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Advances in Space Research 40 (2007) 1827–1834

Three-dimensional global simulation of multiple ICMEs’interaction and propagation from the Sun to the heliosphere

following the 25–28 October 2003 solar events

C.-C. Wu a,f,*, C.D. Fry b, M. Dryer c,b, S.T. Wu a, B. Thompson d, Kan Liou e, X.S. Feng f

a CSPAR/University of Alabama, Huntsville, AL 35899, USAb Exploration Physics International, Inc., Huntsville, AL 35806, USA

c NOAA Space Environment Center, R/E/SE, 325 Broadway, Boulder, CO 80305, USAd NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

e JHU/APL, Laurel, MD 20723, USAf Key State of Laboratory for Space Weather, Chinese Academy of Sciences, Beijing 100080, China

Received 1 November 2006; received in revised form 12 June 2007; accepted 13 June 2007

Abstract

This study performs simulations of interplanetary coronal mass ejection (ICME) propagation in a realistic three-dimensional (3D)solar wind structure from the Sun to the Earth by using the newly developed hybrid code, HAFv.2+3DMHD. This model combinestwo simulation codes, Hakamada–Akasofu–Fry code version 2 (HAFv.2) and a fully 3D, time-dependent MHD simulation code.The solar wind structure is simulated out to 0.08 AU (18 Rs) from source surface maps using the HAFv.2 code. The outputs at0.08 AU are then used to provide inputs for the lower boundary, at that location, of the 3D MHD code to calculate solar wind andits evolution to 1 AU and beyond. A dynamic disturbance, mimicking a particular flare’s energy output, is delivered to this non-uniformstructure to model the evolution and interplanetary propagation of ICMEs (including their shocks). We then show the interactionbetween two ICMEs and the dynamic process during the overtaking of one shock by the other. The results show that both CMEsand heliosphere current sheet/plasma sheet were deformed by interacting with each other.� 2007 Published by Elsevier Ltd on behalf of COSPAR.

Keywords: Sun: flare; Sun: coronal mass ejection; Sun: interplanetary shock; 3D globe MHD simulation

1. Introduction

The first time-dependent 3D simulations of interplane-tary shock propagation were performed by Han et al.(1988). Using this model, some parametric studies utilized3D MHD simulations of interplanetary magnetic fieldchanges at 1 AU as a consequence of an interaction witha flat heliospheric current/plasma sheet (HCS/HPS,

0273-1177/$30 � 2007 Published by Elsevier Ltd on behalf of COSPAR.

doi:10.1016/j.asr.2007.06.025

* Corresponding author. Tel.: +1 301 286 2327.E-mail addresses: wuc@cspar.uah.edu (C.-C. Wu), gfry@expi.com

(C.D. Fry), murray.dryer@noaa.gov (M. Dryer), wus@cspar.uah.edu(S.T. Wu), Barbara.j.thomspan@nasa.gov (B. Thompson), kan.liou@jhuapl.edu (K. Liou), fengx@spaceweather.ac.cn (X.S. Feng).

Wu et al., 1996) and also with a tilted HCS/HPS(Wu and Dryer, 1997). In addition, Dryer et al. (1997) usedthe code to simulate the April 14, 1994, interplanetaryCME and its propagation to Earth and Ulysses (in thesouthern hemisphere at �4 AU). Wu et al. (2005a) recentlyperformed a parametric study, via 3D MHD simulations,of the shock time of arrival at Earth. In a more recent study(Wu et al., 2007a), we found that the background non-uni-formity of the solar wind plasma and IMF is of negligibleconsequence for shock wave arrivals provided the energyoutput of the solar disturbance is unusually large, e.g.,1034 ergs or higher. All of these studies, however, werelimited by having a lower boundary at 18 Rs (where Rs =solar radius = 6.95 · 105 km) and with an ideal steady state

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solar wind condition. This motivated us to relax thisrestriction and to perform a global three-dimensional(3D) numerical simulation from the Sun to the Earth.Therefore, we linked the space weather-validated kinematic3D Hakamada–Akasofu–Fry version 2 (HAFv.2) model(cf., Fry et al., 2001; Dryer et al., 2004) to the full 3DMHD model of Han et al. (1988). Thus, solar surface mag-netograph observations can now drive, continuously, theHAFv.2 model and, then, the Han et al. model throughoutthe heliosphere. We will refer to this hybrid model, hence-forth, as ‘‘HAFv.2+3DMHD’’.

