Adv. Space Res. Vol. 12, No.8, pp. (8)249(8)255, 1992
02731177/92 $15.00 Copyright @ 1992 COSPAR
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THE FIELD OF THE JOVIAN MAGNETOSPHERE, INCLUDING CONTRIBUTIONS OF THE MAGNETOPAUSE SURFACE CURRENTS Irene M. Engle Physics Department, U. S. NavalAcademy, Annapolis, MD 214025026, U. S. A.
ABSTRACT An idealized largescale Jovian magnetospheric fieldhas been computed by calculating the contribution due to the currents on the surface of the magnetopause (calculated from theory). This contribution is added to those of a model current system in the magnetic equatorial plane and the intrinsic dipole field of the planet. Convenient spherical harmonic representations of the field in the region inside the magnetopause have been developed. The Voyager observation model is compared with the Pioneer observation model. INTRODUCTION Pioneer 10 measurements (Smith et a!., 1974) near the Jovian equatorial plane indicated that Jupiter’s magnetosphere was, at the time of those observations, highly inflated by a thin equatorial corotating current sheet. Work by a number ofinvestigators, including Barish and Smith (1975), Beard and Jackson (1976), Engic and Beard, (1980), and references cited by them led to the idealized global Jovian magnetosphere (Engle and Beard) corresponding to those Pioneer 10 observations and the internal sources deduced therefrom. Later observations by the Voyager I and II spacecraft also observed a corotating current sheet resulting in a somewhat inflated magnetosphere; however, the character of the deduced current sheet was that it was smaller in radius (on the order of something less than or equal to 60 Jovian radii) than that of the earlier Pioneer observation (which was on the order of 100 Jovian radii). For the Pioneer model calculation, Engle andBeard created a model of a thin equatorial corotating plasma sheet which began at about 17.8 RJ and continued out to 100 RJ, which was also adopted as the subsolar point distance. The current density of that sheet varied with distance p from the planet center as p~L7. For the more recent Voyager calculation, a thick equatorial plane corotating plasma sheet model developed by Connerney, Acuna, and Ness (1981) was adapted for the purpose of the calculation of the Voyager model global magnetopause and the currents thereon. Parameters used in the Connerney Ct al model of the current sheet was a half thickness of 2.5 RJ, an inner edge at 5 Rj and an outer edge, coincident with subsolar distance, at 60 Rj from the planet center. The Connerney et al model current density varied inversely with distance p. In each case, the intrinsic planetary magnetic field was represented by a planetcentered dipole. Sample magnetic fieldlines for the net fields associated with the (8)249
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internal sources foreach ofthe models are displayedin Figure 1. THE CALCULATION Each mode! calculation began with the construction of a threedimensional zeroorder magnetospheric boundary surface (magnetopause) by assuming a balance of solar wind pressure with magnetic pressure due to the net magnetic field of sources internal to the magnetopause. The differential equation for the magnetosphere boundary is given by
ci S ~
(1)
where ~ is the internal magnetic field at the boundary, ~ is the unit vector ‘in the direction of the incident solar wind, and ci~ is the unit vector normal to the magnetopausesurface In each case, the calculated surface was then used to calculate magnetopause surface current densities associated with the redirected solar wind particles. These currents were in turn used to calculate their additional contribution to the net magnetospheric field. A new surface is then constructed and the cycle repeated until a convergence is achieved. A final selfconsistent surface will have currents such that the magnetic field calculated therefrom will just cancel the net magnetic field due to interior sources at all points outside the magnetopause. Within the magnetopause, the magnetic field due to the surface currents is added to the other contributions to produce a model of the net magnetosphericfield. RESULTS Figure 2 shows the final noonmidnight plane meridian shapes of the Voyager and Pioneer models. At first glance, the two models seem to be remarkably similar in shape. For comparison purposes, the dotted line in the figure presents a corresponding zeroorder “dipole” magnetopause with the same subsolar point distance as the Voyager model. As cylindrical symmetry of the interior sources is assumed in each model, the equatorial magnetopause shape differs little from that resulting from an assumed internal dipole of sufficient strength to have a comparable subsolar distance, and is thus not shown. For each model, the components of magnetic field attributable to the surface currents were calculated for an extensive array of points inside the magnetopause. Purely as a convenient means ofdisplaying the general characteristics of the model field, these field component values were fit to a spherical harmonic expansion. The details for the Pioneer model are presented in Engleand Beard(1980), and the details for the Voyager model are included in a manuscript (by this author) submitted for publication to J. Geophys. Res. The resulting functions were added to the functions representing the interior sources in order to obtain a net magnetospheric field model. Figure 3 displays sample magnetic field lines for each of the models in the same noonmidnight plane meridian. Final subsolar point magnetic field values were 4.534 nT for the Pioneer model and 14.41 nT for the Voyager model, respectively. Comparison of Figure 3 with Figure 1 shows the effect of the solar wind and resulting surface currents on the overall magnetosphericfield.
