4.3 Density and Temperature Isocontours

To illustrate our new 2-D model of the IPT and the effect of choosing values of $\kappa_i = 2$ and $A_{0i}=3$, we present contours of plasma density in Figure 7.

Figure 7: Contours of particle density in the meridian plane for System III longitude of 292$^\circ$. The x-axis gives distance from Jupiter ($R_{J}$), the y-axis gives centrifugal altitude ($R_{J}$). $\kappa _i=2,A_{0i}=3,\kappa _e=2.4,A_{0e}=1.2$. All contour levels are spaced by factor of 2. The electron contours decrease from 3200cm$^{-3}$. The contours for O$^+$, S$^+$ and S$^{++}$ decrease from 1600cm$^{-3}$ and the contours for O$^{++}$ and S$^{+++}$ from 80cm$^{-3}$ .

The torus densities are presented in the meridian plane for a longitude of 292$^\circ$(where the magnetic and centrifugal equators coincide). In order to allow direct comparison with [ Bagenal, 1994, figure 8] we have used the $O_4$ + current sheet magnetic field model. Apart from the differences at the centrifugal equator already discussed, the most notable difference is that the plasma is more tightly confined to the equator at distances beyond about 8${\rm R_J}$, producing an appearance more of a plasma sheet rather than a sharp outer boundary of a torus.

We have also plotted in figure 8 the contours of proton density. It is worth noting that the inputs density and temperature for protons (green lines on figure 4) are very badly known, especially because protons have dropped below the energy threshold of the PLS detector [ Bagenal, 1994] and so the proton density we obtain at the equator (green line on top of figure 6) has a bad reliability (it is however compatible with an upper limit of $60 {\rm cm}^{-3}$ derived from whistler wave analysis [ Crary et al. 1996]).

Figure 8: Contours of proton density in the meridian plane for System III longitude of 292$^\circ$, with $\kappa _i=2,A_{0i}=3,\kappa _e=2.4,A_{0e}=1.2$. The contour levels are spaced by factor of 2.

Nevertheless, we may observe that the maximum proton density is offset from the centrifugal equator (about 8$^\circ$centrifugal latitude). As noted before, the latitudinal structure of the Io torus depends fundamentally on the heavier ions (oxygen and sulfur) which dominate the composition and which more strongly experience the confining centrifugal force than the protons. This results in a rather high electrostatic potential $\Phi_e$ (see figure A2 in appendix) in order to confine the electrons similarly as the heavy ions so as to preserve the plasma neutrality. The consequence on the protons is that the confining centrifugal force is weaker at the equator than the electrostatic force, and this tends to spread them out of the centrifugal equator.

Figure 9: (Left) Contours of temperature for $e^-$, $S^+$ and $O^+$ in the meridian plane for System III longitude of 292$^\circ$. The x-axis gives distance from Jupiter ($R_{J}$), the y-axis gives centrifugal altitude ($R_{J}$). $\kappa _i=2,A_{0i}=3,\kappa _e=2.4,A_{0e}=1.2$. All contour levels are spaced by factor of 2. The electron contours increase from 1eV. The ions contours increase from 10eV.
(Right) Temperature contours assuming an adiabatic L-dependence at the centrifugal equator of L$^{-3}$ (orange line on figure 6). Coloured curves are the trajectories of Ulysses (red) and of Voyager 1 (green).

Figure 9 (left) presents isocontours of temperature for electrons, $S^+$ and $O^+$. The temperature has a minimum at the equator and increases (due to velocity filtration) with latitude. Notice that the latitudinal temperature gradients are stronger for the heavier (sulfur) species than for the oxygen species. We have also plotted Figure 9 (right) the temperature contours obtained assuming that the equatorial temperature decreases adiabatically with radial distance (L$^{-3}$). The spacecraft trajectories of Voyager 1 (green) and Ulysses (red) have been superposed for illustrating how one would expect a temperature increase to be observed by Ulysses on its roughly North-to-South trajectory and by Voyager 1 beyond $7{\rm R_J}$, while the equatorial temperature is assumed to decrease with distance from Jupiter.