JOURNALOFGEOPHYSICALRESEARCH,VOL.???,XXXX,DOI:10.1029/, The role of the Hall effect in the global structure and dynamics of planetary magnetospheres: Ganymede as a case study J. C. Dorelli,1 Alex Glocer,1 Glyn Collinson,1 G´abor T´oth2 Abstract. We present high resolution Hall MHD simulations of Ganymede’s magne- tosphere demonstrating that Hall electric fields in ion-scale magnetic reconnection lay- ers have significant global effects not captured in resistive MHD simulations. Consistent with local kinetic simulations of magnetic reconnection, our global simulations show the 5 development of intense field-aligned currents along the magnetic separatrices. These cur- 1 rents extend all the way down to the moon’s surface, where they may contribute to Ganymede’s 0 aurora. Within the magnetopause and magnetotail current sheets, Hall currents in the 2 reconnection plane accelerate ions to the local Alfv´en speed in the out-of-plane direc- n tion, producing a global system of ion drift belts that circulates Jovian magnetospheric a plasma throughout Ganymede’s magnetosphere. We discuss some observable consequences J of these Hall-induced currents and ion drifts: the appearance of a sub-Jovian ”double 2 magnetopause” structure, an Alfv´enic ion jet extending across the upstream magnetopause and an asymmetric pattern of magnetopause Kelvin-Helmholtz waves. ] h p - 1. Introduction Larmor radii or inertial scale lengths over which collision- e less reconnection physics dominates. While there was some c a The rapid reconnection-driven response of magneto- early evidence suggesting that Hall reconnection produced p spheric convection to changes in the orientation of the ex- Petschek-like [Petschek, 1964] configurations that rendered s ternal magnetic field is one of the great puzzles of magne- the reconnection rate insensitive to the system size [Shay . tospheric physics. The nearly collisionless magnetospheric et al.,1999],subsequentHallMHDsimulationsofmagnetic cs plasma should effectively shield it from changes in the ex- island coalescence – in which reconnection is driven by the ternalfield. Intheresistivemangetohydrodynamics(MHD) i ideal MHD instability of a system of magnetic structures s limit, magnetospheric reconnection should occur in vanish- with characteristic scale λ (the island wavelength) – sug- y ingly thin extended current sheets on time scales much too gested that the reconnection rate (both the instantaneous h slow[Parker,1957;Sweet,1958]toexplainmagneticstorms rate and the coalescence time) should scale like (d /λ)1/2, p and substorms. Either there is some anomalous plasma re- i where d is the ion inertial length [Dorelli and Birn, 2003; [ sistivity(e.g.,producedbyturbulence)enhancingtheSweet- i Parkerreconnectionrate,orhigher-ordertermsintheGen- Dorelli,2003;KnollandChacon,2006]. Recentelectromag- 1 eralized Ohm’s Law (e.g., the Hall effect, electron pressure neticPICsimulations[Karimabadietal.,2011]oflargescale v anisotropy, or electron inertia) are somehow preventing the islandcoalescenceareconsistentwiththeearlierHallMHD 1 formation of extended electron-scale current sheets. results in some ways (predicting a coalescence time that 0 The important role of Hall electric fields in allowing fast scaleslike(di/λ)1/2),buttheyneverthelesssupporttheidea 5 reconnectiontooccurinthelimitofverysmallplasmaresis- thatthemaximuminstantaneousreconnectionrateisinsen- 0 tivity was only beginning to be appreciated in the late 90’s sitive to the island size (at least over the limited parameter 0 [Biskamp et al., 1995, 1997; Ma and Bhattacharjee, 1996; range so far accessible by PIC simulations). . Shay and Drake, 1998; Shay et al., 1999], culminating in Moving from two to three dimensions produces a 1 the“GEM(GeospaceEnvironmentModeling)Reconnection much richer reconnection landscape. Breaking the two- 0 Challenge” results summarized in Birn et al. [2001]. While dimensional symmetry permits plasma instabilities (e.g., 5 there is still debate about the specific physical mechanisms oblique tearing modes [Galeev et al., 1986; Daughton et al., 1 involved–e.g.,Arethedispersivepropertiesofwhistlerand 2011]) that would have been suppressed in two-dimensions. : kineticAlfv´enwavesplayingthedominantrole[Mandtetal., Recently, Daughton et al. [2011] have argued that collision- v 1994; Rogers et al., 2001]? Are finite Larmor radius effects less magnetic reconnection in a realistic three-dimensional i playing a crucial part [Hesse et al., 1999, 2001]? – there is X magnetosphere should produce extended electron-scale cur- generalagreementthatsimplyincludingtheHallterminthe rent sheets that in turn become unstable to secondary flux r GeneralizedOhm’sLawisahugeimprovementoverresistive a rope formation, ultimately resulting in a turbulent recon- MHD,producingreconnectionratesthatarecomparableto nection layer. those observed in full particle-in-cell (PIC) simulations. Unfortunately, high performance computing capabilities It is less clear how the GEM Reconnection Challenge re- arenotyetadvancedenoughtopermitevenHallMHDsim- sults“scaleup”toverylargesystemslikeplanetarymagne- tospheresorstellarcoronalactiveregions,whosecharacter- ulations of an Earth-sized magnetosphere; the same disper- istic scales L are many orders of magnitude larger than the sive waves that may play a role in producing fast reconnec- tion also make the Courant-Lewy-Friedrichs time step pro- hibitivelysmallforexplicitcodes. Thus,itisnotsurprising