JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A1, PAGES 483-492, JANUARY 1, 1999

Three-dimensional propagation of coronal mass ejections (CMEs) in a structured solar wind flow 1. CME launched within the streamer belt

D. Odstr•il 1'2 Cooperative Institute for Research in Environmental Sciences, University of Colorado/National Oceanic and Atmospheric Administration, Boulder, Colorado

V. J. Pizzo

Space Environment Center, National Oceanic and Atmospheric Administration, Boulder, Colorado

Abstract.

A three-dimensional (3-D) numerical hydrodynamic model is used to investigate the temporal and spatial evolution of large-scale solar wind structures. A tilted- dipole outflow configuration is specified at the inner boundary near the Sun, and a structured, corotating solar wind (SW) flow is established by dynamic relaxation. Time-dependent variation of the pressure and velocity at the inner boundary is applied to generate transient structures within the streamer belt. The dynamical interaction of a coronal mass ejection (CME) with the corotating coronal streamer belt flow between 0.14 and 5.04 AU is then investigated. Numerical results show that the motion and appearance of a CME can be strongly affected by its interaction with the velocity and density structure of the background SW. The initial shape and density distribution of the CME is distorted in all dimensions; it is compressed where•the CME is trapped between slow streamer belt and high-speed coronal hole flows, and it is distended where the CME penetrates into the trailing edge of the preceding high-speed stream. Thus a given CME can be observed with substantially different properties at different locations; the shock strength as well as the stand-off distance between the shock front and the CME driver gas can vary considerably across the structure, and the density profile through the disturbance can adopt different forms depending on location. Merging of CME and corotating interaction region shocks and thermodynamic structures as demonstrated in this simulation complicate the interpretation of single-spacecraft observations.

1. Introduction

The two fundamental classes of large-scale solar wind (SW) disturbances in the heliosphere, corotating and transient, have their origins in the solar corona, whose properties change drastically and systematically over the course of the solar cycle (see a review by Gosling [1996]). Corotating disturbances arise from the dy- namic coupling between solar rotation and spatial vari- ability in the expanding, global SW. The steady spatial

1On leave from Astronomical Institute, Ond•ejov, Czech Republic.

2Also at Space Environment Center, National Oceanic and Atmospheric Administration, Boulder, Colorado.

Copyright 1999 by the American Geophysical Union.

Paper number 1998JA900019. 0148-0227/99/1998JA900019509.00

structure is composed of alternating patterns of slow flow (with high-density and low-temperature plasma) as an interplanetary extension of the coronal streamer belt and of fast flow (with low-density and high-temperature plasma) emerging from coronal holes (see a review by Schwenn [1990]). Interactions between fast and slow corotating SW streams result in a compression at the leading edge of the fast stream and a rarefaction in the trailing portions of the fast stream [Gosling et al., 1978]. The compression region is known as a corotating inter- action region (CIR), and it is flanked by forward and reverse shocks, which are usually formed beyond 2 AU.

Large-scale transient interplanetary disturbances are mainly caused by coronal mass ejections (CMEs) that propagate through the background SW and generate large-amplitude waves and/or shocks. There was a nearly 1:1 association of shocks observed by Helios 1/2 and CMEs in the coronagraph's field of view directed toward Helios that were faster than about 400 km/s [Schwenn, 1986]. While the exact nature of CME ini-

483

484 ODSTR½IL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT

tiation is yet to be resolved, it is assumed that the so- lar magnetic field plays an important role because of its energetic potential. Recently, Gosling e! al. [1994] pointed to qualitative observational differences between interplanetary disturbances caused by CMEs ejected into fast and slow SW. High-latitude CMEs usually propagate at about the same speed as the background fast stream, and they can generate a well-defined shock structure (observed first as a forward- and then as a reverse-like shock) driven by expansion of high-pressure plasma. Low-latitude CMEs propagating sufficiently faster than the background slow stream can generate a shock-pair structure (forward and reversed shocks) driven by bulk-flow collision. Coronograph observations indicate that many CMEs originate within or near the coronal streamer belt [ttundhausen, 1993]. This sug- gests the importance of simultaneous consideration of both corotating and transient SW structures because strong mutual interactions can be expected in inter- planetary space. Exciting new issues relating to inter- actions of this sort have been raised by data received from the Ulysses spacecraft in its trek over the poles of the Sun (see •eophysical •esearch Letters special sec- tion: Ulysses Observations From Pole-to-Pole, œœ(23), •).

