A numerical study on the acceleration and transit time of coronal mass ejections in the interplanetary medium

A numerical study on the acceleration and transit time of

coronal mass ejections in the interplanetary medium

J. Americo Gonzalez-Esparza, Alejandro Lara, and Eduardo Perez-TijerinaInstituto de Geofısica, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico

Alfredo SantillanComputo Aplicado-DGSCA, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico

Nat GopalswamyNASA Goddard Space Flight Center, Greenbelt, Maryland, USA

Center for Solar Physics and Space Weather, the Catholic University of America, Washington, D. C., USA

Received 26 November 2001; revised 14 March 2002; accepted 19 March 2002; published 28 January 2003.

[1] Recently, an empirical model of the acceleration/deceleration of coronal massejections (CMEs) as they propagate through the solar wind was developed using near-Sun(coronagraphic) and near-Earth (in situ) observations [Gopalswamy et al., 2000, 2001a].This model states and quantifies the fact that slow CMEs are accelerated and fastCMEs are decelerated toward the ambient solar wind speed (�400 km/s). In this work westudy the propagation of CMEs from near the Sun (0.083 AU) to 1 AU using numericalsimulations and compare the results with those of the empirical model. This is aparametric study of CME-like disturbances in the solar wind using a one-dimensional,hydrodynamic single-fluid model. Simulated CMEs are propagated through a variableambient solar wind and their 1 AU characteristics are derived to compare withobservations and the empirical CME arrival model. We were able to reproduce the generalcharacteristics of the prediction model and to obtain reasonable agreement with two-pointmeasurements from spacecraft. Our results also show that the dynamical evolution offast CMEs has three phases: (1) an abrupt and strong deceleration just after their injectionagainst the ambient wind, which ceases before 0.1 AU, followed by (2) a constant speedpropagation until about 0.45 AU, and, finally, (3) a gradual and small deceleration thatcontinues beyond 1 AU. The results show that it is somewhat difficult to predict the arrivaltime of slow CMEs (Vcme < 400 km/s) probably because the travel time depends not onlyon the CME initial speed but also on the characteristics of the ambient solar wind andCMEs. However, the simulations show that the arrival time of very fast CMEs (Vcme >1000 km/s) has a smaller dispersion so the prediction can be more accurate. INDEX

TERMS: 2164 Interplanetary Physics: Solar wind plasma; 2111 Interplanetary Physics: Ejecta, driver gases, and

magnetic clouds; 2139 Interplanetary Physics: Interplanetary shocks; KEYWORDS: ejecta, CMEs,

interplanetary, numerical simulations

Citation: Gonzalez-Esparza, J. A., A. Lara, E. Perez-Tijerina, A. Santillan, N. Gopalswamy, A numerical study on the acceleration

and transit time of coronal mass ejections in the interplanetary medium, J. Geophys. Res., 108(A1), 1039, doi:10.1029/2001JA009186,

2003.

1. Introduction

[2] Coronal mass ejections (CMEs) originating on thefront side of the solar disk can reach the Earth and causegeomagnetic storms, provided they have appropriate mag-netic field orientation. In order to assess the geoeffective-ness of the front side halo CMEs, we need to know (1) whena CME would occur and whether it would reach the Earth ornot, (2) when the CME would arrive at the Earth if it isindeed heading toward the Earth, and (3) whether it has the

appropriate magnetic field configuration to make an effec-tive coupling with the Earth’s magnetosphere.[3] Recently, Gopalswamy et al. [2000, 2001a] correlated

near-Earth observations of interplanetary CMEs (ICMEs)detected by the Wind spacecraft with their near-Sun counter-parts observed by the Solar and Heliospheric Observatory(SOHO) coronagraphs. They found that, in general, theCMEs were subject to a mean Sun-Earth acceleration andthat the acceleration was approximately proportional to theCME initial speeds. They estimated the initial halo CMEspeeds from 2.5 to 25 solar radii analyzing the CME movieframes of the SOHO/LASCO coronographs and neglecting