that most Earth-scale global magnetosphere simulations to 1GeospacePhysicsLaboratory,NASA-GSFC,Greenbelt, datestilluseresistiveMHD,eitherrelyingonnumericalre- Maryland,USA. sistivity or ad hoc current-dependent “anomalous” resistiv- 2CenterforSpaceEnvironmentModeling,Universityof ity to produce fast reconnection. While it has been known Michigan,AnnArbor,Michigan,USA. since the GEM Reconnection Challenge that one can eas- ilyachievereconnectionratescomparablewithobservations Copyright2015bytheAmericanGeophysicalUnion. andkineticsimulationsbyusingcurrent-dependentresistiv- 0148-0227/15/$9.00 ity models with appropriately dialed free parameters (e.g., 1 X - 2 DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS Otto [2001]), it is by no means clear that simply getting ion drifts). However, the picture that emerged from this therightlocalreconnectionrateistheonlywaythatkinetic previous work was incomplete in important ways. The par- scalephysicsinfluencesglobalmagnetosphericstructureand ticlesimulationsofWinglee[1994]weretwo-dimensionaland dynamics. In this work, we address this basic question: did not properly capture the impact of non-MHD drifts on Does the local structure of collisionless magnetic reconnec- thethree-dimensionalconvectionpattern(aswewilldemon- tion (specifically, the Hall current structure within the ion strate below). The Winglee [2004] simulations, while three- inertial region) influence the global structure and dynam- dimensional, used cell sizes a factor of ∼ 8 larger than the ics (viz., convection and field-aligned current patterns) of ioninertiallength,implyingthationscaleeffectswerelikely planetary magnetospheres? swamped by numerical dissipation. As we will see below, it WhileEarthmaystillbeoutofreachofpresentdayHall iscrucialthatoneresolvetheioninertiallengthwithatleast MHD codes – and even Mercury pushes the high perfor- 5computationalcellsperioninertiallengthinthreedimen- mance computational envelope – Jupiter’s third Galilean sions to see significant differences between the resistive and moon, Ganymede, provides us with an ideal opportunity Hall MHD global convection patterns. to begin addressing these questions. The distance between Previous multi-fluid simulations of Ganymede [Paty and the surface of the moon and the upstream magnetopause is Winglee, 2004, 2006; Paty et al., 2008] that included the aboutafactorof10largerthantheoxygenionskindepthin Hall effect have achieved resolution comparable to that of thesurroundingJovianmagnetosphere(e.g.,Kivelson et al. thesimulationsdescribedhere; however,thispreviouswork [2004]),providinguswithad /L<<1magnetospherethat i focusedontheeffectsofionosphericoutlow(separatelymod- is still computationally tractable. Ganymede is also unique elingthehydrogenandoxygenpopulations)anddidnotdis- inthattheJovianmagnetosphericmagneticfieldisstrongly cusstheimpactofHall-mediatedreconnectionontheglobal anti-alignedwithGanymede’sdipole,sothatmagnetopause patternoffield-alignedcurrentsandconvection. Further, it reconnection is strongly driven by nearly steady upstream conditions,asituationanalogoustotheconditionsthatdrive is not clear from these simulations how the enhanced iono- enhanced magnetospheric convection and magnetic storms spheric outflow impacted the ability to resolve the ion iner- in Earth’s magnetosphere. Finally, we have several Galileo tial length: di ∼n−io1n/2, implying that more oxygen flowing flybys under essentially steady magnetospheric conditions, outintothemagnetospheremakesitmoredifficulttoachieve allowing for a relatively straightforward observational test >5computationalcellsperdi. Incontrast,thepresentwork of our simulations. doesnotexploretheroleofionosphericoutflow,focusingin- Recent high resolution resistive MHD simulations of stead on the global effects of ion-scale reconnection (which Ganymede’s magnetosphere by Jia et al. [2008, 2009] have are much more difficult to resolve in the presence of signif- producedaglobalpictureofGanymede’smagneticfieldthat icant ion outflow). We plan to explore the effect of iono- agrees well with Galileo magnetometer observations for the spheric outflow in future work using the multi-fluid models six Ganymede flybys (e.g., reproducing such basic features developed by Glocer et al. [2009]. asthelocationandshapeofthemagnetopause). Whilethis may seem at first glance to support the idea that ion-scale physics does not have a significant impact on Ganymede’s 2. Simulation setup global magnetic field structure, it is important to note that only two of the flybys (G8 and G28) crossed the upstream We performed our simulations using the BATS-R-US magnetopauseatlocationscloseenoughtothereconnection global Hall magnetohydrodynamics code developed at the site to test predictions about global convection and field- University of Michigan [Powell et al., 1999; To´th et al., aligned current patterns. The G7 and G29 flybys did not 2008]. The Jovian magnetospheric plasma and field param- sample the central tail current sheet (where, as we will see eters were the same as those used by Jia et al. [2008] for below, most of the reconnection-driven convection is con- their simulation of the Galileo G8 flyby. The Jovian mag- fined),andtheG1flybywastooclosetothemoon’ssurface netospheric plasma and field parameters were the same as to sample the tail current sheet. Thus, simply comparing those used by Jia et al. [2008] for their simulation of the a simulation to a few Galileo flybys