# The Io, Europa and Ganymede auroral footprints at Jupiter in the
ultraviolet: positions and equatorial lead angles

###### Abstract

Jupiter’s satellite auroral footprints are a consequence of the interaction
between the Jovian magnetic field with co-rotating iogenic plasma and the
Galilean moons. The disturbances created near the moons propagate as Alfvén
waves along the magnetic field lines. The position of the moons is therefore
”Alfvénically” connected to their respective auroral footprint. The angular
separation from the instantaneous magnetic footprint can be estimated by the
so-called lead angle. That lead angle varies periodically as a function of
orbital longitude, since the time for the Alfvén waves to reach the Jovian
ionosphere varies accordingly. Using spectral images of the Main Alfvén Wing
auroral spots collected by Juno-UVS during the first forty-three orbits, this
work provides the first empirical model of the Io, Europa and Ganymede
equatorial lead angles for the northern and southern hemispheres. Alfvén
travel times between the three innermost Galilean moons to Jupiter’s northern
and southern hemispheres are estimated from the lead angle measurements. We
also demonstrate the accuracy of the mapping from the Juno magnetic field
reference model (JRM33) at the completion of the prime mission for M-shells
extending to at least 15 RJ. Finally, we shows how the added knowledge of the
lead angle can improve the interpretation of the moon-induced decametric
emissions.

JGR: Space Physics

Aix-Marseille Université, CNRS, CNES, Institut Origines, LAM, Marseille,
France Southwest Research Institute, San Antonio, Texas, USA University of
Texas at San Antonio, San Antonio, Texas, USA School of Cosmic Physics, DIAS
Dunsink Observatory, Dublin Institute for Advanced Studies, Dublin, Ireland
STAR Institute, LPAP, Université de Liège, Liège, Belgium Department of
Astrophysical Sciences, Princeton University, Princeton, NJ, USA Institute for
Space Astrophysics and Planetology, National Institute for Astrophysics, Rome,
Italy Sapienza University of Rome, Rome, Italy Department of Electrical
Engineering and Information Science, National Institute of Technology (KOSEN),
Niihama College, Niihama, Japan Johns Hopkins University Applied Physics
Laboratory, Laurel, MD, USA Institut de Recherche en Astrophysique et
Planétologie, CNRS-UPS-CNES, Toulouse, France Minnesota Institute for
Astrophysics, School of Physics and Astronomy, University of Minnesota,
Minneapolis, MN, United States NASA Goddard Spaceflight Center, Greenbelt, MD
20771, USA Space Research Corporation, Annapolis, MD 21403, USA

V<EMAIL_ADDRESS>
Over 1600 ultraviolet spectral images of the Io, Europa and Ganymede
footprints from Juno are analyzed

Empirical formulae for the Io, Europa and Ganymede lead angles derived from
Juno data are provided

Alfvén travel time estimates are derived, constraining the Alfvénic
interaction at the 3 innermost Galilean moons

## Plain Language Summary

The interaction between the Jovian magnetospheric plasma and the Galilean
moons gives rise to a complex set of phenomena, including the generation of
auroral spots magnetically related to the moons and the generation of radio
emissions. The magnetic perturbations local to the moons propagate at a finite
speed along the magnetic field lines, and reach the northern and southern
Jovian hemispheres where they produce the auroral spots. Studying the position
of these auroral spots and how they vary over a complete Jovian rotation
provides information about the magnetic mapping, as they map directly to the
actual physical positions of the moons. The magnetic field model derived from
Juno’s prime mission is in good agreement with the observation of the
satellite footprints. This paper provides information about how the
electromagnetic perturbation resulting from the interaction propagates at a
finite speed to create auroral spots, leading to an angular shift between the
instantaneously magnetically-mapped position of the moon and the auroral
footprint, a quantity also known as the ”equatorial lead angle”. The present
work provides an empirical fit of the equatorial lead angle for Io, Europa and
Ganymede derived from Juno data.

##  1 Introduction

Jupiter’s volcanically-active moon Io is a major source of plasma within the
Jovian magnetosphere. Over a ton per second of sulfur dioxide escapes from the
moon as a neutral cloud around the moon. High-energy electrons trapped in
Jupiter’s magnetosphere dissociate and ionize the neutral material, producing
ions which get picked up by Jupiter’s strong rotating magnetic field, forming
the Io plasma torus. The plasma is then radially transported outwards over the
timescale of several weeks as a plasma sheet with a typical scale height of
about 1 RJ (1 RJ = 71492 km), and confined around the centrifugal equator,
near the magnetic equator, i.e., the points along the magnetic field lines
that are farthest from the spin axis of Jupiter [<]e.g.,¿[]Acuna1983,
Belcher1983.

Evidence of the magnetospheric interaction at Io was discovered early on
through the detection of decametric radio emission [Bigg (1964)]. The
subsequent Voyager 1 measurements near Io led to formalize the interaction
model at the moon resulting in the generation of an Alfvénic disturbance
[Neubauer (1980), Goldreich Lynden-Bell (1969), Acuna . (1981), Belcher .
(1981)]. These Alfvén waves propagate to Jupiter along the magnetic field
lines towards both polar regions, and their multiple reflections off of the
plasma density gradients along the way were later proposed to be responsible
for the multiple Io-controlled decametric radio arcs observed [Gurnett Goertz
(1981)].

When the Alfvénic perturbations reach high Jovian latitudes, they accelerate
electrons towards and away from Jupiter, as well as protons, leading to the
generation of the auroral footprints and decametric radio waves [SLG. Hess,
Delamere . (2010), Szalay, Bagenal . (2020)], which were initially detected in
the infrared (IR) and later in the ultraviolet (UV) [Connerney . (1993),
Clarke . (1996), Prangé . (1996)]. Detection of the Europa and Ganymede
auroral footprints using the Hubble Space Telescope (HST) followed shortly
after [Clarke . (2002)].

The overall strength of the moon-magnetosphere interaction depends on the
magnetic field strength, the plasma density, the conductivity, as well as the
electron acceleration efficiency [Saur . (2013), Sulaiman . (submitted)].
Because Jupiter’s magnetic dipole is tilted from its spin axis by about 10
degrees, the plasma sheet sweeps through the Galilean moons twice every
$\sim$10 hour-rotation period. In the reference frame centered about the
plasma sheet, the moons travel up and down the sheet, experiencing denser
plasma condition at its the center. The multiple reflections of the Alfvén
waves on Alfvén speed gradients, such as near the ionosphere, create multiple
auroral spots, whose relative position, morphology, and distribution is
modulated by the moon centrifugal latitude, as reported by remote sensing
observations [<]e.g.,¿[]Bonfond2008, Mura2018.

