Resistive MHD Simulations of Ganymede's Magnetosphere 2

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A12, 1491, doi:10.1029/2001JA005072, 2002

Resistive MHD simulations of Ganymede’s magnetosphere 2. Birkeland currents and particle energetics Wing-Huen Ip1 and Andreas Kopp Max-Planck-Institut fu¨r Aeronomie, Katlenburg-Lindau, Germany

Received 27 August 2001; revised 22 January 2002; accepted 11 April 2002; published 31 December 2002.

[1] The Birkeland current flows generated by Ganymede’s magnetospheric interaction with the Jovian magnetosphere are simulated by using a resistive MHD code. The total 5 field-aligned current is estimated to be Ik 6.6 Â 10 A. The power delivered to the Jovian auroral zone and to Ganymede’s polar surface via energetic charged particle bombardment is about 6 Â 109 W. Ions and electrons could gain as much as 2.9–48 keV at the reconnection site of the magnetopause. The production rate of oxygen and water 25 26 molecules from the associated ion sputtering effect (QII 10 À 10 molecules/s, QI 1–4 Â 1026 molecules/s) can be derived from polar cap precipitation of the ambient Jovian energetic ions. Because Ganymede’s Birkeland current system is highly time-variable in response to the Jovian magnetic field variations, the ‘‘footpoints’’ of the accelerated ion beams could have rapid changes and hence the motion of the hotspots of the oxygen airglow emission as observed by the Hubble Space Telescope. INDEX TERMS: 5737 Planetology: Fluid Planets: Magnetospheres (2756); 6218 Planetology: Solar System Objects: Jovian satellites; 7827 Space Plasma Physics: Kinetic and MHD theory; 7843 Space Plasma Physics: Numerical simulation studies; KEYWORDS: Birkeland currents, Ganymede, Jupiter, magnetosphere, MHD simulations, satellite magnetosphere interactions

Citation: Ip, W.-H., and A. Kopp,Resistive MHD simulations of Ganymede’s magnetosphere, 2, Birkeland currents and particle energetics, J. Geophys. Res., 107(A12), 1491, doi:10.1029/2001JA005072, 2002.

1. Introduction orientation of the external Jovian magnetic field. To some extent, this effect could be related to the time variability of [2] An important result of the Galileo mission to the the oxygen airglow emission at the polar regions of Gany- Jovian system concerns the discovery that Ganymede, the mede [Feldman et al., 2000; see also Hall et al., 1998]. This third Galilean satellite, possesses an intrinsic magnetic field is because the contraction and expansion of Ganymede’s [Kivelson et al., 1996, 1998, and references therein]. This is polar caps could control the total flux of precipitating the first case of a magnetosphere found inside another energetic charged particles from the Jovian magnetosphere. magnetosphere (and yet inside the heliosphere). Because In turn, the sputtering rate of the oxygen atoms and of the nature of the sub-magnetosonic Jovian plasma flow in molecules at the icy surface will be modulated. Ganymede’s vicinity, the interaction of these two magneto- [3] As in the case of the Jupiter-Io interaction [Goldreich spheres can be described – locally and to a first-order and Lynden-Bell, 1969; Neubauer, 1980; Herbert, 1985; approximation – by the superposition of the vacuum dipole Kopp et al., 1998], the electrodynamical coupling of Gany- field of Ganymede to a uniform Jovian magnetic field. mede’s magnetosphere with the Jovian magnetosphere is However, because of the dynamic pressure of the corotating facilitated by a current system connecting Ganymede to plasma such vacuum field picture must be subject to Jupiter’s ionosphere which may be confirmed by the possible modification. Kopp and Ip [2002], Paper I hereinafter, have detection of spotty Jovian auroral emission at the footpoint of employed a numerical model to study the three-dimensional Ganymede’s flux tube by the Hubble Space Telescope MHD interaction process of Ganymede. In that work, the [Clarke et al., 1999, 2001; J.T. Clarke, private communica- main focus is on the topology of the magnetic field lines and tion, 2001]. It is the purpose of this work to provide a its time variation under different local plasma conditions. preliminary description of Ganymede’s magnetospheric cur- They have shown that, as expected, the satellite magnetic rent system and some of its potential physical consequence. field lines are slightly stretched out on the downstream side. Note that Feldman et al. [2000] and Eviatar et al. [2001a] Furthermore, they showed that the magnetospheric config- have previously invoked the presence of Birkeland currents uration can be significantly changed as a result of the to explain the excitation of Ganymede’s ultraviolet auroral