Numerical hydrodynamic (HD) and magnetohydro- dynamic (MHD) simulations represent an important tool in our understanding of global SW dynamics, but most computational studies have been devoted to in- vestigation of quasi-steady ½orotating flows [e.g., Pfxxo, 1994a, b; Pfxxo • Go•f•, 1994], or to the propaga- tion of interplanetary shocks in a homogeneous medium (e.g., see reviews by Pizzo [1985] and Dryer [1994]). At- tention has recently turned toward more realistic simu- lations where interplanetary disturbances propagate in a structured, corotating SW flow. For example, Odstr•i•

1

et al. [1996a, b] used a 2•-D MHD model to simulate a CME interacting with a thin hellospheric plasma sheet

2. Numerical Model

Large-scale phenomena in the interplanetary medium are described by a system of HD equations. These equa- tions govern the macroscopic spatial and temporal re- sponse of the SW to variations in initial and boundary conditions.

2.1. Mathematical Description

The ideal one-fluid, single-temperature HD approxi- mation with constant ratio of specific heats, ? (= 5/3), is used. The equations are

0

+ v. (pv) - 0,

(pv) + v. (pvv) - •2 '

o

oq() + v. - -rv. (v), where p is the mass density, V is the bulk flow velocity, P is the isotropic thermal pressure, (7 is the gravitation constant, Ms is the solar mass, and E is the thermal energy density. An additional equation,

__0 + v. v) - 0 cot '

where pc is the injected plasma density, is solved simul- taneously to trace material motions.

Spherical coordinates are used, and the three inde- pendent spatial variables are the radial position r, the meridional (colatitude) angle O, and the azimuthal (lon- gitude) angle T.

2.2. Method of Solution

The computational domain is the sector of a sphere defined by pairs of boundaries at fixed radii (inner and

in the equatorial plane. These simulations showed sig- outer), at fixed meridional angle (north and south), and nificant distortion of the shock front. Subsequent sim- 'at fixed azimuthal angle (east and west). The post- ulations with a 2-D HD model demonstrated that the

parts of a single CME straddling both high- and low- speed flows would evolve radically differently in the two regions [Riley et al., 1997b]. The demarcation between the slow- and high-speed region, however, was treated as a conical, axisymmetric boundary, and the complex in- teractions associated with a true "ballerina-skirt" flow

configuration were not included. Recently, Hu [1998] used a 2-D MHD model to simulate propagation of in- terplanetary shocks in the equatorial plane and showed a significant influence of the hellospheric current sheet on shock parameters.

In this paper, numerical simulations are used to inves- tigate the temporal and three-dimensional spatial evo- lution of large-scale SW structures in the hydrodynamic approximation. The aim is to identify how interplane- tary disturbances can be modified by dynamic interac- tions with the pre-existing global background flow, and how this affects their appearance, as observed by space probes.

tion of the inner boundary is set at 0.14 AU (• 30 Rs), and the outer boundary is set at 5.04 AU. The meridional and azimuthal domains span 30ø-150 ̧, and 0ø-180 ̧, respectively. The inner boundary lies in the supersonic flow region, just outside the outer field view of the LASCO C3 coronagraph. The outer boundary is chosen to cover most of the heliocentric distance range observed by the Ulysses spacecraft.

Numerical integration of the HD equations is per- formed on a uniform spatial mesh with Ar -- 0.01 AU and A0 = Ag = 1.5 ̧ (490x80x120 grid points). This spatial resolution represents a compromise be- tween computer memory considerations and spatial res- olution requirements for tracking propagating dynamic structures. The time step for numerical integration is dictated by stability conditions for explicit schemes.

The time-dependent, 3-D, HD equations are solved by a modified Total-Variation-Diminishing high-resolution Lax-Friedrichs (TVDLF) algorithm. This explicit finite- volume scheme, incorporating dimensional splitting, has

ODSTR•IL AND PIZZO' CME PROPAGATION WITHIN STREAMER BELT 485

been shown to be robust and efficient for a range of test problems [Tdth and Otistrail, 1996].

2.3. Boundary Conditions

The inner boundary (r = 0.14 AU) chosen here lies in the supersonic flow region, thereby simplifying the numerical solution. The inner boundary conditions are prescribed values of the dependent variables as de- scribed below. Free-flow conditions are imposed at the outer boundary and meridional boundaries, where zero- order extrapolation of the dependent variables is used. The azimuthal boundaries are periodic and antisym- metric, so background values in northern and southern hemispheres are related across the azimuthal bound- aries as

o, - 0 o) - o - o, - o) ,

where F represents values of SW parameters. Solar ro- tation is included, and all structures rotate along the inner boundary with an azimuthal velocity of 1.64171 x 10 -4 deg s- x, corresponding to the 25.38-day mean side- real period of solar equatorial rotation.