In this study, we use this newly developed global 3Dsimulation model to simulate part of the Halloween 2003events that are described observationally by Veselovskyet al. (2004) and Gopalswamy et al. (2005) and, previously,with a 1.5D MHD numerical simulation by Wu et al.(2005b, 2006, 2007a). In related works, Odstrcil et al.(2004, 2005), who presented an approach to the simulationof the 12 May 1997 flare/CME/shock event during solarminimum, were mainly concerned with the interplanetarydifferences caused by various coronal outflow models(cf., Arge and Pizzo, 2000 and variations thereof) forsmall-scale structures in the pre-event background solarwind. These authors concluded: ‘‘It is always an advantageto use different models for the same problem improved inthe future. Not only can one obtain higher confidencein predicted features and effects, but also the differencesin results are very helpful in estimating their accuracy, inunderstanding the physics, and in learning what shouldbe improved in the future.’’ The present work is presentedin this spirit. We will use a different assumption from thatused by Odstrcil et al. (2004, 2005) for mimicking the solarorigin and launch of the ICMEs (interplanetary coronalmass ejections). Other techniques (cf., ‘‘loss-of-equilib-rium’’) for launching CMEs and flares, CMEs withoutflares, or flares without CMEs (cf., Zhang et al., 2001)are considered to be beyond the scope of this paper. Wewill use the classical deterministic initial boundary valueproblem wherein changes in one or more observable phys-ical conditions (cf., any one or more of emerging magneticflux, pressure increases generated by reconnection, etc.) caninitiate a deviation from the steady state.

Our goal is to provide a validation procedure for thenewly coupled model described above. As noted in the firstparagraph, the HAFv.2+3DMHD model can be drivencontinuously and, therefore, can be used as a second gener-ation operational tool, the first being the HAFv.2 model(Fry et al., 2001). The numerical simulation model isdescribed in Section 2; observations are discussed in Sec-tion 3; and simulation results are described in Section 4.Discussion and conclusions are given, respectively, in Sec-tions 5 and 6.

2. Simulation model

The non-uniform background conditions of the solarwind plasma and IMF are essential for the model coupling

of the corona to the solar wind modeling codes. We use thishybrid model to simulate CME/ICME/Shocks propagat-ing from the Sun to the Earth and beyond with a realisticsolar wind background condition.

As noted in Section 1, HAFv.2+3DMHD combinestwo simulation codes, Hakamada–Akasofu–Fry code(HAFv.2) (Fry et al., 2001 see, also, references therein)and a fully three-dimensional, time-dependent MHD simu-lation code (Han et al., 1988; Detman et al., 1991, 2006).We briefly summarize below two basic steps: (i) from theSun to 2.5 Rs, thence to 0.08 AU and (ii) from 0.08 AUto the Earth and beyond. That is, source surface data at2.5 Rs, provided by NOAA (http://sec.boulder.noaa.gov),are input to the HAFv.2 model. The output from thismodel at 0.08 AU (18 Rs) are then input to the 3D MHDmodel.

2.1. Model for simulating CME/ICME/Shock from 1.0 Rs to

0.08 AU (18 Rs)

This physics-based code is a kinematic model, HAFv.2(Fry et al., 2001). The model uses a modified kinematicapproach to simulate the solar wind conditions out to18 Rs with data from Carrington Rotation maps (2.5 Rs),provided by NOAA’s Space Environment Center, as theinput. The output of HAFv.2 at 18 Rs (0.08 AU) providesinputs for the time dependent 3D MHD solar wind model.The pre-event, globally non-uniform, solar wind plasmaand IMF (interplanetary magnetic field) co-rotating systemis driven by a time series of photospheric magnetic mapscomposed from daily solar photospheric magnetograms(http://wso.stanford.edu). Use of these data to providesolar wind velocity and radial IMF at 2.5 Rs is describedby Arge and Pizzo (2000). Table 1 lists the three differentflow velocity pulses provided to the HAFv.2 code at2.5 Rs. This type of study has been carried out by Fryet al. (2001) and Wu et al. (2000) and is of the kind notedin a previous 3D MHD simulation by Wu et al. (in press)for the 12 May 1997 event.

