Y

2012 vol-. 53, NO.2

IMF ROTATIONS FOLLOWING INTERPLANETARYSHOCKS: THEIR INFLUENCE ON THE INTERACTIONWITH MAGNETOSPHERE

o' GoNCHARoV, r. ŠapnÁNrovÁ, z. NĚtr,tpČBKl. pŘecH

Praha

Received August 6, 20 I 2Revised October 10. 2012

IP shocks are often accompanied with a rotation of the interplanetary magnetic field (IMF)over a large angle and this rotation can modify interaction process. The study discuses the

interaction of the IP shock followed by an IMF rotation with the Earth magnetosphere withmotivation to separate their effects. The results are based on the global MHD modeling ofsuch interaction and are compared with observations.

1. Introduction

Moving toward Earth, an IP shock undergoes an interaction with the Earth's bowshock, magnetosheath, and magnetopause, and modification inside the magneto-sphere. This train of interactions have been studied by several authors using magne-tohydrodynamic (MHD) modeling or using the Rankine-Hugoniot (R-H) conditions.Spreiter et al. ll994l, Zhuang et al. 119811, Ivanov tI964l, Dryer et al. [1961], Dryter

119131, Shen et aL. 119121, Grib et al. [1919] have shown that the interaction of an

IP shock with the bow shock (a fast reverse shock) creates three discontinuities - the

fast reverse shock, a fast forward shock, and a contact discontinuity between them.

Later, Grib U9821, Pushkar et al. 119911, Grib and Pushkar 12006) found thatthe interaction of the IP and bow shocks results in a train of different discontinuitiesand that the number of these discontinuities changes with the distance from the Sun-Earth line. The authors investigated an oblique interaction between the solar wind fast

Charles University Prague, Faculty of Mathematics and Physics, Prague, Czech Republic

The authors thank all spacecfaft teams for the magnetic field and plasma data. Also, the eÍŤbrt of theCCMC staff in preparation of the special model runs is greatly appreciated. The present work was partlysupported by the Czech Grant Agency under Contract205l09l01l2, and partly by the Research Plan MSM0021620860 that is financed by the Ministry of Education of the Czech Republic. O. Goncharov thanksalso to the Grant Agency oť Charles University for a support (GAUK 102508).

Key words and phrases. interplanetary magnetic field, interplanetary shocks

E- mail adire s s.' goncharov.oleksandr@ gmail.com

AC1A L]NIVERSITATIS CAROLINAE - MATHEMATICA ET PHYSICA

19

shock wave and the bow shock front and concluded that the discontinuity interactiondepends on the IMF orientiltion.

MHD simulations [e.g., Yan et a\.,1996, samsonov et a\.,2006] predict that anIP shock-bow shock interaction generates a following sequence of discontinuities: afast shock propagating into the magnetosheath with a speed lower than that in thesolar wind fsamsonov et a|.,20061, and three new discontinuities - a forward slowexpansion wave, a contact discontinuity and a reverse slow shock.

on the other hand, the interaction between a fast shock and the magnetopauseresults according to the R-H conditions lGrib, 1972, Grib et al.,1979lin a rarefactionwave propagating toward the bow shock; similar results were obtained by the 2-DMHD simulation of wu et al. [2003]. Moreover, Grib et al. 119791predicted rharthe interaction of this rarefaction wave with the bow shock leads to another reflectedrarefaction wave which moves toward the magnetopause. From this prediction, onecan assume that the chain of wave transformations can repeat many times.

In this paper, we try to find a method to classify the different discontinuities thatare created as a sequence of the interaction of an IP shock and the following IMFrotation with the bow shock. Such study is actual and important because a statisticalanalysis of lP shocks during the last six years shows that JOo/o of shocks is followedby the IMF rotation and in 68vo of these cases, the rotation of the IMF B, componentwas observed within first 20 minutes after the shock arrival. For demonstration ofan influence of the IMF rotation on the interaction, we have selected a representativeexample with favorable positions of the spacecraft in the solar wind (wIND) and inthe magnetosheath (Geotail). In this example, data measured by wIND are used as aninput to a global BATS-R-US (a Block Adaptive-Tree Solar-wind Roe-type upwindScheme) MHD model. Since discontinuities reflected from the magnetopause and/orfrom some internal magnetospheric boundary or even from the ionosphere can playan important role in the interaction process, we use three BATS-R-US runs. The com-parison of results with the Geotail observations shows a good qualitative agreementbut we conclude that an identification of different discontinuities is possible only withthe MHD model supporl.