Extensive campaigns using the Hubble Space Telescope (HST) have allowed
categorizing the variable morphology of the Io footprints structure as a
function of the location of Io with respect to the plasma sheet [Gérard .
(2006), Bonfond . (2008), Wannawichian . (2013)]. These studies showed that
the Main Alfvén Wing (MAW) spot was sometimes preceded by a leading spot,
named the Transhemispheric Electron Beam (TEB) spot, for a very specific range
of sub-Io Jovian longitudes. In that case, the Alfvén waves generated in the
wing of the interaction region later reached Jupiter’s ionosphere. This means
the beam of electrons generating the TEB spot was accelerated anti-planetward
by the MAW on the opposite hemisphere, then travelled along the magnetic field
line throughout the torus, unaffected by the higher plasma torus density there
[Bonfond . (2008), SLG. Hess . (2013)].

The Juno mission has brought a wealth of new observations that significantly
enhanced our understanding of the moon-magnetosphere interaction [Bolton .
(2017), Connerney . (2017)]. Juno crosses the magnetic shells connected to the
orbits of Io, Europa and Ganymede at least twice per orbit. Not only did Juno
measure the field and particles within the magnetic fluxtube connected to the
discrete auroral footprint spots or tail, but it also provided unprecedented
infrared and ultraviolet observations both at the highest spatial resolution
ever achieved [Mura . (2018)], and with viewing geometries not accessible from
HST [Hue, Greathouse . (2019)].

Prior to Juno, there was a debate regarding the processes responsible for the
footprint tail emission. One set of studies favored a quasi-steady current
system transferring angular momentum from the Jovian ionosphere to the sub-
corotating plasma in the moon wakes, and which would be characterized by beams
of electron discrete in energies [<]e.g.,¿[]Goldreich1969, Hill2002,
Delamere2003, Su2003. Other studies suggested it results from the multiple
bouncing of the Alfvén waves generated at the moons, which would be
characterized by bidirectional electron populations with broadband energy
distributions [<]e.g.,¿[]Bonfond2009, Hess2010, Bonfond2017b, Crary1997,
Jacobsen2007.

Early Juno measurements demonstrated the Alfvénic nature of the interaction
associated with the Io footprint tail [Szalay . (2018), Damiano . (2019),
Gershman . (2019), Sulaiman . (2020), Sulaiman . (submitted), Szalay,
Allegrini . (20202)]. Szalay2018, Szalay2020b showed that the electron energy
flux, obtained by the multiple Juno-JADE measurements along the Io footprint
tail, is a function of the angular separation along Io’s orbit between the
moon and the MAW spot tracked from Jupiter’s ionosphere to the satellite
orbit. This angle is also known as ”Io-Alfvén tail distance”. Juno measured
upward ion conics, i.e. protons with angular distribution concentrated along
the loss-cone, detected simultaneously with ion cyclotron waves, showing that
energetic ions are also generated from moon-magnetosphere interaction [Clark .
(2020)], as well as low-energy ion acceleration in the vicinity of the Main
Alfvén Wing, both near the ionosphere and near the Io torus boundary [Szalay,
Bagenal . (2020)]. Additionally, the cyclotron maser instability (CMI) driven
by a loss-cone distribution has been established as a major process at Jupiter
in generating hectometric and decametric emissions, induced or not by the
Galilean moons [Louarn . (2017), Louarn . (2018), CK. Louis . (2020)].

Alfvénic acceleration processes were also observed when crossing the fluxtube
connected to Ganymede’s footprint tail [Szalay, Allegrini . (20201)]. One
particular Ganymede fluxtube crossing (on PJ30, 8 Nov. 2020), during which
Juno was connected for the first time to the leading-most Ganymede auroral
spot, brought a set of in-situ and remote sensing measurements consistent with
what was expected during a TEB crossing [Hue . (2022)]. Unlike for Io and
Ganymede, crossing through the fluxtube connected to the Europa footprint tail
showed signs of electron distribution resulting at least in part from
electrostatic acceleration processes [Allegrini . (20201)]. Whether this is a
fundamental difference of the interaction at Europa, or that it actually also
corresponded to a TEB crossing remains to be ascertained by additional studies
of the Europa footprint tail crossings. Radio emissions are also observed
associated with Ganymede’s interaction [CK. Louis . (2020)].

The scope of this paper is to process the ultraviolet auroral footprint
observations performed from the first perijove (PJ, hereafter) on 8 Aug 2016
until PJ43 (5 Jul 2022) with the ultraviolet spectrograph on Juno (Juno-UVS).
Section 2 describes the observations and data reduction procedure. In section
3, the reported satellite footprint locations are compared against the
predicted satellite footpaths from the magnetic field model JRM33 [Connerney .
(2022)]. From the position of the MAW spot of the satellites, the equatorial
lead angle can be estimated using a magnetic field model. The equatorial lead
angle is the angular shift, calculated along the orbital motion of the moons,
between the actual position of the moons and the position of the MAW footprint
mapped instantaneously to the orbital plane of the moon. We then calculate the
equatorial lead angles for Io, Europa and Ganymede and provide an empirical
fit on section 4, as well as estimates of the Alfvén travel times for each of
the three moons. We subsequently discuss the lead angle variation measured in
section 5. Finally, in section 6, we present an additional example on the use
of the lead angle for the interpretation of the Ganymede-induced decametric
emission.

##  2 Juno-UVS observations

Juno is a spin-stabilized spacecraft placed in a polar and highly eccentric
orbit around Jupiter since July 2016 [Bolton . (2017)]. Each orbit, Juno
performs a close flyby of the northern polar region first, reaches closest
approach at lower Jovian latitudes at an altitude of about 4000 km, and then
flies above the southern polar region. Because Juno’s orbit is highly
elliptical and because its closest approach velocity with respect to Jupiter
is about 58 km/s, it takes Juno about 2 hours to fly from north to south pole.
This implies that the spatial resolution of the remote sensing instrument such
as UVS varies drastically over the course of a perijove observation sequence.
As the mission is progressing, the orbital period, which was initially around
53 days, was reduced to a shorter orbit, and will be reduced down to 33 days
around PJ75 (15 Aug 2025). Each major orbital period reduction follows a
Galilean moon flyby. Juno’s orbit precesses over time and the sub-spacecraft
PJ latitude increases as the mission continues. The viewing window of UVS over
the northern and southern auroras grows increasingly more asymmetric with the
mission, with the viewing window of the northern aurora decreasing over time.

Some of the magnetospheric goals of Juno include performing in-situ
measurements of the particle population in Jupiter’s magnetosphere using an
electron and ion sensors suite, while remotely sensing the associated infrared
and ultraviolet aurora they may trigger on Jupiter or on the Galilean moons
[Bagenal . (2017)]. The Ultraviolet Spectrograph (UVS) is a photon-counting
imaging spectrograph operating in the 68-210 nm range [Gladstone . (2017)].
Each spin of Juno, UVS records a swath of UV emission along its 7.2∘-long
slit, with a typical point-source integration time of 17 ms. The point-spread
function (PSF) and spectral resolution are respectively 0.1∘ and 1.3 nm, at
best [Davis . (2011), Greathouse . (2013)], meaning that UVS can resolve
features on Jupiter down to 60 km at PJ. Because Juno is flying above both
auroral regions at higher altitude, UVS can rather resolve features in the
$\sim$150-400 km range there. Counts recorded on the detector are then
converted into brightness using the instrument effective area derived from
thousands of stellar observations recorded throughout the mission in between
PJ observation sequences [Hue, Gladstone . (2019), Hue . (2021)].