2.2. Model for simulating CME/ICME/Shock from 0.08 AU

to the Earth and beyond

The numerical 3D MHD scheme used in this analysisis an extension of the two-step Lax–Wendroff finite dif-ference method (Lax and Wendroff, 1960). We foundthat using the Lax–Wendroff (L–W) method is still avalid approach (see next paragraph). The details of thecomputational procedures can be found in the work ofHan et al. (1988) and Detman et al. (1991). When usingthe two-step Lax–Wendroff finite difference method, thegoverning equations are required to be written in conser-vation form. A complete description of this conversioncan be found in Han (1977). The governing equations,for an ideal, single fluid, perfect gas, include conservationof mass, equation of motion, conservation of energy, andinduction equation.

Table 1Flares, CMEs’ speed, and shocks (observed at 1 AU) during October 25–29, 2003

Events

Occurrence of flaresa Class Location VSb VCME

c Shock

0552 UT, 2003-10-25 LDE M1.7/SF N00W15 316 585 0854 UT, 2003-10-28d

0617 UT, 2003-10-26 LDE X1.2/3N S18E33 1302 1245 0150 UT, 2003-10-281102 UT, 2003-10-28 X17/4B S15E08 1875e 1800 0600 UT, 2003-10-29

a The flare time is listed as the radio metric Type II start time that is close to the maximum of the soft X-ray emission in 1–8 A.b Estimated coronal shock speed, km/s, based on metric Type II radio drift (Dryer et al., 2004).c CME speed, km/s, based on near real time estimates listed in Dryer et al. (2004).d Actually, this time marks the arrival of the directional discontinuity, DD, as discussed in the text as a product of the interaction of two shocks (Wu

et al., 2005b).e Based on an average of several real-time radio observatory reports (Dryer et al., 2004).

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The computational domain for 3D MHD simulation is aSun-centered spherical coordinate system (r, h, /) with ther-axis in the ecliptic plane. Earth is located at r = 215 Rs,h = 0�, and / = 0�. The domain covers �87.5� 6 h 687.5�; 0� 6 / 6 360�; 18 Rs 6 r 6 285 Rs. An open bound-ary condition at both h = 87.5� and h = �87.5� is used sothat there are no reflective disturbances. A constant gridsize of Dr = 3 Rs, Dh = 5�, and D/ = 5� is used. The twoangular grid sizes are chosen to be equal to those providedby the photospheric magnetic maps discussed by Arge andPizzo (2000). The radial grid size, at this time, is chosen tobe also large but still sufficient to provide insight for globalstructures such as shocks. We emphasize the point thatthese pulses generate coronal mass motions that exceedthe local characteristic fast mode speed, thereby generatingshocks (Wu et al., 2006). Thus, no CME model, per se, isrequired, although we still do not understand the CMEgenerating mechanism, nor whether a 3D realistic orreliable, CME model exists. For example, performing a3D MHD simulation, Odstrcil et al. (2004, 2005) studiedthe May 12, 1997, magnetic cloud event by adding apressure pulse (4 times the original density magnitude) at�0.1 AU to simulate an empirical CME cone model’spropagating from 0.1 AU to 1 AU.

3. Observations

We were motivated to study the interplanetary conse-quences of only a small subset of the flares and shocks fore-cast and described by Dryer et al. (2004) in real time and byVeselovsky et al., 2004. Our choices included several of thelargest solar events (during a three-day period) that wereaccompanied by metric Type II shocks that were detectedin real time. We did not consider the flares that were notso associated. A summary of the three chosen flares duringthe period from October 25 to October 28, 2003, is given inTable 1. The first one took place at 0552 UT, 25 October inAR0484 at N00W15 as a long duration event (LDE) M1.7/SFflare. The second one occurred at 0617 UT, 26 October inAR0486 at S18E33 as another LDE X1/3N flare. The thirdone was observed at 1102 UT, 28 October, also in AR0486at S15E08, as the X17/4B flare, followed by a halo CME.(Note that there was another one that took place

(Dryer et al., 2004) at 2042 UT, 29 October, as an X10/2Bflare in AR0486 at S15W02. We did not simulate thisevent.)

