A&A615, A89 (2018) 
https://doi.org/10.1051/0004-6361/201732308 
©ESO 2018 
Astronomy&AstrophysicsShock location and CME 3D reconstruction of a solar type II radio burst with LOFAR 
P. Zucca1,D.E. Morosan2,A.P.Rouillard3,R.Fallows1,P.T. Gallagher2,J. Magdalenic4, K.-L. Klein5, 
G. Mann6,C.Vocks6,E.P. Carley2,M.M. Bisi7,E.P.Kontar8,H.Rothkaehl9,B. Dabrowski10, 
A.Krankowski10,J. 
Anderson11,A.Asgekar1,12,M.E. Bell13,M.J. Bentum1,14,P. Best15,R. Blaauw1,F.Breitling6, 

J.W.Broderick1,W.N.Brouw1,16,M. Brgen17,H.R. Butcher18,B. Ciardi19,E.de Geus1,20, 

A. 
Deller21,1,S.Duscha1,J. Eislfel22,M.A.Garrett23,24,J.M.Grießmeier25,26,A.W.Gunst1,G.Heald27,1,M.Hoeft14, 

J. 
Handel28,M. Iacobelli1,E. Juette29,A. Karastergiou30,J.van Leeuwen2,31,D. McKay-Bukowski32,33,H. Mulder1, 

H. 
Munk34,1,A.Nelles35,E.Orru1,H.Paas36,V.N.Pandey1,8,R.Pekal37,R. Pizzo1,A.G.Polatidis1,W.Reich38, 

A. 
Rowlinson1,D.J.Schwarz39,A. Shulevski16,J. Sluman1,O. Smirnov40,41,C. Sobey42,M. Soida43,S. Thoudam44, 


M.C.Toribio16,1,R.Vermeulen1,R.J.vanWeeren16,O.Wucknitz38, andP. Zarka5 <BR>
(Affliations canbefoundafterthereferences) 
Received16November2017/Accepted24 March2018 
ABSTRACT 
Context. TypeIIradioburstsareevidenceofshocksinthesolar atmosphereandinner heliospherethatemitradiowavesrangingfrom sub-meter to kilometer lengths. These shocks maybe associated with coronal mass ejections (CMEs) and reachspeeds higher than the local magnetosonic speed.Radio imagingof decameterwavelengths (20–90 MHz)is now possible withtheLowFrequencyArray (LOFAR), openinga newradio windowin whichtostudy coronal shocksthat leavethe inner solar corona and enterthe interplanetary medium andto understandtheir association withCMEs. Aims. Tothisend,westudyacoronalshockassociatedwithaCMEandtypeIIradiobursttodeterminethe locationsatwhichthe radio emissionisgenerated, andweinvestigatethe originofthe band-splitting phenomenon. Methods. ThetypeIIshock source-positionsandspectrawereobtainedusing91simultaneoustied-arraybeamsofLOFAR,andthe CMEwasobservedbytheLargeAngleandSpectrometricCoronagraph(LASCO)onboardtheSolarand HeliosphericObservatory (SOHO) andbytheCOR2A coronagraphofthe SECCHI instruments on boardthe SolarTerrestrialRelation Observatory(STEREO). The3Dstructurewasinferredusingtriangulationofthecoronographicobservations.Coronalmagnetic feldswereobtainedfroma3D magnetohydrodynamics(MHD)polytropicmodelusingthephotospheric felds measuredbythe HeliosphericImager(HMI)onboard the Solar Dynamic Observatory(SDO) as lower boundary. Results. The typeIIradio sourceofthe coronal shockobservedbetween50 and70 MHzwasfoundtobe locatedattheexpanding fank ofthe CME, wherethe shockgeometryisquasi-perpendicular with θBn ∼ 70◦. The type II radio burst showed frst and second harmonic emission;the second harmonic sourcewas cospatial withthe frst harmonic sourceto withinthe observational uncertainty. This suggests that radio wave propagation does not alter the apparent location of the harmonic source. The sources of the two split bands were alsofound to be cospatial within the observational uncertainty, in agreement with the interpretation that split bands are simultaneousradio emissionfrom upstream anddownstreamofthe shockfront. Thefast magnetosonic Machnumber derivedfrom this interpretationwasfoundtolieintherange1.3–1.5.Thefast magnetosonicMachnumbersderivedfrom modellingtheCMEand the coronal magnetic feld aroundthe typeII sourcewerefoundto lieintherange1.4–1.6. 
Key words. Sun: corona – Sun: coronal mass ejections (CMEs) – Sun: radio radiation 
1. Introduction (Claßen&Aurass 2002;Choetal. 2005;Gopalswamy2006)and 
