof17eventswithatrailingHSS,for 11 of them a coronal holewas present at the Sun, located to the east of the sourceregionoftheCMEcases),theremainingcases(6outof17)haveadatagaporthesourcecouldnotbeidentified.Sincecoronalholesarethesourcesoffastsolarwind,weconcludethattheyarethesourcesoftheHSSstrailingtheMCsandcausingthedensitypeaksattherearboundariesofMCs.

Fortheseevents,apeakinmagneticfieldintensityshouldbeexpectedtooasaresultofthecompression.Thispeak isnotvisible in thesuperposedepochanalysisofFigure2.Firstly,this isbecausetheseplots includeall theMCs, inparticularcaseswithan intrinsicdensityenhancement(correspondingpartlytoaweakermagneticfield).Furthermore,themagneticfieldenhancementisfrequentlystackedwiththeenhancedfieldoftheMC(thisisdifferentfor thedensity,which is typically comparable insideandoutsideMCs). However, limitingtheanalysistocaseshavingatrailingHSS,wefindanenhancedmagneticfieldfor12outof17 cases, comparable or larger than in the MC, associated with the peak density. Anexample isshownintherightpanelsofFigure4withanunusualpeakofBpresentattherear of theMC. It is associatedwith a positive gradient of plasma velocity and a densitypeak.Finally,the5remainingcaseswithoutincreaseinBcorrespondtoweakHSS.

Wewouldliketopointoutthat,whenusingtheinsitudata,weonlyhavealocalsnapshotofthecloudevolvingintime.Forexample,anovertakingflowcouldinteractwithaMCcloseto the Sun, compressing theplasmaat an early stageof its propagation and creating thedensitypeak.Thisfastflowandtheassociatedinteractioncouldbemostlyoveratthetimeoftheobservationsat1AUandthereforeitwouldnotbepossibletoassociatethefastflowwiththecorrespondingdensitypeak.Theoppositemayalsooccur,i.e.theinteractiontakesplaceatthemomentofobservationsat1AU,butwithouthavingasufficienttimetobuildastrong density enhancement. This indicates that a one-to-one association between theobserveddensitypeaksandtheircausescannotalwaysbeexpected.

5.3 Expansion

Ingeneral,magneticcloudsareexpandingstructures.Suchexpansion,whenstrongenough,couldgenerateapeakindensityclosetotheboundariesofthefluxrope.SeveralMCswithrear proton density peaks also exhibit signatures of strong expansion. The dimensionlessexpansionrateζ(Gulisanoetal.,2010),isshownforeachcloudinTable2.Apositivevalueoftheexpansionfactorindicatesthatthecloudsareexpanding.TheleftpanelsofFigure4

14

showanexampleofastronglyexpandingMC,withadistinctdensityincreasejustaftertherearedgeofthecloud.

Valuesofζintherange~0.8–1correspondtotheexpansionneededforthecloudtobeintotalpressurebalancewiththesurroundingsolarwind(DémoulinandDasso,2009).Highervaluesofζmaycontributetothecreationofadensitypeak.Wefixathresholdof1forζtoconsiderthattheMCexpansionmaybeapossiblesourceforthedensitypeakatthetrailingedge of aMC. Table 2 shows that sixMCs from the total of 22 events showing the reardensitypeakshave ζhigher than1,meaning thatMCexpansioncouldbeat theoriginofonly27%ofeventswiththedensitypeaks.Furthermore, fromTable2 itcanbeseenthatthereisnosingleeventwheretheexpansioncanbetheonlycauseforthedensitypeaks,soweconcludethattheexpansionisnotanefficientmechanismtoformadensitypeak.

In summary, compression by trailing high speed streams (HSSs) seems to be the mostpromisingexplanationforthecreationofthetrailingdensitypeaksinMCs.Thismechanism,together with intrinsic processes corresponding to flux tubes with different plasma andmagneticfieldproperties,couldexplainthemajorityoftheobservedpeaks.AcombinationoftheaboveeffectscouldalsoexplainwhysomeMCsexhibitmultipledensitypeaksintheirtails.Outof22events, therewereeight cases showingmultipleprotondensitypeaks (anexample is shown in Figure 5). For some of them, a combination of effects (expansion,compression,intrinsicprocesses)ispresent,althoughitisnotobviousifdifferentprocesseswillproduceseparatepeaks.