During the period October 29–November 2, 2003, threeshocks were observed at Earth by ACE/SWEPAM/MAGand ACE/SWICS on October 28, 29, and 30. Two distinctand very intense geomagnetic storms, associated with theX17.2 and X10/2B flares, rank as two of the largest stormsof solar cycle 23. For example, the X17.2 flare (28 October,S15E08 in AR0486), via its associated halo CME andshock wave, was probably responsible for initiating thegeomagnetic storm, via both increased dynamic pressureand southward Bz, that culminated in the Dst = �363 nTindex on October 30, 2003. We will discuss the global sim-ulation of the ICMEs’ interactions and propagation fromthe first two X-flares/CMEs listed in Table 1. The direc-tional discontinuity listed in the last column was, webelieve, formed by the earlier interaction processesdescribed by Wu et al. (2005b, 2007a).

4. Simulation results

4.1. The effect of background solar wind speed

Fig. 1 shows the profile of simulated solar wind speedthat followed the famous flares of October 25, 26, and28. In preliminary attempts to mimic medical magnetic res-onance ‘‘MRI’’ images, we show the solar wind speed onthe surfaces of three angular cones that are centered atthe Sun’s center: 22.5� North; 2.5� North, close to Earth’slatitude in the solar equatorial coordinate system; and22.5� South, representative of a southern heliosphericresponse. The thin solid circle is at 1 AU with the Earthat 0� heliolongitude. Thus, the East limb (relative to Earth)is at the top, 90� East; and the West limb is at the bottomof each panel, 90� West. The outer boundary of the simu-lation is at �290 Rs. The non-uniformity of the entire glo-bal structure of the CME/ICME/Shock at Earth andelsewhere within the inner heliosphere is apparent.

Figs. 1a,f,k show the solar wind speed profiles at1800 UT on October 25 which is �12 h after a flare, locatedat N00W15, occurred at 0552 UT on October 25, 2003.These profiles show that the ICME has already passed

Fig. 1. The simulated profiles of velocity using the HAFv.2+3DMHD model during the period of October 25–29, 2003. The top, middle, and bottompanels represent, respectively, the constant conical angles of 22.5�N, 2.5�N, and 22.5�S.

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18 Rs. The brighter blue spiral stripes represent the solarwind that emanated from a solar coronal hole; several ofthese zones are marked in dotted ovals. Earth’s locationis marked in Fig. 1f. Figs. 1f,b,g,l show the solar wind pro-files at 0000 UT on October 27 which is �18 h after the sec-ond flare was observed at S18E33, 0617 UT, on October26, 2003. It is clear that the ICME’s central axis (subjec-tively defined) is directed into the southern hemisphere.The ICME’s size is larger in that direction than in the eclip-tic plane or northern hemisphere. Figs. 1b,g,l,c,h,m showthe process of the overtaken ICME’s interaction. Addition-ally, the dashed ovals show the feature of the stronglyattenuated backside portion of the large ICME. Figs.1d,e,i,j,n,o show the solar wind speed profiles at 0200 UTand 2200 UT, respectively, on October 29, 2003, whichwas �15 and �35 h after the third flare was observed at1102 UT on October 28, 2003. The solid arrows showa deformation of ICME structure that propagatedfaster than the adjacent western material due to the fasterbackground flow and lower density from the coronalhole. Finally, Figs. 1e,j,o show that the ICME arrived inthe southern hemisphere earlier than at the equator or inthe northern hemisphere. This effect is clearly due to theICME’s source location at S15E08.

4.2. The deformation and overtaking of ICMEs

Fig. 2 shows an additional set of medically-inspired‘‘MRI’’ global density (upper row) and velocity (lowerrow) profiles that followed the flare/CMEs of October25–28, 2003. These profiles are in the Earth’s meridianplane from 1800 UT, October 25, 2003, to 2200 UT, Octo-ber 29, 2003. The temporal snapshots for the five columnsare for the same times as in Fig. 1. Figs. 2a,f show thesteady state solar wind condition, primarily, but also witha very small density and velocity increase for the ICMEfrom the first flare (Table 1). The location of Earth, indi-cated in Fig. 2e, is in the center of the meridional plane.The simulated ICME in Figs. 2b,g is from the second flareduring this epoch: namely, the X1.2/3N flare at S18E33 onOctober 26, 2003, at �0617 UT which is the metric Type IIstart time that is nearly coincident with the soft X-ray max-imum. Fig. 2, in the other views, shows the velocityresponse that followed this and the other flares. Thelightly-dotted ovals (inclined to the south) call attentionto the heliospheric plasma/current sheet (HPS/HCS) andits boundaries with the solar wind stream from the polarcoronal holes. The HPS/HCS, located near the solarecliptic plane, is clearly seen as well as its subsequent

