• Abstract and Figures
• Public Full-text

GEOPHYSICAL RESEARCH LETTERS, VOL. 22, NO. 23, PAGES 3275-3278, DECEMBER 1, 1995 Magnetosheath flow near the subsolar magnetopause- Zwan-Wolf and Southwood-Kivelson theories reconciled DavidJ. Southwood I and Margaret G. Kivelson2 Instituteof Geophysicsand PlanetaryPhysics. University of California.Los Angeles Abstract. We reconcilethe superficiallycontradictory theories the flow upstreamof the magnetopause,the magneticfield should of flow immediately upstreamof the subsolarmagnetopause. decreaseand the gaspressure and plasmadensity should increase We show that the formation of a layer of enhancedfield and whilst Zwan and Wolf [1976] predict a region where the field depresseddensity immediately adjacent to the magnetopauseas increasesand the densityand pressuredecrease. Southwoodand predictedby Zwan and Wolf appearsto requirethe presence Kivelson[1992] acknowledgedthe differencebetween the Zwanand upstreamof a regionof enhancedpressure and field rarel•tction Wo/f[1976]predictions and their own theory. It is thepurpose of aspredicted by Southwoodand Kivelson. We thusargue that the thispaper to link thesetwo apparentlycontradictory notions and to detachedregions of enhanceddensity and the depletion layer arguethat not only do botheffects occur in practicebut they arepart adjacentto the magnetopauseare actually manifestationsof a of one and the same effect. singlephenomenon. The models of the solar wind flow around the Earth's magnetospherein the gas dynamic limit include the field only Introduction kinematically [Spreiter and Alksne, 1969; 1970]. The approach would be entirely adequateif the gas pressurebehind the shock The structureof the magnetosheathfield and flow patternnear everywheregreatly exceededthe magneticpressure. As Zwan and the magnetopauseis of greatinterest in solarterrestrial physics, the Wo/f[1976] point out, it is implicit in Alksne's[1967] calculations region marking as it does the interface between solar wind and that there alwayswill be a regionnear the magnetopausewhere field terrestrialplasma regimes. The problemis complexbecause of the pressureis important. The kinematiccalculations based on the gas anisotropicnature of magnetohydrodynamicbody forces and the dynamic code predict that the field grows without limit as one allied fact that there are three separatewave modes.Gas dynamic approachesthe magnetopause[see also, Sonnerup,1980]. This fact studiesofthe flow around the magnetosphere weredone with great on its own does not mean that the field necessarily hasto grow large successbySpreiter and co-workers [Alksne, 1967: Spreiter and nearthe boundary; it simply means that an approach thatignores the Alksne,1969: 1970] but these treatments inevitably broke down in fieldforce gives an inadequate description. Recently, some full the immediate vicinity of the subsolarmagnetopause as the MHD simulations[Wu, 1992] have shownboth a densitydepletion magneticfield wastreated kinematically but not self-consistently. and upstreamof that a densityenhancement which may representa In 1976, Zwan and Wolf [1976] analyzed the flow near the combination of Southwood-Kivelson and Zwan and Wolf effects stagnation streamline. They showed that near the subsolar appearingin the results. magnetopausea depletionlayer would form in which the density The net magneticbody forcej x B is alwaysperpendicular to the would decreaseand the magneticfield increase.This was one of the magneticfield and so the stressesexerted by the magneticfield on earliestworks attemptingto model the flow near the magnetopause the plasma are fundamentally anisotropic. Furthermore, small includingthe field forces. Subsequently,a variety of observations disturbances in the medium generate three distinct indicatedthe presenceof a layerjust outsideof the magnetopause magnetohydrodynamic(MHD) wave modeswhose propagationis in which the field was enhancedand the plasmadensity depressed as also stronglyaffected by the field direction. Both the phenomena Zwan and Wolf had predicted[Crooker et al., 1979]. discussedby Zwan and Wolf [1976] and those discussedby Motivated to explain the regions of compresseddensity and Southwoodand Kivelson [1992] are associatedwith the slow MHD rarified magneticfield detectedby the ISEE I and 2 spacecraftby mode. Although only the latter work relies explicitly on Song et al. [1990; 1992] in the magnetosheath,Southwoodand considerationsof its properties, the slow mode gives rise to Kivelson [1992] adopteda different approachto look at the flow compressionand rarefactionof the field and plasmapressure with immediately upstreamof the magnetopause.They discussedthe the property that the respective pressureschange in antiphase. formationof slow modedisturbances in the magnetosheathflow Indeed for the caseof propagationat