UVS is equipped with a scan mirror that allows its field of regard to be
shifted up to $\pm$30∘ away from the spin plane. Juno’s spinning nature
combined with UVS’ mirror pointing capability allows building up complete maps
of Jupiter’s aurora by co-adding consecutive swaths of data. The best temporal
resolution of UVS is constrained by the spin rate of Juno and cannot be less
than 30 seconds.

The satellite auroral footprints represent a direct magnetic mapping to a
given orbital distance, through the prism of the sub-Alfvénic interaction
around each moon. It is worth differentiating at this point magnetic mapping
from Alfvénic mapping. The Main Alfvén Wing spot is Alfvénically connected to
the physical position of the moon, which differs from the instantaneous field-
line tracing magnetically connecting the moon and Jupiter’s ionosphere.
Because of the Jovian rotation and the moon orbital motion, there is a
displacement of the satellite footprints location between two consecutive UVS
images recorded 30 seconds apart, which can be estimated considering each
moon’s synodic period:

$P^{syn}_{moon}=\frac{P_{J}\,P_{moon}}{P_{moon}-P_{J}},$ (1)

where PJ and Pmoon are respectively the rotation period of Jupiter and orbital
periods of a moon. Relationship (1) leads to P${}^{syn}_{io}$ = 12.89 h;
P${}^{syn}_{europa}$ = 11.22 h; P${}^{syn}_{ganymede}$ = 10.53 h. Over the
course of a Juno spin ($\sim$30 seconds), the moon spans a longitudinal sector
of $\Delta\lambda_{moon}=(360/P^{syn}_{moon})\times 30$, where
$P^{syn}_{moon}$ is in seconds. This leads to
$\Delta\lambda_{io}\,=\,0.23^{\circ}$;
$\Delta\lambda_{europa}\,=\,0.27^{\circ}$;
$\Delta\lambda_{ganymede}\,=\,0.28^{\circ}$ between two consecutive swaths.
Over one Juno spin and using the JRM33 model, this leads to a displacement of
the instantaneous field line from the moon to Jupiter’s northern ionosphere up
to 223 km, 220 km, 191 km, respectively for Io, Europa and Ganymede. In the
south, that same smearing ranges up to 141 km, 136 km, 114 km for Io, Europa
and Ganymede. Note that all longitudes ($\lambda$) quoted in this work are
west longitudes in the System III reference frame, and are calculated
according to the 1965 system 3 rotation period [Dessler (1983)].

In order to increase the signal to noise ratio (SNR), without smearing the
signal of the satellite footprint emission, the choice was made to bin the UVS
data by 2 consecutive spins worth of data. Various auroral emissions may be
present close to the footprints, such as emission from the main oval [Bonfond
. (2021), Ebert . (2021)], injection signatures [<]e.g.,¿[]Bonfond2017, or
increased background radiation [Bonfond . (2018), Kammer . (2019)]. The change
of geometry, background emission and SNR makes challenging extracting the
precise location of the footprints, particularly for the Europa and Ganymede
footprints, generally located rather close to the main oval emission and
auroral injections. For these reasons, the footprint locations were manually
extracted by visual inspection of consecutive series of 2 spins-averaged UVS
data. Since the moons are not in co-rotation with Jupiter, identifying the
satellite footprints over consecutive spins worth of data is achieved by
visually inspecting auroral spots that are in sub-corotation around a
background of mostly corotating auroral emission. Figure 1 shows an example of
consecutive 2-spin averaged spectral image recorded by UVS of the Io, Europa
and Ganymede footprints.

Figure 1: 2-spin averaged Juno-UVS spectral images of the Io and Europa
footprints (panel A), and the Ganymede footprints (panel B) over the southern
hemisphere. The UVS nadir time of the two consecutive spins are listed as UTC
time. The instantaneous moon magnetic footprint positions according to the
JRM33 model is shown as orange dots along the satellite footprints, also
calculated using JRM33 and shown as solid green line. The satellite footpath
of Io from Bonfond2017 is shown as dashed green lines. The solid white lines
show the reference location where the main oval is observed [Bonfond .
(2012)].

The uncertainties in the derived location of the different observed footprints
were calculated as the quadratic combination of the uncertainty due to the
instrument point-spread-function (PSF), and the uncertainty due to the
projected scale height $H$ of the footprint emission curtain. While the former
uncertainty only depends on the distance between Juno and the footprint of
interest, the latter depends on the footprint emission angle as seen by Juno.
The uncertainties on the footprint longitude ($\lambda$), latitude ($\phi$)
therefore reads:

$\sigma_{\lambda,\phi}^{2}=\sigma_{PSF}^{2}+\sigma_{P\,\lambda\,\phi}^{2},$
(2)

where $\sigma_{PSF}$ is calculated as the projection of the $\sim$ 0.1∘ UVS
PSF along the latitude and longitude grid. $\sigma_{P\,\lambda\,\phi}$ is
calculated as the projected extent of the footprint emission curtain, $H$, as
illustrated on figure 2, assuming as a first approximation that the auroral
curtain is vertical. P is given as P = H/tan $\beta$, and $\beta$ = $\pi/2$ \-
$e$ \- $\epsilon$, where $e$ (emission angle) and $\epsilon$ are angles
calculated using NAIF’s SPICE kernels [CH. Acton (1996), C. Acton . (2018)].
$H$ was taken as 366 km, i.e., the typical scale height of a Chapman profile
derived from Io’s MAW spot by Bonfond2010.

Figure 2: Uncertainty calculation on the derived latitude and longitude of the
footprints. Panel A: calculation of the projected height of a typical auroral
footprint vertical emission P along the Juno line of sight. The latitude and
longitude uncertainty ($P_{\phi}$, $P_{\lambda}$) are calculated through the
decomposition of $P$, exaggerated here for illustration purposes, along the
latitude and longitude grid (panel B). $e$ is the emission angle, while
$\beta$ and $\epsilon$ are two angles used to calculate the projection of $P$.

Only the data recorded by UVS when Juno was 1.5 hours about perijove was used,
i.e., when the $\sim$ 0.1∘ PSF projected at 45∘ on Jupiter’s surface was lower
than the typical width of the footprints as previously derived from HST
[Bonfond (2010)]. From PJ1 until PJ43, this results in a set of 211 (Io), 108
(Europa) and 160 (Ganymede) 2-spin averaged UVS images in the north, and 585,
264 and 299 in the south for Io, Europa and Ganymede, respectively. The
projection altitude of the UV data on Jupiter used for this work was 900 km
above the 1-bar level, after Bonfond2010, Szalay2018.