Fig. 2. The simulated profiles of density (N, upper row) and velocity (V, lower row) at a constant meridional angle of 0� (Earth location) using theHAFv.2+3DMHD model during the period of October 25–29, 2003.

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deformation. The shape of the ICME, indicated by the two,dashed arrows and the heavily-dashed ovals, was distortedafter interacting with the HPS/HCS (lightly-dashed ovals).Figs. 2g–h (see the heavily-dashed ovals) show the defor-mation of the merged ICMEs by interacting with eachother and the non-uniform solar wind, becoming twonon-symmetric structures. The leading edges of the twoICMEs (including their shocks) propagated slower in theHPS/HCS region because of the lower speed there.

4.3. Comparison of simulation results with observation

Fig. 3 shows the observed ACE/SWEPAM/SWICS/MAG (black dots) and simulated (dashed lines) solar windplasma and magnetic field data between October 26 and 30,2003. Three shocks (marked by the vertical dotted lines)occurred on October 28, 29, and 30, 2003. The first twoshocks are listed in Table 1. We made no attempt to simu-late the third shock as noted earlier. A directional discon-tinuity, marked DD (discussed in Wu et al. (2005b)), isnoted by a vertical solid line at a smaller velocity increasefrom �600 km/s to 650 km/s at 0852 UT on October 28,2003. The bottom to the top panels of Fig. 3 show solarwind speed, number density, temperature, total magneticfield, and the x-, y-, and z-components of magnetic field.The proton density is not available (Skoug et al., 2004) ina reliable form during the period after 0600 UT, October29, 2003. The simulation results compared to ACE data

look reasonably good for solar wind velocity, number den-sity, and total magnitude of magnetic field. The second(simulated) shock arrived about �12 h later than actualbecause our pulse also for that mimicked flare was notlarge enough. SWEPAM Level 1 data for density, temper-ature, and velocity are not reliable after 1200 UT, October28 because of the energetic proton ‘‘snowstorm’’ from theX17/4B flare and shock wave. The actual temperature plot-ted here is from the ACE/SWICS instrument. We do notsimulate the temperature very well because thermal con-duction and damping of Alfven waves are not included inour model; however, we consider temperature to be a sec-ondary objective at this time. For magnetic field, we getthe general trend and shocks but not the correct ampli-tudes. The transverse component, By, is simulated reason-ably well but not Bx or Bz. So, in general, we still haveopen questions about how to initialize our inputs. As notedabove, we did not attempt to simulate the ICME nor itsshock from the X10/2B flare and CME on October 29,2003.

5. Discussion

Wu et al. (2005a) recently performed a parametric studyconcerning the arrival times of shock passages at Earth byperforming 3D MHD simulations. They demonstrated thatthe shock arrival time at Earth depends on the backgroundsolar wind speeds, the initial speeds of solar disturbances,

Fig. 3. Solar wind plasma and magnetic field data (ACE), and simulationresults (dashed lines) during October 26–30, 2003.

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their size, and their source location on the Sun relative tothe Earth’s central meridian. However, the lower boundaryused (Wu et al., 2005a) is �0.08 AU instead of the surfaceof the Sun. We have initiated basic studies of shocks thathave already evolved from the Sun (thus within�0.08 AU) and by tracking their evolution and interactionsto 1 AU by using a 1.5 D MHD model (Wu et al., 2005b,2007a) for the events discussed here. This earlier work,the latter one in particular, provided the motivation toextend the initialization process to the present 3D MHDhybrid procedure.