recent casestudies(Zimovetsetal.2012;Zuccaetal.2014b;Pick TypeIIradio burstsaretheresultof magnetohydrodynamics etal.2016)usingradiospectralobservationstogetherwithwhite-(MHD)shocksinthesolar atmosphere(Uchida1960;Wild1962; lightandX-rayimagesshowedthat CMEs can initiate mostof Mann et al. 1995), and they can be observed to range from the metric type II (m-type II) bursts. sub-metricto hectometricwavelengths(∼400 to ∼0.4 MHz). The region of the CME that is responsible for driving the Several candidatesfortriggeringanddrivingtheseMHDshocks shock mightbedifferentfor each eventandhasnotyet been have been proposed, such as coronal mass ejections (CMEs), comprehensively identifed. Multiple scenarios have been sug<BR>fares, coronalwaves,erupting loopsor plasmoids, ejecta-like gested,suchasapurebowshockattheCMEfrontandamultiple sprays, and X-ray jets (Pick & Vilmer 2008; Nindos et al. shock scenario in internal parts, or fanks of the CME, pos<BR>2008, and references therein). Magdaleni´sibly also related to blast waves as triggering events (see e.g. cet al. (2010)showed thatin addition totypeIIburstsrelatedtoCMEs,faresmay Claßen&Aurass2002;Nindosetal.2011).Furthermore,asthe 
also beresponsible forthe production ofa shockwavethat shockistriggeredbyapropagatingfronttravellingfasterthanthe 
drives thetypeIIbursts.However,severalstatistical studies magnetosonicwavespeed,travellingdisturbancesinthecorona 
Article publishedbyEDP Sciences A89, page1of 8 
A&A615, A89 (2018) 
can create shocks only in specifc structures with low Alfvén speed.In some cases,thepropagatingwave can alsosteepeninto a shock when it moves towards an environment with decreasing Alvén speed (see e.g. Vršnak&Luli´
c 2000). The scenario is then additionally complicated as the electron acceleration at shocksthatresultsinradio emissionmayberestrictedtoquasiperpendicularregions(Holman&Pesses1983;Baleetal.1999). Therefore,adetailed analysisbyinterferometricradio observations, extreme ultraviolet (EUV) and white-light together with models or data-constrained models of the magnetic feld and AlfvénspeedarenecessarytofullyunderstandthetypeIIburst – CMEparadigm.Several casesofm-typeIIburstshavebeenstudied using radio positional information at frequencies ≥150 MHz with the Nanca¸y radio-heliograph (NRH; Kerdraon & Delouis 1997). In these studies, the radio source location is compared withEUV orX-rayobservations (e.g. Kleinetal.1999;Dauphin etal. 2006;Nindos etal. 2011;Zimovets etal. 2012;Zucca etal. 2014b),whileonlyafew casesofradioburstimagingand white-light CMEs are available (e.g. Maia et al. 2000). The lack of radio positional information compared with white-light CMEs is mainly due to observational constraints. Metric type II burst typically occur inthe low corona (i.e. <2R&#12;); these heights are currentlyocculted in space-borne coronagraphs, whilefor type IIinthe deca-hectometricrange (DH-typeII)at heights >2 R&#12;, where coronagraphs are available, radio imaging observations are unavailable.Radio-heliographic observationsof typeIIradio burstsat109MHzhave beenreportedby Rameshetal. (2012) withthe Gauribidanur radio-heliograph(Ramesh et al.1998), andthere areafew observationsinthe literatureof typeIIradio bursts at 80 MHz (e.g. Gary et al. 1984)using the no longer operating Culgooraradio heliograph(Wild1967).To date,there is no radio positional observation of type II bursts at frequencies <80 MHz.A rangeoflow-frequencyradio imagingarrayshave beendevelopedinthepastyears, such astheMurchisonWidefeldArray(MWA; Tingayetal.2013), which wasrecentlyused for solar observations(e.g.Mohan&Oberoi2017),andtheLOw Frequency ARray(LOFAR; van Haarlemet al.2013).LOFAR operates at frequencies of 10–240 MHz, and it features multibeaming capabilities, whichcanbe usedtoproduce heliographic imagingoftheradio source(Morosan et al.2014,2015;Reid &Kontar 2017). The frequency domain at whichLOFAR oper-atesbridgesthegapbetweenthe metric band andthe currently unexplored imagingofthe decametric band. 
We here use LOFAR tied-array beam imaging and spec-troscopy to study the location of a decametric type II radio burst and understand the region of the CME responsible for triggering the shock and the role of the ambient magnetic feld and fast magnetosonic speed. In Sect. 2 we give an overview of the observational method, and we present the results of the tied-array beam imaging analysis and of the 3D reconstructionofthe CME.In Sect. 3we discusstheresults andpresent the conclusion. 