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A1, 1039, doi:10.1029/2001JA009186, 2003

Copyright 2003 by the American Geophysical Union.0148-0227/03/2001JA009186$09.00

SSH 9 - 1

the projection effects, i.e., assuming that the radial CMEspeed was approximately equal to the expansion CMEspeed. They also showed that this result could be used forspace weather forecasting, by developing an empiricalmodel to predict the 1 AU arrival time of Earth-directedhalo CMEs. In this paper we perform a parametric study ofthe propagation of CME-like disturbances from near the Sunto the Earth and obtain their accelerations and transit times asthey propagate through the ambient solar wind. We comparethe numerical results with the two-point observations as wellas the predictions of Gopalswamy et al.’s empirical model.

2. Simulation Technique

[4] We employ the numerical code ZEUS-3D (version4.2) for our study. This code solves the system of ideal MHDequations (nonresistive, nonviscous) by finite differences onan Eulerian mesh [Stone and Norman, 1992]. In order tosimplify the calculations and to be able to perform a largenumber of different cases, we neglect all magnetic effectsand assume spherical symmetry. These simplified one-dimensional hydrodynamic numerical simulations of inter-planetary disturbances have proved to be very useful inunderstanding the basic physical aspects of the injection andheliospheric evolution of solar disturbances [e.g., Hundhau-sen and Gentry, 1969;Dryer, 1994;Gosling and Riley, 1996;Riley and Gosling, 1998; Riley, 1999; Riley et al., 2001].[5] Following a technique similar to that of Gosling and

Riley [1996], we produced the ambient solar wind byspecifying the fluid speed, density and temperature at aninner boundary located beyond the critical point (Ro = 0.08AU), and then allowing the code to evolve and reach anequilibrium state that mimics the observed values of thesolar wind at 1 AU. After the ambient solar wind has beenestablished we injected a perturbation from the inner boun-dary to simulate the propagation of a CME into theinterplanetary medium. These CME-like perturbations aresquare pulses with a given initial speed characterized byincrements in density and temperature, over a finite extentof time. We include the solar gravity and assume that thesolar wind is an ideal fluid with a ratio of specific heats,g = 5/3. All numerical runs have a resolution of 0.001 AU/zone with an inflow condition at the inner boundary and anoutflow condition at the outer boundary.[6] We are interested in the dynamics of CMEs in the

ecliptic plane and propagating through a variable slowambient solar wind (ASW). Therefore, we consider twodifferent ‘‘slow’’ ASWs (referred to as ASW1 and ASW2)to study the influence of solar wind characteristics on theCME propagation. Table 1 summarizes the characteristics ofASW1 and ASW2 along with the wind parameters at theinner boundary as well as the equilibrium values at 1 AU.Note that ASW1 is slower and denser than ASW2.[7] One of the major problems in numerical modeling is

the initial conditions. Technical limitations make it difficult

to know the precise values of the physical parameters of theemerging solar wind and CMEs near the Sun. In manynumerical studies it is customary to use arbitrary values ofthe physical parameters at the inner boundary that mimic thesolar wind and CME observables at 1 AU. Although someCMEs show a well-defined three-part structure (frontalstructure, cavity, and core) the CME structure is verycomplex in general. In this work we attempt to simulatethe leading part of the CMEs by producing CME pulses withconstant structure. It is believed that the CME leading part isformed of dense hot coronal material [Hundhausen, 1999].Table 2 shows the inner boundary parameters of eightdifferent CME square pulses that we injected against thetwo ambient winds. The CME densities (Ncme) were taken tobe 2 and 10 times the ambient value (No), while the temper-atures (Tcme) were taken to be 1 and 4 million degrees. Thepulse durations (�t) were taken to be 3 and 6 hours. Thedensity values are within the range reported by [Ramesh etal., 2001] and the CME durations were arrived at from theLASCO CME movies (http://lasco-www.nrl.navy.mil orhttp://cdaw.gsfc. nasa.gov), as the time taken by the CMEsto pass through a given point near the 20 R�.