The Field of the Jovian Magnetosphere
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DISCUSSION A major difference in predictions for the two models is the relative strength of the contribution due to the surface currents at locations in the inner magnetosphere, particularly in the vicinity of the orbits of the Galilean satellites. lo, Europa, Ganymede, and Callisto are located at 6, 9.4, 15, and 26 Rj, respectively, from the planet center in its equatorial plane. Despite the approximately 100 tilt of the Jovian planetary dipole and magnetic equator, the orbits of the Galilean Satellites lie within approximately 100 ofthe Jovian magnetic equator. The Pioneer model magnetosphere had a subsolar point distance r0 equal to 100 RJ and a calculated total subsolar point field, B0, of 4.5 nT. Thus, for the Pioneer model, the Galilean satellite orbits lay from 0.06 r0 to 0.26 r0 the values of “normalized” field components arising from the magnetopause surface currents for the Pioneer model in the neighborhood of the satellite orbits ranged from 0.5 B0 to 0.75 B0 in B9 and were considerably smaller for Br. Thus, the surface current field contribution to total magnetic field for that neighborhood would be such as to tend to generally reduce the total field from what it would be without the surface current contribution by a small amount in the range 2.25 nT to 3.8 nT. For the Pioneer data set, the measured magnetic field values at distances corresponding to the orbits of the Galilean satellites were on the order of (100±50) nT. For the more recently calculated Voyager model, the measured total magnetic field in the vicinity of the Galilean satellites is again (100 ±50) nT; however, the different character of the observed size of the magnetosphere and the altered geometry of the equatorial current sheet led to a calculated subsolar point total magnetic field of 14.41 nT for the assumed value of 60 Rj for the subsolar point location. The values of the “normalized” surfacecurrent produced B~in the neighborhood ofthe Galilean satellite orbits range from 0.3 B0 to as large as 0.87 B0 , while the Br could be as large as + 0.3 B0 out at Callisto. Even the B~could reach a magnitude as large as 0.07 B0 at the Callisto orbit neighborhood. Thus, the net normalized magnitude of magnetic field due to the surface currents could be as large as 0.92 B0, or 13.3 nT, which is a significant fraction of the total measured field there. Furthermore, since, in that neighborhood, the 9component of field arising from the surface currents is antiparallel to the 9component due to the internal sources, while the Br is parallel to the interior fieldsource contribution to Br, thus affecting the apparent angle of the magnetic field. The effect is even more pronounced if a smaller subsolar distance parameter is used in the Connerney et al equatorial current sheet model. Inclusion of the effect of these surface currents for a “Voyager”size magnetosphere is thus important when attempting to correctly calculate the planetary magnetic moments and accurately model the corotating current sheet from magnetic field measurements made in the neighborhood of the Galilean satellites’ orbits. 


As each of the completed models assumes that the planetary dipole axis and axis ofthe corotating sheet to be perpendicularto the equatorial plane, the models’ axial symmetry is broken only by the solar wind interaction; the solar wind direction is assumed to be parallel to the ecliptic/equatorial plane and to be a constant vector. Inclusion of the approximately 10°tilt of the magnetic dipole axis with respect to the ecliptic plane and the precession of that axis as a result of Jupiter’s rotation will introduce symmetrybreaking perturbations in the shape, and consequently of the pattern of the currents on the magnetopause. J~.SR12~8Q
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REFERENCES Barish, F. D., and R. A. Smith, An analytical model of the Jovian magnetosphere. Geophys. Res. Lett 2: 269272, 1975. Beard, D. B., The interaction of the terrestrial magnetic fieldwith the solar corpuscular radiation, J. Geophs. Res. 65: 3559, 1960. Beard, D. B. and D. J. Jackson, The Jovian magnetic field and magnetosphere shape, J. Geophs. Res. 81: 3399, 1976. Connerney, J. E. P., M. H. Acuna, and N. F.Ness, Modeling the Jovian Current Sheet and Inner Magnetosphere, J. Geophs. Res. 86: 8370, 1981. Connerney, J. E. P., M. H. Acuna, and N. F. Ness, Voyager 1 Assessment of Jupiter’s Planetary Magnetic Field, J. Geophs. Res. 86: 3623, 1982. Smith, E. J., L. Davis, Jr., D. E. Jones, P. J. Coleman, D. S. Colburn, P. Dyal, C. P. Sonett, and A. M. A. Frandsen, The planetary magnetic field and magnetosphere of Jupiter: Pioneer 10, 1. Geophs. Res. 79: 3501, 1974.
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The Field of the Jovian Magnetosphere
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•.f Figure 1. Jovian magnetic field due to planetary dipole plus corotating ~ Lc11~ntsheet; Pioneer model, with partial Voyager model overlaid J
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