Recently, we applied the HAF+3DMHD code to simu-late CMEs/ICMEs propagating into the realistic solar windduring a solar minimum (e.g., the May 12, 1997) event (Wuet al., in press). In the present study, we simulated multipleevents during the declining phase of solar Cycle 23, i.e.,Halloween 2003 event as shown in Figs. 1 and 2. Fig. 2

shows: (1) the deformation of ICMEs after interaction withthe HPS/HCS; (2) the overtaking and interaction processbetween two ICMEs; and (3) the ability and location of astrong flare that can be inferred when only a backsideCME is observed. Item (3) refers to the thin solid arrowsin Fig. 1i,n,j,o that point to increased speed ‘‘pimples’’(and likely density increases as well) at the ICME/Shockflanks. Expanding on this point, the reader is asked to bea hypothetical observer who would be located (roughly)opposite Earth’s location. Our interpretation is that thecombined shocks (in this particular case) from the flares,listed in the top of Fig. 1, expanded around the Sun tomore than 2p steradians. The combined ICME ejecta weresufficiently compressed so that it might be observed via theThomson effect in the plane-of-sky for this hypotheticalobserver.

Several fully 3D MHD simulations exist for studyingsolar eruptions from the Sun to the Earth. However, eachmodel has its own limitation. For example, Han et al.(1988) first used a 3D, MHD, time-dependent numericalmodel to study supersonic and super Alfvenic MHD flowfrom 18 Rs to 1 AU. Their code can study solar phenom-ena from 0.1 AU but not the evolution of shocks within0.1 AU. Another 3D MHD numerical model used to inves-tigate the temporal and spatial evolution of large-scalesolar wind structures was developed by Odstrcil and Pizzo(1999a,b). These workers studied the evolution of coronalmass ejections launched at several heliographic positionsinto a tilted-dipole ambient solar wind flow which is appro-priate around solar activity minimum and declining phase(Odstrcil and Pizzo, 1999b). However, the 3D model usedby Odstrcil and Pizzo (1999a,b) can only simulate solarwind structures beyond 21.5 Rs. It has the same limitationas the 3D model developed by Han et al. (1988).

Numerical simulations were previously used to study theinteraction of CMEs. Using a 2.5D MHD simulationmodel, Schmidt and Cargill (2004) studied the interactionbetween two CMEs from 1.7 to 32 Rs. They found: (1)the interaction of CME pairs will tend to lead to largemerged structures, at least when the outward CME trajec-tories are close to each other and (2) CMEs ‘‘sticktogether’’ rather than tending to bounce off each other.Thus, they realized that multiple CME compressible inter-actions were inelastic rather than like billiard ball elasticcollisions. Their analysis considered a uniform backgroundsolar wind with no consideration of the IMF. Recently,more extensive 2.5D MHD studies on CME ‘‘cannibaliza-tion’’ have been done with solar minimum type bimodalsolar wind backgrounds together with the HPS/HCS. Inthis work, Xiong et al. (2006a,b) also used a meridian2.5D MHD model to simulate the overtaking of an initialICME by a trailing ICME. Their results, with more exten-sive details, show that the trailing shock first overtakes thepreceding magnetic cloud, then penetrates through it, andfinally merges with the MC’s first shock, forming a strongercompound shock. This process (without the use of a MC)was also demonstrated, together with reverse shock

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formation, in detail by Wu et al. (2005b) in the 1.5D MHDapproximation. We might also mention another studypertaining to the October 28–30, 2003, event within thecontext of an empirical electrodynamical approximation.This non-MHD study by Krall et al. (2006), however,required numerous free parameter adjustments in orderto provide an appropriate MC arrival time at ACE.

The 3D MHD studies have been progressing rapidlywithin the context of the solar minimum bimodal back-ground solar wind and the popular flux rope model formagnetic clouds. Lugaz et al. (2005b) used this approachto study the interaction of two identical CMEs. Two iden-tical CMES were launched in the same direction into thispre-existing solar wind, the second one 10 h after the firstone. This approach followed their earlier work (with a sin-gle ICME) by Lugaz et al. (2005a) who also used an unbal-anced self-similar flux rope within the initially undisturbedcorona in order to cause the disturbance. This latter workalso examined the total mass and energetics of the CME.