3. Results

[8] The eight CMEs in Table 2 were injected againstASW1 and ASW2 with four different initial speeds (Vcme):150, 350, 650 and 1200 km/s. For each one of these pulseswe obtained their speeds at 1 AU. Figure 1 shows thehistograms of the initial and 1 AU (Vicme) speeds of thesimulated CME fronts. We find an effect of speed ‘focusing’as a consequence of the propagation of the CMEs in thesolar wind: slow pulses accelerate and fast pulses decelerateas they travel to 1 AU. The histograms are remarkablysimilar to the observational results of Gopalswamy et al.[2000, Figure 1]. This result has also been shown elsewherenumerically [Gosling and Riley, 1996], and it is due mainlyto the interchange of momentum with the ambient solarwind. In Figure 1, we differentiate between the CME pulsespropagating into ASW1 and ASW2. Note that no CMEfronts propagating in ASW2 have speeds lower than 400km/s at 1 AU. As we would expect the CME frontspropagating in ASW2 reach 1 AU with faster speeds thanthose propagating in ASW1.

3.1. CME Mean Accelerations

[9] Following Gopalswamy et al. [2000], we calculatedthe mean acceleration of each CME pulse from 0.08 to 1.0AU using its speed at 1 AU, initial speed and the transit time(�acme = (Vicme � Vcme)/�tcme). Figure 2 shows the scatterplotof the �acme of the 8 CME pulses versus their initial speeds(Vcme). The symbols connected by dotted and solid lines

Table 1. Physical Characteristics of the Two Ambient Winds

(ASW1 and ASW2) at the Inner Boundary (Ro) and at 1 AU

Ro,AU

Vo,km/s

V1AU,km/s

No,p/cm3

N1AU,p/cm3

To,106K

T1AU,104K

ASW1 0.08 250 287 2100 12.7 0.5 1.7ASW2 0.08 350 426 900 5.1 1.0 3.4

Table 2. Physical Characteristics of the 8 CME-Like Pulses

CME Ncme Tcme, 106K �t, hours

1 2No 1.0 32 2No 4.0 33 2No 1.0 64 2No 4.0 65 10No 1.0 36 10No 4.0 37 10No 1.0 68 10No 4.0 6

SSH 9 - 2 GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES

correspond to CMEs propagating in ASW1 and ASW2,respectively. Similar to Gopalswamy et al. [2000, 2001a],we performed a linear fit to the data points in Figure 2obtaining the following equation: �acme = 1.65 � 0.0038Vcme. The slope is very similar to the slope given byGopalswamy et al. [2000], and it is slightly less steep thanthe slope given by Gopalswamy et al. [2001a]. For the veryslow CMEs (Vcme = 150 km/s) propagating against ASW1the �acme’s cluster around 0.36 m/s2. For higher initial speeds(Vcme � 350 km/s) the data points corresponding to bothambient winds begin to spread, suggesting that differenttypes of CME pulses with the same initial speed andpropagating against the same ambient wind can be subjectedto different �acme’s. In other words, the mean accelerationdepends not only on the initial CME speed and the type ofambient wind, but also on other CME characteristics (Ncme,Tcme, �t). Table 3 shows the average values of the �acme ofthe 8 CME pulses (Table 2) and their corresponding stand-ard deviations as a function of Vcme: columns 2–3 corre-spond to CMEs propagating in ASW1, columns 4–5 toCMEs propagating in ASW2 and columns 6–7 to all theCMEs (combining the results of both ambient winds). Thefastest CMEs (Vcme = 1200 km/s) present the largestdispersion of �acme’s in both ambient winds, but the averagevalues of CME acceleration are similar for both ASW1 andASW2 (Table 3), implying that the ambient wind has asmaller effect on their propagation than in the case of theother CMEs with slower initial speeds.