is not sufficient to ad- Galileo G8 flyby. Ganymede’s dipole moment was set to dress the impact of ion-scale physics on global magneto- M = −716.8nT, M = 51.8nT and M = −18.0nT X Y Z spheric structure; MHD may get the basic size and shape in GphiO coordinates (where X points in the direction of ofthemagnetopauserightandstill(aswewilldemonstrate the incident Jovian magnetospheric flow, Y points along below) fail to correctly capture the global convection and the Ganymede-Jupiter line and Z is parallel to the Jovian field-aligned current patterns. spin axis). The Jovian magnetic field components were set In what follows, we describe our use of global Hall MHD to B = 0nT, B = −6nT and B = −77nT. The simulations of Ganymede’s magnetosphere to demonstrate X Y Z inflow velocity was V = 140km/sec, V = 0km/sec, thatthelocalion-scalestructuresobservedintheGEMRe- X Y V = 0km/sec. The Jovian magnetospheric mass density connection Challenge (and all subsequent kinetic reconnec- Z and pressure were set to ρ = 56amu−cm−3 and 3.8pPa, tion simulations) have significant impacts on Ganymede’s respectively. convection and field-aligned current patterns. Specifically, While BATS-R-US provides the option to run the Hall the Hall “out-of-plane” magnetic field quadrupole pattern model with several non-ideal contributions included in that has become one of the defining characteristics of col- Ohm’slaw,E=−V×B/c+J×B/(nec)−∇p /(ne)+ηJ lisionless magnetic reconnection generates a new system of e (here,Vistheplasmabulkvelocity,Bisthemagneticfield, field-aligned currents that map directly from the reconnec- c is the speed of light, J is the current density, n is the tionsitesallthewaydowntothemoon’ssurface,modifying the region-1 type current system that supports the Alfv´en plasmanumberdensity,eistheelectroncharge,andηisthe wing structure close to the moon. Further, the same Hall plasmaresistivity),theresultspresentedhereusedthemuch current system produces a new J×B force that acceler- simpler Ohm’s law: EHALL ≡ −V×B/c+J×B/(nec). atesionstotheirlocalAlfv´enspeedoutofthereconnection Our neglect of the electron pressure gradient and resistiv- plane, introducing large asymmetries to the classic Dungey ity terms was motivated by our desire to test, in the global [1961] convection pattern. magnetosphericcontext,thetwoprimaryresultsoftheGEM Inpreviouspioneeringwork,Winglee[1994,2004]empha- Reconnection Challenge papers (summarized in Birn et al. sized some of the effects described in this paper (in partic- [2001]): 1) EHALL is the minimally complex Ohm’s law re- ular, the impact of Hall physics on the field-aligned current quired to produce reconnection rates comparable to those systems and the important role of non-MHD perpendicular observedinfullPICsimulations,2)thereconnectionrateis DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS X - 3 Figure 1. Hall effects appear when the dissipation scale is sufficiently smaller than d , so that the i ion and electron bulk velocities become decoupled in thin d scale current sheets. To achieve this scale i separation,whilestillrecoveringthelargescaleAlfv´enwingstructureatlargedistancesfromthemoon, we used a nested grid in which the highest resolution of 1/32R was concentrated near the moon (left G panel). This allowed us to achieve a resolution of 5−10 computational cells within the d scale current i sheet(rightpanel). Thus,sincethenumericalschemeconcentratesnumericalresistivityatthegridscale, this strategy achieves the required separation between d and the dissipation scale. i insensitive to the plasma resistivity when the J×B/(nec) and magnetotail current sheets required at least 5 compu- termisincludedinOhm’slaw. Aswewillseebelow,relying tational cells per d ; thus, for the results presented here, i onnumericalresistivityalsoallowsustomoreeasilyachieve we chose a computational mesh consisting of several nested a significant separation (factor of ∼5−10) between di and uniform grids with the innermost grid having a cell size of the dissipation scale. ∆X = ∆Y = ∆Z = 1/32R ≈ 83km and dimensions G The Hall and electron pressure terms introduce whistler L = 7R ,L = 4.5R ,L = 4R (see Figure 1). This X G Y G z G and kinetic Alfv´en wave dynamics, respectively, both of innermost grid was chosen to properly resolve the ion iner- which alter the structure of the reconnection layer in qual- tialscaleinaregioncontainingtheupstreammagnetopause itatively similar ways (e.g., Rogers et al. [2001]). Thus, by and magnetotail current sheets. The outer grid extended neglecting the pressure gradient term in Ohm’s law, we are to 64R to capture the Alfv´en wing structure far from the leaving out potentially important kinetic Alfv´en wave dy- G region of interest in the inner magnetosphere. namics. ThekineticAlfv´enwavephysics,however,doesnot Our strategy was to focus on resolving the d scale, rely- strongly influence the current sheet structure or reconnec- i ingonnumericalresistivityη tobreaktheMHDfrozenflux tion rate for small guide fields; thus, neglecting it is appro- constraint. Our reliance on numerical resistivity was made priate for the G8 flyby case considered here. Future simu- necessarybythefactthatHalleffectsdonotbecomesignifi- lationsofotherGalileoflybyswherethereconnectionguide field is moderately large will require inclusion of the elec- cantuntilthedissipationscalelη isafactorof5−10smaller tron pressure gradient term. In any case, simply including than di; however, resolving