Discussion

Some anticorrelation between and can also be seen in some of the results of the particle analyzers aboard Voyager, although it has not been quantified ([Scudder et al. 1981]; [Sittler and Strobel 1987]). However, as we said, Voyager mainly explored the variations with Jovicentric distance near the equator, whereas Ulysses mainly explored the variation with latitude. Indeed, the region involved in Fig. 2 spans in full latitudinal extension but only in Jovicentric distance. Owing to that special trajectory and to the general predominance of the latitudinal gradient over the radial one, most of the variation observed here in and can be ascribed to the change in latitude. This is confirmed by the approximate latitudinal symmetry exhibited in Fig.1 (whereas the small variation in Jovicentric distance should be responsible for most of the slight asymmetry observed; we will return to this point in Section 5.3.).

The presence of the Jovian magnetic field - with the corresponding very small particle gyroradii - makes the physics of the latitudinal and radial variations basically different, since they take place respectively along and across . With the largest density and smallest temperature measured here in the vicinity of equator (i.e., cm with K), the free path of thermal electrons for Coulomb collisions with like particles ([Spitzer 1962]) is . Since , the mean free path is larger away from the equator, and still larger for suprathermal electrons. Other free paths, such as those corresponding to Coulomb encounters with ions and/or with the hot electron population - or to collisional ionization or excitation, or recombination - are of the same order or larger, as are ion free paths (see [Strobel 1989]). On the other hand, one sees in Fig.1 that typically increases by a factor of two - whereas decreases by a factor of four - over about latitude, which corresponds to a distance of only 1 along field lines. This is much smaller than the free paths estimated above. Thus the time for a particle to move over a characteristic scale length along is short compared to other time scales. The reverse is true in the radial direction, since the time scales for diffusion perpendicular to are expected to be very large (see for example [Siscoe and Summers 1981]).

The polytrope relation found here over more than one decade in density is incompatible with the assumption of constant (bulk) temperature along field lines made in the torus models (see [Divine and Garrett 1983], [Bagenal and Sullivan 1981], [Bagenal 1994]), since, as we said, our measured temperature is mostly sensitive to the bulk cold electron population. It would also be difficult to explain our results by longitudinal asymmetries ([Desch et al. 1994]), since such an explanation would require an ad-hoc four-fold temperature variation over longitude, being, by chance, adequately symmetrical.

Our results are also incompatible with an adiabatic ( = 5/3), or CGL ([Chew et al. 1956]) double-adiabatic behaviour. In particular, with an anisotropic distribution, our measurement gives the temperature perpendicular to ([Meyer-Vernet et al. 1993]), and the results are then incompatible with the CGL relation B, since B varies by less than 15 % over latitude. This is not surprising since with free paths so large as compared to the scale height, the traditional fluid closure approximations are not expected to be applicable; the existence of important parallel electric fields strongly violates the CGL ordering scheme further; (anyway, one would not expect to find an adiabatic or double-adiabatic behaviour along field lines, since they are perpendicular to the mean bulk velocity, so that the fluid energy equation has no component parallel to .)

With these large free paths, one should use a microscopic plasma description, i.e., take explicitely the velocity distribution into account. In this case, it is well known that with an isotropic Maxwellian, the temperature should be constant along field lines (see Section 4.3), which is incompatible with our results. Adding a hot Maxwellian tail to the distribution ([Sittler and Strobel 1987], [Bagenal 1994]) cannot explain our results either, since our measurement scheme is roughly insensitive to the hot component; (we will return to this point in Section 4.5). Now, what would happen with an anisotropic Maxwellian, i.e., the so-called bi-Maxwellian? The problem has been formulated in detail by Chiu and Schulz (1978), and applied in particular to Jupiter by Huang and Birmingham (1992) without considering the problem of accessibility in phase space. Under that assumption, which is relevant in the latitude range considered here, the sense of anisotropy expected in the torus ( ) should produce a decrease of with latitude ([Huang and Birmingham, 1992]). To yield a temperature increase, the sense of anisotropy should be opposite; moreover, the relative increase should then be necessarily smaller than that of B, i.e., rather small, whatever the anisotropy factor.

Hence, a microscopic plasma description cannot explain our results if the (bulk) velocity distribution is a Maxwellian or a bi-Maxwellian.

This is not surprising with the above parameters since the collisions are not expected to be sufficient to drive the distributions to local Maxwellians (or bi-Maxwellians) in the presence of the latitudinal gradient. Even if the free paths of thermal particles were not so large, the presence of the suprathermal particles - which have free access to still larger distances since the free paths increase as the fourth power of the velocity - should preclude the achievement of local thermal equibrium. The basic importance of such a non-local behaviour in space plasmas was first noted by Scudder and Olbert (1979) in the context of the solar wind.