Positioning the inner boundary in the supersonic flow region has only a small effect on the formation of a cotorating structured background SW, as discussed by Pizzo [1989]. Larger effects may be expected for CMEs, and proper specification of CME initiation remains an open question.

3. Description of the Simulation

SOLAR MAGNETIC ROTATION

DIPOLE AXIS AXIS

EAST • WEST

•:,•;•i::•?:,•i•::•;•i•::•::::•::i?:::•::i::•::::::•i::• •:: .. ::::•::•:•::•;•-.• -.•.• • • •::•i:::::: ............. 5,• *,• •..• • •

•]gure 1. Schematic view of outflow conditions at the inner boundary (0.1& AU). The streamer bek is spec- ified as a high-densiW, ]ow4emperature, slow-velocity structure tilted with respect •o •he rotation axis. The gas pressure and momentum flux density are held con- s•ant across the entire inner boundary. The CME is introduced as a time-dependen• pulse centered within [he streamer be]I, using a 30ø-wide spatial profile and 12-hour duration (with i-hour •empora] ramps). The maximum pulse density is •wice as large as the slow stream value, the radial velocity and temperature are equal to •he fast stream values, and the pressure is 8 times higher than the background values.

The numerical simulation is done in two stages: es- tablishment of the steady tilted-dipole flow, followed by computation of transient disturbances propagating in that background.

3.1. Corotating Background Flow

We use the numerical relaxation technique to obtain the steady state within the whole domain of interest, by fixing parameters of the SW outflow along the inner boundary and integrating SW parameters in the com- putational domain starting from arbitrary values.

The tilted-dipole structure is specified at the inner boundary, R0, as shown in Figure 1. The axis of the streamer belt is inclined at an angle c• to the solar ro- tation axis. The radial velocity profile normal to the tilted equatorial band is given by

- V, - + 2 x

[_tanh (• - •x h •-•2 '• •k•-•/ tanh( ]

gross latitudinal SW structure observed by Ulysses [see Pizzo and Gosling, 1994; Phillips e! al., 1995].

The density varies according to the relation

- , with the result that the radial kinetic momentum flux density is constant across the flow structure at the inner boundary. Thh temperature T, is adjusted according to the relation

- ,

so that the total gas pressure is also constant on R0. In this paper, the tilt angle a - 20 ø, and the tran-

sition zone parameters are • - 75 ø, •2 - 105 ø, and A•w - 5 ø. This tilt angle is appropriate during de- clining and minimum phases of the solar cycle. Val- ues of the radial velocity, density, and temperature are V! - 600 km/s, p! - 125 cm -•, and T! - 2000 kK in the fast stream and V• - 300 km/s, p• - 500 cm -•, and T• - 500 kK in the slow stream.

The above parameters produce an ambient back- ground state with velocity 718 (359) km/s, density 2.08

where • is the latitude angle in the tilted coordinate- (8.45) cm -a, and temperature 130 (32.9) kK in the fast system, subscripts f and s denote fast and slow flow (slow) stream at i AU, which are close to typical obser- speeds, • and •2 are the latitudes of the transition vations. For example, Schwenn [1990, Table 3.1] gives zone centers, and A•w is the mean angular width of the average velocity 702 (327) km/s, density 2.73 (8.3) the transition zones between fast and slow flows. This cm -•, proton temperature 230 (34) kK, and electron specification provides a credible approximation to the temperature 100 (130) kK in the fast (slow) SW streams

486 ODSTR(•IL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT

8OO

,,•. 6oo

400

200

103

10 •

, 10

10 ø

10-'

10 -2

10 4

103

¾ O; • " 1

10'

R = 0,14 AU ...........

R= 1AU ...........

_

i i i i i i i i i i , i i i i . , l

, . . ............ . , .

0 30 60 90 120 150 180 0 50 60 90 120 150 180 longitude longitude

R=SAU

,

, ,

,

, ,

,

,, , , , , , , , ,

, , , , , ..... ,

0 50 60 90 120 150 80

longitude

Figure 2. Ambient background state with corotating fast and slow SW streams as a function of heliolongitude at two different latitudes. The velocity (top), density (middle), and temperature (bottom) are shown at the inner boundary (left), R - 1 AU (middle), and/• - 5 AU (right), respectively. Profiles at +15.75 ø latitude are shown as dashed and solid lines, respectively. Periodic, anti-symmetric conditions are imposed at the azimuthal boundaries of the computational domain, as explained in section 2.3. This means that the northern hemisphere profiles (dashed lines) are the same as the southern hemisphere profiles (solid lines) beyond 180 ø longitude, and vice versa, for latitudinal positions away from the equatorial plane. Interaction of fast and slow streams produces a shock-pair structure beyond 2 AU, as identified by vertical dashed lines in 5 AU plots.

for near-Earth observations. These background SW val- ues also produce a reasonable match with Ulysses lati- tudinal observations at larger heliocentric distances [see Riley et al., 1997a].