2. Observation

on July 28,1996 at 1214:35 ur, the WIND spacecraft located far in rhe solar windat(.119 l3;-10)656 RE registered a fast forward shock. About 50 minutes later, at1306:51 UT, the same shock was registered by Geotail located in the magnetosheathat(4;13:,--5)csp Rs. Unfortunately, no other spacecraft was in the solar wind, thusthe shock parameter determination was based on the R-H relations and the WINDdata. Parameters of the lP shock were: shock normal, n : (0.92; -0.06; -0.39),shock speed, V'r' : 339 km/s, and the Alfvénic Mach number, Ms = 2.06. How-ever, we note that the predicted time of the shock propagation from WIND to Geotail

80

Frcune 1. (a) Solar win<

shock through July 28, 19

and the seoond Íbur to (of the IMF magnitude an

density as determined Íio

based on these shock Parameterr 52 minutes. The good match o

were determined ProPerlY. Obse

In Geotail panels, one can identi

shock: 2 - a combination of a fc

and a reverse slow shock; 3 - no

3. Structure of the IP

Based on a comParison of ot

sonov et al. 120061 and Safrankt

lP shock with the bow shock w,

_..-r

teraction

:t that anruities: arat in the

ard slow

etopause

refaction

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reflected

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ities thating IMFtatistical[ollowed

mponent"ation ofientative)) and inied as an

Upwinde and/or

:an playhe com-reement

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lar windlater, at

.osheath

nd, thus

WIND-0.39),. How-Geotail

FrÉ

IG

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ta

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ť

a)

ÍffiĎ?]ms1*íísŮé

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Frcune l. (a) Solar wind and magnetosheath observations of thc IPshock through July 28, 1996. The íirst lbur panels oorrespond to WINDand the seoond Íbur to Gcotail measurements. (b) Temporal proÍilcsof the IMF magnitude and three components; speed; tcmpcrature; andilensity as determincd liom the global MHD model.

based on these shock parameters was 50 minutes, whereas that observed time wasry -52 minutes. The good match of these two times suggests that the shock parameterswere determined properly. Observations of both spacecraft are shown in Figure la.In Geotail panels, one can identify the following discontinuity: I the transmitted IPshock; 2 - a combination of a forward slow expansion wave, a contact discontinuityand a reverse slow shock; 3 - non identified discontinuity; and 4 - a slow shock.

3. Structure of the IP shock front in the magnetosheath

Based on a comparison of observations with a local magnetosheath model, San-sonov et al. 12O06l and Safrankova et al. 120011 suggested that the interaction oftheIP shock with the bow shock would generate a new discontinuity that would follow

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the IP shock front in the magnetosheath. ln their papers, this suggestion was sup-

ported by the modeled profiles of plasma parameters in the subsolar region but Griband Pushkar t20061 have argued that the follow-up discontinuity (ies) would differat diÍŤ'erent intersections of the interacting shocks. Since Geotail is located in the

magnetosheath, we can test this prediction. We prepared MHD simulations of this IPshock using real measurements from WIND as an input data for a global BATS-R-USMHD model. The model solves fully conservative magnetohydrodynamic equationsand uses a high-resolution finite-volume approximate Riemann solver scheme for cal-culation of ideal MHD equations [e.g., Gombosi et a\.,2002].