2. Observations and data analysis 

2.1. LOFAR observations 
On 2013 October 26, a type II radio bursts was recorded using oneoftheLOFAR beam-formed modes(Stappers et al.2011; van Haarlem et al. 2013). The radio burst was observed with theLow Band Antennas(LBAs) operatingatfrequenciesof10– 90 MHz using six stations at the heart of the core combined to effectivelyforma single largestation,a 320m diameter island referredto asthe Superterp. 


Fig. <BR>2. <BR>Dynamicspectrum(fromthebeamreportedwiththe flledblue circleinFig. 1)ofa typeIIradio burstrecorded on2013 October26 at 9:30 UT, showing fundamental (F) and harmonic (H) components, bothsplitintotwo lanes.The spectrumwasobtainedwiththeLOFAR SuperterpLBAantennas. The decreasein sensitivity below 29 MHz is duetothe flterfortheHF band. 
We used91simultaneous beamsto covera feldof viewof ∼16R&#12; centredontheSun.Eachbeamproducesadynamic spec-trumwithhigh time-andfrequencyresolution(10ms;12.5kHz) atauniquespatial locationthatcanbeusedtoproduce tied-array images of radio bursts (see Morosan etal. 2014, 2015). 
The FWHMofthe tied-arraybeam size withthis beam con-fguration is estimated to lie between 1.1 and 2.2 R&#12; from 80 to 50 MHz because of the reduced spatial resolution of the tied-array beam imaging, which uses a baseline of ∼320 m. The locationofthe91 beamsis showninFig. 1. The dynamic spectrum of the type II radio burst is shown in Fig. 2. The 
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P.Zuccaetal.:ShocklocationandCME3DreconstructionofasolartypeIIradioburstwithLOFAR 

Fig. <BR>3. <BR>Panel a: dynamic spectrum of the type II radio burst observed on 2013Oct 26; the harmonic emission is visible from 70 to ∼30 MHz. The specifc timesandfrequenciesatwhichthe locationoftheradio sourceis calculatedare indicatedwithcolouredtriangles. Panelb:runningdifference image of the CME observed withSOHO/LASCO(09:36−09:24 UT) withsuperposed contours of the radio sources (80%, 90%, and 95%)usingthe same colourcodeasforthetrianglesinpanela. 
burst shows fundamental (F) and harmonic (H) emission, and bothlanespresent band-splitting.Radio emissionstarted around 
9:30UT, andthe harmonic componentdriftedfrom70 MHzto 30MHzinapproximately6min.The intensityoftheradiationat a specifc beam location canthenbe usedtoproducea “macropixel”mapatachosen timeandfrequency.Figure 3ashowsthe dynamic spectrumofthetypeIIburstwiththe superposedtriangles indicatingthe frequency and time at whichthe locations of the typeII burstarereportedinFig. 3b. 
The locationoftheradio sourceforthis specifc settingof beam locations (using only the Superterp) can be estimated to lie between 70 and 50 MHz, while below 50 MHz, the larger source size results in emission spilling in the adjacent beam side-lobes. The location of sources below 50 MHz with the tied-array beam mode confguration requires a larger baseline thanthe Superterp (see Morosan et al. (2014, 2015)for full core tied-array observations) or a full knowledge of the beam shape.Figure 3b showsthe contours (80%, 90%, and 95%)of theradio emission fuxat70,65,60,55,and50MHz,following the harmonic emission band from 09:31:10 UT to 09:32: 58UT. These contours are superposedtotherunning difference image of the CME observed with SOHO/LASCO (09:36−09: 24 UT). The radio sources are located in the fank of the CME and appeartoshowatrendofmotion consistentwiththe lateral expansion ofthe fank (indicatedbythe black arrow). However, with this set of observations and with the effects of scatteringandrefractioninthe coronaatthesewavelengths(Kontar et al. (2017)report a size increase around 20 arcminutes and a potential shift up to ∼5 arcmin for LOFAR frequencies), we do not take into account any source motion for this study. When metric or decametric radiation propagates through the corona, it is both refracted and scattered by turbulent plasma processes that may affect the apparent positions of the radio sources. For this reason, we did not estimate the speed of the radio sources but we compared their positional centroid (indicatedinFig. 3bby thereddot) with white-light observations. The position of the type II radio burst at different frequencies wasfoundtobe locatedwithinthe uncertaintiesatthe fankof the CME. 