Figure 2 shows the ambient background state along two azimuthal lines at the inner boundary, R - 1 AU, and R - 5 AU. Interaction of corotating fast and slow SW streams produces a shock-pair structure beyond 1- 2 AU as shown in 5 AU plots. The fast stream (with velocity 724 kin/s) extends from 0 ø to 10 ø, the reverse shock is at 100 , the forward shock is at 300 , the slow stream (with velocity 345 kin/s) is from 300 to 70 ø, and the reverse and forward rarefaction waves are from 700 to 1800 . All these structures lie in the southern hemi-

sphere (at 15.750 below the equatorial plane) and they repeat in the northern hemisphere for longitudes from 1800 to 3600 . However, the flow configuration in this pe- riodic, two-sector pattern is anti-symmetric across the 0ø/1800 azimuthal boundaries, so that the fast stream in the northern hemisphere has north-south gradients and flow components reversed in sign.

3.2. Coronal Mass Ejection

The CME is introduced at the inner boundary as a time-dependent pulse situated within the slow stream,

centered where it crosses the heliocentric equator, as shown in Figure 1. The input pulse has the following spatial

- Q0 + and temporal

I Qo+/kQpt/rr 0 < t < 7'r , Q(t) - Qo+AQp 0 _• t-rr _< rd , Qo+AQp(2r•+r•-t)/r• 0 < t-r•-r• < r• ,

profiles, where the quantity Q refers to the radial veloc- ity V•, the density p, and the temperature T. Further, Q0 is the background value, AQp is the amplitude of the pulse, • is the radial position from the pulse center, •0 is the full pulse radial extent, r• is the ramp dura- tion (linear transition between the background and con- stant pulse values), and r• is the pulse duration. These functional relations define cosine spatial and trapezoidal temporal profiles, respectively.

The pulse diameter 2•0 - 30 ø, the pulse ramp du- ration r• - 1 hour, and the pulse duration r• - 12 hours. Maximum values of the radial velocity, density, and temperature are V• - 600 km/s, p- 1000 cm -a, and T- 2000 kK. Thus the density in the CME pulse is twice the slow stream value and the radial velocity

ODSTRQIL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT 487

•a-_)65.25o

w •b=)74.25o

w

RADIAL VELOCITY (kin/s) CASE I INJECTED DENSITY (cm -3) ,..300 •,':•'•' ';,,; .......... i 800 DAY 12 0.50 I • 7.50

Plate 1. Global view of the CME interaction with the structured background SW, 12 days after its launch from the inner boundary near the Sun. Distributions of the radial velocity (gray scale) and injected mass (color scale) are shown in six azimuthal slices (a through f) between r = 0.14 and 5 AU and between • = 0 ø and 180ø; and six meridional slices (g through 1) between r = 0.14 and 5 AU and between 0 = 30 o and 150 ø. Note that the injected mass is normalized to 1 AU data by pc = pc(r/to) 2, where r0 = 1 AU.

=87.

RADIAL VELOCI• (kin/s) INJECTED DENSI• (cm -3) Iog,o DENS• (cm -3) 500 ...... :. - 800 O.0D ..... --.. 0.75 0.01 •tt1't"1"1 !,.,I • • • • l' '• 7.50

CASE • DAY 12

Plate 2. Detailed view of the CME interaction with the structured background SW, 12 days after its laun& from the inner boundary near the Sun. Distributions of the radial velocity (gray scale), injected mass (color scale), and total density (contours) are shown in azimuthal slices (panels a through d) between r - 2.5 and AU and between • - •0 ø and 130 ø. Note that the injected mass is normalized to 1 AU data by p• - p•(r/ro) •, where r0 - 1 AU.

488 ODSTR(•IL AND PIZZO' CME PROPAGATION WITHIN STREAMER BELT

and temperature are equal to the fast-stream values. The pressure is eight times higher than the background value. The CME diameter is smaller than the mean ob-

served values (Hundhausen [1993] gives average width 47 o and median width 44ø), and CMEs are observed to contain considerable internal structure, which is lacking in our pulse characterization. Nonetheless, the simple pulse configuration we have selected suffices to illus- trate the basic dynamic processes involved in 3-D CME propagation in a structured background medium. Com- plexity can be added once we obtain a firm grasp of the primary dynamic issues.