a resistive layer of thickness lη the Hall term at least captures the de-coupling of electron with 5−10 cells when lη is itself a factor of 5−10 smaller and ion bulk velocities which is completely absent in resis- than di would require 25−100 computational cells per di, tive MHD, and this electron-ion decoupling below the ion andthisiscurrentlystilloutofreachwithpresentdaycom- inertial scale allows magnetic reconnection to occur on an puters. Thus,relyingonnumericalresistivitywithlη ∝∆X Alfv´enic time scale that is comparable to that observed in allowed us to accurately resolve d scale structure with the i resistive MHD with current-dependent anomalous resistiv- minimal number of computational cells per d . While this i ity. approach raises questions about how the results depend on Our Hall MHD model also neglects ion pressure theresistivitymodel,wepointoutthatprodigiousnumerical anisotropies and gyro-viscous effects (e.g., the well-known evidencefromHallMHDsimulationsstronglysuggeststhat “gyro-viscous cancellation” effect [Hazeltine and Meiss, theHall-mediatedreconnectionrateisinsensitivetothedis- 1992]inthemomentumequation). Whiletheseeffects–and sipation physics (e.g., see the GEM reconnection challenge otherfiniteLarmorradius(FLR)effects–mayalsohaveim- papers [Birn et al., 2001]). Consistent with these past re- portantconsequencesforthestructureofGanymede’smag- sults, we have found in our convergence tests that the d netosphere, we will see below that the Hall term in Ohm’s i scalestructuresbegintoconvergewhen∆X <d /5,despite law already captures globally significant ion drifts that are i the fact that the resistivity is numerical. absent in MHD . Indeed, we argue below that many of the We imposed inner boundary conditions on cells within a neweffectsobservedinourGanymedesimulations(e.g.,the sphereofradius1.0R . Themassdensityandtemperature asymmetric “double magnetopause” boundary layer) have G attheinnerboundarywereinitiallysetto550amu/cm3and alsoappearedinmulti-fluidsimulations[Benna et al.,2010] 20eV, respectively (consistent with Jia et al. [2008]) and andhybridsimulations[Mu¨ller et al.,2012]ofMercuryand can be explained (at least qualitatively) by two-fluid mag- thenallowedtofloat(withzeroradialderivative)thereafter netic reconnection physics. (incontrasttoJiaetal.[2008],whofixedthesevaluesatthe For the parameters described above, the Jovian magne- inner boundary). While Jia et al. [2008] surrounded their tosphere ion inertial length was d ≈ 450km = 0.17R . innerboundarywithaconductingshell(tomimictheiono- i G Convergence experiments in which we compared results sphere) and imposed zero bulk velocity at the solid surface at increasingly higher resolutions demonstrated that accu- inside this conducting shell (thus allowing magnetospheric rately capturing the Hall effect within the magnetopause convection to drive ionospheric convection), we allowed the X - 4 DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS (a) (b) (c) (d) Figure 2. WhiletheHalleffectdoesnothavemuchimpactonthelargescaleAlfv´enwingstructure, it has a dramatic impact on the pattern of field-aligned currents near the moon. Figures (a) and (c) show the resistive MHD case, while (b) and (d) show the Hall MHD case. Streamlines of the magnetic field projectedintotheplaneareshownin blue, andbulk velocitystreamlinesareshowningreen. Theblack dashedlineshaveslope±cos−1(V /V );whereV istheambientJovianco-rotationvelocity,andV is in A in A the Alfv´en speed based on the ambient Jovian density and magnetic field. The lower right panel shows the characteristic quadrupolar out-of-plane magnetic field pattern that characterizes Hall reconnection. These out-of-plane fields are supported by field-aligned currents that merge into the Alfv´en wings and extend all the way down to the moon’s surface. azimuthal components of the bulk velocity to float (zero Future work will incorporate a more realistic model of the radial derivative), while the radial component of the bulk interaction of magnetospheric plasma with Ganymede’s icy velocitywaschosensothatflowintothemoon’ssurfacewas surface. absorbed and flow out of the moon’s surface was zero. The Before running the Hall MHD case, we ran a resistive magneticfieldattheinnerboundarywastreatedbysplitting MHD case with identical boundary conditions but using an anomalous resistivity of the following form: η = η + offEarth’sdipolefieldandsolvingforthenon-potentialfield 0 η (J/J −1),limitedby0andη =2×1010m2/s(here, B (e.g., see Tanaka [1994]; Powell et al. [1999]). The total A C max 1 J isthemagnitudeofthecurrentdensity;η =1×109m2/s, fieldwasinitializedtoGanymede’sdipolefield(i.e.,B =0) 0 1 η =2×109m2/s and J =1×10−7Am−2 are constants) andthenB wasallowedtofloatwithzeroradialderivative A C 1 Aswewillseebelow,ourresultsforthiscasearecomparable thereafter. Given the large uncertainties in the ionospheric tothoseofJiaetal.