2.2. CME multi-viewpoint triangulation 
On 2013 October 26, during a period of intense solar activity, a series of CME were observed with the Large Angle and Spectrometric Coronagraph (LASCO; Brueckneretal.1995)on boardtheSolar and Heliospheric Observatory(SOHO; Domingo et al.1995)andwiththeCOR2Acoronagraphofthe SECCHI (Howard etal. 2008)instruments on boardtheSTEREO(Kaiser et al. 2008)mission. The frst CME appeared in LASCO/C2 at 07:00 UT, and it was then followed at 09:12 UT by the CME associated with the type II radio burst presented in this work. A third CME appeared again at 09:48 UT. Owing to the multiple passages of the CMEs, the coronal environment was signifcantlydisturbed. The longitudinal separation between SOHO and STEREO-A was 148◦ on 2013 October 26. Based on this multi-viewpoint dataset, the 3D surface of the expanding CME canbereconstructed usingthe methodfrom Rouillard et al. (2016).Figure 4 shows someexamplesofthe3Dreconstruction technique. The CME front is ftted with an ellipsoid, and panels(a)and(b)showtherunning-difference imagesat 
09:24 UT and 10:00 UT in which the superposed red crosses were manuallyobtainedto matchthe CME front observed from LASCO C2. As the CME is propagating in a disturbed corona because of the passage of the previous CME, the white-light front selection was not straightforward and required a careful manual selection. The obtained points that matched the CME front at different times were then used to ft the surface of an ellipsoid at each time step and obtain a set of three param-eters. The ellipsoid central position is defned in heliocentric coordinates (radius, latitude, and longitude). These ellipsoids where then visually compared to match the CME observed by the COR2A coronagraph viewpoint. After the parameters of the successive ellipsoids were obtained, we interpolated these parameters at steps of 150 seconds to generate a sequence of regularlytime-spaced ellipsoids.To computethe3Dexpansion speedofthe surfaceofthe CME,wedeterminedfora pointPon the ellipsoidattimetthe locationofthe closestpointontheellipsoid at a previous time-step t − δt by searchingforthe shortest distancebetweenpointPandallpointsonthe ellipsoidattime 
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Fig. <BR>4. <BR>Panel a: running-difference image of the CME observed with LASCO C2 at 09:24 UT. The superposed red crosses represents the manually selected CME front used to ft the ellipsoid. Panel b: same image as panel a at 10:00 UT. Panel c: resulting projected ellipsoid surface with the related red crosses extracted from the CME running-differenceimageat 09:25UT,andat10:00UTin paneld. 
t − δt.We then computed the distance travelled between these two points and dividedthisbythe time interval δt =150 seconds to obtain an estimate of the speed at P. This approach slightly underestimatestheCMEfront speed,butitreturnsasimpleestimationofthe speedinthe direction perpendiculartothe CME surface. 
Figure5ashowsthe CMErunning-difference image(09:36− 
09:24 UT) with superposed contours of the 50 MHz source at 
09:32:58 
UT and the centroid of the radio sources from 70 to 50 MHz between 09:31:10 and 09:32:58 UT (same sources as reportedinFig. 3), indicatingtheaveraged position wherethe type II emission was recorded (red dot). Figure 5b compares the location of the type II radio source centroid with the CME expansion speed. A detailed comparison of the radio source positions withthe shockfront observedin white lightis notpossible because the time cadence of LASCO/C2 is limited. The typeII signatureis observedtopropagatebetween 09:31:10and 