[10] Slow CMEs (Vcme � 350 km/s) propagating inASW1 have lower �acme when the CMEs have higherincrease in density, lower increment in temperature andlonger duration (CME 7 in Table 2). For CMEs with Vcme =650 km/s lower value of �acme results when they propagateagainst ASW2 with higher increase in density and temper-ature and longer duration (CME 8 in Table 2). For thefastest CMEs (Vcme = 1200 km/s) the largest decelerationresults when propagating against ASW1 with lower initialincrement in density and shorter duration (CMEs 1–2 inTable 2).

3.2. CME Transit Times

[11] The CME transit time (dtcme) is the key parameter forspace weather forecasting. Figure 3 shows the scatterplot ofdtcme’s from 0.08 to 1.0 AU versus Vcme. There is a largedispersion in the dtcme’s the slowest CMEs (Vcme = 150 km/s),which tends to diminish for faster CMEs (Vcme � 350 km/s).Note that the dtcme’s for these faster CMEswhich propagate inASW1 (dotted lines) or in ASW2 (straight lines) overlap,showing that CMEs with the same initial speed but withdifferent characteristics and propagating through differentambient winds can have the same dtcme. Table 4 shows theaverage values of the dtcme’s and their corresponding standarddeviations as a function of Vcme. The slowest CMEs (Vcme =150 km/s) have an average dtcme of 135 hours propagating inASW1 and of 96 hours propagating in ASW2, whereas, thefastest CMEs (Vcme = 1200 km/s) have an average dtcme of 47hours propagating in ASW1 and 42 hours in ASW2. For thevery fast CMEs the transit time depends mainly on the CMEinitial speed, in agreement with the results reported byGopalswamy et al. [2000, 2001a].[12] For a given initial speed, the CMEs with lower

dtcme’s are the ones that propagate against ASW2 and thosehaving the initially longer injection duration and higherincrease in density or in temperature (CMEs 6–8 in Table2). On the other hand, regardless of their initial speeds, theCMEs with longer dtcme’s were the ones propagating againstASW1 and those having shorter injection durations (CMEs1–2 in Table 2).

Figure 2. CMEs mean acceleration from 0.08 to 1.0 AU(acme = (Vicme� Vcme)/�tcme) versus their initial speeds. Thecharacteristics of the different CME pulses are described inTable 2.

Figure 1. Frequency histograms of CME speeds (top) at theinner boundary and (bottom) their corresponding CME frontspeeds at 1 AU. The CME pulses were injected against twodifferent ambient winds: ASW1 and ASW2 (see Table 1).

GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES SSH 9 - 3

[13] It is interesting that Figure 3 shows a contrary behav-ior than the one commented on in Figure 2. In Figure 2 thehighest dispersion of mean accelerations occurs with thefastest CMEs (Vcme = 1200 km/ s), but in Figure 3 the highestdispersion of transit times occurs with the slowest CMEs(Vcme = 150 km/s). This shows that there is not a simplerelation between the CME mean acceleration and the CMEtransit time.

3.3. Evolution of the CME Velocity and Acceleration

[14] From Figure 1 we know that there is a ‘‘focusing’’ ofCME speeds from the Sun to 1 AU due to the interactionwith the ambient wind, but this does not tell us how theCME speed changes with the heliocentric distance. Sincethe code is able to track the front of the CME pulse as itpropagates in the solar wind, we can study the changes inCME velocity and acceleration as a function of heliocentricdistance. Figure 4 shows the plots of the CME front speedversus heliocentric distance for CME 3 (Table 2) injectedwith four different initial speeds against ASW1. The slowestCME (Vcme = 150 km/s) suffers an abrupt acceleration justafter the injection and then rapidly reaches the speed ofASW1 (thick line in Figure 4) at about 0.1 AU. On the otherhand, the fastest CME (Vcme = 1200 km/s) suffers an abruptdeceleration attaining a speed of about 806 km/s just before0.1 AU and then propagates with a constant speed until atabout 0.45 AU, beyond which it gradually decelerates. Notethat in this case the speed difference between the CME frontand the ambient wind is still large at 1 AU. CMEs with in-between speeds display an intermediate behavior comparedto the extreme cases.[15] This abrupt acceleration/deceleration of the 4 CME