MCStart(1)

MCEnd(2)

Numberof

trailingPeaks(3)

HSS(4)

ζ(5)

Trailingdensitypeakorigin(6)

CorrespondingCME(7)

Solarfeatures(8)

1998

03/0413:00 03/0606:00 2 Y 0.69 O 02/2812:48 CH

1999

02/1814:00 02/1910:00 1 N 0.86 I Datagap 08/0921:00 08/1017:00 2 Y 0.43 I,O NA

2000 02/1217:00 02/1300:00 1 N 0.01 I 02/1002:30 07/1521:00 07/1610:00 2 Y 1.88 E,I,O 07/1410:54 CH,FIL08/1205:00 08/1305:00 1 N 1.21 E,I 08/0916:30 11/0622:00 11/0718:00 1 N 1.77 E,I 11/0318:26

2002

15

03/1923:00 03/2016:00 1 Y 0.79 O,I 03/1523:06 CH03/2412:00 03/2522:00 1 Y 0.60 O 03/2017:06 CH04/1803:00 04/1902:00 1 Y 0.62 O,I 04/1503:50 CH08/0112:00 08/0123:00 1 Y 0.69 O 07/2923:30 CH,FIL

2003

06/1718:00 06/1808:00 1 Y 0.34 O 06/1401:54 CH,FIL11/2010:00 11/2102:00 1 Y 1.14 E,I,O 11/1808:50 CH,FIL

2004

04/0402:00 04/0517:00 2 Y 0.82 O Datagap 07/2215:00 07/2301:00 1 Y -3.88 O 07/2013:31 CH07/2414:00 07/2515:00 2 Y 1.27 E,O 07/2207:31 CH08/2919:00 08/3022:00 2 Y 0.47 I,O NA

2005 05/2007:00 05/2105:00 1 Y 0.89 I,O 05/1613:50 CH06/1505:00 06/1609:00 2 Y 1.02 E,I,O Datagap 07/1714:0 07/1804:00 1 Y 0.86 O NA 12/3113:00 01/0111:00 1 Y 0.86 O,I NA

2006 08/3020:00 08/3115:00 2 N 0.98 I Datagap

Table2.Summaryofthemagneticcloudeventswhereaclearpeakindensity isseenclose(within30%ofthecloudduration)totherearboundaryofthecloud.Columns1and2listthestartandendtimes of the MCs (from the R&C list). Column 3 shows the number of trailing peaks identified.Column4stateswhetherahigh-speedstream(HSS)signatureispresentbehindthecloud.Column5showsthedimensionlessexpansionrateζdefinedbyGulisanoetal.(2010),withpositivevaluesofthis factor indicating that the cloud is expanding, andwith the value ζ = 1 set as a threshold forconsideringexpansionasasourceforthereardensitypeak.Column6givestheprobableoriginoftherearprotondensitypeak,whereEindicatesMCexpansion,IindicatesanintrinsicpropertyoftheplasmaflowatorclosetotheSun,andOstandsforanovertakingflow.Column7detailsthedateand time of the corresponding CMEon the Sun,with “Data gap” corresponding tomissing SOHOdata (EIT and/or LASCO), and NA standing for the cases where no association with a solarcounterpartcouldbefound.Column8listsanyrelatedsolarfeature:CHmeansthatacoronalholewaslocatedeastofthesourceregionoftheCME,FILstandsforafilamenteruptionclearlyidentifiedinrelationtotheCME.

