Magnetic Field Changes in the Inner Magnetosphere of Jupiter
C. T. Russell, Z. J. Yu, K. K. Khurana and M. G. Kivelson
While the outer magnetosphere of Jupiter is very dynamic, powered ultimately by mass loading at the moon Io, the magnitude of the magnetic field in the inner and middle magnetospheres is very steady. Small deviations with orbit to orbit variations of typically 5 nT do occur presumably due to variations in the magnetodisk current. In order to develop an index of the magnetodisk current we examine existing models of the interior and exterior field and modify them for secular variation and local time variations. While we use the radial range from 11 to 12 jovian radii for computing our index, we show that the same results would be obtained over a wide range of radial distances.
That the jovian magnetosphere was a very dynamic place was known well before the first visitation by the Pioneer 10 and 11 spacecraft from observations of the radio emissions that Jupiter generates [Burke and Franklin, 1955]. The control of these emissions by the phase of Io , the discovery of the Io torus [Brown and Chaffee, 1974], and its probing by the Pioneer and Voyager spacecraft led to an appreciation that Io provided the engine for these disturbances. However, initially the Io control was believed to derive from unipolar induction in which currents through Io or its ionosphere were generated by the potential drop created by the flow of the torus past Io. In fact it is now evident that much of the flow is diverted around Io and that the coupling of the Io torus to the ionosphere, in order to accelerate the plasma added to it by Io, is responsible for the field-aligned current system observed [Russell and Huddleston, 2000]. The plasma added at Io sets up a circulation system because the mass cannot build up forever. This circulation carries flux tubes gradually outward over many rotations of the plasma. The magnetic forces dominate over the plasma forces until about 25 RJ [Russell et al., 1999]. The centrifugal force becomes so strong that a large JxB force is needed to maintain force balance. This is provided by a stretched field configuration or magnetodisk that circles the planet. Like the Earthís ring current, this magnetodisk current weakens the field in its interior but unlike the Earthís ring current we do not have a monitor of the strength of the jovian ring current. It is the purpose of this paper to present such an index.
The terrestrial magnetosphere is ringed with magnetometers on the surface of the Earth. The Dst index is created continuously from four low to mid-latitude measurements with a quiet day baseline removed. At Jupiter we must rely on orbital measurements that are available only occasionally at low altitudes interior to the ring current and at a pair of local times each orbit. Despite the limitations of the temporal and spatial aliasing that are present, we proceed because of the insight that will result on the statistical behavior of the currents.
The magnetodisk begins about 25 RJ but we expect some variability of the currents inside this distance and it is best to measure the effect of these currents as far inside this distance as possible. However, the perijove of the Galileo orbit was initially about 11 RJ and if we wish to have a uniform index throughout the mission we must construct it from data outside this distance as possible. Figure 1 shows that the range of distances available during the first 20 orbits from mid 1996 to mid 1999 perijove was restricted to the region outside of 9 RJ. Beginning on orbit C21 perijove was lowered to 6 RJ. Figure 1 also shows the expected internal magnetic field from the O6 model , illustrating the growing sensitivity of the Galileo magnetometer to the internal field on these orbits. In order to characterize the magnetodisk current we will have to remove the effects of the internal field and the steady external field. The model for the currents by Khurana  is our starting point for removing the external currents but these currents are symmetric and as we show below it is clearly evident that these are local time effects. The O6 model too must be modified because there are secular variations in the internal magnetic field. In the next two sections we discuss how we deal with these modi-fications. In the section following these two we show the calculation of the index and test it.
|Figure 1. Inward radial extent of selected Galileo passes together with the expected magnetic field variation due to the three dipole terms in the equatorial plane on orbit C23. The h11 and g11 terms represent the projection of the dipole in the equatorial plane and define the longitude of the dipole moment.|
The Secular Variation
The Galileo spacecraft orbits Jupiter in its rotational equator. This enables it to measure all the dipole, quadrupole and octopole terms except the go2 term. If we expect temporal changes of the order of 1% similar to those of the terrestrial magnetic field since the time of Pioneer and Voyager we would expect to see changes in the dipole terms of the order of 4 nT at 10 RJ, and 20 nT at 6 RJ. Given enough coverage with periapsis of the order of 10 RJ we might eventually obtain an accurate measure of the secular variation but it is clearly more accurate to obtain the secular variation from the lower periapsis data. We do not attempt at this time to deduce the secular variation of the orders higher than the dipole as these will be much smaller in magnitude at these distances. Thus we proceed by removing our best estimate of the external field [Khurana, 1997] and the internal field terms of quadrupole and higher using the O6 model of Connerney . Then we find dipole moments to the residuals for each orbit in which we have fairly complete coverage inside 15 RJ. We fit only integral numbers of rotation.