The results of simulations are shown in Figure lb and one can seen similar dis-continuities which can be identify as: (l) Expansions of the density, velocity, tem-perature, and magnetic Íield can be attributed to the decelerated front of the originalIP shock because it has a character of the fast wave; (2) An increase of the magneticfield and density but the decrease ofthe speed and temperature can be probably attrib-uted to a combination of the slow shock, rarefaction wave, and contact discontinuity;(3) An increase of the density and magnetic field and no change of the velocity and

temperature can be distinguished by the magnetic field rotation and represents a tan-

gential discontinuity or Alfvén wave; (4) A decrease of the density, and the increaseof the temperature, velocity, and magnetic field are typical for a slow shock.

However, in both data and simulations, the IP shock was followed by the IMFrotation. Since an arrival of this rotation roughly coincides with the time of the bestidentified discontinuity, we performed new simulation runs with artificial timing ofthe follow-up IMF discontinuity in order to SepaÍate the effects of the IP shock and

IMF rotation (Figure 2). For this task, the input data for the model were modified and

new two runs of the model were requested:(l) The simulation grid in the critical region of the dayside magnetosphere and

magnetosheath was 0.06 RE in order to identify accurately the discontinuitiesin the model results. The time step of the calculation was 3 s, in accord withthe best WIND resolution of the plasma data;

(2) The input data were complemented with a five-minute interval with con-stant values of parameters that delayed the follow-up IMF discontinuity (Fig-ure 2a).

(3) The input data with constant post-shock conditions (Figure 2b) were used.

Figure 3 presents the results of runs of global MHD simulations. The first run thatis shown in the top panels basically repeats the run show in Figure 1 but it uses a

signiÍicantly enhanced spatial resolution, especially in critical regions of the daysidebow shock and magnetopause. This procedure allowed us a more detailed analysis ofthe influence of the IMF rotation. The different discontinuities identified in the model

data are distinguished with vertical lines and numbered. In all panels of the figure,

1 represents an arrival of the original IP shock. A compound discontinuity predictedby Samsonov et al. t20061 is denoted as 2. The further discontinuity induced bythe IP shock bow shock interaction identified in the first run (Figure 3) coincidences

82

aE

ř-É

z

1248 1300lime

Frcuns 2. Two model rur

discontinuity (dashed lin,

shifted by 5 minutes; (b)

with the upstream IMF discontinvelocity, and density is 3. Howerof the magnetic field is a product

the magnetic field decrease wherthe second and third panels ofFi

The absence of the IMF rotati

generated by the IP shock - bowdecrease of the magnetic field ar

eters (5 and 6). It is a question

of the magnetosheath profile du

al. 120111 or if it would be treat

boundaries. However, the in-phathe latter as a more probable exp

In the second run, an arrival ,

a large increase of the magneticfollowed by a new tangential dis

tion - bow shock interaction 8. T

x

sup-

Gribďiffer

n the

ris IP{-usÍions

r cal-

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FIcune 2. Two model runs with different timing of the Íbllow-up IMFdiscontinuity (dashed linc). (a) In the run 2, the IMF B" rotation wasshifted by 5 minutes; (b) in the run 3, the rotation was deleted.

with the upstream IMF discontinuity characÍerized by increases of the magnetic field,velocity, and density is 3. However, the second and third runs reveal that the increaseof the magnetic field is a product of the arrival of the IMF rotation because we observethe magnetic field decrease when this arrival is delayed or absent, as it can be seen inthe second and third panels ofFigure 3.

The absence of the IMF rotation allows us to identify a set of new discontinuitiesgenerated by the IP shock - bow shock interaction: number 4 is characterized by thedecrease of the magnetic field and density and following oscillations of both param-eters (5 and 6). It is a question if their oscillations are connected with the scanningof the magnetosheath profile due to a oscillatory motion in this region Nemecek etal.l20l1l or if it would be treated as a product of the IP shock interaction with theboundaries. However, the in-phase changes of the magnetic field and density suggestthe latter as a more probable explanation.

