THE UNIPOLAR INDUCTOR MYTH: MASS ADDITION OR MOTIONAL ELECTRIC FIELD AS THE SOURCE OF FIELD-ALIGNED CURRENTS AT IO

C. T. Russell1,2 and D. E. Huddleston3



1Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567
2
Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095-1567
3
Hughes Space and Communication Company, El Segundo, CA 90245

 Adv. Space Res., 26(10), 1665-1670, 2000.

ABSTRACT

The nature of the interaction of Io with the Io torus has undergone an important paradigm shift due to the many results of the Galileo flyby and the reinterpretation of the Voyager data. The main obstacle to the flowing plasma appears to be mass loading. Only a small fraction of the flux tubes that are flowing toward Ios cross section at infinity join up with the Io magnetic field and flow slowly across Ios polar caps. The mass pickup on these flux tubes is heated much less than on the tubes that flow near to but around Io. Both Voyager and Galileo data show this deceleration and deflection. The slowed plasma in the wake is accelerated up to corotational velocities by 6 RIo downstream. This picture is much different than the original picture of Io as a unipolar inductor in which an electric potential drop of 500 kV appeared across Io. In fact, the potential drop is only about 50 kV. The current flowing along magnetic field lines in the vicinity of Io, however, is much greater than heretofore believed. The original theories did not take into account the size of the mass-loading region or the closure currents associated with the bent field lines. Thus they assumed that the currents would be limited by the Alfven conductance and the size of Io. The field-aligned current system appears to be much larger than previously proposed and shifted downstream. This downstream shift has important consequences for the possible size of the Io intrinsic field. It may be larger than originally proposed. The location and source of these current systems does not affect their capability of generating the potential drops along the magnetic field that were postulated to be responsible for radio emissions. The low potential drop across Io evidenced by the small fraction of the wake stream lines that intersect Io and the low pickup ion temperature produces cold, slow flowing flux tubes that can interchange with the hot torus tubes just inside the Io orbit, producing the cold plasma torus.

INTRODUCTION

The discovery of the Io-control of the jovian decametric radiation (Bigg, 1964) was quickly followed by the interpretation of this control in terms of field-aligned currents generated by a potential drop across Io due to the 57 km/s that a corotational flow would have relative to Ios orbital velocity about Jupiter (Piddington and Drake, 1968; Goldreich and Lynden-Bell, 1969). Figure 1 shows a schematic illustration of the proposed mechanism that has been classically called a unipolar inductor (e.g. Acuna et al., 1983).

Hill et al. (1983) have a more restrictive definition of the unipolar inductor that requires closure of the current in the ionosphere but we note that most recently this term has also been used for a fully mass loaded model (Hill and Pontius, 1998). As we use it here, the term refers to what causes the observed current. If the current comes from a potential drop across Io or its ionosphere then Io is acting as a unipolar inductor. If the current arises from mass loading it is not. In the unipolar inductor mechanism the current is limited by the shear in the magnetic field produced by an Alfven wave propagating the news of the interaction to the ionosphere. For the conditions of the Voyager Io flyby this current was estimated to be a total of 2.8 MA integrated over in two "wings", one above Io and one below (Acuna et al., 1981). The discovery of bends in the magnetic field during the Voyager encounter led to the declaration that the unipolar inductor model had been confirmed. However, these bends in the field have another interpretation, one consistent with a predominantly mass-loaded interaction. In this paper we review briefly what we know about interactions of magnetized flows with a magnetized object so that we can most accurately interpret the Galileo and Voyager observations. We show that a self-consistent picture arises with strong currents closing along field lines and a very little potential drop across Io. This refinement leaves intact the explanation for the radio emissions in terms of beaming emissions generated by the field-aligned currents, but changes the location and extent of those currents.

THE MOON, VENUS AND COMETS

The solar wind interaction with the Moon applies a potential drop across it, as proposed in the unipolar inductor model for Io, but the low conductivity of the lunar soil allows no significant current to flow through the Moon in response to this potential drop. The net result is shown in Figure 2. The solar wind is absorbed by the Moon and a cavity is formed in the plasma. Behind the Moon the plasma expands into the wake region to fill the cavity at some distance downstream (see e.g. Russell, 1993a).