[2008]andthusserveasagoodstarting conductivity–andthecomplexnatureofinteractionofpre- pointfromwhichtoassessimportanceoftheHalleffect. We cipitating electrons and ions with Ganymede’s atmosphere testedavarietyofboundaryconditions(notreportedhere), and icy surface (an interaction that involves both sputter- and found little impact on the final results. ing of neutrals and the production of secondary electrons FortheresistiveMHDsimulations,theBATS-R-UScode fromthesurface)–webelievethisisareasonablefirststep. was run in“local time stepping” mode (in which each grid DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS X - 5 Figure 3. In resistive MHD (left panel), the magnetospheric convection and field-aligned currents (FAC) are symmetric about the Jovian magnetospheric inflow direction, exhibiting the classic Dungey convection(greenarrowsonthedensityplaneandpurplearrowsontheinnersphere)andregion-1FAC (blue-whitecolorbarontheinnersphere)patterns. Inconstract,theHallsimulation(rightpanel)shows strong asymmetries in both the convection and FAC patterns. In the Hall simulation, Jovian magneto- spheric plasma appears to enter Ganymede’s magnetosphere along the sub-Jovian flank, populating the plasma sheet with Jovian magnetospheric plasma (in contrast to the resistive MHD case, in which the wake region is more or less devoid of Jovian magnetospheric plasma). Note the pronounced bending of reconnected field lines (green tubes) out of the reconnection plane in the Hall case. cellisadvancedatthelargesttimesteppossiblefornumer- which produces the classic quadrupolar out-of-plane mag- ical stability) until a quasi-steady state was reached; then, netic field pattern shown in the lower right panel of Figure “time-accurate”timesteppingwasused. FortheHallMHD 2 – generates a new system of field-aligned currents that runs,weusedtwodifferentinitialstates: 1)localtimestep- are most intense near the upstream and downstream edges pingasfortheMHDsimulations,2)thefinaltime-accurate of the polar cap. The global convection pattern also shows MHD state. We ran the simulations in time-accurate mode largeasymmetries,withJovianmagnetosphericplasmaflow- long enough to reach a quasi-steady state (∼10 minutes of ing into Ganymede’s wake region through the sub-Jovian simulated time was found to be sufficient for Ganymede’s flank. We demonstrate below that all of these effects are small magnetosphere). We obtained similar results in both directly driven by Hall electric fields within the upstream cases, giving us confidence that the final Hall MHD state magnetopauseanddownstreamtailcurrentsheetsand,thus, presentedbelowwasnotinfluencedbytheinitialcondition. should be present to some degree in all planetary magneto- spheres (e.g., Mercury and Earth) for which convection is 3. Results driven by collisionless magnetic reconnection. Figure 4 shows a closer view of the FAC and convection Figure 2 shows an overview of the Hall and resistive patternsinthepolarcap. TheresistiveMHDcaseshowsan MHD simulation results. The two upper figures show the anti-symmetricpatternofFACintothemoon’satmosphere, X (GphiO) component of the bulk velocity for the resis- withparallelcurrentdensitiesofabout0.05µ−A/m2 (con- tive(left)andHall(right)runs,showingthatthelargescale sistent with those reported by Jia et al. [2008, 2009]). In Alfv´en wing structure is not significantly modified by the theHallcase,theFACpatternisdistortedbythereconnec- Hall effect. Reconnection at the upstream magnetopause tionFACsystem,andnowthemostintensecurrentdensities and downstream tail current sheets, however, produces the appear in bands centered at the upstream and downstream characteristic quadrupolar out-of-plane magnetic field pat- edges of the polar cap. The polar cap convection pattern tern(lowerrightpanel). Theout-of-planefieldissupported in the Hall case shows localized acceleration channels near by a system of intense field-aligned currents (FAC) that theupstreamanddownstreampolarcapboundaries,bothof merge into the large scale Alfv´en wings far from the moon, whichareassociatedwiththebendingofthemagneticfield but these currents also extend all the way down to the linesoutofthereconnectionplanesinthemagnetopauseand moon’s surface. magnetotail current sheets (labelled “JxB” in the figure). Looking at the X−Y plane (Figure 3), however, reveals We will refer to these acceleration channels as “Harang-like that the Hall effect introduces significant asymmetries into discontinuities,”sincetheyaresimilarinappearancetothe the global convection and FAC patterns. In resistive MHD, HarangDiscontinuityobservedintheeveningsectorconvec- Jovian magnetospheric plasma flows around the upstream tion electric field of Earth’s ionosphere. magnetopausesymmetrically,producingadensitycavityde- TheHallreconnectionphysicsisconfinedtod scalelay- voidofJovianmagnetosphericplasmainGanymede’swake. i ersand,asshowninFigure2,haslittleimpactonthelarge This is the classic Dungey [Dungey, 1961, 1963] convec- scale Alfv´en wing structure. However, Hall electric fields tioncycle,drivenbymagneticreconnectionattheupstream magnetopause and downstream tail current sheets. Asso- appear to have a dramatic impact on the global convection ciated with this symmetric convection pattern is an anti- pattern in the X −Y plane. Figure 5 shows cuts of cur- symmetric pattern of FAC, most pronounced on the flanks rentdensitymagnitudeandbulkvelocitystreamlines(green andvanishingattheupstreamanddownstreamedgesofthe linesandarrows)intheX−Y planefortheresistiveMHD polar cap. run (left panel) and the Hall run (right panel). The MHD In contrast, in the Hall MHD simulation Jovian magne- case shows the classic Dungey convection pattern, with tail tospheric plasma enters Ganymede’s magnetosphere along reconnection driving flow jets moonward and tailward from the sub-Jovian flank, filling Ganymede’s wake with Jovian anXlineorientedmoreorlessalongtheY axisabout2RG magnetospheric plasma. The bending of the reconnected downstream of the moon. Note the symmetric pattern of field