It is worth noting, returning to the 1.5D MHD context,that Wu et al. (2005b, 2006, 2007a) simulated the overtak-ing of two forward fast mode shocks (as in the 2.5D and3D studies mentioned above) as well as the collisionbetween forward and reverse fast mode shocks using multi-ple ICME interactions during the period of October 25–November 1, 2003. The Wu et al. studies not only simu-lated the real solar events by mimicking solar flare inputsto interplanetary space, but the results also matched, viatuning only the single required free parameter, the flares’pressure pulses, with the unusual ACE solar wind velocityobservations. There is no flux rope structure in the Wuet al. studies. Fortunately, this omission is not a handicap(perhaps considered as such by some workers since thisstructure is used by the authors mentioned above). Wemake this comment with the support of Richardson andCane (2005) who showed that only �15% of all ICMEsmeasured at Earth during Solar Cycle 23 (1996–2005) wereof the magnetic cloud (flux rope) category.

The present study, also neglecting consideration of fluxropes, used the newly developed HAFv.2+3DMHD modelto simulate the interaction of ICMEs for the period ofOctober 25–29, 2003, the dates of their associated solarflares. The background solar wind includes the inhomoge-neity caused by stream-stream interactions, not merely thebimodal solar wind. The study showed the overtaking of anICME by a second one from behind in several cases. Weshowed that the slower ICME was, as expected, totallyovertaken by the fast shock as in the general case 2.5Dcases studied by Xiong et al. (2006a,b). We interpretedtheir fast shock as being followed by the second ICME thatwas generated, not as a flux rope (as in their first ICME),but by compressed plasma and IMF ejecta as a conse-quence of their initializing pressure pulse. This approach,with a single ICME, was examined by Lugaz et al.(2005a) who used the same unbalanced self-similar fluxrope within the initially undisturbed corona in order tocause the disturbance. This work provided realistic

3D-calculated energetics and mass of the ICME. Theshock’s propagation speed (or ‘‘leading edge’’ of theICME) was affected by the upstream solar wind speed asshown in our ‘‘magnetic resonance imagery’’ plots (seeFigs. 1b–c, g–h, l–m, Figs. 2b–c, and g–h). It is difficultto tell what the effect of the ICMEs’ interaction is on theirsize changes after interaction since the size of the fastICME is bigger than the slow CME in this study. Theanswer would require more detailed studies to make a finalconclusion. For example, we would have to simulate twoseparate cases wherein each simulation should consideronly a single ICME. Then, we could compare the sizesbetween the individual pre-collision ICME (either the slowor faster one) with the merged ICME. That kind of study,however, is beyond the scope of the present one.

6. Conclusions

This study performs a simulation example of coronalmass ejection and shock propagation that includes a realis-tic 3D solar wind structure from the Sun to the Earth. Thefollowing statements are concluded. (1) This simulationprocedure can provide a tool to link the general cases ofICME at 1 AU to their solar sources, as well as to identifythe possible origins of shock formation due to CME inter-action. We refer to an example shown in Figs. 1c,h,m whentwo ICMEs and their shocks collide. The 3D interactionshould, in principle, be studied in higher resolution as inthe 2.5D examples of Xiong et al. (2006b). (2) The resultscan be extended to simulate a variety of coronal and helio-spheric observations, including the essential ambient med-ium’s non-uniformity provided by the HAFv.2 model in acontinuous temporal mode. (3) The results also help under-standing the effect of background solar wind speed on thepropagation of ICMEs and their deformation by interact-ing with the heliosphere plasma/current sheet. (4) Theresults help understanding the procedure of multipleCMEs’ overtaking each other. (5) The arrival times ofICMEs/Shocks at 1 AU are affected by the location ofsolar sources. (6) Both CMEs and HCS/CPS weredeformed by interacting with each other.

Acknowledgements

We thank the ACE PI teams for management and pro-viding ACE solar wind plasma and magnetic field data.C.C.W. and M.D. are supported partially by NASA GrantNNG08GG80G. M.D. acknowledges the hospitality of theNOAA Space Environment Center. S.T.W. wishes toacknowledge support of this work via National ScienceFoundation (NSF) Grant ATM0310115 and NASA GrantNAG5-12843. K.L. acknowledges the support of NASAGrant NNX06AB88G. X.S.F. was supported by NSFCGrants 40621003 and 40536029. X.S.F. and C.C.W. werealso supported in part by the International CollaborationResearch Team Program of the Chinese Academy of

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Sciences. We thank the reviewers for their constructivecomments.

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