The
overall structure of the main auroral spots is consistent with the
expectations from ray-tracing models (e.g., Hinton et al., 2019). Our
model indicates that the spacing of the main and reflected Alfvén wings
is consistent with previous work and depends upon the density profile
along the flux tube. Furthermore, the structure of the field-aligned
currents produced by the model is consistent with the transverse
displacement in secondary spots observed by JIRAM (Mura et al., 2018).
The results suggest that this may be due to the generation of
field-aligned currents at the surface of Io and its ionosphere. In
addition, the secondary structure in the currents is consistent with the
reflection of Alfvén waves from the boundary of plasma torus, which can
occur over time scales of about a minute. However, one puzzle in the
results is that when the parallel electric fields due to current
limitation are included, these secondary reflections do not produce
significant potential drops.
The complicated structure after the passage of the RAW suggests that the
waves are subject to phase mixing, particularly while passing through
the dense plasma torus. This makes the current structure more
complicated, especially after the passage of the reflected Alfvén wing.
Recently, Schlegel and Saur (2022) considered the effect of different
travel times on the alternating spots and concluded that this was only a
minor effect. However, in our model, the difference in the passage time
of an Alfvén wave from one ionosphere to another between L=5.90 and
5.95, a difference of about 1 Io radius, is 22.5 seconds in the
low-density model and 30.6 seconds in high-density model, much larger
than their assumed time of 3.7 seconds. In addition, the RAW spot occurs
after the wave has traveled through the torus 1.5 times, so the
difference is 50% larger. So it appears plausible that the travel time
difference, i.e., phase mixing, can be an important effect down the tail
from the main spot. This may be related to the bifurcated auroral tail
sometimes seen downstream from main spot (Szalay et al., 2018; Mura et
al., 2018).
In summary, this new model for the propagation of Alfvén waves generated
by Io has revealed some interesting points and raised some questions
about this interaction:
- The model confirms that reflections from the torus boundary are
significant and give rise to the overall pattern of currents,
indicating that the spacing of auroral emissions is dependent on the
density along the flux tube. The transmission through the torus
boundary is stronger in the high-density case since the density
contrast is not as large, leading to higher currents at the ionosphere
for this case.
- The Alfvén wave pattern depends strongly onthe position of Io within
the plasma torus. The main and reflected Alfvén wings are farther
apart and the magnitude of the currents is stronger in the northern
hemisphere when Io is in this hemisphere.
- In addition to the main reflections, there are weaker secondary
reflections of waves bouncing between Jupiter’s ionosphere and the
plasma torus. These may be responsible for the continued auroral
emissions between the MAW and RAW spots. These secondary reflections
appear to be particularly strong in the hemisphere opposite to the
location of Io.
- The field-aligned currents due to the main Alfvén wing (MAW) have a
characteristic U-shape due to the generation of field-aligned currents
at the Jupiter-facing and anti-Jupiter side of Io. The repetition of
this shape due to the secondary reflections may be related to the
structure of the auroral emissions as seen by JIRAM (Mura et al.,
2018).
- The length of the footprint tail is a function of the conductance in
Jupiter’s ionosphere. A conductance of 0.1 S leads to strong
dissipation of the wave on each bounce, while for a 10 S conductance
the waves can persist for many bounces. However, the tails extending
over 100° in longitude reported by Mura et al. (2018) may require more
than the linear propagation of the Alfvén waves.
- The currents produced by Io are strong enough to lead to potential
drops of up to 100 kV along the main Alfvén wing. However, the current
limitation due to these potential drops keeps the currents in the
secondary reflections limited, so that it is not clear from the
present work how particles are accelerated by these reflected waves.
- At long distances along the tail, phase mixing and the presence of
multiple reflected waves can complicate the structure of the currents.
For high conductance in the ionosphere, the upward and downward
currents can reverse with the upward currents appearing on the high
latitude side of the footprint.
While this model shows some interesting features, there are still many
unanswered questions. Although our model includes the electron inertial
effect thought to be responsible for the electric field producing a
broadband electron distribution, there does not seem to be significant
electric fields produced by this effect. This may be due to the large
size of Juno with respect to the electron inertial length. However, if
the currents are strongly filamented, the importance of the electron
inertial effect would be increased. Including the possibility of a
turbulent cascade to smaller scales (Hess et al., 2010; Saur et al.,
2002) or ionospheric feedback effects (Lysak, 1991; Lysak and Song,
2002; Moirano et al., 2021) would give a more complete understanding of
the propagation of Io-generated Alfvén waves in Jupiter’s magnetosphere.