JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 86, NO. A13, PAGES 11,401-11,418, DECEMBER 1, 1981 Solar Wind Flow About the Terrestrial Planets 1. Modeling Bow ShockPosition and Shape JAMES A. SLAVIN AND ROBERT E. HOLZER Instituteof Geophysicsand PlanetaryPhysics, University of Californiaat LosAngeles, Los Angeles, California 90024 Generaltechnique for modeling the position and shape of planetarybow waves are reviewed. A three-parameter methodwas selected to model the near portion (i.e., x' > - 1Roo)of theVenus, earth, and Mars bow shocks and the resultscompared with existing models using 1 to 6 freevariables. By limitingconsideration to the forward part of thebow wave, only the region of theshock surface that is mostsensitive to obstacleshape and size was examined. In contrast,most other studies include portions of themore distant downstream shock, thus tending to reducethe planetarymagnetosphere in question to a pointsource and constrain the resultant model surfaces to be paraboloid or hyperboloidin shapeto avoiddownstream closure. It wasfound by thisinvestigation that the relative effective shapesof the near Martian, Cytherean, and terrestrial bow shocks are ellipsoidal, paraboloidal, and hyperboloidal, respectively,in responseto theincreasing bluntness of theobstacles that Mars, Venus, and earth present to the solarwind. The position of theterrestrial shock over the years 1965 to 1972showed only a weakdependence onthe phaseof thesolar cycle after the effects of solarwind dynamic pressure on magnetopause location were taken into account.However, the bow waveof Venuswas considerably more distant around solar maximum in 1979than at minimumin 1975- 6 suggestinga solar cycle variation in itsinteraction with the solar wind. Finally, no significant deviationsfrom axial symmetry were found when the near bow waves of theearth and Venus were mapped into the aberratedterminator plane. This finding is in agreementwith the predictions of gasdynamic theory which neglects theeffects of theIMF onthe grounds of theirsmallness. Farther downstream where the bow wave position is being limitedby theMHD fastmode Mach cone, an elliptical cross section is expectedand noted in theresults of other investigations. INTRODUCTION vieet al., )977;Russelland Greenstadt, 1979; Slavin et al., 1980]. Themagnetic field observations in Figure 1 showa seriesof quasi- Amongthe majorearly discoveries of the spaceprogram was the perpendicularshock crossings by, from top to bottom, Mariner 10, presenceof a bow shockupstream of the earth(e.g., Spreiterand PioneerVenus, Isee 1, and Mariner 4. In each casethe upstream Alksne[1970], Dryer [1970], and referencestherein). Given the precursorsare quite small in amplitude,the transition layer thick- largecollisional mean free path of solarwind particles (i.e., h -,• ! nesson the order of theion inertiallength, and the jump in thefield AU) it mighthave been expected at thetime that the magnetosphere magnitude'strong(i.e.,approaching (y + 1)/(y- 1)for the trans- wouldrepresent a small (i.e. ,'--, 10 -3 •.) scatteringcenter as opposed versecomponent). Under these favorable conditions, bow shock to an obstacledeflecting fluid throughthe formationof a standing crossingsmay be unambiguously identified in the experimental data bow wave. Thus planetarybow shockscomprise some of our recordswith precision limited only by the instrument sampling rate earliest,and perhaps most striking, observational evidence for the andthe relative velocity of theshock. However, it mustbe noted existenceof the microscaleplasma processes that allow the solar that the determinationof bow wave location is complicatedon wind to exhibitbulk fluid propertieson spatialscales much smaller occasionby "quasi-parallel"conditions when the angle between thanthe physicaldimensions of the planets.Further, the thickness theshock surface normal and the upstream interplanetary magnetic of the transitionlayer within whicha portionof the plasmaflow field becomessmall. In theseinstances there is a broadeningof the energyis convertedto internalenergy, turbulence, waves, and regionover which the plasmais "shocked"and an increasein suprathermalparticles has beenfound to be small in comparison turbulenceboth upstream and downstream [e.g., Greenstadt, 1970] with the shockstand-off distance. Hence, the bow wave may, for makinga judgement as to theshock location less certain and some- somepurposes, b• considered a mathematical discontinuity ashas timesdifficult in the absenceof plasmaas well as magneticfield beendone in obtainingboth gasdynamic [Spreiter and Jones, 1963; data. However,the relativenumber of passesduring which a dis- Dryer and Faye-Petersen,1966; Spreiter et al., 1966;Dryer and tinctcrossing fails to be recorded is notlarge [e.g.,Fairfield, 1971; Heckman,! 