1 emission. We have investigated such electrodynamical effect Now at Institute of Astronomy and Institute of Space Science, National by using a different approach which is capable of providing a Central University, Chung-Li, Taiwan. three-dimensional view of the Birkeland current system. In Copyright 2002 by the American Geophysical Union. section 2 we will briefly describe the simulation procedure. 0148-0227/02/2001JA005072$09.00 In section 3, the numerical results will be discussed. In the

SMP 42 - 1 SMP 42 - 2 IP AND KOPP: BIRKELAND CURRENTS IN GANYMEDE’S MAGNETOSPHERE final section, we will consider possible effects of such current flows on Ganymede’s ionosphere and the related surface-sputtering process.

2. Model Calculations

[4] Details about the numerical procedure can be found in Paper I. The numerical code integrates the basic equations of the resistive MHD by means of a leapfrog scheme. In a resistive regime, the induction equation becomes parabolic and is integrated by a Dufort-Frankel scheme. As usual, r, v and P denote plasma pressure, velocity, and gas pressure of an ideal gas with adiabatic index g = 5/3. Further quantities are B, the magnetic field, j, the electric current density and h, the resistivity. If we write s = rv for the momentum density, the (unnormalized) equations are: @r ¼ÀrÁs þ r_; ð1Þ @t @s ¼ÀrÁðÞÀrsv P þ j Â B þ r_v; ð2Þ @t @B ¼rÂðÞÀrv Â B h Â j þ hÁB; ð3Þ @t @P r_ ¼ÀrÁðÞþPv ðÞg À 1 PrÁv þ hj2 þ P : ð4Þ @t r The source terms r_, r_v and (r_/r) P refer to Ganymede’s mass loading, where the last two terms have been neglected here (see Paper I). The coordinate system is the standard system for satellite-magnetosphere interactions, i.e. x is the flow direction, y points towards Jupiter and z is the main direction of Jupiters’s background field. As described in Paper I, we use an O6 model for Jupiter’s background with a superimposed field which is used to fit the Galileo data. Ganymede’s field is a slightly tilted dipole according to Kivelson et al. [1996]. The plasma parameters are the same as in Paper I.