Venus is at the opposite end of the spectrum. It generates an ionosphere strong enough to deflect the solar wind flow. Thus streamlines of the solar wind move around Venus so that there is almost no potential drop applied to Venus at all. Venus also adds mass to the deflected streamlines. This slows down the flow along these streamlines and the magnetic field that threads these slowed regions gets stretched out in a tail-like fashion (see e.g. Russell, 1993b). This interaction is sketched in Figure 3. The bend in the field behind Venus is equivalent to a current that through the JxB force accelerates plasma in the downstream direction so that it eventually reaches (and exceeds) the solar wind velocity and the bends are removed. We note that the magnetic field component crossing the current sheet is stronger near Venus than further downstream.

This force, associated with the pressure gradient, is also pointing downstream in the sense to accelerate the plasma and this force is also part of the JxB force. In the case of Venus the momentum to accelerate the tail plasma comes from the solar wind. At Jupiter, Io must get this momentum from the planetary ionosphere by the field-aligned current system. The ions that are picked up by the flow have a thermal velocity equal to their bulk flow velocity. Thus particles that are picked up in a slowly flowing region may be cold relative to the ions picked up in the more rapidly flowing regions. The JxB acceleration process does not heat the picked up ions. Only the bulk velocity is affected.

Fig. 1. Schematic illustration of the unipolar inductor mechanism originally proposed by Piddington and Drake (1969) and Goldreich and Lynden-Bell (1969) to explain the observations of Bigg (1964). (After Acuna et al., 1983)

On the time scale required to diffuse into the Venus ionosphere the vectorial average interplanetary magnetic field is zero. Thus, under most circumstances the vast majority of the ions produced in the vicinity of Venus are born in the field-free ionosphere. However, at comets the neutral cloud is not confined to the near-nucleus region and the interplanetary magnetic field permeates the ion production region. In this situation the cometary mass loading process creates the obstacle to the flow in contrast to the case at Venus where mass loading the flow is a minor consideration in the process of obstacle formation (see e.g. Russell, 1993b). The physics of the cometary tails on the other hand is not much different than that of the Venus tail, albeit the length of a comet tail far exceeds that of the Venus tail because of the much greater mass loading at comets. At Io the mass loading is directly onto the jovian magnetic field for two reasons: the jovian field has penetrated Io over the eons and the mass loading region extends well away from Io as we discuss below.

Fig. 2. The interaction of the solar wind with the Earth's Moon when the interplanetary magnetic field is perpendicular to the solar wind flow (Russell, et al., 1993a). Fig. 3. The interaction of the solar wind with Venus. The plasma and its associated flux tubes moving close to Venus are slowed down in the interaction and pickup mass from the Venus exosphere. Behind Venus the magnetic forces (curvature and pressure) accelerate the plasma back up to and beyond the solar wind velocity (Russell et al., 1993b).

CONSISTENCY OF VOYAGER AND GALILEO FLOW DATA

The signature seen in the Voyager magnetic field data as it passed 11 RIo beneath Io can be interpreted in terms of a slow down in the flow ahead of Io and a deflection to the side given some simplifying assumptions: gradients only in the corotation direction; and normal corotational flow at Voyager 1, joined by straight field lines to altered flow close to Io (Russell, 1999). The principle behind this calculation is that, if the field line begins to become more horizontal along the flow direction, the plasma has slowed on the part of the field line near Io but has not slowed near Voyager. If the field line changes direction to point more radially inward or outward, the flow must have been deflected inward or outward near Io (but not at Voyager). After the flow terminator is crossed the plasma accelerates and turns into the wake, in a manner very consistent with the Galileo data. Figure 4 shows the superposition of the Voyager and Galileo flows in the corotation frame. Since the assumptions are at best only correct to zeroth order, Voyager and Galileo data are consistent in the direction and location of the slowing and deflection, and in the magnitude of the effects. These two data sets suggest that the region of disturbed flow around Io extends to the order of 5 RIo. If the flow is slowed or deflected, then we expect also to find field-aligned currents in these regions that are attempting to resume strict corotational flow. A third set of flow data was obtained in the Io wake by dual-station occultation measurements shown in Figure 5 (Hinson et al., 1998). These data show slow flow in the wake accelerating to corotational velocities at 6 RIo. Taken as a whole these data suggest that the Alfven wing extends from just upstream of Io to at least 6 RJ downstream. The field-aligned current system that is capable of accelerating this with the observed Galileo plasma densities is 2.6 MA. This current is in addition to the current associated with the initial ion mass pick-up (Goertz, 1980) that has been estimated to be similar in size. We note that the Goertz (1980) current arises when ionization occurs in a fast flow. The wake acceleration is of plasma created in a slow flow.

