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MHD Simulations of Current Systems in Planetary Magnetospheres: Mercury and Saturn

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MHD Simulations of Current Systems in Planetary Magnetospheres: Mercury and Saturn To appear in: AGU Monograph on Magnetospheric Current Systems MHD Simulations of Current Systems in Planetary Magnetospheres: Mercury and Saturn Tamas I. Gombosi∗ International Space Science Institute, Hallerstr. 6, CH-3012 Bern, Switzerland Darren L. DeZeeuw, Clinton P.T. Groth, Kenneth C. Hansen, Konstantin Kabin, Kenneth G. Powell The University of Michigan, Ann Arbor, Michigan Abstract. The study of planetary magnetospheres can provide valuable insight into a wide range of phenomena and processes acting in the terrestrial magnetosphere. This paper uses global MHD simulations to investigate the large scale configuration and current systems in two very different planetary magnetospheres. Mercury has a weak intrinsic magnetic moment and it is exposed to a high density, very variable solar wind. It has no ionosphere or plasmasphere and its slow rotation is unimportant. Under typical conditions in the solar wind, Mercury’s magnetosphere is very “open”, the last closed field-line being at a latitude of 40◦–50◦. At the other end of the spectrum, the interplay between solar wind and planetary rotation driven processes, combined with strong plasma sources, generates new and interesting configurations and current systems in the magnetosphere of Saturn. In particular, our simulations predict two current systems connecting plasma sources in the rings/icy satellites region and in Titan’s torus to the high-latitude regions of Saturn’s ionosphere. 1. Introduction spheric configuration and associated current systems in two vastly different planetary magnetospheres. Among magne- The planets Mercury, Earth, Jupiter, Saturn, Uranus and tized planets Mercury has the weakest intrinsic magnetic Neptune possess significant intrinsic magnetic fields. Since field (its magnetic moment is about 3,000 times smaller than the underlying plasma-physical processes are the same in the terrestrial magnetic moment), while Saturn’s magnetic these magnetospheres, qualitative or quantitative analogies moment is the second largest among all solar system planets with the terrestrial magnetosphere can help us to understand (580 times larger than the magnetic moment of Earth). Mag- poorly sampled planetary magnetospheres. Conversely, sim- netospheric current systems in these two planetary magneto- ilarities in planetary magnetospheres, in spite of differences spheres clearly exhibit many of the most interesting features in configurations, plasma and energy sources and sinks, can relevant to Earth and many astrophysical magnetospheres. help us to understand better the full range of phenomena and This paper uses global MHD simulations to study the processes in the Earth’s magnetosphere. Planetary magneto- large-scale configuration of the Hermean and Kronian mag- spheres help us to extend observed magnetospheric phenom- netospheres. The high performance BATS-R-US simulation ena into different parameter regimes. The study of magne- code has been developed at the University of Michigan and tospheric current systems is a very powerful tool in gaining it solves the equations of ideal magnetohydrodynamics on a global perspective of the multiscale coupling between var- an adaptively refined grid [Powell et al., 1999]. The code ious regions in planetary magnetospheres. has been successfully used to simulate solar system plasmas In this paper we investigate the large-scale magneto- ranging from the 3D expansion of solar wind [Groth et al., 1999] to the interaction of the heliosphere with the magne- ∗On leave from the The University of Michigan, Ann Arbor, Michigan 1 2 GOMBOSI ET AL. tized interstellar medium [Linde et al., 1999], to the mag- formulation B1 does not have to be small, therefore this de- netospheres of Earth [Gombosi et al., 1998; 1999], Venus composition is completely general. [Bauske et al., 1998], Saturn [Hansen et al., 1998], comets [Gombosi et al., 1996; Haberli¨ et al., 1997], and to the 3. Mercury magnetospheric interaction of planetary satellites, such as Io [Combi et al., 1998], Europa [Kabin et al., 1998a] and Titan Mercury’s magnetosphere is surprisingly poorly studied, [Kabin et al., 1998b]. and consequently, poorly understood. It has been visited only by Mariner 10, which encountered Mercury three times 2. Model between March 1974 and March 1975 (however, one of the three encounters was so far upstream that it completely The BATS-R-US (Block Adaptive-Tree Solar-wind Roe- missed the magnetosphere). type Upwind Scheme) code solves the governing equations The first estimate of Mercury’s magnetic moment was 3 of ideal magnetohydrodynamics. The high-resolution fi- between 284 and 358 nT RM [Ness, 1975]. However, the nite volume solution scheme is based on an approximate poor spatial coverage during the two magnetospheric flybys Riemann solver for magnetohydrodynamics [Powell, 1994; of Mariner 10 make the evaluation of the intrinsic