09:32:58 
UT, while the coronagraph images were taken at 9:24 and 9:36 UT. However, even without high time-cadence observationsin white light,theradio emissionisfoundtobe located at the fank region where the CME expansion speed calculated with the 3D reconstruction is ∼370 kms−1. The fanks of the CMEarenotthefastest expandingregionsoftheCME surface. The apex shows a propagation speed of about 500 km s−1. The radio emission, however, is located at the fank of the CME, indicatingthatother parameters suchasthe shockgeometryand theMach numberplay akey roleingeneratingtheradio emission from the shock. To estimate the Mach number along the CME expanding surface, we started reconstructing the ambient corona electron density using a combination of SDO/AIA and SOHO/LASCO data as describedby Zuccaet al. (2014a). Subsequently, we usedthe model called magneto-hydrodynamic around a sphere polytropic (MASP) developed by Predictive Sciences Inc.(Linkeretal.1999).MASPisa3DMHDpoly<BR>tropic model that adopts the photospheric magnetograms from SDO/HMIasthe inner boundaryconditionofthe magnetic feld. The full details of the interpolation technique used to derive 



Fig. <BR>5. <BR>Panel a:running-difference image withsuperposed contour of the type II harmonic emission at 50 MHz at 09:32:58 UT andthe centroid of the position of the radio sources from 70 to 50 MHz from 09:31:10UTto 09:32:58(reportedinFig. 3b). Panelb:CME 3D speed surface reconstruction from multi-viewpoint observations; the radio source centroidis indicated withthe pink circle. 
the coronalfast-magnetosonic speedfromthe3D MHD model results at all points on the surface of the CME is described in Rouillardetal. (2016). 
Afterwe estimatedthe ambientfastmagnetosonic speed,the Machnumberwas obtainedbycalculatingtheratiobetweenthe expanding CME front speed and the fast-magnetosonic speed. Figure6showsa3D viewofthereconstructedexpanding CME surface usingthe techniquefrom Rouillard et al. (2016). The viewpoint is chosen to allow the overview of the CME speed (a), magnetic feld orientation θ (b), andthefast magnetosonic Machnumber(c)oftheapexand upper fankoftheCME simultaneously. For each panel the line of sight (LOS) is indicated with a purple arrow, and the location of the the type II radio burstis indicatedbythered circle. The typeIIradio emissionis recordedatthe fankoftheCMEinaregionwherethespeedof the expanding CME reaches ∼370 kms−1 and the Mach numberrangesfrom1.4to1.6 and withthe orientationofthe B-feld θ ∼ 70◦ (Fig. 6). 


2.3. Band-splitting and multi-lanes 
Type II radio bursts typicallypresent two bright bands of emission witha frequency ratio of ∼2. These are commonlyaccepted to bethe emission ofthe fundamental and frst harmonic ofthe 
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P.Zuccaetal.:ShocklocationandCME3DreconstructionofasolartypeIIradioburstwithLOFAR 

