SOME SIMPLE GUIDELINES TO THE INTERPRETATION OF THE MAGNETIC SIGNATURES SEEN AT THE GALILEAN MOONS

C. T. Russell

 

Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics,
University of California, Los Angeles, CA 90095-1567, USA

Adv. Space Res.,26(10), 1653-1664, 2000

 

ABSTRACT

Io, Europa, Ganymede and Callisto all interact with a flowing magnetized plasma, that of the nearly corotating jovian magnetosphere. The plasma conditions at each differ as there is a strong variation in the properties of the magnetosphere with radial distance. The properties of the moons vary as well. Thus each of the moons has a unique interaction. In order to understand how to interpret these signatures we examine first the limiting field induced in a permeable moon to determine what size fields demand intrinsic sources. We also examine the implications for remanent field sources imposed by the Runcorn theorem. Electrical conductivity in the ionosphere and interior to the moons can exclude the time varying portion of the external magnetic field. This exclusion can be used to probe for subsurface oceans beneath the crust. In addition to these effects, Europa and Io have sufficient atmospheres that they add mass to the incoming flow. The evidence for this mass loading and its effects on the jovian magnetosphere are reviewed as are its effects on the more classic signatures described above. When all these effects are considered we conclude that Io may have an intrinsic field with a moment as large as 1013 Tm3 although it is possible that this signature results from permeable material within Io. Europa has a conducting interior, most probably due to a saltwater ocean near its surface. Ganymede has an intrinsic field that is dynamo driven and Callisto has a conducting layer like that of Europe. Earlier observations by Voyager can readily be interpreted in terms of this mass loading scenario. The slowed cold flow behind Io provides a suitable source via the interchange instability for the cold torus well inside the orbit of Io.

INTRODUCTION

The Galilean moons are four quite different worlds, as varied as the four terrestrial planets. Io is the most volcanically active body in the solar system. Europa is covered with ice, but shows evidence of recent disruption of that ice and much tectonic activity on the surface that in turn suggests the presence of an ocean of water beneath that ice. Ganymede has a much older icy surface. It is the largest of the four moons and is the largest moon in the solar system. Callisto has the most ancient surface and is also completely covered with ice. None of the moons has an extensive atmosphere. Except above active volcanoes the maximum atmospheric column density at Io is 1015/cm2 (Ballester et al., 1994). Yet despite its weakness the Io atmosphere is important for the interaction with the jovian magnetosphere as the ions it produces through sputtering are nearly sufficient to block the oncoming torus plasma. The Europa atmosphere is much weaker and is not dynamically important except when the moon crosses the equatorial plane. At Ganymede and Callisto, there are no known effects of the atmosphere on the interaction.

The interactions with the magnetosphere are also dependent on the properties of the magnetospheric plasma: its density, temperature and velocity as well as the velocity of the waves that can travel in the plasma. These properties are listed in Table 1. A few words are in order about the parameters listed therein. First we note that the corotational velocity, i.e. the velocity at which plasma moves around Jupiter in lock-step with the planetís rotation, is close to the observed velocity at all moons, save Callisto, where the observed velocity is 33% less. This implies that the magnetospheric plasma is slipping relative to the ionospheric plasma at Callisto. This in turn implies a parallel electric field, probably in the ionosphere, that decouples the two regions. A parallel electric field in turn can accelerate electrons into the atmosphere causing aurora. Thus we expect that the magnetic field lines in the vicinity of Callisto enter the auroral ionosphere of Jupiter and this appears to be the case. Secondly the ratio of the magnetic field strength to the plasma density rises precipitously with radial distance from a value of 0.5 nT/ion/cc at Io, to 9 at Europa, 25 at Ganymede and 50 at Callisto. If as we expect, the plasma and field are slowly moving outward from Jupiter this ratio should rise as the field lines stretch in the absence of significant new sources of plasma. In a dipole field the ratio will rise in proportion to the jovicentric distance r as the volume of the flux tube increases with radial distances roughly as L4 and the magnetic field decreases as L-3. Perhaps surprisingly this measure of stretching is greatest from Io to Europa and least from Ganymede to Callisto, suggesting that there is much scattering of the plasma in the Io torus that acts to stretch the region of plasma proportionately more than field line itself stretches.