4. Results and Discussion

The 3-D dynamic interaction leads to complex dis- tributions of SW parameters that are difficult to un- derstand. We present results of the global structure, structural details and temporal profiles of the primary SW parameters in Plates 1, 2 and Figure 3, respectively. Note that the CME was centered at 0 = • = 900 and the displays show cuts through the flow distribution at a number of locations with respect to the centerline of the disturbance.

4.1. Global Structure

Plate 1 shows global views of the CME interaction with the tilted-dipole corotating ambient flow 12 days after its launch from the inner boundary near the Sun. Plate la through If and lg through 11 show the radial velocity and injected mass density, in slices of constant latitude and longitude, over the whole computational domain.

The model CME is injected as a pulse of plasma shaped roughly like a prolate spheroid, with the long axis in the radial direction. The excess radial momen-

tum and thermal pressure in the pulse drive a rapid evolution near the Sun. The choice of input parameters leads to a piston-driven initial interaction [Hundhausen, 1972]. However, as the CME pushes through the heart of the slow, dense streamer belt flow, its excess mo- mentum is quickly dissipated, a compression is built up at its front, and the disturbance abruptly decelerates. Rarefaction waves are also generated in the immediate wake of the injected pulse which further erode the piston from the rear. A short distance from the inner bound-

ary, then, the CME undergoes a severe compression in the radial direction, which, coupled with the gas over- pressure within the input pulse, leads to a strong lat- eral expansion of the CME structure. Thus the ejecta, which were initially confined to a 300 cone, spread out over • 600 at larger heliocentric distances. The lat- eral spreading of initially narrow disturbances is well known from early 2-D HD simulations [De Young and ttundhausen, 1971, 1973].

As a consequence of the combined effects of radial flow collision, lateral material expansion, and interac- tions with the background velocity and density struc- tures, the 12-day-old CME depicted in the panels of

Plate 1 exhibits a bent and twisted pancake structure. In particular:

1. The CME, as measured by the distribution of in- jected mass (color), propagates slower near the helio- graphic equator and faster at high latitudes, which pro- duces the bowed shape of the ejecta in Plate li and lj. At low latitudes, the CME plows most directly into the slow, dense streamer belt flow and is retarded. By contrast, the high-latitude extensions of the CME are pulled rapidly outward by the fast flow toward the poles.

2. A systematic twist in the east-west orientation of the ejecta structure is evident in Plate la through lf. North of the equator the CME conforms to the follow- ing high-speed stream and its long axis is nearly aligned with the spiral stream front. South of the equator, how- ever, the orientation shifts as the CME lies nearly per- pendicular to the spiral. This is because the western (left) edge of the CME is embedded in a faster part of the background flow structure. Similarly, the north- south orientation of the CME front varies systematically with latitude and longitude.

3. The CME is most compressed (thinnest ejecta structure) north of the equator, where it is caught be- tween the slow, dense streamer flow ahead and the over- taking fast stream behind. In the south, it is distended by the gradients in the background flow.

Hammond et al. [1995] present observations of a CME by two spacecraft separated by 200 in heliographic lat- itude, and they infer that CMEs can be significantly distorted in latitude (see their Figure 5). Such distor- tions can be explained by large systematic differences in background SW velocities. In our simulation, the out- ward concave shape of the CME arises in two stages; initially, the CME undergoes strong lateral expansion near the Sun, whereupon the high-latitude portions are advected outwards rapidly by the fast background flow off the equator. The material near the original cen- terline of the disturbance remains mired in the slow streamer belt flow at low latitudes.

4.2. Structural Details

Plate 2 shows detailed views of the CME interacting with the corotating streamer belt at larger heliocen- tric distances. In these panels the colorations indicate the injected mass density, the greyscale shading indi- cates the velocity, and the contour lines (logarithmically spaced) denote the total (injected plus swept-up ambi- ent) density. The contours are useful for visualizing the location and strength of shock fronts in the simulation. The following features can be identified:

1. The maxima of the total density and of the injected density (i.e., the CME material) appear at different lo- cations. This separation is especially pronounced where the CME shock structure merges with the corotating shock structure (Plate 2b and 2c). Local merging of CME and corotating structures can thus produce much greater compression of the ambient density than either alone.