Fig. <BR>6. <BR>3D reconstruction of the coronal ambient parameters. Panel a: CME speed, panelb:magnetic feld orientation withrespecttothe per-pendicular directiontothe CME front, and panel c:fast magnetosonic Machnumber.TheLOSis indicatedwiththepurplearrow,andtheradio source centroidisshownwiththeredcircle.The modelledCMEfront is reported at 09:36 UT in all panels. 
local plasma frequency (see e.g. Wild & Smerd 1972; Mann etal.1995;Aurass1997;Gopalswamy&Thompson 2000;Pick &Vilmer 2008). These two bright bands often appear to show a distinct separation into two sub-bands with an average frequency ratio of ∼1.23(Vršnak et al. 2001; Du et al. 2015)in bothfundamental and harmonic emission. This phenomenon is knownas band-splittingofthetypeIIradioburst,anditsorigin is still controversial. One explanation that found observational evidenceinthe past(Smerd et al.1974;Vršnaket al. 2001)and recently(Zimovetset al.2012; Zuccaet al.2014b)isthatthe two lanesoriginatefroma simultaneousradio emissionfromthe upstream anddownstreamregionofa shock. Holman&Pesses (1983)suggested that band-splitting might also result from a planar shockfront moving non-radially across curved magnetic feld lines. Another interpretation of band-splitting is that the two sub-lanesaretheresultof emissionfromtwodifferentparts of the shock front with similar expanding speeds, where the coronal ambientproperties suchasthe electron density,magnetic feld, and Alfvén speed are different (see e.g. McLean 1967; Schmidt& Cairns2012).In additiontothe band-splitting phe<BR>nomenon, type II radio bursts mayalso show multiple separate lanes(Nelson& Melrose 1985). These multiple lanes cannot be explained with a simple upstream and downstream emissionfroma single shockfront.Recently, Zimovets& Sadykov (2015)reported an observation withthree separate lanes. Using observations fromthe NRH(Kerdraon& Delouis1997),they showed distinct locations of the radio sources associated with the different lanes. They proposed a scenario in which two lanes are paired and originate from the upstream and down-stream of a shock front, while the third lane was found to have its origin in another location and resulted from a different shockfront. 
The typeII burstobserved on2013October13withLOFAR presentsbothband-splittingand multiple lanes.Adynamic spectrum showingthe band-splitting and multiple lanesinthe typeII burst is shown inFig. 7a. Band-splitting is visible in both fun<BR>damental (indicated with red stars and marked F and Fa) and harmonic emission (indicated with orangestars and markedH and Ha). The type II radio burst shows also a second harmonic band of emission, marked 2Ha. This is the second harmonic emission of the Fa lane, while the second harmonic emission oftheF laneis not clearlydiscernible asitis superposed with the Ha emission lane. Multiple lanes other than the different ordersof emissionoftheFandFa pair are alsopresent. These areindicatedinthedynamicspectrumwiththeblackarrows,and theyareevidentstartingfrom 09:34UT, wherethe typeII signature becomes more complex. Theradio source positionsforthe lanesH andHa andthe second harmonic 2Ha are indicatedin panel b using the same colour code as the triangles in panel a, while no spatial information could be inferred for the F and Fa bands with the current beam setting as these lanes are below 50 MHz. Sources are superposed over the LASCO white-lightrunning-differenceimageoftheCMEat 09:36UTin panelb. LanesHandHa(the temporalevolutionof laneHais reported in Fig. 3)resulting from band-splitting are located in the fankoftheCME.PanelcshowsthefastmagnetosonicMach number estimated withthe3Dreconstructionoverthe CME sur-face. The positions of the radio sources of the band-splitting lanes (H and Ha) are superposed in the 3D reconstruction with the two triangles, using the colour code of the triangles in panelaand indicatingtheLOSpathwith apurple line.Thetwo source locationsareinaregionwheretheMachnumberishigher than1.Inparticular,lanesHandHaarelocatedinaregionwhere the fast magneto-sonic Mach number is in the range 1.4–1.6. Withintheresolutionofthis observation,thetwo sources(Hand Ha) are located in the same region. This is in agreement with the band-splitting interpretation of emission ahead and behind the shockfront. Whenwe considerthis interpretation,thefast magnetosonic Mach number can be estimated by calculating the compression ratio inferred from the frequency split in the type II harmonic lane. The average value of the compression ratio from the band-splitting along the frst harmonic emission lanes is X =1.45. We estimated the fast magneto-sonic Mach number using the method described by Vršnak et al. (2002), usingEq.(9)oftheir manuscript. Thefastmagnetosonic Machnumber MFM = MA/(1 + βγ/2)1/2 assuming a polytropic index γ = 5/3, has a value of 1.32–1.35, using a plasma-tomagnetic pressure ratio β between 0 and 2, respectively. For a value of γ = 1 (uniform coronal temperature), the Mach number is estimated as MFM =1.36 –1.54 and is in this case 
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Fig. <BR>7. <BR>Panel a:dynamic spectrumofthetypeIIradioburstobservedon2013Oct26,showing band-splittinginboththe fundamental(FandFa) andtheharmoniclanes(HandHa)andaseriesof multi-lanes (indicatedby theblack arrows).Thesecondharmonic emissioncanalsobeseen andismarkedwith2Ha.The locationoftheradio sourcesforthetwo split-lanesresolvedfor50and65MHzat09:31:30UTare indicatedinthe dynamicspectrumbythebrownandyellowtriangles,respectively.The secondharmonicofthetypeIIradioburstis indicatedat75MHzwiththe blue triangle. Panelb:running-difference image ofthe CME observed withSOHO/LASCO(09:36−09:24 UT) withsuperposed contours of the radio sources(80%,90%,and95%)ofthetwosplitlanesHandHaat09:31:30UT.The source locationofthe secondharmonicat 09:32:45using the colourcodeofthetrianglesinpanelaisalsoshown. Panel c: reconstructed CME Machnumber. The locations of the type II split-lanes are superposed. TheLOSis indicatedbythe purple line. 
comparable withthe Machnumber estimated withthe3D CME reconstruction(1.4–1.6). 