Table 1. Properties of the Galilean moons and the magnetospheric plasma at their location

Body

Io

Europa

Ganymede

Callisto

Radius (km)

1815

1565

2640

2420

Distance from Jupiter (RJ)

5.91

9.40

15.00

26.39

Orbital period (days)

1.769

3.551

7.155

16.689

Eccentricity

0.004

0.009

0.002

0.007

Corotation Velocity (km/s)

75

119

180

334

Observed velocity (km/s)

62-74

98

138

236

Orbital velocity (km/s)

17.3

13.7

10.9

8.2

Relative corotation vel. (km/s)

45-57

84

127

228

Density (cm-3)

4000

~50

~4

~0.2

Corotational Dynamic Pressure (nPa)

185

6

1

0.2

Electron temperature (K)

5x104

5x105

1.5x106

1.5x106

Ion temperature (K)

5x105

6x105

7x105

106

Thermal Pressure (nPa)

30

0.8

0.1

0.01

Magnetic Field (nT)

1800

450

100

10

Alfven speed (km/s)

130

300

250

300

Sound speed (km/s)

19

26

37

40

Magnetosonic speed (km/s)

133

310

250

300

Beta

0.02

0.01

0.03

0.2

Notes: Dynamic pressure and Alfven speed calculated using an ion mass of 22 amu. 1 RJ = 71,400 km; Dynamic pressure is given relative to moonís orbital motion with observed velocity. Plasma parameters follow those provided by Belcher (1983).

The rapid fall off in density has an important effect on the Alfven speed that might be expected to drop rapidly with radial distance because of the rapid fall off of the magnetic field strength, as it does in the Earthís magnetosphere. In fact the Alfven speed remains nearly constant because of the rapid decrease in the density with radius, and remains much greater than the sound speed everywhere. Thus the speed of the compressional magnetosonic fast mode is dominated by the Alfven speed everywhere and itself does not vary much with radial distance, about a factor of 2 from Io to Callisto.

It is important to understand clearly the effects of the finite permeability, and electrical conductivity on the signatures of the magnetic field around a moon-sized body in the jovian magnetosphere because we wish to determine the strength of any intrinsic magnetic field. Further we need to examine what limits exist on the strength of any remanent field because we cannot simply separate remanent from dynamo-driven sources at Jupiter as we can at Earth using crustal associations and absence of temporal variations. At the jovian satellites we must argue based on the allowable strength of dipolar fields arising form these sources. In the sections that follow we examine first the theoretical constraints on the signatures due to permeability, remanent magnetism, and electrical conductivity. Then we address the effects of mass loading and the evidence for it at Io and Europa.

PERMEABILITY

The simplest interaction between the jovian magnetosphere and one of its satellites would occur if the magnetosphere were a vacuum and the moon had no atmosphere, ionosphere, or interior dynamo. The jovian magnetic field would be still affected in this simple scenario by the permeability of natural materials. Iron, nickel and cobalt have very high permeabilities at temperatures below the Curie temperature that for iron is 1043K. Above the Curie temperature these materials have a much smaller permeability that decreases inversely as temperature. At some temperature below the Curie temperature natural materials can retain magnetization in the absence of a magnetic field. This natural remanence depends on the properties of the material.

To understand the limits of permeability in providing the signatures we see at the Galilean satellites it is instructive to review magnetic effects seen near slabs and spheres of permeable material. While this is "text book" material, it seems not to be widely understood. Figure 1 shows the magnetic induction, B, magnetic intensity, H, and magnetization, M, for slabs of finite permeability in the upper two rows. When the magnetic induction is along the normal of the slab, the lines of magnetic induction are continuous along the normal but the magnetic intensity H is discontinuous along the normal. The magnetization M, of course, is only in the material layer. If there is a discontinuity in the permeability in the plane containing the magnetic field, then the magnetic induction in the slab and in free space is different but the magnetic intensity is the same. If the permeability of the slab becomes infinite as illustrated in the lower left-hand panel, then the magnetic intensity in the slab goes to zero. If the geometry of the material is spherical and the permeability is infinite, then we can quickly calculate the magnetic induction everywhere as follows. On the equator along the line perpendicular to the external field the magnetic induction at the surface is zero because it is zero inside the sphere and its tangential component is continuous. For this to occur in free space just outside the sphere the magnetic induction caused by the permeability of the sphere must be equal and opposite to the externally applied magnetic induction, Bo. From symmetry the field of the permeable sphere must be dipolar. If so the induction at the poles is twice that at the equator. Adding the external field to the field induced by the permeability of the sphere we obtain a total magnetic induction of 3 Bo at the top and bottom of the sphere. Thus the maximum field that can be produced by the permeability of a moon is three times the jovian field at that point. Table 2 gives the average external field at each of the moons along its rotation axis as well as the time-varying model magnetic field, radially outward in the equatorial plane in which the moon orbits. The peak-to-peak variation is twice this value as the moon moves from one side of the magnetic equator to the other. Also listed is the maximum magnetic moment that can be produced by magnetic induction in a highly permeable moon.