MASS LOADING

If one integrates the mass flow during the Galileo wake passage in the region where the stream lines intersect the moon, then a mass loading rate of only a few tens of kg is found (Russell et al., 1997). (Note that in the final copyedit of that article the region of integration of this estimate was omitted from the text). However, there is strong evidence that closer to 1000 kg/s are added to the torus by Io (Hill et al., 1983). If we accept this number and the typical flow velocity reported by Frank et al. (1996) of 45 km/s near Io, we can calculate the effective cross-section that the mass loading region exhibits to the flow. This value is 43 Io cross-sections or a radial extent of 6.5 RIo. That distance is quite consistent with the region of disturbed flow shown in Figure 4. In short, the mass-loading region must be extended both because there is little of the required mass in the wake region and because the disturbed region (in this otherwise low beta nearly incompressible plasma) extends far from Io in the direction away from Jupiter. Finally, the temperature of the picked up ions also gives a clue to the nature of the interaction since the thermal velocity of the picked up ion equals the bulk velocity at the pick up point. At the edges of the interaction region where the flow velocity increases as it expands behind Io the picked up ions are their hottest. In the center of the wake where the flow is slowest they are coldest (Frank et al., 1996).

Fig. 4. A superposition of the flow vectors obtained by extrapolating the magnetic perturbation seen by Voyager to the neighborhood of Io, and of the flow vectors seen by Galileo (Russell et al., 1999; Frank et al., 1996). Data are in the corotation frame. Fig. 5. The velocity of the wake plasma behind Io measured by interferometric observations during an occultation (Hinson et al., 1998).

SUMMARY AND CONCLUSIONS

While the rate of mass loading of the Io torus in the geometric Io flux tube is less than many of the earlier estimates of near-Io mass loading, the effect of the mass loading on the field-aligned currents is greater than previously estimated because the reacceleration of the cold plasma was not included. The newly added plasma slows the flow in front of Io, while the magnetospheric ends of the field continue to move past Io at nearly their undisturbed velocity. The disturbance caused by the mass loading moves along the magnetic field at the Alfven velocity and the shear in the field is limited by the finite velocity in this sub-Alfvenic flow but, since the disturbance in the flow extends far (6 RIo at least) behind Io, the total current is not limited by the size of Io as it was in the early unipolar inductor model that closed all this current through Io and its ionosphere. The wake currents increase the vertical field in the region immediately behind Io. Since the field strength in this region was used to estimate the possible intrinsic field of Io and the effect of the Io field is to depress the field here, the Io moment may be greater than the initial value estimated perhaps exceeding 1013 Tm3.

The observations made by Voyager 1 and Galileo in their Io flyby passes are quite consistent in this regard. The magnetic perturbation seen by Voyager and the flow disturbance seen by Galileo are very similar. It is important to note that mass pickup in the region to either side of Io where the flow is accelerated (in closing behind Io) is picked-up with a high thermal velocity, i.e. equal to the super-corotational velocity at that location. The flow passing directly over the moon that is moving much slower than the surrounding torus plasma produces cold plasma. This cold plasma is consistent in temperature and composition with the cold torus plasma seen by Voyager. It is quite probable that on flux tubes that intersect Io, more hot plasma is absorbed by Io, than cold ions picked up, despite the higher cold density near Io. Thus the emptier, cold tubes could move inward due to their buoyancy. Perhaps more importantly the flux tubes in the hot torus inside the Io orbit are moving much more rapidly than those in the Io wake region with its cold plasma. Thus, the centrifugal force should cause the hot tubes to interchange with the cold tubes. The colder the tube the further in it should move because these tubes also are the slowest moving. These tubes also should have their plasma confined close to Io and close to magnetic equator where the most sputtering might be expected. Thus, as observed, we would expect the cold torus to be narrowly confined in latitude.

The picture of mass-loading as the source of the field-aligned currents rather than a large potential drop across an electrically conducting body does not alter the original explanation that field-aligned currents generate the decametric radio emissions that are controlled by Io. Much of the treatment of the interaction of Io and its environment has in fact been correct and the present differences between researchers may be as much due to semantics as to real physical differences.

ACKNOWLEDGMENTS

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

REFERENCES

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