##  3 Satellite footprint locations

Measuring accurately the location of the satellite footprint emission gives a
precise magnetic mapping of the orbital position of the moons. Comparing the
observed footprint position of, e.g., Io, against the predicted magnetic
mapping of that moon gives an estimate of the mapping accuracy. Earlier
magnetic field models of Jupiter were constructed using in-situ spacecraft
measurements as well as the Io footprint location derived from IR and UV
observations. This initially allowed Connerney1998 to constrain the VIP4
model, using observations of the Io footprints in the IR. When employing a
larger set of Io footprint observations obtained in the UV, the method was
extended by Hess2011 to produce the VIPAL magnetic field model. That model
additionally included the longitudinal constraint on the Io footprint
location, which originates from the finite Alfvén travel time between the
interaction region near the moon to Jupiter’s ionosphere. Later, Hess2017
further constrained Jupiter’s magnetic field model by adding also Europa’s and
Ganymede’s auroral footprint locations to produce the ISaAC magnetic field
model.

The position of the Io, Europa and Ganymede footprints are presented in figure
3, and are plotted against the satellite footpath contours predicted from the
JRM33 model [Connerney . (2022)], combined with the Juno-era current sheet
model [Connerney . (2020)]. Unlike the HST observations, UVS observed the
footprints from a wide range of emission angles ($e$ on figure 2) from 1∘ to
77∘, as well as from a wide range of altitude, from 0.3 RJ to 2.6 RJ.

Figure 3: Extracted position of the Io, Europa and Ganymede Main Alfvén Wing
footprints in the north (top panels) and south (bottom panels), using Juno-UVS
data recorded from perijoves 1 to 43 and color-coded according to the emission
angle observed by Juno-UVS. The solid red lines show the reference oval from
Bonfond2012. The black dotted line show the satellite footpaths as predicted
from the JRM33 model [Connerney . (2022)].

Because of the precession of Juno’s orbit, Juno-UVS gets an increasingly
shorter look over the northern aurora as the mission progresses. This causes a
greater density of footprint position measurements in the south, despite the
rapid increase of Juno’s altitude over the south pole during the outbound leg.
The magnetic field model obtained after the completion of the prime mission
(JRM33) predicts a magnetic footpath for the satellite in very good agreement
with the Juno-UVS observations [Connerney . (2022)]. One region which
previously showed significant differences between the observed and predicted
satellite footprint location is the auroral kink sector, at longitudes from
80∘ to 150∘ in the northern hemisphere only, for which Grodent2008 suggested
the inclusion of a magnetic anomaly to the existing magnetic field model at
that time, in order to better fit the footprint location. Early Juno
measurements for instance showed significant differences between the predicted
Europa footprint location in that sector, and the observed one [Allegrini .
(20202)]. JRM33 is now in very good agreement with the observed MAW spot
positions in that sector for all 3 inner Galilean moons.

Despite the more extended UVS coverage than HST in the south, there are
several longitude gaps in the northern MAW observation not covered by Juno-UVS
as of PJ43. For the northern Io MAW spot, there are gaps at footprint
longitudinal sectors of 260∘-280∘; 100∘-118∘; 342∘-20∘. For the northern
Europa MAW, the gaps are 300∘-80∘; 175∘-206∘; 215∘-238∘; 250∘-290∘. For the
northern Ganymede MAW, the main longitude gap is 280∘-130∘. The MAW footprint
latitude/longitude locations for Io, Europa and Ganymede are provided in the
supporting information. The difference in coverage with previous HST
observations can be compared with figures 1 and 2 showed in the supporting
information of Bonfond2017b.

By binning the measured MAW positions over 1.5∘-wide longitudinal sector to
minimize the measurements scattering, and only considering the MAW spot
position recorded at emission angles lower than 20∘, one can assess the
accuracy of magnetic field models, such as JRM33, while limiting the
uncertainty resulting from the range of viewing geometries. For Io, the
average distance between the JRM33-computed reference footpath and the
observed MAW positions is 511 $\pm$ 28 km in the north and 274 $\pm$ 64 km in
the south. For Europa, these numbers are 141 $\pm$ 26 km in the north and 322
$\pm$ 61 km in the south. For Ganymede, these numbers are 213 $\pm$ 44 km in
the north and 343 $\pm$ 64 km in the south. These numbers provide an order-of-
magnitude estimate in mapping uncertainty between the model and the
observations, and vary slightly ($\sim$10%) depending on the way the UVS data
is binned (e.g., longitudinal and emission angle binning).

The position of the MAW spot of the moons, together with a magnetic field
model, is a key ingredient to estimate the equatorial lead angle, which is the
focus of the next section.

##  4 Lead angles

The equatorial lead angle ($\delta$) is the angular separation between the
position of the moon and the magnetically-mapped MAW footprint onto the
orbital plane. The lead angle is determined by the sum of the physical
processes occurring between the interaction region around the moon and
Jupiter’s ionosphere. In this work that uses Juno-UVS data, it is calculated
by:

  1. 1.

measuring the position of the MAW spot at a given time t0,

  2. 2.

determining the position of the moons at the same time t0 from the
ephemerides,

  3. 3.

tracing back the position of the MAW spot in the moon orbital plane using a
magnetic field model,

  4. 4.

calculating the longitudinal difference between the moon and the back-traced
MAW spot, hence the equatorial lead angle.

Juno in-situ instruments provided invaluable measurements of the particle
distribution on the magnetic field lines connected to the satellite footprints
and tails, such as measurements connected to Io [Szalay . (2018), Clark .
(2020), Sulaiman . (2020), Sulaiman . (submitted), Szalay, Allegrini .
(20202)], Europa [Allegrini . (20201)] and Ganymede [Szalay, Allegrini .
(20201), CK. Louis . (2020), Hue . (2022)]. Szalay2020b showed that the
exponential decrease in precipitating electron energy flux, obtained from the
Juno-JADE instrument when Juno was magnetically connected at various distances
downstream the Io footprint tail, was better organized when considering the
angular separation along Io’s orbit between Io and an Alfvén wave back-traced
from Jupiter’s ionosphere to the moon orbital plane, as the power decays
farther from the moons for each subsequent bounce of the initial Alfvén wave
generated near the moon. Further, Sulaiman2023 showed the Poynting fluxes and
field-aligned currents to similarly exhibit a decay as a function of the same
downtail angle. That quantity, coined ”Io-Alfvén tail distance” by
Szalay2020b, wraps up the knowledge of the equatorial lead angle within. Here,
we provide critical updates unique to Juno’s observational platform allowing
for the calculation of Alfvén angles for Io, Europa, and Ganymede.

Figure 4: Northern lead angle for Io (top), Europa (middle) and Ganymede
(bottom) using Juno-UVS dataset of the Main Alfvén Wing from PJ1 until PJ43.
The vertical solid black lines indicate the location when the moons are at the
center of the plasma sheet. The red lines correspond to the best fit obtained
with eq. (3). The red-dashed lines correspond to the 3$\sigma$ uncertainty on
the fit parameters. Figure 5: Same as figure 4 for the south.