967; Spreiterand Stahara, 1980a,b] andMHD [Sprei- Olsonand Holzer, 1975]and the study of minorchanges in shock ter andRizzi, 1974] solutionsto the continuumdescription. positionas a functionof itsstructure [Formisano etal., 1973;Auer, Theseremarks find relevancein Figure 1 which bringstogether 1974]is outside the intended domain of thiswork. Accordingly, the samplesof theshock observations that have been made at eachof the resultsof this studymay not be strictlyapplicable to the highly terrestrialplanets: Mercury [Ness et al., 1975],Venus [Slavin et al., quasi-parallelportions of planetarybow waves. Observations have 1980], earth [Russelland Greenstadt,1979], and Mars [Smith, alsoshown that shock motion may occur at speeds of 10-102km/s 1969].Magnetometer observations are preferentially displayed here [Holzeret al., 1966;Greenstadt et al., 1972]in responseto chang- becauseof their ability to makehigh time resolution(e.g., 1-10 ing upstreamparameters and interactionswith solar wind Hz) measurementsrelative to those of the plasma instruments. discontinuitiesto produce multiple encounters between spacecraft However,with someexceptions that will be discussedlater, there is andthe shock even when the probe velocity is as great as ,-• 11 km/s generallygood agreementamong the particlesand fields experi- suchas was the casefor Mariner 10 at the time of the observationsin mentsas to the locationof the shockover length scales greater than Figure1. The treatmentof multipleencounters in boundarymap- thetransition layer thickness, •c/topi [e.g.,Vaisberg, 1976; Ogil- pingproblems varies from study to studyand is consideredin the next section.Mean valuesof the variousinterplanetary parameters changewith distancefrom the sunas can be seen,for example,in Copyright¸ 1981by the AmericanGeophysical Union. Papernumber 1A 1147. 11,401 0148-0227/81/001A- 1147 $01.00 11,402 SLAV•NAND HOLZER: FLOW ABOUT THE PLANETS 6O be highlydesirable to explorethe regionbetween the bow wave and the denselower atmosphereof eachplanet with particlesand fields 4O experiments.However, suchprograms have been restricted largely to the earth. Further,the examinationof flow throughany volume, suchas the magnetosheath,is limited to statisticalstudies if the 20 boundarylocation and boundaryconditions are not known at the time of the individualobservations as is the casewith singlespace- craft measurements[e.g., Hundhausenet al., 1969; Howe and 40 Binsack, 1972]. Owing to the naturalvariability of the solarwind and the planetaryresponse both the bow shocksand the magneto/ 20 ionopausesof planetsare in nearlycontinuous motion [e.g., Holzer et al., 1966;Slavin et al., 1980]. This pointis illustratednot only by the multiple boundarycrossings in Figure 1, but also Figure 2, La 40 whichplots average daily locationof the Venusbow shockmapped o.,..,,. into the solarwind aberratedterminator plane as observedby Pio- 20 neer Venus during its first 225 days in orbit. As is the caseat the earth, large fluctuationsare present.They have been studiedby Slavin et al. [1979a,b; 1980] and attributedto changesin not only ionopauseheight and solarwind Mach number,but alsothe solar wind interactionthrough the effects of varyingsolar corpuscular and electromagneticradiation on the ionosphereand neutral atmos- 5 Mars phere.At Mercury andMars still lessdata are availablewith noneof it havingbeen taken at low altitudeson the dayside(see reviews by Ness [ 1979],Russell [ 1979], andSiscoe and Slavin [ 1979]). Hence, Time at this time the study of solar wind flow about theseplanets as a Fig. 1. Quasi-perpendicularbow shocksat Mercury,Venus, Earth, and group is still reducedthe temporal variability of these physical Marsare displayed as adapted fromNess et al. [ 1975],Slavin et al. [ 1980], systems,the overall paucity of observations,and the limitationsof Russelland Greenstadt [1970], and Smith [ 1969].In timethe top 3 panels spanseveral minutes each, while the Mars encounter covers about 12 hours. single spacecraftmeasurements to an examinationof bow wave Multiple encountersdue to shockmotion are evidentin the Mercury and position, shape,and variability. Venusprofiles. The time spentin themagnetosheath at Mars appears small In this paperwe reporton the findingsof the first of the two part owing to the compressedtime scaleand the grazingnature of the high- studyof this subject.As will be describedbelow, Part 1 modelsthe altitudeMariner 4 fly-by aswell asany variations associated with bow wave motionat the time of the meaurements(Note: Greenstadt [ 1970] hasdeter- shapeand location of the bow wavesof Venus,earth, and Mars by a minedthat the final (i.e., exit) shockcrossing at Mars mayhave fulfilled the singlestandard technique for thepurpose of comparingtheir relative requirementsfor being