2. Shock strengths are greatest, and the entire struc- ture narrowest, where the forward and reverse shocks of

ODSTRQIL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT 489

CASE 1 - POINTo R=3 AU e--80.25 e •=71.25 e

40o . . "; , '"' .11 ,

,,i R=3,NJ e=80.25 ø •=90.75 ø ":-:•;:i•i•i!!•::•ii:i!!•:•i!•? ? R=3 AU e=80.25 ø ff=!08.75 ø ....... ':

• , .... • • ............ • • ß , -. ........ , .'

z 0.01 ........................

POINT e CASE I - POINT f CASE I - POINT d :•;..- .... ;"':•:•:•:::i: CASE I - R=5 AU •'=89.25 ø •=71.25 ø '. '.:•:::?:i::; R-5 AU e=89.25 ø •=90.75 ø ... R=3 AU •=89.25 ø •=108.75 ø :::•!!?i!?::'"•::'" .:.-::.•:'.

:• 4oo ....

,o 0.01 .... ' I

....... ,.... ............ .... 1ooo1 ................ • '" ' ' ';" •'"' ' I :::;

I •'•:::•

10-•! ß . ; .............. : ......... ., • J O. ....... v I

10 "4 •'• ' • ..... '"" ?'::::...::.'.:... •!•?:::i . ..... "

CASE 1 - POINT g :•.¾..:.."?:.:::;ii:;:.. CASE 1 - POINT h ::•.::.-:: :. ..... CASE 1 - POINT i ......... '"•-':":..-. R,,=5 AU $-'104.25 e •==71.25 e ;::• .... R=5 AU 8=104.250 .•-'90.75 e -' .... R==$ ALl 8•104.25 ø •,=108.75 ø

• 400 ....... ' I '••1 ........ • . I

10 ' :::. I '" ' ' ' :*"*;*:. ' ' / , , ......,., ..,t.., ...:., :... ,.,,.,.-. , , .. , ,

,go ' z 0,01 ............... I

..... ...... ........ ..... .... ! .. ,ø-'- ' "'"" '"-"----"'• .... .... •,.,:.., ,...,r... .... ....... .... I''; .... ;'''•'' ' -'I "--•-'-' a' •o..• .......................... , .... I

4 6 8 10 12 144 6 $ 10 12 144 6 8 10 12 14 DAY DAY DAY

Figure 3. Temporal profiles of interplanetary disturbances generated by CMEs launched within the slow streamer belt flow. Schematic views of the initial outflow conditions are included at the top-right of each panel and the location of the observing point (at 3 AU) is projected onto that region for easier orientation. Radial velocity, total number density, temperature, and thermal pressure are shown from top to bottom. The dashed line (in the total number density plots) shows the injected number density. Shaded areas indicate intervals where the injected mass densities exceed 5% of the maximum values; these regions define the main body of the CME material. Vertical dashed lines indicate the forward and reverse shocks, generated by the CME.

490 ODSTROIL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT

the CME and the corotating stream merge into a single paired structure (Plate 2a and 2b). Although the CME has the same speed as the fast stream initially, it decel- erares at larger heliocentric positions because there is no "piston" to overcome the resistance of the background SW and because lateral expansion of the CME dissi- pates its excess radial momentum density. The CME is then overtaken by the fast corotating stream and is entrained into its inclined leading edge.

3. The region between the shock and the leading edge of the injected CME material (the stand-off distance) varies with latitude and longitude. The stand-off dis- tance is very small where the CME is overtaken by the corotating fast stream (Plate 2a and 2b) and the gap increases when the CME propagates within the slow stream (Plate 2c) or within the rarefaction region be- hind the fast stream (Plate 2d). In addition, the gap between the CME leading edge and the shock is larger to the west (greater longitudinal angle), as indicated in Plate 2b through 2d. The CME propagates in a background SW characterized by 3-D gradients in phys- ical parameters; regions with higher temperatures have higher sound velocity, pressure waves propagate faster, and they form more distant and weaker shocks.

4. The forward shock generated by the CME is weaker in the southern hemisphere where it propagates into the trailing edge of the corotating streamer belt. The shock front can be identified by the coalescence of these con- tours (a larger density jump involves more contours) ahead of the CME. There is a well-developed shock ahead of the CME in Plate 2b and 2c and there is a

smaller density jump around the CME propagating in the trailing region behind the corotating stream (Plate 2d). This, together with the enhanced width of the den- sity transition zone, suggests that the front is reduced locally to a pressure wave, not a shock.