Figures 4 and 5 display the equatorial lead angle in the north and south,
respectively, inferred from Juno-UVS and using the JRM33 magnetic field model
[Connerney . (2022)] combined with the Juno-era current sheet model [Connerney
. (2020)], and color-coded according to the perijove it was recorded at. The
lead angle depends mainly on the travel time variation of the Alfvén waves
through the higher plasma density region of the plasma sheet. Assuming a
plasma sheet around Jupiter with uniform and constant plasma density to first
order, one would expect a sinusoidal modulation of that angle with the
latitudinal separation between the moons and the central part of the plasma
sheet over the course of a Jovian rotation [SLG. Hess, Pétin . (2010)].
Figures 4 and 5 are adjusted with a Fourier series, such that:

$\delta=a_{0}+\sum_{n=1}^{\infty}a_{n}\,\cos nw\lambda+b_{n}\,\sin nw\lambda$
(3)

The best fit parameters of equation 3 were estimates using a least-squares
minimization technique [<]MPFIT package,¿[]Markwardt2009, and are listed on
Table 1. In order to assume periodicity in the fit, the measured lead angles
were replicated in the $[-2\pi:4\pi]$ interval. Because of the sparsity of the
Europa and Ganymede data, fitting the data with higher order Fourier series
introduces oscillations. The lead angle data on these two moons is therefore
fitted using a first order Fourier series. For Io, a second order Fourier
series best reproduces the observations, based on the weighted sum of squared
residuals, though producing larger uncertainties of the retrieved fit
parameters.

The averaged values of the northern and southern Io lead angles are 4.3$\,\pm
0.7$ degrees and 4.1$\,\pm 0.6$ degrees, respectively. For Europa, these
values are 5.8$\,\pm 0.9$ degrees in the north, and 7.0$\,\pm 0.5$ degrees in
the south. For Ganymede, the averaged northern and southern lead angles are
12.3$\,\pm 1.3$ degrees and 13.0$\,\pm 1.3$ degrees, respectively. The
uncertainties in the averaged lead angle is calculated using the 3-sigma
uncertainties of the derived fit parameters, and are tighter in the south, due
to the denser dataset. The averaged northern and southern lead angles value
overlap for each individual moon, meaning that the Alfvén travel time is
similar between hemispheres.

| North | South
---|---|---
Io |  $\delta$ = 4.26 + 2.64 $\cos$ $\lambda$ \+ 0.50 $\sin$ $\lambda$ |  $\delta$ = 4.14 - 1.89 $\cos$ $\lambda$ \- 0.70 $\sin$ $\lambda$
| \+ 0.20 $\cos$ 2 $\lambda$ \+ 0.126 $\sin$ 2 $\lambda$ | \+ 0.22 $\cos$ 2 $\lambda$ \- 0.12 $\sin$ 2 $\lambda$
Europa |  $\delta$ = 5.78 + 3.29 $\cos$ 0.99 $\lambda$ \+ 1.41 $\sin$ 0.99 $\lambda$ |  $\delta$ = 7.06 - 3.37 $\cos$ $\lambda$ \+ 0.15 $\sin$ $\lambda$
Ganymede |  $\delta$ = 12.45 + 6.16 $\cos$ 0.98 $\lambda$ \+ 3.64 $\sin$ 0.98 $\lambda$ |  $\delta$ = 12.97 - 5.39 $\cos$ 0.99 $\lambda$ \- 4.50 $\sin$ 0.99 $\lambda$
Table 1: Best fit of the northern and southern lead angles for Io, Europa and
Ganymede, with $\lambda$ the SIII West-longitude of the moon.

The Alfvén travel times can be approximated using measurements of the
equatorial lead angle. The quantity $\delta_{moon}$/360 is the orbital
fraction over which the Alfvén wave travels from the interaction region to the
Jovian ionosphere. If the moons were static, or far slower than the angular
rotation of Jupiter, the Alfvén travel times could be estimated by multiplying
this ratio by the Jovian orbital period. However, since the orbital period of
the moon is not negligible when compared with the Jovian rotation period
(especially for Io), the synodic period of the moon has to be accounted for.
The Alfvén travel times can then be approximated using equation (4).

$t_{A}=\frac{P^{syn}_{moon}\times\delta_{moon}}{360},$ (4)

where $P^{syn}_{moon}$ is the synodic period and $\delta_{moon}$ the measured
equatorial lead angle of the moon of interest. The range of Alfvén travel
times are listed in Table 2, and displayed on Figure 6. The derived Io Alfvén
travel times are consistent with the modeled travel times by Hinton2019.

| North | South
---|---|---
Io |  $t_{A}^{min}$ = 3.9 $\pm$ 1.5 minutes |  $t_{A}^{min}$ = 4.6 $\pm$ 1.3 minutes
|  $t_{A}^{max}$ = 15.4 $\pm$ 1.5 minutes |  $t_{A}^{max}$ = 13.5 $\pm$ 1.3 minutes
Europa |  $t_{A}^{min}$ = 4.1 $\pm$ 1.7 minutes |  $t_{A}^{min}$ = 6.9 $\pm$ 1.0 minutes
|  $t_{A}^{max}$ = 17.5 $\pm$ 1.7 minutes |  $t_{A}^{max}$ = 19.5 $\pm$ 0.9 minutes
Ganymede |  $t_{A}^{min}$ = 9.3 $\pm$ 2.4 minutes |  $t_{A}^{min}$ = 10.4 $\pm$ 2.0 minutes
|  $t_{A}^{max}$ = 34.4 $\pm$ 2.4 minutes |  $t_{A}^{max}$ = 35.1 $\pm$ 2.2 minutes
Table 2: Range of northern and southern hemisphere Alfvén travel times for Io,
Europa and Ganymede estimated from the measured lead angles. Figure 6: Alfvén
travel times for Io (top), Europa (middle) and Ganymede (bottom), estimated
from the equatorial lead angles measured by UVS. Blue-shaded area for Io comes
from Hinton2019.

The lead angle shows considerable variability at a given SIII longitude, well
beyond the observational uncertainties. Since this quantity accounts for the
sum of the physical processes occurring between the interaction region around
the moon and Jupiter’s ionosphere, it is affected by plasma density variations
encountered by the Alfvén waves within the torus and potential magnetic field
strength variations. For Io, Hinton2019 estimated that the Alfvén travel times
to Jupiter’s southern ionosphere at $\lambda^{Io}$ = 200∘ ranged from 11 min
to 13.5 min solely based on torus density variations on the order of 50%
caused by variation in Io’s volcanic activity [Yoshikawa . (2017)]. Based on
Io’s synodic period, a 2.5 min variation in Alfvén travel times corresponds to
a longitudinal shift of about 1.5∘, which is fully consistent with the lead
angle variations observed between perijoves. However, Hinton2019 also
predicted a variation in the Alfvén travel times to Jupiter’s southern
ionosphere at $\lambda^{Io}$ = 30∘ from 2 min to 3 min, leading to a predicted
shift in lead angle of 0.6∘, which appears smaller than the measured variation
in lead angle in that longitude sector. The origin of this discrepancy is not
clear, and could be due to either underestimating the uncertainties of the
lead angle, uncertainties in the magnetic field model or simplifications in
modeling the plasma sheet spatial variability.