pulses just after their injection in Figure 4 are due mainly to

the difference in speed and momentum between the CMEfront and the ambient wind. In the case of the fastest CME(Vcme = 1200 km/s) the newly injected CME material cannotoverflow the slower ambient wind ahead and the largedifference in dynamic pressure produces a pair of shockwaves: a forward shock accelerating the slower ambient windand a reverse shock decelerating the CME front. After thisabrupt encounter there is an equilibrium between the shockedCME front and the shocked wind and the front propagates at aconstant speed driving the forward shock until a point (�0.45AU) where its dynamic pressure is not enough anymore todrive the shock and then it begins to decelerate. The case ofthe CME initiated with Vcme = 650 km/s is similar, but theCME front begins to decelerate closer to the Sun.[16] Figure 5 shows the plots of the acceleration profiles

versus distance of the four CMEs shown in Figure 4. In thefour cases close to the inner boundary there is a very strongand complex interaction between the CME front and theambient wind ahead. Although the magnitude of acceler-ation is different in each plot, the values beyond 0.1 AU arevery small compared to those near the injection point. It isinteresting to compare the values of the simulated CMEaccelerations in Figure 5 with the estimated CME acceler-ations between 2.5 and 25 solar radii as inferred from theLASCO C2 and C3 observations: the measured CMEaccelerations are comparable to those obtained by thesimulated CMEs near the injection point. In fact the abruptdeceleration of the fastest CME (Vcme = 1200 km/s) seemsto be very large but it is not outside of the range of theobserved values [Gopalswamy et al., 2001b]. The measuredacceleration of SOHO/LASCO CMEs is in the rangebetween �386 and 703 m/s2(http://cdaw.gsfc.nasa.gov/),whereas the CME accelerations computed with other space-craft and Earth based coronagraphs are in the range between�218 and 3270 m/s2 [St. Cyr et al., 1999].[17] It is remarkable that the simulated CMEs have

accelerations similar to those inferred from the observations.However, we should keep in mind that this simulationoriginates beyond the critical point and in reality the inter-action between the CME and the ambient wind starts quitenear the Sun in the sub-Alfvenic region. This implies that thestrong interaction which produces the abrupt decelerationshown in Figures 4 and 5 in reality it should occur moregradually throughout a longer interval of heliocentric dis-tance. Note that the one-dimensional simulations overesti-mate the interaction between the injected CME and theambient wind since the code does not solve the azimuthaland meridional flows that relieve pressure stresses.

3.4. Comparison with Observations

[18] Figure 6 is similar to Figure 2 except that we havesuperposed observed data based on two-point measurements

Table 3. Averaged Mean Accelerations From 0.08 to 1 AU of the 8 CMEs (Table 2) and Their Associated

Standard Deviations (Std.) as a Function of Their CME Initial Speeds

Vcme, km/s

CMEs in ASW1 CMEs in ASW2 All CMEs (16)

acme, m/s2 Std., m/s2 acme, m/s2 Std., m/s2 acme, m/s2 Std., m/s2

150 0.36 0.07 0.92 0.16 0.64 0.31350 0.05 0.12 0.58 0.25 0.32 0.33650 �0.63 0.24 �0.15 0.39 �0.39 0.401200 �2.40 0.91 �2.0 0.96 �2.20 0.93

Figure 3. CME travel times from 0.08 to 1.0 AU againsttheir initial speeds.

