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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  10 A. The power delivered to the Jovian auroral zone and to Ganymede’s polar surface via energetic charged particle bombardment is about 6  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  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  B þ r_v; ð2Þ @t @B ¼rÂðÞÀrv  B h  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 corre- sponding 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  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  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.
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