5. The reverse shock has a much smaller angular ex- tent than the forward shock. It can be identified in

Plate 2c through 2d by the large number of density con- tours at the back side (facing the Sun) of the CME. This shock is, in general, weaker than the forward shock. A special case is shown, however, in Plate 2d, where the reverse shock is stronger. This is because the shocks in this region are generated mainly by the CME expan- sion, and the reverse shocks produced by this mecha- nism are stronger than the forward shocks propagating outward into the trailing edge of the preceding high- speed stream.

The injected CME had initially 8 times larger inter- nal pressure and twice larger velocity than the back- ground slow streamer. The evolution of the CME in this example is thus characterized mostly by collision between fast CME and slow background flows. This produces the shock-pair structure at the leading edge of the CME material and results in high pressures and densities within the body of the CME. The flow collision effect is weaker in the lateral edges of the CME, where expansion effects driven by the internal overpressure are more pronounced. However, this expansion is weak, and pressures and densities remain at or above background

values, contrary to what is observed in overexpanding CMEs at high latitudes [Goslin9 at al., 1994].

4.3. Temporal Profiles

Figure 3 shows simulated spacecraft temporal profiles at nine different locations at 3 AU. These locations are

chosen to illustrate the differing appearances of the dis- turbance, as observed by a hypothetical space probe. Observing points a, b, and c (top row of Figure 3) are located north of the pulse center. The temporal profiles correspond to the part of the CME interacting with the leading edge of the following high-speed stream. Ob- serving points d, e, and f (middle row of Figure 3) are located at the latitude of the pulse center. The temporal profiles correspond to that part of the CME propagat- ing within the main part of the slow streamer belt flow. Observing points g, h, and i (bottom row of Figure 3) are located south of the pulse center. The temporal pro- files depict the part of the CME propagating within the trailing edge of the preceding fast stream. The resultant shocks/waves can be described as follows:

1. The CME is trapped by the leading edge of the following fast stream and it is sandwiched within the CIR at points a and b. The merged CME and CIR for- ward shock is observed just ahead of the leading edge of the CME material at point a and with a small stand-off distance at point b. The CME plasma is highly com- pressed and passes by in a relatively short time. The CME and CIR reverse shocks are observed as merged at point a. The reverse CME wave follows the reverse CIR shock at point b. The merged shocks are stronger and cause large density compressions.

2. The CME propagates just ahead of the leading edge of the following fast stream at points c and d. The forward transient shock is well ahead of the leading edge of the CME material. The velocity rise across the CME indicates compression of the CME plasma. The reverse shocks/waves are weak, and they are observed within (point c) or toward the rear (point d) of the CME plasma. At larger heliocentric distances along the same radial line, the structure will evolve toward that seen at points a and b.

3. The CME propagates almost wholely within the slow stream at points e and f. The forward and reverse CME shocks are well developed. They originate at the leading edge of the CME due to collision of high-speed CME plasma with the background slow stream.

4. The CME propagates in the trailing region of the preceding fast stream (points g, h, and i). Maximum to- tal and injected mass densities appear toward the rear part of the CME. The "N"-profile of the velocity re- flects the initial expansion of the over-pressured CME. However, the pressure within the CME is higher ev- erywhere than the surrounding ambient values. This indicates that the collisional interaction of the high- speed CME with the background slow stream exceeds the over-pressure expansion effects. Low-latitude CMEs (those propagating at relatively high velocity within the slow stream) follow a different evolution than high- latitude CMEs (which propagate with the same velocity

ODSTR•IL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT 491

as the fast stream). It is interesting to note that the rel- ative intensities of the forward and reverse CME shocks

differ in the two cases. There is a strong forward shock but no reverse shock at point g, while there are weaker forward shocks and stronger reverse shocks at points h and i. This effect was observed by Ulysses and simu- lated using a 1-D HD code by Gosling et al. [1998].

5. Conclusions

We have used a 3-D ideal HD model to investigate dynamic phenomena associated with a CME launched from within the middle of the coronal streamer belt.

Simulations of CMEs propagating outside the streamer belt will be undertaken in future work.