6 SummaryandConclusions

InthisworkwepresentananalysisoftheinternalstructureofMCsobservedat1AU.Weappliedasuperposedepochmethodto63eventsdetectedbyACEattheL1point,observedbetween1998and2006.Weobtainedanensembleprofile foreachplasmaandmagneticfieldquantity,whichrepresentsanaverageateachpointofthecloudoveralltheevents.Byperformingsuchananalysis,wehaveidentifiedseveralMCcharacteristicsthatwereknown

16

tobepresentinindividualevents,butcannowbegeneralizedtoalargesampleofMCs,asshownbythetypicalmagneticcloudprofilesconstructedinthisstudy.Theyinclude:

• Protondensityandtemperaturepeakbeforethefluxrope,thatisaconsequenceofthehotanddensematerialaccumulatedthere(MCsheath).

• TheprotontemperatureandtheplasmabetaarelowthroughoutthedurationoftheMC.

• Theexpansionofthecloudismarkedbythenegativeslopeofthespeedprofileandthelowprotontemperature.

• TheO+7/O+6profileexhibitsaclearenhancementthroughoutthedurationoftheMC,indicatinghightemperaturesinthesourceregionofthecorrespondingCME.

• Thepeak inthemagneticfieldmagnitude insidemagneticclouds isnotsymmetric,which is a consequence of the combined effect of the MC expansion, a possiblespatial asymmetry within the flux rope, and its asymmetric interaction with thesurroundingsolarwind.

• Magnetic field vector fluctuations, normalized to themean field strength, are lowthroughout the duration of the MC, thus confirming that the low magnetic fieldvariationcanbeconsideredasaveryrobustparameterfortheidentificationofMCboundaries, which is also consistent with the analysis of ultra-low-frequencymagneticfieldfluctuationsinMCsbyKilpuaetal.(2013b).

• Theintervalsofdecreasedvaluesoftheplasmabetaarealsoaverygoodproxyforthefluxropeduration.

Furthermore, new insights into the internal characteristics of MCs were found in ouranalysis:

• Log-normaldistributionfunctioncanbeusedtodescribethedistributionofplasmaandmagnetic field parameters near the center ofMCs. This is in agreementwithprevious works that find log-normal distribution functions for parameters withinICMEs(MitsakouandMoussas,2014;Guoetal.,2010),andinthesolarwindat1AU(BurlagaandLazarus,2000andreferencestherein).Suchdistributionsarebelievedto indicate a consequence of the presence of non-linear multiplicative processes(e.g.MontrollandShlesinger,1982).

• The O+7/O+6, and the alpha-to-proton number density ratio (two parameters thatcharacterizethefluxropewhen itwasmuchclosertotheSunthan1AU),presenttypical ICME values for a period extendedwell beyond the defined flux rope rearboundary,aresultconsistentwiththereconnectionbetweenthefluxropeandthemagnetic field of the ambient solarwind. In particular, theO+7/O+6 values show aslowerrecoveryratetobackgroundsolarwindlevelsattheMCrearcomparedtothefastriserateattheMCfront.Thiscouldbeanindicationofthepresenceofa longbackregioninmagneticclouds.Then,thetypicalMCshouldbeerodedat1AU.This

17

is an important result since studies focusing on the characteristics ofMCs and inparticularthemagneticfieldstructureshouldtaketheerosionprocessintoaccount,forexampleinthefluxropefittingprocedure(e.g.,Lavraudetal.2014;Ruffenachetal.,2015).

• There are proton density peaks observed around the trailing edge of a significantfraction of the studiedMCs (22 out of 63). For 17 of these 22 events, there wasevidence of a trailing fast-stream compressing the cloud, while 6 events showedstronginternalexpansion,and4eventswereassociatedwithafilamentattheSun.The overtaking fast flows scenario is sufficient to explain most of the observedproton density peaks. Finally, proton density increases could also be attributed toother intrinsic processes occurring close to the Sun (the plasma structure ofmagneticloopsintheeruptingregion,reconnectionoutflows,etc.).

• SomeeventspresentmorethanoneprotondensitypeakintheMCtail,whichmaybeafurtherindicationofmultipleprocessescreatingthedensityenhancement.