lines (green tubes) out of the reconnection plane – Kelvin-Helmholtz (KH) waves on the flanks, driven by the X - 6 DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS JxB JxB Harang-like Discontinuities Figure 4. The resistive MHD polar cap convection pattern shows the classic symmetric Dungey cycle, driven by magnetic reconnection at the upstream magnetopause and tail current sheets. Plasma flows uniformlyoverthepolarcapfromtheupstreamsidetothedownstreamside,andtheFACpatternshows the familiar relationship between flow shear (responsible for magnetic field line bending in the magne- tosphere) and current density. In the resistive MHD case, the current densities are most pronounced in the flanks. In contrast, the Hall MHD convection pattern exhibits large asymmetries, driven by field linebendingassociatedwithHallreconnection. ThefieldlinebendingproducesnewJ×Bforcesonthe ions, generating new “Harang-like” discontinuities in the convection pattern. flowshearbetweenthereconnectionreturnflowandtheJo- 4. Comparison with Galileo magnetometer vian co-rotation inflow. observations IntheHallcase(rightpanelofFigure5),largescalebulk flow channels appear, flowing in the −Y direction within To test the model predictions described above, we probe themagnetopauseandmagnetotailcurrentsheets(magenta our simulated magnetosphere with a virtual Galileo probe arrows in the figure). These jets produce an asymmetric corresponding to the G8 flyby. The G8 flyby crossed the pattern of KH waves on the upstream magnetopause, with upstreammagnetopauseatabout0.75R abovetheX−Y G larger amplitude oscillations appearing on the sub-Jovian plane. Since upstream magnetopause reconnection should sideofthemagnetopause. Qualitatively,theasymmetrycan be occurring continuously and more or less steadily (given be explained by the asymmetry in the flow shear between the steady strongly southward JMF conditions), the G8 in- the incoming Jovian co-rotation flow (blue arrows) and the boundmagnetopausepassshouldhavebeenanidealoppor- upstream magnetopause current sheet jet (magenta arrow). tunity for the Galileo magnetometer (see the overview by Jovian magnetospheric plasma enters Ganymede’s magne- Kivelson et al.[1998])toobservetheout-of-planeHallelec- tosphere through the sub-Jovian flank, returning along a tric field in the exhaust region above the reconnection site. thickented sub-Jovian boundary layer to join with the up- Not surprisingly, previous comparisons with resistive MHD stream magnetopause jet. The resulting high flow shear on by Jia et al. [2008] did not see the expected Hall fields, but thesub-Joviansideofthemagnetopauseproduceslargeam- theydidnotethepresenceoflargeamplitudemagneticfield plitude KH waves there. fluctuations near the magnetopause crossings. Later, Jia A similar effect explains the patchy appearance of the etal.[2010]usedresistiveMHDsimulationstointerpretthe tailcurrentdensityintherightpanelofFigure5: KHwaves observed magnetic field fluctuations as the result of bursty drivenbythetailionjetcausethecurrentsheettoundulate reconnection producing large scale flux rope structures, or inandoutoftheX−Y plane,producingtheappearanceof Flux Transfer Events (FTEs), similar to those observed at currentdropoutsintheplane. Figure6showshowtheseKH Earth’smagnetopause(seethereviewby[Elphic,1995]). In waves develop in the tail current sheet. The arrow glyphs what follows, we argue that these large scale magnetic field showtheplasmabulkvelocity,paintedbymagnitude,show- fluctuationsontheinboundcrossingareinfactsteadystate ing how plasma flowing into the tail current sheet interacts structures associated with collisionless reconnection. withthecurrentsheetjettoproducelargeflowshearonthe Figure 7 compares observed (blue lines) and simulated anti-Jovianside,wheretheKHwaveamplitudesarelargest. (greenlines)magneticfieldcomponentsalongtheG8flyby. DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS X - 7 High Flow Shear Low Flow Shear Figure5. TheHalleffectproduceslargeasymmetriesinGanymede’sconvectionpattern. Theleftpanel shows the classic Dungey convection pattern for the resistive MHD case, in which plasma is accelerated bothmoonwardandtailwardawayfromanXlinemoreorlessalignedwiththeY axis. IntheHallcase (rightpanel),fastionjetswithintheupstreammagnetopauseandtailcurrentsheetsallowJovianmagne- tosphericplasmatocirculatethroughoutGanymede’smagnetosphere,enteringfromthesub-Jovianflank andreturningalongathickenedsub-Jovianboundarylayertojoinwiththeupstreammagnetopausejet. This asymmetric circulation pattern produces a corresponding asymmetric pattern of Kelvin-Helmholtz waves on the upstream magnetopause. Figure 6. The Hall effect produces an ion jet in Ganymede’s magnetotail current sheet. This in turn produces a large flow shear on the anti-Jovian side of the current sheet (toward the right in the plot). Here, we show a cut plane at X = 2.5 (Y is horizontal and Z is vertical), showing how the resulting Kelvin-Helmholtz (KH) waves cause an undulation of the current sheet that appears as small scale cur- rent density drop-outs in the right panel of Figure 5. The arrows show bulk velocity color coded by magnitude. The top two panels show the resistive MHD results, and tween the simulated and actual magnetopause shapes may the bottom two panels show the Hall results. The left pan- produce observable systematic differences in the magnetic field components in the closed field line region (which be- elsshowthemagneticfieldcomponentsalongthepublished