##  5 Variability in magnetospheric conditions and lead angle

The scatter in lead angle shown in figures 4 and 5 implies significant
variations in the magnetospheric conditions at the moons. Because the lead
angle depends on the Alfvén travel times from the interaction region to the
ionosphere, any temporal or spatial changes in the plasma density, structure
of the plasma sheet, or even magnitude of the magnetic field in these regions
need to be considered. We briefly discuss here the spatial and/or temporal
variations of such quantities.

Neutrals escaping Io are dissociated and ionized by impacts from
magnetospheric electrons [Bagenal Dols (2020)]. They are then picked up by the
rotating magnetic field and brought up to near-corotation by transferring
angular momentum from the Jovian ionosphere to the magnetosphere through a
system of field-aligned currents, and regulated by the ionospheric
conductivity [Hill (1979)]. The radial transport of plasma then occurs through
the centrifugally-driven flux tube interchange, in which plasma-loaded flux
tube moves radially outward from its production source by the E $\times$ B
drift, and are replaced by inward-moving flux tubes containing less mass
[<]e.g.,¿[]Thomas2004. The typical transport timescale of plasma from the Io
to the Europa orbital distances was estimated to be in the $\sim$30-80 days
[Bagenal Delamere (2011)].

Plasma survey at various distances across the magnetosphere have been
performed thanks to the previous Jupiter missions, and is being extended now
with Juno [<]see, e.g., reviews of¿[]Bagenal2015, Bagenal2020. Density in the
plasma sheet generally decreases by five orders of magnitude from 6 RJ to 30
RJ [Bagenal . (2016)]. Because of Jupiter’s magnetic dipole tilt, magnetic
field measurements from in-situ spacecrafts are characterized by regular sign
changes in the radial component of that field associated with a plasma sheet
crossing. Although previous in-situ plasma measurements performed in the
middle magnetosphere of Jupiter showed a well-structured plasma sheet,
variations in magnetic field measurements have been reported, indicating
spatial and temporal variations of the current sheet position
[<]e.g.,¿[]Krupp2004.

Since the early Pioneer 10 and 11 missions, the magnetic field has been known
to be distorted near the centrifugal equator, where the field is radially
stretched outwards by the presence of the plasma sheet currents. An empirical
model of the magnetodisk using the Voyagers measurements that accounts for a
system of azimuthal currents circulating in the centrifugal equator were
constructed to account for this effect [Connerney . (1981)]. The extensive
data collected by Juno demonstrates that the magnetic field in the middle
magnetosphere is less stretched than previously thought. This led
Connerney2020 to revise the empirical magnetodisk model, and to add a radial
current that contributes to the azimuthal component of the magnetic field
(BΦ), and designed to account for the transfer of angular momentum of the
radially outflowing plasma. Orbit-by-orbit measurements of the radial current
system contributing to the BΦ component show significant variations, which
might suggest a modulation in the angular momentum transfer that affects the
plasma outflow [Connerney . (2020)]. Vogt2022b used magnetic field
measurements from Juno as well as previous missions to survey the magnetic
field condition near the orbit of Ganymede. They found that the expected
temporal variability obtained from fit of the current sheet results in a 10-20
% variability in the magnetic field components, and is longitude-dependent.
Understanding and tracking the variability of the plasma sheet current is
crucial as they may induce a displacement of the footprint location,
especially for Ganymede [Vogt . (2022), Promfu . (2022)]. The variation in the
Ganymede footprint position are large enough to be easily detected and thus is
important to track magnetospheric changes.

Huscher2021 used Juno-JADE data at or near the plasma sheet crossing to survey
the plasma density from Juno’s first 26 orbits at radial distances beyond 17
RJ. The plasma sheet density structure can show significant variability in
spatial structure, sometimes smaller than 1 RJ, over timescale of minutes, and
between Juno orbits. At the same radial distance within the plasma sheet, the
peak charged density of heavy ions measured by Juno-JADE can differ by about
one order of magnitude between orbits. For instance, data from a few number of
orbits indicated plasma density uniformly low (e.g., PJ12 and PJ26). Juno will
be traversing the equatorial Io-Europa region as the extended mission
progresses, and more results are expected.

In order to investigate temporal variability in the plasma sheet properties,
figure 7 present the lead angle deviations from the best fit obtained on
figures 4 and 5. Juno-UVS lead angle measurement is subtracted from the lead
angle fit at the particular $\lambda$ the data was recorded at. A
positive/negative value for that quantity, called here $\Delta_{LA}$,
corresponds to the case where the Alfvén travel time was longer/shorter than
the travel time derived from equation (4), respectively. A longer Alfvén
travel time may translate into the situation where either (i) the local plasma
sheet density was higher than nominal, (ii) the plasma sheet vertical extent
increased, (iii) the local magnetic field amplitude decrease with respect to
it nominal value, or a combination thereof.

The consistently lower density reported by Huscher2021 using Juno-JADE during
the inbound section of Juno’s orbit 12 throughout the magnetosphere may cause
the Alfvén travel time to become temporarily shorter for that orbit, until the
plasma density return to their nominal level. This would translate to a
negative $\Delta_{LA}$, and is roughly consistent with the $\Delta_{LA}$
measured for Io (south), Europa (south) and Ganymede (both north and south) on
PJ12. A couple of issues with that interpretation are that (i) Juno-JADE only
measured the densities from 17-50 RJ, i.e., from Ganymede and beyond, (ii) the
JADE data were recorded several days prior to the UVS data (1-3 days,
depending on the orbit number). Lower plasma density in the middle
magnetosphere measured by JADE may be a consequence of a temporary slowdown of
the mass loading from Io, implying lower densities in the inner magnetosphere
prior to PJ12. This means that UVS should have recorded consistently negative
$\Delta_{LA}$ on, e.g., PJ11, which is not the case.