Once this is done we learn two very interesting things. First, the longitude of the dipole has scarcely changed in System III over 25 years. Since the System III rotation period was defined to order phenomena associated with the magnetic field this constancy of the longitude indicates that the System III period is accurate as defined to within 3 msec. While the longitude has remained fairly constant, the tilt angle has not. It has increased from about 9.3o to 9.8o. Finally, the magnitude of the dipole moment has increased about 1.5% over the period from 1975 to 2000. In order to quote precise numbers we need to study the calibration of each of the magnetometers involved very carefully but to proceed with our exercise we need only adjust the Galileo data for the apparent changes. We note that at the distance for which we calculate our index, the secular change of the dipole field is less than 1 nT over the 5 years of the Galileo mission so the secular variation will not affect our calculation of a magnetodisk index. Even at the orbit of Io the secular change of the dipole magnetic field is only about 6 nT from 1995-2000.
Local Time Variation
The model of the external variations that we use in our calculations has no local time variations but we expect the magnetotail to produce such an asymmetry in the vertical magnetic field near Jupiterís equator. In order to determine this local time effect we subtract the Khurana  model external field and the internal field [Connerney, 1992] adjusted for the apparent secular variation since its epoch (1977) and map the residual field versus local time. This is shown in Figure 2. The map shows a generally positive perturbation on the afternoon side and a generally negative perturbation in the morning sector. The negative perturbation is large in the predawn hours than the positive perturbation post dusk. In a solar wind interaction dominated magnetosphere we would have expected symmetry around midnight with equal (negative) perturbations on either side. In the corotationally dominated jovian magnetosphere we expect asymmetry as the flux tubes expand in the afternoon and contract in the morning. To fully resolve this local time behavior we need more coverage but for our index calculation these data should suffice. We note again that this local time pattern is not due to the secular variation over the period in which Galileo has drifted in local time around Jupiter. The effect is far too small over the period of the study.
|Figure 2. The average local time radial variation of the external contribution to the dipole with the secular varying internal terms and the Khurana  symmetric model removed.|
The next step in our index calculation is to subtract the baseline local time variation in Figure 2 from the individual orbit residuals to produce a trace such as that shown in Figure 3 that shows the residual versus local time and radial distance. On this orbit it is everywhere positive. The variations from a constant value are caused by temporal variations in the external field, and imperfections in our removal of the internal field. Our index is calculated by averaging all the values obtained on a single orbit from the radial range 11-12 RJ using only orbits for which both inbound and outbound data are available.
|Figure 3. The residual field on orbit C21 with the local time-radial distance variation in Figure 2 removed.|
To check if our index is robust we also calculate it at other distances as well and cross compare these other possible indices with our closer one. We examine this comparison in the next section. We recall that the reason for choosing the distance range from 11-12 RJ for the index was based on the more continuous coverage available at that distance.
Cross Checking the Index
Figure 4 shows a plot of the magnetodisk current index calculated at 10-11 RJ versus that at 11-12 RJ. The slope is 0.97, the intercept of the best-fit line is -0.94, and the correlation coefficient is 0.9. There is some variation about this line that we interpret as due to the real temporal variation of the magnetosphere on a variety of time scales. Repeating this for 1 RJ bins from 6 to 7 RJ, out to 15-16 RJ, we obtain the radial variation seen in Figure 5. The bottom panel shows that the correlation coefficient is high, >0.6, over the entire range. The slope of the correlation plots shown in the middle panel peaks about 10 RJ. We attribute this possibly to the effect of the magnetodisk currents being largest here, but the accuracy of our technique is less in the region inside of 9 RJ as indicated by the finite intercept of the lower altitude fits.
|Figure 4. The index calculated at 10-11 RJ compared with that at 11-12 RJ.|
|Figure 5. Results of cross-correlations of indices from 7.5 to 15.5 RJ with that at 11.5 RJ.|
Figure 6 shows the index plotted versus time with orbit numbers of several exceptional passes indicated. There seems to be a general trend from negative values indicating a weaker field and a stronger magnetodisk current early in the mission to a positive field, indicating a weaker magnetodisk current later in the mission. The fact that the exceptional orbits are isolated suggests that the magnetodisk is disturbed for relatively short periods of time, much shorter than an orbit. We also note that orbit C3 does appear to have a weaker current sheet than on adjacent orbits as judged from in situ observations [Russell et al., 1999].
|Figure 6. The magnetodisk current index calculated at 11-12 RJ for all passes on which data were available for both inbound and outbound passes.|
Summary and Conclusions
Our attempt to define a jovian magnetodisk current index akin to the Dst index for Earth has led us to perform a study of both the internal and external magnetic field models. It seems that there has been a secular change from the Pioneer/Voyager epoch until the Galileo-epoch of about 1.5% in magnitude with a half degree tilt change but the longitude has not changed significantly. Thus the System III period does not need adjusting at this time. There clearly is a local time variation in the external field. Even though Galileo has not made a complete circuit in local time, we can determine this variation well enough to be sure of its reality. The index we create appears to be robust. It matters little whether we calculate it at 11-12 RJ inside or outside this distance. The index appears to be correctly registering the changes in the magnetodisk but these changes appear to be sustained for only short periods, much less than the orbital period or there would be more orbit to orbit coherence.
The authors thank S. Joy and J. Mafi for their efforts with the Galileo data reduction. This work was supported by the National Aeronautics and Space Administration from grant JPL 958510 administered by the Jet Propulsion Laboratory and research grant NAG5-8938.
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