come distorted near the magnetopause). To explore this G8 trajectory. While there is good qualitative agreement, effect,weintroducedasmalloffsettothepublishedG8tra- the simulated probe shows a somewhat larger BX than ob- jectory(+0.05RGintheXdirection,and+0.05RGintheZ served. This is not surprising, since small differences be- direction). Thisoffsetwaschosentoimprovetheagreement X - 8 DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS Figure 7. ComparisonsofoursimulationswiththeGalileomagnetometerobservationsfortheG8flyby show good overall agreement. The left panels show the comparison using the published G8 flyby coor- dinates. Green lines show the simulation results, and blue lines show the data. The right panels show theresultsofaddingtothesimulatedprobeanoffsetof+0.05R intheX andZ positioncomponents. G The top panels show the resistive MHD case, and the two bottom panels show the Hall MHD case. between simulated and observed B components, and the notattemptedtoidentifyitinFigure8(thoughitisobvious X offsettrajectorywillbeusedinallfurtherdiscussionbelow. in Figure 9). For reference, the GphiO magnetic field com- Because of the G8 trajectory crosses the magnetopause ponentsarereproducedinthetoptwopanels,withresistive at a finite Y location, the reconnection plane is not aligned MHD on the left and Hall MHD on the right. As expected, with the GphiO X −Z plane. Thus, the Hall out-of-plane transformingthedataintoinboundmagnetopauseBNCco- field would be expected to produce large perturbations in ordinateseliminatesthenegativeB excursion,leavingonly both the X and Y components. However, rotating into a X anenhancedB excursion. Thisisconsistentwithwhatwe “Boundary Normal Coordinate” (BNC) system (where the Y observe in the Hall simulation (right panels of Figure 8): new X unit vector points along the magnetopause outward The small negative B perturbation in the top right panel normal, the Z unit vector points northward tangent to the X at about 15.8hours has been transformed away in the bot- magnetopause, and the Y unit vector completes the right- handedsystem)wouldbeexpectedtoeliminatethepertur- tomrightpanel,andthesmallpositiveBY excursioninthe bation in the new X component, leaving only the new Y top right panel has been enhanced in the lower right panel. (out of the local reconnection plane) component. This is Similarly,whenviewedintheinboundBNCcoordinatesys- exactly what we observe, as we show now below. tem, a large positive BX perturbation appears on the out- Figure 8 shows the data transformed into BNC coor- boundcrossing. Wehavelabelledtheseperturbations“Hall dinates corresponding to the inbound outer current sheet Fields” in Figure 8. crossing,andFigure9showsathree-dimensionalviewofthe While these features are somewhat difficult to see in the offset G8 flyby trajectory (green line) through our resistive line plots of Figure 8, they appear very clearly in the 3D (toppanel)andHall(bottompanel)simulations. Wedeter- view of Figure 9. The resistive MHD case in the top panel mined the BNC normal direction by inspection of this plot of Figure 9 shows that there is no field line bending out of for the inbound magnetopause crossing. The corresponding the reconnection plane as the simulated probe crosses the coordinateaxesareshowninwhite. Notethattheaxisnear magnetopauseboundarylayer. Incontrast,Hallcaseinthe theoutbound(upper)crossingissimplytranslatedfromthe bottom panel shows clearly that there is significant bend- inbound (lower) crossing, to simplify the interpretation of ing out of the reconnection planes of both the inbound and Figure8,whichplotsthecomponentsinthesingleinbound outbound crossings. For the inbound crossing, it is obvi- current sheet BNC coordinate system. The yellow rectangles in Figure 8 show where the simu- ous that the perturbed field is predominantly in the BNC latedprobeentersandexitstheoutermagnetopausecurrent Y direciton, while the perturbed field is in the X direction sheet,whichappearsasanobviousreversalintheB com- for the outbound crossing when viewed in the local BNC Z ponent. Thesecondcurrentsheetcrossingislessobviousin coordinate system for the inbound crossing. This is exactly both the simulations and the data and, therefore, we have what is observed in the data. DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS X - 9 Hall Fields Figure 8. The Hall perturbations become particularly clear in Boundary Normal Coordinates (BNC). Here, the left panels show the resistive MHD case, and the right panels show the Hall case, with yel- low rectangles indicating the boundaries of the outer magnetopause current sheet in the simulations. The perturbations marked “Hall Fields” in the lower right panel show the out-of-plane magnetic field structure in the reconnection exhausts as they are crossed by the simulation probe. Note that similar structures are observed in the actual magnetometer data. AnotherinterestingfeatureoftheG8Galileomagnetome- 5. Physics of the ion drift belts ter data is the series of large amplitude waves that appear (most clearly in the magnetic field magnitude) as Galileo is While the appearance of the out-of-plane magnetic field exiting Ganymede’s magnetosphere on the sub-Jovian side. isanexpectedandwell-understoodconsequenceoftheHall These waves do not appear in the MHD simulations, but effect,thedramaticdistortionofGanymede’sglobalconvec- they do appear in the Hall simulations (compare the up- tion pattern