Figure 1. Schematic showing the magnetic induction, magnetic intensity and magnetization for slabs with surfaces perpendicular and parallel to the magnetization. The lower two panels show the field, for a slab and a sphere with infinite permeability.

 

 

Table 2. Magnetic field at each of the Galilean Satellites

 

Io

Europa

Ganymede

Callisto

Average magnetic field around orbit [nT]

1958

443

98

30

Variable field around orbit [nT]

336

81

31

21

Maximum induced moment [Tm3]

1.2x1013

1.7x1012

1.8x1012

4.3x1011

Observed moment [Tm3]

1013

<4.6x1011

1.4x1013

<2x1011

The observed moment of Io (Kivelson et al., 1996; Khurana et al., 1997a) Europa (Kivelson et al., 1997b) and Callisto (Khurana et al., 1997b), all are smaller than the maximum induced moment but not that of Ganymede (Kivelson et al., 1997). Thus the moments (or their upper limits) could be explained by the presence of permeable material. In order to explain the Io moment in terms of permeable material though requires a large amount of iron. We return to this point later after examining the Io magnetic signature in greater detail.

REMANENT MAGNETIZATION

The signature at Ganymede cannot be due to magnetic induction in a permeable material simply on the grounds it is too large. Moreover, the multiple passes of Galileo past Ganymede have shown that the magnetic dipole is fixed in the moon and does not move with the external field. There are two possible sources for such magnetism: a remanent field that was captured by the magnetic materials in Ganymede either impressed by an internal dynamo, or by Jupiter itself; or due to an internal dynamo, active today. In any case if we propose a source for the Ganymede field we must also explain why the other moons have not this source.

Since Europa is the smallest moon and Callisto is the most distant and most uniform, least dense moon, we might excuse these two from dynamo production since any dynamo activity in their interiors should have been the first to cease. Io has a tidal heat source to keep its interior active, albeit that heat source is concentrated in the outer layers. Ganymede being largest should have retained dynamo action the longest all other factors remaining equal. While this makes a plausible case for active dynamos at Ganymede and possibly Io, we must examine the alternative scenario, that remanent magnetism can produce the signatures seen there.

There are two possible external sources of a magnetizing field: the field of Jupiter and an internal field. In either case the magnetizing field must have been very strong at Ganymede because naturally occurring minerals do not pick up a strong remanent field. Since the jovian field strength varies rapidly with increasing radial distance we would expect Io and Europa to be more strongly magnetized than Ganymede, if Jupiter were the source of magnetization. For the same reason that Ganymede is the most likely candidate for present day dynamo action, we assume for the time being that it is possible that Ganymede was also the only one with an ancient dynamo that caused remanent magnetization. This scenario has several difficulties. First, natural dynamos (e.g. the Earthís and the Sunís) reverse periodically. To use an internal dynamo to magnetize a planetary body in a coherent sense requires a suspension of this hitherto general property. (This difficulty also extends to Jupiter as the magnetizing source). Second, if the material is magnetized in a dipolar fashion then it has no external field (Runcorn, 1975). This is illustrated in Figure 2. Runcornís theorem is also true for any multipolar magnetization. The only way around this theorem is to disrupt the dipolar magnetization with non-linear effects or inhomogenities. Crary and Bagenal (1998) have probed the limits of this theorem. They find that a field such as Ganymedeís can be produced only with large values of remanent magnetization and specific thermal histories that are very restrictive. It is extremely unlikely that such scenarios occurred.

Figure 2. The magnetic induction (left) produced by a dipolar magnetization (right).