SSH 9 - 4 GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES

(asterisks). These 18 ‘observed’ mean accelerations wereobtained correlating in situ observations of ICMEs from twospacecraft (Helios 1 and PVO) located at heliocentricdistances ranging from 0.63 to 0.91 AU and near Sunobservations of the corresponding CMEs by the Solwindcoronagraph [Gopalswamy et al., 2001a, Table 1]. For theseevents the pairs of observing spacecraft were in quadrature,so the problems in inferring the CME initial speed towardthe spacecraft in the interplanetary medium were mini-mized, thus improving the accuracy in the estimation ofthe CME mean acceleration. The behavior of CME accel-eration in Figure 6 can be divided into two velocity regimes:for slow CMEs (Vcme � 400 km/s) the simulation resultsagree very well with the observed data, while for the fastCMEs (Vcme > 400 km/s), the simulated decelerations areless than the observed data. This suggests that we under-estimate the interaction from near the Sun to 1 AU for fasterCMEs with the ambient wind in our simulations and alsothat some of the initial conditions for the fast pulses areunrealistic (e.g., some pulses have an excess of dynamicpressure given by the highest increment in density: Ncme =10No). These high speed pulses contain too much densematerial, which provides the disturbance too much inertia.[19] Figure 7 is similar to Figure 3 except that we have

superposed 47 observational data points. These data pointswere obtained by combining in situ measurements ofICMEs by WIND and coronagraphic observations of thecorresponding CMEs by SOHO [Gopalswamy et al., 2001a,Table 2]. Contrary to the previous Figure 3, the observa-

tional points in Figure 7 are not based on limb measure-ments of CMEs but on halo CMEs propagating toward theEarth, implying that in this case there is more uncertainty inthe estimation of the CME radial initial speeds. The numer-ical results of slow CMEs (Vcme � 400 km/s) propagating inboth ambient winds agree very well with the dispersion ofthe observed data. However, for CMEs with Vcme = 650 km/spropagating in ASW2 the simulation values are below theobserved data indicating that the simulated CMEs propagatefaster than the observed ones, in particular those pulses withhigher increase in density (CMEs 6–8 in Table 2). Thisdisagreement between numerical and observational resultsmight be explained by the fact that we have only a fewobserved points within this range of initial speeds; presum-ably with more observational points in this range we wouldhave a similar dispersion, but this also it could mean thatsome of the initial conditions in the CME simulations wereunrealistic. Finally, the numerical results for the fastestCMEs (Vcme = 1200 km/s) agree well with the observed

Table 4. Average Transit Times From 0.08 to 1 AU of the 8 CMEs (Table 2) and the Associated Standard

Deviations (Std.) as a Function of Their CME Initial Speeds

Vcme, km/s

CMEs in ASW1 CMEs in ASW2 All CMEs (16)

�tcme, hours Std., hours �tcme, hours Std., hours �tcme, hours Std., hours

150 135 18 96 11 116 25350 107 14 82 11 95 18650 76 11 63 7 67 111200 47 8 42 5 44 7

Figure 4. Evolution of the CME front speed versusheliocentric distance. CME 3 (see Table 2) was injectedagainst ASW1 (Table 1) with four different initial speeds.Note that the extended acceleration of the ASW1 may be anartifact of the polytropic approximation.

Figure 5. Evolution of the CME front acceleration versusheliocentric distance corresponding to the four cases inFigure 4.

GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES SSH 9 - 5

data. For these CMEs the effect of the ambient wind isnegligible as can be seen in Table 4.[20] In Figure 7 we have also plotted the curves of CME

travel prediction time by Gopalswamy et al. [2000, 2001a].In their model they assumed that the motion of a CMEpropagating from the Sun to 1 AU can be approximated bythe simple equation: S ¼ Vcmet þ 1

2�acmet

2 (where Vcme is theinitial speed and �acme is a constant acceleration whichdepends only on the initial speed: acme = 1.22 � 0.003Vcme in Gopalswamy et al. [2000], and �acme = 2.19 � 0.005Vcme in Gopalswamy et al. [2001a]). Although the simulatedCMEs have different accelerations at different heliocentricdistances (Figures 4–5), it is interesting that the predictioncurve by Gopalswamy et al. [2000] is contained completelyin the region covered by the numerical pulses propagatingin ASW1. In general, the numerical pulses propagating inASW2 with initial speeds in the range of 150–500 km/stend to have lower transit times than the ones predicted bythe curves. The improved version of the prediction curvereported by Gopalswamy et al. [2001a] seems to have abetter agreement with the observations in the range of thoseCMEs with initial speeds between 600 km/s and 1000 km/s.