AcknowledgementsL. R. and A. N. Z. acknowledge support from the Belgian Federal Science Policy Officethrough the ESA-PRODEX program. Luciano Rodriguez acknowledges support from theEuropeanUnionSeventhFrameworkProgramme(FP7/2007-2013)undergrantagreementnumber 263252 (COMESEP). SOHO is a project of international cooperationbetween ESAandNASA. This researchhasbeenpartially fundedby the InteruniversityAttractionPolesProgrammeinitiatedbytheBelgianSciencePolicyOffice(IAPP7/08CHARM).Thisworkwaspartially supported by Argentinean grant UBACyT 20020120100220, PICT-2013-1462, PIP-11220130100439CO (CONICET), PIDDEF 2014-2017 Nro. 8, and by the Argentina-BelgiumagreementbetweentheFNRSBelgium(V4/325M)andMINCyTArgentina(BE/13/07).Thiswork was also partially supported by a 1 month invitation of P.D. to the Instituto deAstronomíayFísicadelEspacio,andbya1monthinvitationofS.D.totheObservatoiredeParis.S.D.ismemberoftheCarreradelInvestigadorCientífico,CONICET.E.K.acknowledgessupportfromAcademyofFinlandproject1267087.

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Figures

21

Figure 1. CME of 15 March 2002. Observed as a full halo by SOHO LASCO-C2 (right panel). ThecorrespondingeruptionisseeninthesourceregionNOAAAR9866closetodisccenter,ascapturedby SOHO EIT (left panel). Both are running difference images, where the previous image issubtractedfromthecurrentone.

22

Figure2.SuperposedepochprofilesofplasmaandmagneticfieldcharacteristicsmeasuredbyACEforthemagneticcloudsofourlist.Eachplotwascreatedbyapplyingasuperposedepochmethodto63MCs.Eventswithadatagaplargerthan20%werenotusedintheanalysis.Sincethenumberofdata gaps varied between individual instruments, the number of MCs used varied for eachparameter(seethenumberofconsideredeventsinsideeachpanel).Panelsreadinglefttorightandtop to bottom are (a) interplanetary magnetic field intensity, (b) solar wind speed, (c) protontemperature,(d)protonnumberdensity,(e)plasmabeta,(f)O+7/O+6relativeabundance,(g)alpha-to-protonnumberdensityratioand(h)normalizedmagneticfieldvectorvariance. MCperiodsaremarkedbytheblueareas.Errorbars(ingrey)representthestandarddeviationsofthemean(blackcurve),andtheredcurveisthemedian.

23

Figure3.ProbabilitydistributionfunctionsoftheplasmaandmagneticfieldparameterspresentedinFigure 2 for our dataset ofmagnetic clouds (taken from the center of theMCs). N indicates thenumberofpointsusedinthedistributionshown,theredlineisthelog-normalfitderivedusingtheparametersµandσofthedistributionfunction(seeEquation3).Themedianvalueisindicatedasavertical dashed line. The red shadowed rectangle marks the area between the inferior and thesuperior percentile of the data (50-33/2 = 33.5% and 50+33/2 = 66.5% of themaximum of thecumulativedistributionfunction),toshowthespreadingofeachobservableinthedistribution.

24

Figure4.Examplesof individualprofilesofplasmaandmagnetic fieldparameters intwomagneticclouds.Thepanelsfromtoptobottomareinterplanetarymagneticfieldintensity,solarwindspeed,protonnumberdensity,protontemperature,plasmabeta,normalizedandun-normalizedmagneticfield vector variance. The blue regions refer to themagnetic cloud passage. Left: the event on 6November 2000, for which the causes of the plasma density peak at the cloud trailing edge are

25

plausiblytheexpansionofthecloudandanintrinsicstructurefoundexactlyaftertherearboundaryofthecloud.Right: theeventon22July2004, forwhichafaststream,seen inthevelocityprofilerightafterthemagneticcloud,couldbethecauseofthedensitypeakseeninsidethefluxrope,closetoitsrearboundary.

26

Figure5. Exampleof aMC (1998/03/04)wheremultiplepeaks are seen close to the rearboundaryoftheMC.Theformatisthesameasinfigure4.

27