3. Current Flows

[5] The nominal case when the dipole moments of Jupiter and Ganymede are both parallel to the z-axis is shown in Figure 1. Figure 1a depicts the configuration of the Gany- median magnetic field geometry and Figure 1b is for the symmetrical pattern of the electrical current flows in the y-z- plane, perpendicular to the plasma flow. It can be seen that the magnetopause at the equatorial region and the corresponding magnetic field surface separating the open and closed field regions define a Birkeland current system. In our simulations, the current density j is computed by using the relation rrÂB = m0j for corresponding values of the magnetic field at different grid points. As expected, the largest magnetic field changes can be found at the region (i.e., the magnetopause) where the magnetic field lines reconnect [Kivelson et al., 1998]. The field-aligned current originated at the magnetopause will connect to Ganymede’s polar ionosphere. Because the atmosphere of Ganymede is Figure 1. (a) Magnetic field lines and (b) field lines very tenuous it is not certain whether its electrical con- connected to Ganymede of the current density in the y-z- ductivity would be large enough to support the current flow. plane for the nominal case of two parallel dipoles, (c) the Eviatar et al. [2001a] suggested that the so-called pickup 2 field-aligned current density in nA/m at z =2R . conductivity generated by the gyro-motion of the new G pickup ions [Ip and Axford, 1980; Goertz, 1980] could be IP AND KOPP: BIRKELAND CURRENTS IN GANYMEDE’S MAGNETOSPHERE SMP 42 - 3 effective. A pair of (upward and downward) Birkeland magnetic field. That is, from rÂB = m0j we have j Á B/ currents will thus be beamed towards the Jovian ionosphere. m0h where ÁB is the magnetic field difference (ÁB 2 B0), Figure 1c shows the distribution of the field-aligned (paral- j is the current density. The integral of j across the magneto- lel) current density in a cross section of the Ganymede flux pause layer is J jh ÁBm0. Therefore, the total current 2 tube. The peak current density (jk) is 17.8 nA/m and the generated at the magnetic field reversal zone will be I 5 total current flow can be estimated to be 6.6 Â 10 A from ÁBW/m0. Now, given a potential (È) across the magneto- the present numerical results. In comparison, the total pause, the power to be delivered to Ganymede’s magneto- Birkeland current of Io is about 3 Â 106 A according to sphere via the Birkeland currents will be: Neubauer [1980]. In our work the spatial resolution is Z limited by the minimum grid size used (0.085 RG 224 P jEd3 x km, 1 Ganymede radius, RG = 2634 km). It is therefore likely that the actual current flows could be more restricted I È Á BWÈ=m0 ð5Þ in their distribution and hence the peak value of jk should be higher than given here. We will return to this point later. [6] At Ganymede’s orbital distance, the Jovian magnetic With a corotating plasma flow speed of v0 150 km/s and a field is subject to strong modulation by the warping of the field strength of B0 120 nT, the corresponding convective plasma current sheet. Kivelson et al. [1998] have shown electric field will be E = v0B0 0.018 V/m and the total how variable the Jovian magnetic field direction could be potential across the magnetopause will be È 47 kV if the during four different close flybys of the Galileo spacecraft at approximate dimension of the cross-tail electric field is L 9 Ganymede. Figure 2 compares the patterns of the Birkeland 2RG. The corresponding value of P will be 6.0 Â 10 W current systems for the nominal case and the three encoun- for ÁB 2B0 240 nT and W 0.25 RG. ters G2, G7 and G8. Figure 2a shows how the orientation of [8] The total flux of magnetospheric charged particles the field-aligned current along the flux tube could swing drifting into the reconnection region is N_ n0vD WL where around. The cross-sectional plots in Figure 2b are even n0 is the magnetospheric particle density and vD is the more instructional in the sense that they show how asym- plasma drift velocity. Because vD E/B0, N_ n0W È/B0, metric and localized jk could be at G2 and G7. This implies the total flux varies between a minimum value of 7.8 Â that the Birkeland currents projected back to Ganymede’s 1023 particles/s and a maximum value of 1.3 Â 1025 À3 auroral zone could be highly filamentary in nature. Could particles/s if n0 3–50 cm [Frank et al., 1997]. This such features be related to the rapid time-variations (i.e., flux variation will probably be in tune with the oscillation from orbit to orbit (1.6 hours interval) of the Hubble of the Jovian current sheet relative to Ganymede. Hence the Space Telescope) of the so-called hotspots of the oxygen average kinetic energy per particle obtained after the airglow emission detected by Feldman et al. [2000]? reconnection process at the magnetopause [Kivelson et 2 [7] As one of the two possible electron acceleration al., 1998] will be EP/N_ (2B0/m0)/n0 2.9À48 keV. mechanism (the other one is stochastic heating of iono- This is interesting because this energy range is sufficient for spheric plasma waves), Eviatar et al. [2001a] described how (a) the production of energetic electrons to generate the electrodynamical interaction of Ganymede’s magneto- enhanced ionization of Ganymede’s oxygen atmosphere; sphere with the Jovian magnetic field should lead to the and (b) the production of energetic ions to generate formation of a field-aligned electric field (Ek) and hence enhanced surface sputtering of Ganymede’s icy surface. If charged particle acceleration. The present MHD formulation most of the ions of magnetopause origin are protons, the also permits the existence of parallel electric fields [e.g. sputtering yield Yi 10 [Shi et al., 1995] and the source Kopp, 1995, and references therein]. However, the numer- strength (QI) of the sputtered oxygen atoms and water ical computation is complicated and highly dependent on a molecules will be of the order of 1025 –1026 neutrals/s. 26 number of uncertain parameters (i.e., the resistivity of the The surface sputtering rate of QII 1–4 Â 10 molecules/ magnetospheric plasma). Because the Birkeland current s (termed component II) because of the Jovian magneto- system is basically generated by the magnetic field recon- spheric charged particles precipitating into Ganymede’s nection at the upstream magnetopause, it is useful to polar cap [Ip et al., 1997] might be compared to the 25 26 compute the maximum energy to which charged particles above-mentioned source strength (QI 10 –10 mole- can be accelerated within the reconnection region. The cules/s). Of special note is that the sputtering process of the actual acceleration process depends, however, on the micro- second component which is regulated by the Birkeland physics involved [cf. Kopp et al., 1998]. Because we are currents could be highly localized at the boundary of the merely interested in a rough estimate, the following ana- polar cap as illustrated in Figure 2. This effect will further lytical model may be applied to Ganymede’s magnetosphere amplify the appearance of hotspots in the oxygen airglow in analogy to the terrestrial magnetosphere [e.g., Cowley, emission. Lastly, it is interesting to note that, in spite of 1980], where the magnetopause is described by a flat differences in the details of the sputtering calculations (i.e., rectangular structure of length L (in the horizontal direction) the omission of low-energy ions by Ip et al. [1997]), more and width W (in direction parallel to the magnetic field). recent work by Paranicas et al. [1999] and Cooper et al. The Jovian magnetic field and the intrinsic magnetic field of [2001] all reported a total gas production rate of a few times Ganymede (both assumed to be locally antiparallel and of 1026 molecules/s. the same magnitude B0) are separated by a thin current sheet [9] Feldman et al. [2000] mentioned that a puzzle of the of thickness h. A simple way to estimate the possible energy observed oxygen airglow of Ganymede has to do with the delivered to Ganymede is by computating the total current absence of limb-brightening effect which is to be expected flow created at the magnetopause via reconnection of the in an extended source region in the atmosphere. In this SMP 42 - 4 IP AND KOPP: BIRKELAND CURRENTS IN GANYMEDE’S MAGNETOSPHERE IP AND KOPP: BIRKELAND CURRENTS IN GANYMEDE’S MAGNETOSPHERE SMP 42 - 5