 

CONDUCTIVITY EFFECTS

A perfectly conducting sphere will exclude an externally applied magnetic field forever as sketched in Figure 3, but over the age of the Galilean moons and with the expected conductivity of their cores the Jovian field should have penetrated through the entire moons long ago. However, on each orbit the magnetic field varies as the moons change latitude and to a certain extent radial distance. Since this variation occurs on the time scale of a fraction of a day to days this variable field does not penetrate far into even moderately conducting materials such as seawater. Such a signature is equivalent to an induced dipole orthogonal to the inducing field. This is 90o from the induced dipole caused by the permeable response to the same varying magnetic fields. Such a conductivity effect has been reported for both Europa and Callisto (Khurana et al., 1998). The externally varying field is shown in Figure 4 for both moons. It is this field that appears to be excluded by a near surface conducting layer.

Figure 3. The exclusion of an external field by a conducting shell. Figure 4. The variable magnetic field seen at Europa and Callisto over an orbit (after Khurana et al., 1998)

MASS LOADING SIGNATURE

When ions are created in a moving magnetized plasma, they are accelerated by the electric field of the plasma and gyrate with a "thermal" velocity perpendicular to the magnetic field equal to the perpendicular velocity of the plasma and drift with a bulk velocity of the plasma to perpendicular to the field. If the mass addition rate becomes comparable to the rate of convection of mass into the volume in which mass addition is occurring then conservation of momentum dictates that the incoming flow is slowed. If the mass-loading region has a curved surface the pressure gradient force is at a varying angle to the incoming flow and the incoming flow is deflected and slowed. If the thermal pressure in the mass loading plasma exceeds the dynamic pressure in the flowing plasma, a field free region can be produced in the mass loading region on time scales less than that for the diffusion of the field into the region. Such field free regions are observed both at Venus and at comet Halley.

Mass loading within the jovian magnetosphere is different than in the solar wind because the external field maintains its direction over periods of time long compared to the diffusion into the conducting body of the moons and its ionosphere. Moreover the field strength at Io has such a high pressure that a typical planetary ionospheric density would have to exceed about 109 electrons/cm3 if the temperature of the ionosphere were similar to that of the atmosphere before a diamagnetic cavity could be formed. Thus we expect to find a rather uniform field at Io depressed slightly by the diamagnetic effect of the picked up ions and bent in the region of slowed flow.

It is instructive to calculate the mass of the Io torus that intersects Io each second. This amounts to 87 kg/sec for a density of 4000/cm3 arriving at Io with corotational velocity. If a ton of ions per second were added to this small region of the torus then the resulting velocity would be only 5 km/sec. To slow the plasma down from the expected corotational velocity of 57 km/s to the observed 45 km/s would require the addition of 23 kg to each stream tube of the cross section of Io. This value is very similar to that found by integrating the mass flux seen as Galileo crossed the Io wake [Russell et al., 1997]. If we use the canonical ton per second (Hill et al., 1983), then the incoming velocity would be slowed from 57 to 45 km/s if that mass were spread out over a cross section of 43 Ios or radial distance from the center of Io, or 6.5 RIo. This dimension is similar to that in which the largest plasma disturbances are seen as shown below.

Once the plasma is slowed, the magnetic field piles up at Io and in its wake. Because the flow, well above and below Io, is not slowed by mass loading the field lines bend. This bending acts to accelerate the flow back to corotational velocities. The bent field lines constitute the Alfven wing of Io. This definition differs from the original definition that was restricted to the tubes that passed through Io itself, and the currents in the mass-loaded Alfven wing are potentially much larger than those originally calculated for Io. These currents serve to increase the field strength in the wake region. Since this "enhanced" field was used in the estimates of the possible intrinsic magnetic field of Io and the intrinsic field reduces the field in the wake, the possible moment of Io is significantly greater than initially estimated.

Figure 5. Voyager 1 trajectory past Io (after Acuna et al., 1981)

Both Voyager 1 and Galileo have made passes by Io. Figure 5 shows the Voyager orbit past Io and Figure 6 shows the resulting magnetic field perturbation that was thought to agree with the original unipolar inductor model.

Figure 6. The magnetic perturbation as Voyager 1 passed Io (after Acuna et al., 1981).