a large angle to the field, the upstreamof the magnetopause.The Zwan and Wolf effectpredicts presshrechanges in the wavemore or lessbalance. The group exactlythe oppositephenomena to thosepredicted by Southwood velocity of the wave mode is stronglyguided by the magneticfield andKivelson [1992]. Acrossa compressionalslow front standing in undermost conditions. Dungey [1968] likens the mode to a wave in a pipe (aligned along the field) althougha wave in an elastictube might be a betteranalogy. •Department of Physics, Imperial College of Science, To understandthe dynamicalfunction of the slow mode, let us Technologyand Medicine,London SW7 2BZ, U.K. 2Departmentof Earth and Space Sciences,University of startby noting that an ideal planar slow MHD mode wave satisfies California,Los Angeles,CA 90024-1567 the coplanaritytheorem. In other words, the backgroundmagnetic field, the wave velocitychange, the magneticfield changeand wave normalall lie in the sameplane. It followsthat a standingwave can Copyright1995 by the American Geophysical Union. modify the velocity of the flow in the plane of the upstreamfield and flow. If we take the plane containingthe upstreammagnetic Papernumber 95GL03131 field and velocityto be the X, Y plane, we concludethat, in steady 0094-8534/95/95GL-03131503.00 state, slow waves standingin the flow will serve to modify the 3275 3276 SOUTHWOOD AND KIVELSON: ZWAN-WOLF & SOUTHWOOD-KIVELSON MERGED velocity only in this plane. One can note that the diversionin the Z Zwan and WoWs 'thin tube approximation'is an analogyand as direction would introduce intermediate mode disturbances. suchis not fully rigorous. An individualtube of the magnetosheath doesnot actually retain its identity and so there are elementsof the Review of Zwan and Wolf [1976] scenariowhich are not completelyexplained, as we now discuss. As the tube moves towards the magnetopause,one expects Zwan and Wo/f[ 1976] considerthe evolutionof a singlethin flux transversepressure balance to be more or less maintained. The tubemoving in fro.m the solarwind as illustratedin Figure1. The compressionof the tube increasesthe magneticfield magnitudebut incident solar wind field is assumedto lie in the Y direction, the case the corresponding enhancement in magnetic pressure cannot we shalluse throughout the remainderof the paper.As the plasmain actually act to push plasmaalong the field (the "squeezing"effect the tube crossesthe bow shock,it receivesa tangentialacceleration describedby Zwan and Wolf [1976]). Only a gradient in gas that sets up motion parallel or antiparallelto the field in order to pressurealong the field can push the plasma in such a direction. deflect the plasmaaway from the nose of the magnetosphere.This Both the assumedoutflow along the field from the stagnation motion cannot but decreasethe number of particles per unit flux streamlineimposed at the bow shockand the increasingcontribution near the part of the tube incident on the nose and this is the first of the magneticcomponent to pressurebalance seem to be working source of the depletion effect. One can envisagethat as the flux to make the gaspressure near the constrictiondecrease. This is the tube moves towardsthe magnetopausethe number density on the oppositeto what is requiredto sustainthe outflow itself. tube near Y= 0 decreasesand the magneticfield rises.It would seem We proposea resolutionof the paradoxthat the Zwan and Wolf that to sustainthis motion behind and away from the shock, the and Southwoodand Kivelsontheories predict different behavior by shock must be strongestnear the nose so that there is a pressure linking the two theories. Already in Zwan and Wolf [1976], the gradientalong the field directioneverywhere to maintaina net force authorspointed out their solutioncorresponds to a slow mode wave along the field direction. The pressureon the stagnationstreamline expandingalong the flux tube. However,implicit in their pictureis (i.e. the streamline at Y = 0) would decrease towards the the paradoxalluded to above. They describea slow mode signalin magnetospherenose and to maintainperpendicular pressure balance which the field increasesand the pressuredecreases behind the the magnetic field pressurewould rise, thus creating a region wave as the wave propagatesalong the flux tube away from the nose adjacentto the magnetopausein which the field is enhancedand the region.Yet, the pressuregradient in sucha wave pulseis exactlyas plasmadensity is depleted. we have describedin the previousparagraph; it would exert a force The secondsource of depletion that Zwan and Wolf identi•j is to pushmaterial back towardsthe nose. Sucha motion in isolation associated with compressional stress near the nose of the is opposite to what we have concludedoccurs behind the bow magnetosphere.

Load more

  4

Copy Link