The equations are modeled in a frame co-rotating with Jupiter’s
magnetosphere. In this frame, Io moves westward at a speed of 57 km/s,
leading to an emf of VIoB 0 of 120
mV/m. This effect is included in the second term in the equation forE ν in equation . Io is modeled as a cloud of
conductivity which is constant over the diameter of Io and falls off as
the distance squared in Io’s ionosphere. As noted above, the simulation
is based on magnetic coordinates, so that Io moves in a plane inclined
about 10° from the magnetic equator. Similarly, the mass density in the
Io plasma torus is centered on the centrifugal equator. We use two
density profiles: a “high-density” case based on the density model of
Dougherty et al. (2017), and a “low-density” case based on the model
considered by Ray et al. (2009). These densities are taken to be
independent of longitude along the centrifugal equator. The density and
the resulting Alfvén speed cA are plotted in
Figure 1, with Figures 1a and 1b giving the density for the low- and
high-density cases, respectively,
while
Figures 1c and 1d show the corresponding Alfvén speed profiles. The
high-density case results in a density of 200 cm−3 at
a radial distance of 2 RJ, while the low-density case
has 0.1 cm−3 at this altitude. The trajectory of Io in
magnetic coordinates is plotted as a solid line in these figures. These
models have a total Alfvén transit time from one ionosphere to the other
of 16 minutes in the high-density case and 12 minutes in the low-density
case. These values are comparable to the one-way transit times between
12.5 and 15 minutes in the model of Hinton et al. (2019).