2.4. Second harmonic emission 
The second harmonic emission (three times the fundamental emission) is rarely observed in type II radio bursts. The type IIradio burst observed on2013October26byLOFAR showed this emission in the dynamic spectrum. This emission lane is marked as 2Ha in Fig. 7. The tied-array beam source reconstruction was used to locate the source position of the second harmonic lane 2Ha. The radio source position at 75 MHz of the 2Ha lane is indicated with blue contours in Fig. 7b. The position is comparable within the beam size with the location of the frst harmonic lane Ha, suggesting that the second and thirdharmonic emissionoriginatefromthe same sourceregion. This fndingisinagreementwith Zlotniketal. (1998), wherethe authorswere ableto measurethe source locationof another type II burst showing frst and second harmonic emission. Using the NRH imaging bands at 327and 435 MHz, theyconcluded that their observations were in agreement with the frst and second harmonic lane of the type II radio burst coming from the same source. This confrmation usingLOFAR suggeststhatradiowave propagation does not signifcantlyalterthe apparent location of the harmonic source even at low frequencies such as 65 and 75MHz. 


3. Conclusion 
Wehavepresentedastudyofthe typeIIradio burstobserved on 2013October 26.Wewere ableforthe frst timeto estimatethe spatial locationofthetypeIIradioburstatfrequenciesbetween (70–50 MHz) using the LOFAR LBA antennas. This complex typeIIradioburstwascomposedofapairofsplit lanesobserved at fundamental, frst, and second harmonic emission and of several multi-lanes.The locationofthetypeIIradio signaturewas compared with the CME front reconstructed in 3D. The fast magnetosonic speed and the B-feld orientation were used to estimate the shock Mach number and the shock magnetic feld geometryalongtheCME surface.Wehavefoundthattheradio signatureofthe shockis locatedatthe fankofthe CME.Inpar-ticular,the band-splittingofthetypeIIfrstharmonic emissionis locatedinthe fankofthe CME wherethe Machnumberranges between1.4and1.6andthe confgurationisquasi-perpendicular, θBn ∼ 70◦. This study provides observational evidence on the location of the type II emission in the region with quasi-perpendiculargeometryand Mach numbergreaterthan1. This is the region where particles can effciently be accelerated to higher energiesby shock drift acceleration(Holman&Pesses 1983; Mann& Klassen 2005). Thequasi-perpendiculargeom<BR>etry related to a signature of a type II radio burst was recently found alsoby Salas-Matamoroset al. (2016).In addition, mul<BR>tiple lanes in the type II emission may be explained with the radio signature comingfrom differentregionsofthe shockfront where the local plasma conditions are favourable for quasi-perpendicular shocks andforthegenerationof associatedradio emission. However, the observations we presented do not allow identifying the spatial position of these lanes. We were able to locate the source position of the frst harmonic split lanes, which wasfoundtobe consistent with the emission ahead and behindtheexpanding shockfrontinthe CME fank.A compa-rableMachnumber(1.3–1.5)was calculated independentlyfrom the band-splitting in the dynamic spectrum assuming this scenario. However, other scenarios cannot be excluded since the observation we presented does not provide a defnite answer to the band-splitting phenomenon. The location ofthe second harmonic emission was also identifed. It was located within the beam size in a common source region with the frst harmonic emission. This confrms previous fndings and excludes that in thisevent,radiowavepropagation signifcantlyaltersthe apparent locationoftheradio sourceofthe secondharmonic emission. Radio observationswithbetterresolutionarenecessarytoclearly describe the origin of the different emission lanes and to inter-pretthem.In particular,LOFAR observations using simultaneouslyimaging and tied-arraybeam willreducethe uncertainties of the radio source location, and will allow determining the 
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P.Zuccaetal.:ShocklocationandCME3DreconstructionofasolartypeIIradioburstwithLOFAR 
location of fainter radio sources. Questions remain about the number of events with shocks at the fank of CMEs, about the necessityofaquasi-perpendiculargeometryin typeII emission, and about the nature of the band-splitting and multi-lane phenomena. Multi-viewpoint observations together with imaging campaigns usingLOFAR areimportantfor solvingtheremaining unknowns of the type II radio emission, the related fne structures, and the relationship between CME expansion and ambient medium parametersinproducingtheradio emission. 
Acknowledgements. This paper is based on data obtained with the International LOFAR Telescope (ILT). LOFAR (van Haarlem et al. 2013) is the Low Frequency Array designed and constructed by ASTRON. It has facilities in several countries that are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation undera joint scientifc policy.We arealsogratefultotheSTEREO, SDO, and LASCO team for the data access. A. P. Rouillard acknowledges funding from the French “Agence Nationale de la Recherche” under contract number ANR-17-CE31-0006-01. 