Our results show that the motion and appearance of a CME can be strongly affected by its interaction with background structures and by velocity variations within the background SW. The initial shape of the CME is distorted in all dimensions, the CME is com- pressed where it is caught up in the leading edge of the background stream structure, and it is distended where it propagates into the trailing edge of a preceding high- speed stream. Because of the systematic background velocity distribution (fast outflow over the poles, slow outflow near the ecliptic), the high-latitude parts of the CME tend to travel faster than the near-equatorial part. A given CME can thus be observed with different prop- erties at different locations: the shock strength varies with position (the shock being stronger where it is over- taken by and merged with the fast stream front); the stand-off distance between the shock and the leading edge of the injected CME material can vary dramati- cally (the forward shock of the CME may even merge with the forward shock of the corotating stream); and total and injected densities and shock strengths may maximize at different locations. This presentation fo- cussed upon results at large heliocentric distances to fa- cilitate basic understanding of the ongoing Ulysses mis- sion. Interactions with the ambient structure also take

place between the Sun and I AU, and analysis of the evolution in the inner heliosphere will be undertaken in a subsequent study. Distortions of interplanetary disturbances caused by background velocity gradients inside i AU are generally similar to, but smaller than, those presented here. A major exception is the inter- action at the leading edge of the fast stream, since the CME becomes trapped and compressed only at larger heliocentric positions where corotating shock-pair struc- ture develops. The 3-D nature of the SW thus leads to increasingly complicated structures with increasing dis- tance from the Sun.

The magnetic field was neglected in our computa- tions. In general, this approximation has little effect on overall SW dynamics because the kinetic energy and momentum of the plasma is typically much larger than the magnetic energy and momentum in interplanetary space. For example, the typical SW values given in sec- tion 3.1 and the typical magnetic field intensity 3.28 (3.45) nT in the fast (slow) SW streams at I AU [Mar-

ian[ and Neubauer, 1990] imply a plasma beta (ratio of internal to magnetic pressures) of 2.9 (4.0), and dy- namic, internal, and magnetic pressures of 1125 (742), 12 (19), and 4.3 (4.7)pPa (10 -•2 Pa), respectively. Thus the dynamic pressure is completely dominant in undisturbed SW at I AU. Also, interplanetary obser- vations indicate that CME structures most commonly occur without magnetic cloud signatures [Gosling, 1990; Richardson and Cane, 1993; Bothmet and $chwenn, 1996]. However, many CMEs do contain an internal magnetic field structure that is much more intense than the typical interplanetary magnetic field. For example, Suess [1988] lists typical values for the velocity, density, temperature, and magnetic induction inside magnetic clouds at I AU as being about 400 km/s, 11 cm -a, 40 kK, and 12 nT, respectively. The corresponding plasma beta is 0.21, and the dynamic, internal, and magnetic pressures are 1472, 12, and 57 pPa, respectively. Thus the dynamic pressure is also dominant inside magnetic clouds at i AU. Suess [1988] suggested that magnetic clouds expand passively as they move away from the Sun and that the low-beta conditions inside the cloud

should enable them to resist being distorted into shell- like objects. Cargill et al. [1994] demonstrated that flux tubes with internal magnetic field do resist dynamic de- formation and suggested that deformation of magnetic clouds takes place relatively close to the Sun, within 0.5 AU. We therefore expect that inclusion of the magnetic field would tend to reduce the compression and distor- tion effects seen in this simulation and that the near-Sun

expansion of the overpressured pulse used to character- ize the input CME would also be affected, perhaps sub- stantially. However, CMEs propagating beyond I AU are likely to suffer large distortions, even with a mag- netic cloud, since the kinetic momentum density domi- nates with increasing heliocentric distance. The effects should be particularly pronounced where the CME in- teracts with a high-speed stream front. We intend to add the magnetic field to the model in the near future to assess these effects, to map out the draping of the ambient magnetic field, and to study more realistically the evolution of the CMEs enroute to I AU.

Despite the simplifications made in this paper, our re- sults show that a single interplanetary disturbance can appear radically different at different locations. The 3- D interactions between transient and corotating struc- tures produce a rich set of dynamic phenomena and merit further computational and observational studies.

Acknowledgments. This work has been performed at the N OAA Space Environment Center and was supported by NASA grants NAGW-4616 and NAGW-4582, as well as by grant A303707 from the Academy of Sciences of the Czech Republic. Final computations were done at the NASA Cen- ter for Computational Sciences at the Goddard Space Flight Center. The authors are grateful to R. Zwickl for helpful discussion and to the referees for useful comments and sug- gestions.

The Editor thanks Volker Bothmet and another referee

for their assistance in evaluating this paper.

492 ODSTRQIL AND PIZZO: CME PROPAGATION WITHIN STREAMER BELT

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Du•an Odstr•il, Astronomical Institute, 25165 Ond•ejov, Czech Republic (e-mail: odstrcil@@asu.cas.cz)

Victor J. Pizzo, NOAA, Space Environment Cen- ter, 325 Broadway, Boulder, CO 80303, USA (e-mail: vpizzo@@sec.noaa.gov)

(Received April 10, 1998; revised September 8, 1998; accepted September 8, 1998.)