4. Discussion and Conclusions

[21] The ambient solar wind has a strong influence on thepropagation of CMEs in the interplanetary medium. FastCMEs decelerate and slow CMEs accelerate as a conse-quence of interchange of momentum with the solar wind. Inour numerical simulations the dynamical evolution of theCME pulses have different phases with heliocentric dis-tance. For example, the front of the fast CMEs suffer a verystrong deceleration just after their injection against theambient wind, then it propagates at a constant speed untilat about 0.45 AU, from which gradually decelerates. Weshould keep in mind that this simulation originates beyondthe critical point and in reality the interaction between theCME and the ambient wind starts quite near the Sun in thesub-Alfvenic region. This implies that although the netCME deceleration from near the Sun to 1 AU is reasonablymodeled here, the strong interaction adjoin to the injectionpoint, should in reality occur more gradually throughout a

longer interval of heliocentric distance. In general, thenumerical results of CME mean accelerations from 0.08to 1.0 AU agree very well with the observable data for theCMEs with initial speeds �500 km/s (Figure 6). However,for faster CMEs the numerical results predict lower meandecelerations than the observed data. This suggest that theinitial density increments associated with fast CMEs shouldbe small.[22] The results of the numerical study are in good

agreement with the observed data of CME transit times(Figure 7). The study shows that it is difficult to predictwhen a slow CME (Vcme < 400 km/s) would reach the Earth.For these cases the travel time depends not only on theCME initial speed, but on the ambient wind and other CMEcharacteristics. However, the simulations show that thearrival time of very fast CMEs (Vcme > 1000 km/s) has asmaller dispersion and therefore predictions can be madewith reasonable accuracy. For these cases the predictionmodel by Gopalswamy et al. [2000, 2001a] seems to do agood job.[23] The comparison between the parametric study and

the observational data points helps us test the initial con-ditions of the CME pulses. It is found that in general, thoseCME pulses with high increments in density (Ncme = 10No)tend to disagree with the observations. A study of the initialconditions for specific CME events is underway and will bepublished elsewhere.[24] Finally, it is remarkable that the one-dimensional

simulation is able to capture most of the dynamic behaviorof CMEs in the interplanetary medium, consistent with theempirical model and the observations. Problems such as theneglect of magnetic fields, assumptions of spherical symme-try and homogeneity of the ambient solar wind, and the innercomputational boundary conditions too far from the Sunneed to be considered in future simulations. The magneticfield plays a predominant role in the origin and evolutionnear the Sun of the CMEs [Wu et al., 2001]. Including themagnetic field in our simulations would allow us to study theCME evolution close the Sun. On the other hand, the strengthand orientation of the magnetic magnetic field inside the

Figure 6. Observational data of CME mean accelerationssuperposed on the numerical results presented in Figure 2.

Figure 7. Observational data of CME travel times versustheir initial speeds superposed on the numerical resultspresented in Figure 3. The prediction curves from theempirical model of Gopalswamy et al. [2000, 2001a] are thethick lines as marked.

SSH 9 - 6 GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES

CME are crucial to predict the interaction between the CMEand the Earth’s magnetosphere. Furthermore, to fully addressthe problem of CME dynamics in the interplanetary mediumwe must consider the relative contribution of the dynamic,thermal and magnetic pressures to the total pressure. As wascommented in the discussion of Figures 4–5, this one-dimensional simulation overestimates the interactionbetween the newly ejected coronal material and the ambientwind because it neglects the azimuthal and meridionalmotions of the plasma which help to relieve pressure stresses.In reality the initial interaction between the CME and theambient wind should occur more gradually throughout alonger heliocentric range. Further work in three dimensionswould help to solve this problem.