Although no clear temporal trends can be distinguished from figure 7, a
Lomb–Scargle periodogram analysis on these time-series reveals a period in the
400-500 days range for Io. This may be consistent with the periodic
brightening of Loki Patera, the most powerful volcano on Io, as monitored in
the infrared. The periodicity of such brightness was thought to be correlated
with periodic changes in Io’s eccentricity and semimajor axis, about 480 and
460 days, respectively [de Kleer . (2019)]. Io is the main supplier of plasma
in the Jovian magnetosphere. Changes in Io’s volcanic activity affect the
radial circulation of mass and energy in the middle magnetosphere over time
scales of tens of days. For instance, DeKleer2016 have characterized the
location and appearance of hot spots on Io in the near-IR and found widespread
activity from Aug–Sep 2013 and from Oct 2014-May 2015. Around the same time,
the Hisaki telescope monitored the torus ion emission lines of the Jovian
system in the 55–145 nm range [Yoshikawa . (2014)]. Enhancements in the sodium
emission line [Yoneda . (2015)], as well as sulfur and oxygen emission lines
[Tsuchiya . (2018)] was detected from mid-Jan until mid-Mar 2015, over
sensibly different timescales. During the Cassini era, temporal changes in the
emissions from the major sulfur and oxygen ions torus species was suggested to
be related to the changes in outgassing from Io [Delamere . (2004), Steffl .
(2006)]. However, tying together changes in the brightness of Io’s volcanoes
with enhancements in the various emission lines of the torus (e.g., sodium,
oxygen and sulfur), to ultimately derive changes in mass supplied to the torus
is not straightforward and still unclear.

The present work provides an empirical fit of the equatorial lead angle for
Io, Europa and Ganymede derived from Juno data, from which the averaged Alfvén
travel time is derived. It also demonstrates how, by accounting for these lead
angle values, the interpretation of the moon-induced decametric radio
emissions can be improved, as demonstrated below. Understanding the effect of
magnetospheric conditions on the lead angle variability is beyond the scope of
this work, and deserves a dedicated study.

Figure 7: Time series of the measured lead angle deviation from the best fit
shown in figures 4 and 5. Red squares and black triangles correspond to the
northern and southern lead angle data. The blue-shaded regions correspond to
the uncertainty from the northern lead angle fit parameters shown in figure 4.

##  6 Application to modeling of the moon-induced decametric emission

The knowledge of the lead angle is also important for the interpretation of
the moon-induced decametric emissions [<]e.g.,¿[]Hess2010b, Marques2017,
Louis2019, Lamy2022. This section illustrates the added benefit from the
equatorial lead angle knowledge in a case related to the interpretion of the
Ganymede-induced decametric radio emission. These emissions are thought to
originate from the cyclotron maser instability (CMI), a wave-particle
instability where a circularly polarized wave resonates with the gyrating
motion of an accelerated electron population [Wu Lee (1979), Wu (1985),
Treumann (2006)]. That mechanism was confirmed using Juno in-situ measurements
[Louarn . (2017), Louarn . (2018), CK. Louis . (2020)]. These radio emissions
are produced along the magnetic field lines, at a frequency close to the
electron cyclotron frequency (proportional to the magnetic field amplitude),
and beamed along the edges of a thin hollow cone on the order of a degree in
thickness. The opening angle of this cone is dependent on the electron energy
[S. Hess . (2008)]. In order to interpret the moon-induced decametric
emission, modeling tools such as the Exoplanetary and Planetary Radio Emission
Simulator [<]ExPRES, ¿[]Hess2008, Louis2019 require knowledge of both the lead
angle and electrons velocity. Because the directionality of these radio
emissions depend both on the electron energy and the lead angle, this may lead
to situations where non-unique solutions exist, in order to reproduce the
observed decametric radio arcs. The knowledge of the active field line (where
the radio emission sources are located) and thus the lead angle, constitutes
one of the main sources of uncertainty in determining the electron energy
responsible for the radio emission [SLG. Hess, Pétin . (2010), Lamy . (2022)].
Previous estimate of the absolute lead angle values were not accurate enough
mostly because of the uncertainty in the magnetic field models as well as the
uncertainties in the Europa and Ganymede measured footprint positions from HST
[SLG. Hess, Pétin . (2010)], leading to non-physical cases with negative lead-
angle.

Several datasets of moon-induced decametric radio emission were recorded by
the Radio and Plasma Wave Science (RPWS) instrument on Cassini [Gurnett .
(2004)] on 17 November 2000, prior to the Jupiter flyby. Figure 8 shows the
analysis of a decametric arc induced by Ganymede, and previously studied by
Louis2017. RPWS data is shown on panels A and B as time-frequency
spectrograms, corresponding to a Ganymede-D decametric arc, i.e., emitted on a
field line connecting Ganymede and Jupiter’s southern hemisphere around
Jupiter’s dawn side. Because the waves amplified by the cyclotron maser
instability are circularly polarized, panel A shows the time-frequency
spectrogram corresponding to the degree of circular polarization, for better
contrast. During the observation of the Ganymede-D arc (from $\sim$22:00 to
$\sim$02:00), the longitude of Ganymede varies from 348∘ to 133∘.

Figure 8: Panel A: Cassini-RPWS time-frequency spectrogram of circularly
polarized radio emission. Panel B: Cassini-RPWS time-frequency spectrogram.
Panel C: ExPRES simulation of a Ganymede-D decametric arc without lead angle.
Panel D: ExPRES simulation using the lead angle derived from this present
study. Panel E: ExPRES simulation combining the lead angle derived from this
present and refraction effect on the emission. This simulations have been
produced using the Version 1.2.0 of ExPRES [CK. Louis . (2023)]

.

Panel C shows the best fit to the data, prior to this work, using the ExPRES
radio modeling [CK. Louis . (2019)]. This assumes (i) the radio emission is
created by a loss-cone electron distribution with energies of 3 keV, (ii) the
JRM33 magnetic field model, and (iii) no equatorial lead angle. Note that we
consider here a simplistic mono-energetic case, as Juno clearly observed
electrons distributed as a power-law extending well above and below 3 keV
[<]e.g.,¿[]Szalay2018. Although it was previously presented by Louis2017, this
application differs slightly from that earlier work which assumed the ISaAC
magnetic field model [SLG. Hess . (2017)]. Panel D shows simulations using
ExPRES considering the equatorial lead angle fit derived from the present
work. The best fit of the data is obtained considering electrons with energies
ranging from 10-15 keV. When accounting for refraction effects on the beamed
radio emissions, the fit can be improved by considering electrons of energies
ranging 5 to 15 keV (panel E). Refraction effects are occuring when the radio
emissions are emitted in a region with decreasing electron cyclotron frequency
(fce). In which case, the emission can not propagate due to the cut-off
frequency at fce, and the radio wave is reflected until it reaches a region
with increasing fce [Galopeau Boudjada (2016), CK. Louis, Lamy, Zarka,
Cecconi, Imai . (2017), CK. Louis . (2021)].

The addition of the knowledge on the equatorial angle, especially for Europa
and Ganymede, improves the predictability and analysis of moon-induced
decametric radio emission. Due to Ganymede’s longitude variation during the
observation of the Ganymede-D arc, based on our new lead angle model, the
error on the active magnetic field line position goes from 5∘ (minimal value
of $\delta$ in the south) to 14∘, which lead to a poor estimate on the
location of the sources. Since the shape of the arc depends mainly on the lead
angle (position of the active field line), the magnetic field model (value of
B, and therefore position of the sources, along the field line) and the energy
of the electrons (value of the emission cone aperture), a too low estimate of
the longitude of the active field line will lead to an underestimation of the
value of the energy of the electrons [SLG. Hess, Pétin . (2010), C. Louis .
(2017)]. This is what is noted in the simulations comparing figures 8A and 8C,
where a lower value of electrons is needed to fit correctly the arc without a
lead angle model.