If we extrapolate the magnetic field vectors as straight lines from Voyager to the plane of Io we get the trace shown in Figure 7 for the extrapolated trajectory. Belcher (1981) has shown that the plasma appeared to be tied to the field so with some assumptions we can use the directional changes in the field also to trace the slowing and deflection of the flow. We assume first that the flow at Voyager is flowing at nearly the unperturbed corotational velocity and that the perturbation in velocity close to Io is much larger than the flow perturbation at Voyager. Then we assume that the perturbation at Io is due only to gradients along the corotational direction so that only the motion of the satellite along the corotation direction leads to changes in the field seen at Voyager. The changes in the field components with time then can be attributed to slowing and deflection of the flow as it approaches Io from upstream. This approximation ignores the fact that some of the changes have occurred because Voyager has moved onto a new streamline that has experienced different perturbations as it flowed toward Io. Thus we can expect only semi-quantitative results but we do not expect to make a qualitative error with this approximation and the velocities that we derive bear this out. The vectors in the Figure 7 show the change in the flow from corotation at each point along the trajectory. We see that the flow slows in front of Io and then is deflected to the side. Further back it accelerates and closes behind Io.

Figure 7. Inferred flow pattern along the extrapolated Voyager trajectory into the plane of Ioís orbit. Figure 8. Flows seen by Galileo referenced to the observed corotational velocity. Original data appear in Frank et al., (1996).

Figure 9. Flow velocity in the Io wake versus distance behind Io (Hinson et al., 1998).

The plasma added in the slow flow region should be quite cold compared to that on the streamline deflected around Io. That expectation is confirmed by the plasma observation on Galileo as shown in Figure 10 (Frank et al., 1996). This leads to a simple explanation for the cold plasma torus seen by Voyager and shown in Figure 11. The cold plasma seen at radial distances less than Io must be the cold wake plasma produced on those streamlines passing directly over and under Io. Its appearance at closer radial distances than Io requires that the cold plasma moves to the inner edge of the hot torus. This can happen if the hot torus produced on the Jupiter side of Io interchanges with the cold torus plasma. This could occur if the total mass on flux tubes intersecting Io and picking up cold ions is less than that of the neighboring hot torus that only gains and does not lose ions as they pass Io. It could also occur if the additional centrifugal force on the hot torus flux tubes inside Ioís orbit due to their more rapid motion made them interchange unstable with the more slowly moving cold tubes. This would explain why the cold torus "cools" so abruptly just inside the orbit of Io. It never contained hot plasma that had to cool. Moreover, the coldest tubes should be moving the slowest and interchange most deeply into the inner jovian magnetosphere as observed. Finally, we might expect the greatest effect to occur as Io crosses the magnetic equator, thus restricting the width in latitude of the cold plasma torus.

Figure 10. Plasma density temperature and thermal pressure observed by Galileo (Frank et al., 1996). Figure 11. The plasma torus as observed by Voyager 1 on its inbound trajectory. The cold plasma seen near the end of this sequence was obtained inside the orbit of Io (after Belcher 1983).

SUMMARY AND CONCLUSIONS

Our examination of Io, Europa, Ganymede, and Callisto has shown that their signatures in the magnetospheric plasma are possibly affected by permeability and certainly affected by conductivity effects. However, there are limits to the size of the perturbation caused by a permeable object. Ganymede's moment exceeds that limit and Ioís apparent moment is very close to the limit. Io is a strongly mass loading object and that mass loading produces a strong field-aligned current. This current acts to reduce the field along the Galileo trajectory through the Io wake and hence early estimates of the Io magnetic moment may be too small. Thus, while Ioís field signature may be produced by a permeability effect, it is more likely due to an internal dynamo whose moment could be as high 1013 Tm3. Ganymede clearly has an intrinsic field whose most probable source is an internal dynamo. At present we cannot tell if it has a magnetic signature associated with a subsurface ocean.

We note that while there are some plasma signatures in the interaction of the magnetosphere with Europa and Callisto, the signature is dominated by the electrical conductivity of the interior that excludes the time varying field at Europaís synodic period with respect to Jupiter. This signature strongly indicates that these two moons have electrically conducting oceans. The perturbed fields seen by Voyager 1 are very consistent with the signatures observed much closer to Io on Galileo. They both may be interpreted in terms of a ton of ions per second added to the magnetosphere over a broad region around Io. The slow cold plasma in the wake region provides a suitable source for the cold plasma torus.

ACKNOWLEDGMENTS

This research was supported by the National Aeronautics and Space Administration through a research grant administered by the Jet Propulsion Laboratory.

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