4.2.3 Variation in temperature measured by Voyager 1

First of all, we should clarify that the temperatures in Figure 6 are the usual perpendicular temperatures, i.e. defined from the moments of order 2 of the anisotropic bi-kappa distribution, and extrapolated to the centrifugal equator by equation 12. We plot the perpendicular temperatures because we wish to compare them with the temperatures measured by Voyager 1. For easier comparison, since these perpendicular temperatures at Voyager 1 were provided as distinct core and halo temperatures (see Figure 4), we have so plotted (dotted line) in Figure 6 a total (core+halo) temperature of these in situ measurements (this temperature can be interpreted also as the total equatorial temperature in absence of the velocity filtration effect).

On examining the radial profiles of temperatures extrapolated to the centrifugal equator with the bi-kappa model (Figure 6) with those measured at the location of Voyager 1 there are substantial differences. One one hand, since the temperatures were poorly-determined by the Voyager plasma instrument, all the ionic species were assumed to have the same temperature. But, when the temperatures are extrapolated to the equator by using our model under this last assumption, we find straightforwardly from equation 12 and A5 that the temperatures of the different ion species will be different at the centrifugal equator, the sulfur (heavier) ions being colder than the oxygen ions for the same charge state. However, this result is mainly a consequence of the lack of discriminating temperature data at Voyager and we will not so discuss it further. On the other hand, because of velocity filtration, the equatorial temperatures are lower than those measured off the equator. This is particularly noticeable beyond 8${\rm R_J}$ where Voyager 1 dipped more than 1${\rm R_J}$ below the equator (see Figure 1). The net result is that the equatorial temperature profile is much flatter than the radial profile measured at the spacecraft, where the temperature was observed to increase substantially with radial distance. Otherwise stated, and as was first pointed out by Moncuquet [1995], a substantial part of the ion temperature increase measured by Voyager 1 beyond 8${\rm R_J}$ can be ascribed to the increasing centrifugal latitude of the spacecraft. This result was confirmed by Thomas and Lichtenberg [1997], who interpreted their ground-based spectroscopic IPT observations at $6{\rm R_J}$, showing a significant increase in perpendicular ion temperature with distance from centrifugal equator, by using the simplified ``kappa model'' of Meyer-Vernet, Moncuquet and Hoang [1995].

One would expect the plasma to cool on expansion as it diffuses radially outwards from Io. The power laws shown in the figure illustrates what one would expect for isotropic adiabatic expansion, i.e. $n\propto L^{-4}$ and $T\propto L^{-8/3}$ [ Herbert and Sandel, 1995], or, because we assume here a substantial ion temperature anisotropy, for adiabatic expansion under conservation of the first adiabatic invariant, i.e. $T_{\perp}\propto L^{-3}$ (and a total density charge which may decrease also as $L^{-3}$ if we assume a constant centrifugal scale height). Thus, our model yields an equatorial temperature profile until $\sim 9.3 {\rm R_{J}}$ (about the Europa orbit) which may be roughly interpreted as the adiabatic cooling of a plasma in radial diffusion, while there is still a ``missing'' heating source beyond this distance in order to fully explain the Voyager 1 PLS temperature data. Our model is also more consistent with UV spectra observations at Voyager 1 and ground-based observations [ Herbert and Sandel, 1995, Thomas, 1995]. Indeed, the vertical distribution of emissions from the torus suggests a decrease in temperature with distance. Note that the temperature anisotropy works in the opposite direction - the perpendicular temperature is greater at the equator when there is significant anisotropy (from equation 12 or [ Huang and Birmingham, 1992] for the bi-Maxwellian case).