moment of Powell et al., 1995]. In this approach, the hydrodynamic Mercury very complicated and the results are highly depen- and electromagnetic effects are solved for in a fully three- dent on the physical assumptions [Ness, 1975; Connerney dimensional tightly coupled manner, rather than in separate and Ness, 1988]. steps [Gombosietal., 1994; Powell et al., 1995; 1999]. A tenuous atmosphere was observed at Mercury by the The code uses a limited reconstruction that ensures second- Mariner 10 spacecraft [Broadfoot et al., 1976]. This atmo- order accuracy away from discontinuities, while simultane- sphere is mainly composed of hydrogen, helium and oxy- ously providing the stability that ensures nonoscillatory so- gen, with traces of sodium and potassium. The H, He, and lutions. In addition, the code employs two accurate approx- O components are thought to be of solar wind origin, while imate Riemann solvers: the Roe [1981] scheme [Powell, sodium and potassium atoms are probably produced by sput- 1994] and the Linde [1998] solver. The resulting scheme tering [Lammer and Bauer, 1997]. The total column density works equally well across a range of several orders of mag- of the neutral atmosphere is estimated to be less than 1012 nitude in plasma β (β is the ratio of the kinetic and magnetic cm−2, which is essentially negligible from the perspective pressures). of magnetospheric interaction. In the Mercury simulations The basic data structure used in the BATS-R-US ap- shown in this paper all atmospheric effects are neglected. proach is that of adaptive blocks [Stout et al., 1997; Powell In our simulation Mercury was approximated by a solid et al., 1999]. Adaptive blocks partition space into regions, nonmagnetic sphere with a radius of RM =2, 440 km. The each of which is a regular Cartesian grid of cells, called a intrinsic magnetic field was approximated by a dipole mo- 3 block. If the region needs to be refined, then the block is re- ment of 330 nT RM , with the magnetic moment vector point- placed by 8 child subblocks (one for each octant of the parent ing south (the same sense as Earth). The surface conduc- block), each of which is a Cartesian grid of cells containing tivity was assumed to be zero, thus neglecting the effects the same number of cells as the parent block. If coarsening of a photoelectron sheath which may form around Mercury is needed, then the 8 children are replaced by their parent. [Grard, 1997]. Magnetic flux was allowed to cross the sur- The blocks in the grid, at their various levels of refinement, face of the planet, but no particle flux could penetrate the are stored in a tree data structure. surface. The boundary conditions on the surface were im- BATS-R-US was specially designed to handle objects posed by utilizing cut cells [DeZeeuw and Powell, 1992], with strong intrinsic magnetic fields. It achieves improved which allows second order (piecewise linear) reconstruction solution accuracy by solving for B1, which is the measure of the boundary geometry. of the deviation of the full magnetic field from the intrin- The upstream plasma flow conditions around Mercury sic field, B◦, and is defined as B1 = B − B◦ . This ap- may vary significantly depending on several factors, includ- proach was first employed by Ogino and Walker [1984] and ing the position of the planet on its trajectory and solar Ogino [1986] (and later applied to Godunov-type schemes activity. In this paper we present simulations for “typi- by Tanaka [1995]) and can lead to improved numerical solu- cal” solar wind conditions near perihelion: n =73cm−3, tions by alleviating the necessity of resolving the often large T = Te + Ti =14eV, B =46nT, u = 430 km/s, spatial gradients associated with the intrinsic fields and by ion-acoustic sound speed a =74.2 km/s, Alfven´ speed ∼ ensuring that the divergence of the intrinsic component of VA = 120 km/s, mean molecular mass 1 amu, and specific the magnetic field is by definition zero. Note that in this heat ratio 1.67. The corresponding ion-acoustic Mach num- CURRENT SYSTEMS IN THE MAGNETOSPHERES OF MERCURY AND SATURN 3 Figure 1. Three-dimensional rendering of Mercury’s magnetosphere. The electric current density is shown in gray scale in the noon-midnight meridian and in a cross sectional plane in the tail. Closed magnetic field lines are shown by dark solid lines, while open magnetic field lines connected to the northern high latitude region are represented by light solid lines. The open-closed magnetic field boundary is marked by a circle. Figure 2. Equatorial (left panel) and noon midnight meridian (right panel) cuts of the Hermean current system. The IMF vector is in the equatorial plane. 4 GOMBOSI ET AL. ber is 5.8 and Alfvenic´ Mach number is 3.6. At Mercury’s pushed together, while they are clearly separated on the dusk orbit the Parker spiral magnetic field forms an angle of 20◦ side. with the solar wind direction. However, we must emphasize In the equatorial plane the current is strongest in a rel- that these parameters may vary significantly. A parametric atively narrow region on the dawn side.
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