This improved estimation of the position of the active field lines, and
therefore of the position of the radio sources, allows reducing the number of
unknowns and to obtain a better, and more reliable, estimate of the electron
energy. For instance, comparing in more details the simulations that account
for the lead angle and refractions effects (figure 8C) with the circularly
polarized radio emission from RPWS indicates that the early part of the radio
emission arc (from 22:00:00 to 22:15:00) are better reproduced with electrons
with lower energies, i.e., 5 keV, while the center and end of the arc are
better reproduced with electrons with energies ranging from 10 to 15 keV. It
is worth noting here that Lamy2022 showed that, in the case of Io, the
electrons energy derived from radio emission analysis is variable as a
function of the moon longitude. It is not surprising here to observe that in
order to reproduce the arc in the time-frequency plane, the energy of the
electrons must vary with time (i.e., the longitude of the moon). Finally, the
ExPRES simulations with the new lead angle model give results that are in
agreement with the Juno in-situ observations recorded during a Ganymede
fluxtube crossing on PJ20, on May 29th 2019, [CK. Louis . (2020)].

##  7 Discussion and Summary

The presented work makes use of 479 and 1148 individual spectral images of the
satellite footprints recorded over the northern and southern auroral regions,
respectively, measured by Juno-UVS from PJ1 to PJ43 (at the exception of PJ2),
i.e., about 6 years of Juno data. From these images, the accurate positions of
the Io, Europa and Ganymede Main Alfvén Wing spots are estimated and compared
with the prediction from the magnetic field model obtained at the end of
Juno’s prime mission, JRM33 [Connerney . (2022)]. The accuracy with
predictions from JRM33 can be estimated while limiting the projection effect
by restricting to data recorded at small emission angles. We selected data
points with emission angle lower than 20∘, which allowed us to reduce the
uncertainty associated to the projected vertical extent of the footprint
emission curtain ($\sigma_{P}$ in 2) while keeping enough data to perform a
statistical analysis. In general, the average distance between the
JRM33-computed moon footpaths and the observed MAW positions is smaller than
500 km, which is equivalent to $<$ 0.4∘ on Jupiter.

Measurements of the equatorial lead angle provide information on how the
Alfvén waves generated around the moon interaction region propagate towards
the Jovian ionosphere. It is an important piece of information for (i)
interpreting the footprint related in-situ measurements made by Juno, (ii)
inferring in-situ conditions of the plasma sheet (e.g., a lead angle greater
than the fit derived here might be caused by a higher than usual plasma
density, or a variation in the magnetic field strength), and (iii) analyzing
the satellite-induced decametric radio emission. Despite the variability in
the measured lead angle at a given moon longitude, a statistically consistent
trend can be derived from the first 43 perijoves. The best fit of the lead
angle for Io is in the 1.8∘-7.2∘ range, with an average calculated as the
arithmetic mean of 4.2∘. For Europa, the lead angle ranges from 2.2∘ to 10.4∘,
with an average of 6.4∘. For Ganymede, the lead angle is in the 5.3∘-20.0∘
range, with an average of 12.7∘. Over an entire Jovian rotation, this
corresponds to Alfvén travel times ranging from 3.9-15.4 minutes, 4.1-19.5
minutes, and 9.3-35.1 minutes for Io, Europa and Ganymede, respectively.

Significant deviations of the lead angle at a given longitude were observed
for all moons. Changes in the magnetospheric conditions, such as plasma
density variations, magnetic field amplitude or spatial structure of the
plasma sheet, are likely responsible for such variations. Comparing the
instantaneous lead angle obtained from the observed MAW footprint positions
with the fit derived may provide an indication of these changes in
magnetospheric conditions. Time series of the lead angle variation with
respect to the best fit does not show a consistent temporal trend for Europa
and Ganymede (see figure 7). For Io, a Fourier analysis shows a tentative
periodic change in the 400-500 days range, which may be attributed to
modulated in Io’s volcanic activity, although a dedicated study on this topic
is beyond the scope of this investigation and deserves a detailed examination.

Modeling the moon-induced decametric arc requires the knowledge of the
equatorial lead angle to constrain with higher accuracy the derived electron
energy causing the emission. When accounting for the equatorial lead angle
values from this work in the ExPRES simulation tool, the derived electron
energy required to reproduce the Ganymede-induced decametric arc is in
agreement with the in-situ measured values from Juno. This method can be
applied for modeling the moon-induced radio emission for which no in-situ
particle measurements data is available.

The main conclusions of this work are listed as follows:

  1. 1.

The reported position of the Main Alfvén wing spots for Io, Europa and
Ganymede agrees well with the JRM33-computed satellite footpath generally $<$
500 km, which is equivalent to $<$ 0.4∘ on Jupiter.

  2. 2.

Empirical formulae for the Io, Europa and Ganymede equatorial lead angles
derived from Juno data are provided.

  3. 3.

The range of equatorial lead angle for Io, Europa and Ganymede is 1.8∘-7.2∘,
2.2∘-10.4∘, 5.3∘-20.0∘, respectively.

  4. 4.

The respective range of Alfvén travel times for Io, Europa and Ganymede,
derived from the lead angle, are 3.9-15.4 minutes, 4.1-19.5 minutes, and
9.3-35.1 minutes.

  5. 5.

Knowledge of the lead angle allows, e.g., better simulating the decametric
radio emission induced by the Galilean moons. By comparing them with the
observations, this makes possible deriving more precisely the energies of the
electrons triggering these emissions. This new derivation is in agreement with
the Juno in-situ measurements.

##  8 Open Research

All the data used in this study are publicly available on the PDS Atmospheres
Node Data Set Catalog https://pds-atmospheres.nmsu.edu/cgi-
bin/getdir.pl?dir=DATA&volume=jnouvs_3001. Juno-UVS calibrated data (Reduced
Data Record) recorded during Juno’s perijove observation sequences were used
here. The corresponding dataset used here contain the string PXXOBS, where XX
= 1 to 43. Cassini/RPWS data display in this article are part of the
Cecconi2017 collection, and has been produced following the ”Circular
Polarization mode” goniopolarimetric Inversion described in section 2.1.3.2 of
Cecconi2005.

###### Acknowledgements.

We are grateful to NASA and contributing institutions that have made the Juno
mission possible. This work was funded by the NASA’s New Frontiers Program for
Juno via contract NNM06AA75C with the Southwest Research Institute. CKL’s work
at the Dublin Institute for Advanced Studies was funded by Science Foundation
Ireland Grant 18/FRL/6199. AHS acknowledges NASA NFDAP grant 80NSSC23K0276.
Hue acknowledges support from the French government under the France 2030
investment plan, as part of the Initiative d’Excellence d’Aix-Marseille
Université – A*MIDEX AMX-22-CPJ-04.

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