Figure 3. (a) Plasma flow in the x-z-plane for the nominal case. The color indicates the amount of the velocity in km/s. (b) Same quantity, but in the equatorial plane. respect, we would like to mention the possible optical relatively small so that the electron-impact induced UV excitation of sputtered oxygen atoms at impact production. radiation is confined to the near-surface region. Ion-beam induced ultraviolet luminance has been observed in ion sputtering experiments on oxygen-containing surfaces [Johnson and Quickenden, 1997; Lee and Lin, 2001]. It 4. Plasma Flows is of interest to investigate whether significant amount of [10] Frank et al. [1997] reported the detection of a strong optical luminance could be excited in a similar fashion. proton outflows during the G1 crossing of Ganymede’s Since such emission should occur very close to the surface, polar cap by the Galileo Orbiter. The flow speed along the no limb-brightening effect is hence created. On the other magnetic field was estimated to be as high as 70 km/s. A hand, a simple solution to this problem is that the scale reinterpretation of these Galileo measurements by Vasy- height of the putative molecular oxygen atmosphere is liunas and Eviatar [2000] and Eviatar et al. [2001b] has

Figure 2. (opposite) (a) Current density (arrows) and the field-aligned current density (grayscale, in nA/m2, the maximum 2 value is 28 nA/m )inthey-z-plane (±5 RG in each direction) for the nominal case (upper left panel), G2 (lower left panel), G7 (upper right panel) and G8 (lower right panel). (b) The field-aligned current density at z =1.2RG for these four cases. SMP 42 - 6 IP AND KOPP: BIRKELAND CURRENTS IN GANYMEDE’S MAGNETOSPHERE led to the identification of the ion composition to be O+ and airglow emission. From this, we can probe and image this pthatffiffiffi the flow speed is correspondingly reduced by a factor of unique magnetosphere. A (=4) to 18 km/s, where A is the atomic mass number. Such ion outflow could be similar to the terrestrial polar [14] Acknowledgments. We thank the two reviewers for very useful wind in which the ionospheric plasma is being accelerated comments and suggestions. This project was supported by the Bundesmi- nisterium fu¨r Bildung und Forschung (BMBF) through the German Space away by ion heating and magnetic mirroring force [Retterer Agency, DLR (Bonn, Germany), under 50 QJ 94010 and the National et al., 1994]. If the convective electric field in the polar cap Council of Taiwan under NSC 89-2111-M-008-017. region is reduced by a factor a, the gyro-speed of the newly [15] Michel Blanc and Lou-Chuang Lee thank John F. Cooper and another reviewer for their assistance in evaluating this paper. created pickup ions will have an initial value of v? av0 where v0 150 km/s. For a 0.25 as indicated by the energetic charged particle observations at G1 [Williams et References al., 1997], the initial thermal velocity of the new ions at Clarke, J. T., J. Ajello, G. Ballester, L. Ben Jaffel, J. Connerney, J. C. Ge´rard, R. Gladstone, W. Pryor, K. Tobiska, J. Trauger, and H. Waite, creation will be v? 40 km/s. 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