was a surprise to us. While the sources of the per left and upper right magnetic field magnitude traces new ion jets are confined to the upstream and tail current in Figure 8). Figure 9 shows that the wave-like feature in sheets, they clearly have a global impact on the structure thesimulatedoutboundcrossingiscausedbytheKHwaves of Ganymede’s magentosphere. The most obvious effect is that are driven by enhanced flow shear on the sub-Jovian the appearance of a new global system of “ion drift belts” thathelpcirculateJovianmagnetosphericplasmathrougout sideoftheupstreammagnetopause(asarguedaboveinthe Ganymede’s magnetosphere. The most striking difference context of Figure 5). To our knowledge, these large ampli- between the classic Dungey resistive MHD pattern and the tude wave-like perturbations observed on the G8 outbound new drift belt pattern is that Ganymede’s wake should be magnetopausecrossinghavenotyetbeeninterpretedasKH filledwithJovianmagnetosphericplasmainathin(ioniner- waves; our interpretation is that these KH waves – appear- tialscale)layeraroundZ =0. Anotherimportantglobalef- ing on the sub-Jovian side but not on the anti-Jovian side fectistheappearanceofasignificantlythickenedsub-Jovian – are a new feature predicted by our Hall model. They boundary layer. are driven by the upstream magnetopause ion jet which, in Figure 10 illustrates our new ion drift belts model of turn, owes its existence to ion-scale structure of the recon- global convection in Ganymede’s magnetosphere. The fig- nection site. Thus, we argue that intermittent upstream ure shows another view of the X −Y cut shown in Figure magnetopause reconnection (and associated flux ropes or 5, this time annotated with a cartoon of the flow topology. FTEs) is not required to explain the large amplitude mag- TheredarrowsshowtheJovianmagnetosphericflow;theor- netic field perturbations observed on the G8 inbound and angeandmagentaarrowsshowtheupstreammagnetopause outboundmagnetopausecrossings. Thesestructurescanbe and tail current sheet ion jets, respectively; the green ar- explained as consequences of steady collisionless reconnec- rows show how plasma of Jovian magnetospheric origin cir- tion: 1)theclassicout-of-planemagneticfieldbending,and culates through Ganymede’s wake region and then back 2) the ion drift that supports the upstream magnetopause upstream, forming a thickened sub-Jovian “double mag- current sheet. Neither of these effects is present in resistive netopause” structure (note that Jupiter is somewhere be- MHD simulations. lowthebottomofthefigure,co-rotatingcounter-clockwise). X - 10 DORELLIETAL.: HALLMHDGANYMEDESIMULATIONS X Y X Y X Y X Y Figure 9. Simulations reveal that Ganymede’s magnetopause has a bifurcated current sheet structure at the location of the G8 flyby (green line). In the resistive MHD case, the current sheet is relatively smooth,andtherearenolargeout-of-planemagneticfieldexcursionsasthesimulatedprobecrossesthe boundarylayerbetweenthecurrentsheets. IntheHallcase,however,theasymmetricpatternofKelvin- Helmholtz (KH) waves is apparent, as are the large out-of-plane excursions of the magnetic field (blue field lines). In both panels, the white X −Y axes show the orientation of the inbound magnetopause crossing Boundary Normal Coordinate (BNC) system. The yellow circles show stagnation points of the flow. As a rectiontotherightoftheY axisandinthepositiveX direc- parcelofJovianmagnetosphericplasmaentersGanymede’s tion to the left of the Y axis. These in-plane current loops wake region on the sub-Jovian flank (1), it splits, with one supportthequadrupolarout-of-planecurrentsystemshown pathmergingwiththetailionjet(2,2’)andtheotherpath schematically by the red and blue ovals, and the resulting circulating back upstream (3) where it merges with the up- J ×B force accelerate ions out of the reconnection plane. This Hall acceleration mechanism illustrated schematically stream magnetopause jet and collides with the incoming in the right panel. Jovian plasma (a) (generating KH waves in the process). Wecanestimatethespeedoftheupstreammagnetopause Meanwhile, the upstream jet (4) collides with the tail jet ion jet by writing down the Y (GphiO) component of the (2’)atstagnationpoint(c’),wheremoreKHwavesarepro- momentum equation: duced on the anti-Jovian flank. The appearance of the Hall-induced ion drift belts is an easilyunderstoodconsequenceoflocalforcebalancenearthe ∂V J B ρV Y ≈− X Z (1) reconnectionXlines. Figure11illustratesthephysicsofthe X ∂X c ion out-of-plane acceleration due to Hall currents in the re- connection plane. In the left panel, the cyan box is the ion where the Hall current is given by Amp´ere’s law: JX ≈ diffusionregion–theregionoverwhichtheionandelectron −(c/4π)∂BY/∂Z, and BY is the amplitude of the out-of- planequadrupolefieldstructure. We approximateequation bulk velocities become de-coupled. In this region, electrons (1) as follows: leadtheionsintotheelectrondiffusionregion(yellowbox), producing an in-plane current in the positive Y direction abovetheX axisandinthenegativeY directionbelowthe V V B B X axis (here, X and Y now refer to the outflow and inflow ρ X Y ≈ Y Z (2) δ ∆ 4π i i directions in the reconnection plane, respectively). Simi- larly, electrons lead the ions out of the electron diffusion where δ and ∆ are the thickness and length, respectively, i i region, producing an in-plane current in the negative X di- of the ion diffusion region. Assuming ρ is approximately