In the second run. an arrival of the IMF rotation is shown as a line 7 and causesa large increase of the magnetic field. This increase propagates downstream but it isfollowed by a new tangential discontinuity which results for the upstream IMF rota-tion - bow shock interaction 8. The rise of the magnetic field magnitude is terminated

13$S t320timé

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05101520250min eftér í3:00

51015m25min aÍter 13:00

IMF rotation with the bow shor

magnetic field, and (3) this incrr

new discontinuity, and finally, (IP shock front in the magnetoshe

Classification of the discontin2 in Figure 3a is the discontinuit'region and described as a combtact discontinuity, and a reverse

t20061 reported a sequence of r

continuity moving downstream a

downstream according to our sinrotational discontinuity, a slow slstream. A similar set of discontiof discontinuities in the data wouare masked by magnetosheath flrrotation of IMF 8,.

Dnvrn M., Mrnnrrr D., AnoNsoN P.: Ir

J. Geophys- Res.72(11),2955 296',

Dnyen M.: Bow shock and its interactiGnrs S.: The interaction of solar wir

B e lo rus sian Ac ad. S c i. 16(6'1, 49TtGnre S. A., BnruNBr-r-r B. E., Dnvsn M..

the bow shock-magnetopause systeGnrs S. A.: Interaction of non-perpend

netosphere, Space Sci. Rev.32,43'Gnrs S. A. eNo PusHxnn E. A.: Asymr

with the bow shock, Geomagn. AertGol,rsosr T., TorH G., oB ZBBuw D., F

hydrodynamics and physics-based2002.

Iv,q,Nov K.: Interaction of running shor

the Eafth, Geomagn. Aeron.4,803-NEuEcEr 2., SepneNrovl J., Kov,qr, A,

interplanetary shock across magnet{

2011.PusHran E., BnnMn'r 'A.., Gnrs S.: MI

shock on the Earlh's bow shock, Ge

SapneNrove J., Nrnncnr 2., PnucH L.,terplanetary shocks near the bow shr

408212,2007.SnnsoNov A. A., NrlrBclx 2., SlnnnN

planetary shock through the magnet

15

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5

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60

4í)

029

15

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5

o

R{]N 3

/jl., |,

,a J

l

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Frcuns 3. Changes of the magnetic field (a) and density (b) obtained as

a result of three model runs; original data and two runs with the shiÍted

IMF rotation aÍter the IP shock.

by another discontinuity 9, after it, the magnetic field and density slowly decrease and

eventually stay almost constant. These magnetic field discontinuities are similar to

those observed in the first run, but the second run reveals that they are accomplishedwith simultaneous changes of the density. The system reaches a steady state in about

20 minutes after the IP shock arrival in the first and second runs, whereas about

1O minutes is enough in the third run where the IMF discontinuity is absent.

4. Conclusions

Based on these results and using an earlier study of the interaction IP shock[MFdiscontinuity with bow shock we can draw several conclusions.

We have analyzed observations of an IP shock in the magnetosheath and compared

data with the BATS-R-US global model. The attention was devoted to global features

of the IP shock-bow shock-magnetopause interaction as well as to structure of the

lP shock front in the magnetosheath. ln simulation results, we see that (l) the IP

shock creates a new discontinuity in the magnetosheath, (2) the interaction of the

84

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,l'I

*-llI;

l__-l

llLJ_t

Il

_*_J

IMF rotation with the bow shock results in a huge increase of the magnetosheathmagnetic Íield, and (3) this increase propagates downstream but it iS followed by anew discontinuity, and finally, (4) we identified three discontinuities that follow theIP shock front in the magnetosheath.

ClassiÍication of the discontinuities is diÍ1]cult but we think that the discontinuity2 in Figure 3a is the discontinuity repofted by Snmsonov et nl. 120061 in the subsolarregion and described as a combination of a forward slow expansion wave, a con-tact discontinuity, and a reverse slow shock. On the other hand, Grib and Pushkar[2006] reported a sequence of a fast shock, a rarefaction wave and a contact dis-continuity moving downstream and followed by a new rarefaction wave also movingdownstream according to our simulations. A more complicated set of a fast shock, arotational discontinuity, a slow shock, and a contact discontinuity would move down-Stream. A similar set of discontinuities was found in the Geotail data. IdentiÍicationof discontinuities in the data would be impossible without model results because theyare masked by magnetosheath fluctuations of a similar amplitude and by a followingrotation of IMF 8,.