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1 ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990AA, Dwingeloo, TheNetherlands e-mail: zucca@astron.nl <BR>
2 Astrophysics Research Group, School of Physics, Trinity College Dublin, Dublin 2, Ireland 3 Institut de Recherche en Astrophysique et Planétologie, 9 Av. du ColonelRoche,31028Toulouse Cedex4,France 4 Solar-Terrestrial Center of Excellence, Royal Observatory of Belgium,Av. Circulaire3,1180Brussels, Belgium 5 LESIA, UMR CNRS8109, Observatoire deParis, 92195 Meudon, France 6 Leibniz-Institut f AstrophysikPotsdam (AIP), An derSternwarte 16,14482Potsdam, Germany 7 RAL Space, Science andTechnologyFacilities Council,Rutherford Appleton Laboratory, Oxfordshire, UK 8 SUPA School of Physics and Astronomy, University of Glasgow, G128QQ, UK 9 Space Research Centre of the Polish Academy of Science, 18A Bartycka 00-716Warsaw,Poland 10 Space Radio-Diagnostics Research Centre, University of Warmia and Mazuryin Olsztyn,Poland 
11 Helmholtz-Zentrum Potsdam, DeutschesGeoForschungsZentrum GFZ, Geodesy and Remote Sensing, Telegrafenberg, A17, 14473 Potsdam, Germany 
12 ShellTechnology Center, Bangalore, India 
13 UniversityofTechnology Sydney,15Broadway, UltimoNSW2007, Australia 
14 EindhovenUniversity ofTechnology, PO Box513, 5600 MB Eindhoven, TheNetherlands 
15 InstituteforAstronomy,Universityof Edinburgh,Royal Observatory of Edinburgh, BlackfordHill, Edinburgh EH9 3HJ, UK 
16 KapteynAstronomicalInstitute,POBox 800,9700AVGroningen, TheNetherlands 
17 University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany 
18 Research School of Astronomy and Astrophysics, Australian NationalUniversity, Canberra,ACT2611Australia 
19 Max Planck Institute for Astrophysics, Karl Schwarzschild Str. 1, 85741Garching, Germany 
20 SmarterVisionBV, Oostersingel5,9401JX Assen, TheNetherlands 
21 Centrefor Astrophysics& Supercomputing, SwinburneUniversity ofTechnology JohnSt,Hawthorn VIC3122,Australia 
22 Thinger Landessternwarte, Sternwarte 5, 07778 Tautenburg, Germany 
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29 Astronomisches Institut der Ruhr-Universität Bochum, Universitaetsstrasse150,44780 Bochum, Germany 
30 Astrophysics, University of Oxford, Denys Wilkinson Building, KebleRoad, OxfordOX1 3RH,UK 
31 AntonPannekoekInstituteforAstronomy,UniversityofAmsterdam, SciencePark904,1098XH Amsterdam, TheNetherlands 
32 Department of Physics and Technology, University of Troms, Norway 
33STFCRutherfordAppleton Laboratory, Harwell Science and Innovation Campus, DidcotOX110QX,UK 
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35 Department of Physics and Astronomy, University of California Irvine,Irvine,CA92697,USA 
36 Centerfor InformationTechnology (CIT),UniversityofGroningen, Groningen, TheNetherlands 
37 Poznan Supercomputing and Networking Center (PCSS) Poznan, Poland 
38 Max-Planck-Institut fRadioastronomie,Auf demHel69,53121 Bonn, Germany 
39Fakultät fPhysik,Universität Bielefeld,Postfach100131, 33501, Bielefeld, Germany 
40 Department of Physics and Elelctronics, Rhodes University, PO Box94,Grahamstown6140, SouthAfrica 
41 SKASouthAfrica,3rdFloor,ThePark,ParkRoad, Pinelands,7405, SouthAfrica 
42 International CentreforRadioAstronomyResearch -CurtinUniver-sity, GPOBoxU1987,Perth,WA6845,Australia 
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44 Department of Physics and Electrical Engineering, Linnaeus University 35195,Vaexjoe, Sweden 
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