[25] Acknowledgments. We are grateful to Pete Riley for providingthe trace subroutine and many useful discussions. This project was partiallysupported by CONACyT project J33127-E. NG was supported by NASA,AFOSR and NSF. The numerical simulations were performed usingUNAM’s ORIGIN-2000 supercomputer.[26] Shadia Rifai Habbal thanks Nancy Crooker and Victor Pizzo for

their assistance in evaluating this paper.

ReferencesDryer, M., Interplanetary studies: Propagation of disturbances between theSun and the magnetosphere, Space Sci. Rev., 67, 363, 1994.

Gopalswamy, N., A. Lara, R. P. Lepping, M. L. Kaiser, and D. Berdichevs-ky, and O. C. St. Cyr, Interplanetary acceleration of coronal mass ejec-tions, Geophys. Res. Lett., 27, 145, 2000.

Gopalswamy, N., A. Lara, S. Yashiro, M. L. Kaiser, and R. A. Howard,Predicting the 1-AU arrival times of coronal mass ejections, J. Geophys.Res., 106, 29,207, 2001a.

Gopalswamy, N., S. Yashiro, M. L. Kaiser, R. A. Howard, and J.-L. Bou-geret, Characteristics of coronal mass ejections associated with long-wa-velength type II radio bursts, J. Geophys. Res., 106, 29,219, 2001b.

Gosling, J. T., and P. Riley, The acceleration of slow coronal mass ejectionin the high speed wind, Geophys. Res. Lett., 23, 2867, 1996.

Hundhausen, A. J., An introduction, in Coronal Mass Ejections, Geophys.Monogr. Ser., vol. 99, edited by N. Crooker, J. A. Joselyn, andJ. Feynman, pp. 1–7, AGU, Washington, D. C., 1999.

Hundhausen, A. J., and R. A. Gentry, Numerical simulations of flare-gen-erated disturbances, J. Geophys. Res., 74, 2908, 1969.

Ramesh, R., C. Kathiravan, and C. V. Sastry, Low-Frequency Radio Ob-servations of the angular broadening of the crab nebula due to a coronalmass ejection, Astrophys. J., 548, L229, 2001.

Riley, P., CME dynamics in a structured solar wind, in Solar Wind Nine,edited by S. R. Habbal et al., AIP Conf. Proc., 471, 131, 1999.

Riley, P., and J. T. Gosling, Do coronal mass ejections implode in the solarwind?, Geophys. Res. Lett., 25, 1529, 1998.

Riley, P., J. T. Gosling, and V. J. Pizzo, Investigation of the polytropicrelationship between density and temperature within interplanetary cor-onal mass ejection using numerical simulations, J. Geophys. Res., 106,8291, 2001.

St. Cyr, O. C., J. T. Burkepile, A. J. Hundhausen, and A. R. Lecinski, Acomparison of ground-based and spacecraft observations of coronal massejections from 1980–1989, J. Geophys. Res., 104, 12,493, 1999.

Stone, J. M., and M. Norman, ZEUS 2-D: A radiation magnetohydrody-namics code for astrophysical flows in two dimensions, I, The hydrody-namics algorithms and tests, Astrophys. J., 80, 753, 1992.

Wu, S. T., M. D. Andrews, and S. P. Plunkett, Numerical MHD Modelingof CME, Space Sci., 95, 191, 2001.

�����������J. A. Gonzalez-Esparza, A. Lara, and E. Perez-Tijerina, Instituto de

Geofısica, UNAM, Ciudad Universitaria, Coyoacan, Mexico D.F. 04510,Mexico. ([email protected])N. Gopalswamy, NASA Goddard Space Flight Center, Code 695.0, Bldg

2, Room 143, Greenbelt, MD 20771-0001, USA.A. Santillan, Computo Aplicado-DGSCA, Universidad Nacional Auton-

oma de Mexico, Mexico D.F. 04510, Mexico.

GONZALEZ-ESPARZA ET AL.: ACCELERATION AND TRANSIT TIMES OF CMES SSH 9 - 7