References

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Dnvpn M.: Bow shock and its interaction with intcrplanetary shocks, Radi.o lci.8,893 901, 1973.Grrrg S.: The intcraction oÍ' solar wind shock waves with tho magnetosphere oi the E'arth, 1{e2.

Belorussian Acad. Sci. 16(6),493 '1.96, 1912.Gnrs S. A., BnluNut.r-t B. E,., DnvBn M., SuuN W.-W: lntcraction of interplanetary shock waves with

thc bow shock magnctopause system, J. Geophys- Res. 84, 5901 5921, 1919.Gr<rs S. A.: Interaction of non-pelpendicular/parallel solar wind shock waves with the Earth's rnag-

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with the bow shock, Geomagn.. Aentn. 46, 411423,2006.Coueosr T., TorH G., oe Zur:uw D., H,rNsEN K., Kanrrv K., Pownll K.: Semirelativistic magneto-

hydrcrdynamics and physics-basod convergence accelcration, J. Comput. Ph.ys. 177, 116 205,2002.

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NeuBcsr Z., SlnnrNrova J., Kov,tr, A., Manrce J., PnncH L.: MHD analysis of propagation of aninterplanetary shock across magnetosphcric boundaries. J. Atmos. Sol.-Terr. Phys.73(l),20,29,20tI.

PusHxirn E., B,tnrr,rrN A., Gnra S.: MHD-apprclximation study oí'the incidencc of the solar windshock on the Earth's bow shock, Geomagn. Aeron. 31,522 525, 1991.

Sa.pn,rNrov,t J.. Nl-l,ll.cex Z., Precu L., SnusoNov A., Koval A', ANonBpov,n K.: Modi Íication of in-telplanetary shocks ncar the bow shock and through the magnctosheath, J. Geoph.y.s. rtes. 112(tt),Á.082t2.2001.

Sensolov A. A., Nr.;nl;cnx 2., S'rnuNrova J.: Numcrical MHD modeling of propagation of intcrplanetary shock through the magnetoshcaÍh, J. Geophys. Rr:s. 111, A082l0' 2006.

lse and

rilar to

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ckAMF

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) the IP1 0f the

85

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doubfe-shock ensemble with thc Earth's bow shock, J. Geophys. Res.77(25),46214644, 1972.

Spnlrrrn J. R. nNo Smnene S. S.: Gasdynamic and magnetohydrodynamic modeling of the magne-

tosheath: a tutorial, Adv. Space Res.14,5-19,1994.Wu C.: Shock wave interaction with the magnetopause, Space Sci. Rev. 107,219-226,2003.YeN M. nNo LBB L. C.: Interaction of interplanetary shocks and rotational discontinuities with the

Eafih's bow shock, "/. Geophys. Res. 101,4835 4848, 1996.

ZuueNc H. C., RussBu C. T., StrrrH E. J., Gosr-rNc J. T.: Three-dimensional interaction of interplan-

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ACTA L]}JIVERSITAl

THERMAL CONVECTBODY WITH FREE SUFOR SATURN'S MOOI\

M. KUCHTA, o' ČADEK, G. ToBIE

Praha, Nantes

ReceivedJune 11,2012Revised October 10, 2012

We present a new numeriing body with freely defc

chanical properties of the

creep mechanisms, its de

density approximation (st

order to track the surface

moon Iapetus, whose topr

history when the spin ratr

model is characterized b;

270 K), the initial rotatior

defining the relative roleters, we systematically er

rameters the body can be

Our results indicate that tl

an external body.

I

The topography of Iapetus, tltwo enigmatic features: an exce

torial ridge reaching heights ofto Thomas et al. 120011, the strc+ 3.1 km and polar rudrusll2.4

Deparlment of Geophysics, Faculty <

Laboratoire de Planétologie et Géod,

The work was supported by project I

Key words and. phrases. thermal con'

E- ma il addre s s: miroslav.kuchta@ gr

86