# Energetic proton losses reveal Io’s extended and longitudinally asymmetrical
atmosphere

###### Abstract

Along the I24, I27 and I31 flybys of Io (1999-2001), the Energetic Particle
Detector (EPD) onboard the Galileo spacecraft observed localised regions of
energetic protons losses (155 keV-1250 keV). Using back-tracking particle
simulations combined with a prescribed atmospheric distribution and a
magnetohydrodynamics (MHD) model of the plasma/atmosphere interaction, we
investigate the possible causes of these depletions. We focus on a limited
region within two Io radii, which is dominated by Io’s SO2 atmosphere. Our
results show that charge exchange of protons with the SO2 atmosphere,
absorption by the surface and the configuration of the electromagnetic field
contribute to the observed proton depletion along the Galileo flybys. In the
155-240 keV energy range, charge exchange is either a major or the dominant
loss process, depending on the flyby altitude. In the 540-1250 keV range, as
the charge exchange cross sections are small, the observed decrease of the
proton flux is attributed to absorption by the surface and the perturbed
electromagnetic fields, which divert the protons away from the detector. From
a comparison between the modelled losses and the data we find indications of
an extended atmosphere on the day/downstream side of Io, a lack of atmospheric
collapse on the night/upstream side as well as a more global extended
atmospheric component ($>1$ Io radius). Our results demonstrate that
observations and modeling of proton depletion around the moon constitute an
important tool to constrain the electromagnetic field configuration around Io
and the radial and longitudinal atmospheric distribution, which is still
poorly understood.

JGR: Space Physics

School of Cosmic Physics, DIAS Dunsink Observatory, Dublin Institute for
Advanced Studies, Dublin 15, Ireland Space and Planetary Science Center,
Khalifa University, Abu Dhabi, UAE Department of Mathematics, Khalifa
University, Abu Dhabi, UAE European Space Agency (ESA), European Space
Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The
Netherlands Leiden University, Leiden, the Netherlands KTH, Royal Institute of
Technology, Stockholm, Sweden Department of Earth and Environmental Sciences,
Ludwig Maximilian University of Munich, Munich, Germany Laboratory for
Atmospheric & Space Physics, University of Colorado, Boulder, CO, USA HLF
Huybrighs and CPA van Buchem contributed equally to this work and are
considered as joint first authors.

Hans<EMAIL_ADDRESS>
Atmospheric charge exchange is a major or dominant loss process of energetic
protons (155-224 keV) during three close Galileo flybys of Io

Proton losses suggest an expanded atmosphere on the day/downstream side and a
lack of atmospheric collapse on the night/upstream side.

Discrepancies between the data and model hint at a global large scale height
atmosphere

## Plain Language Summary

Io is a moon of Jupiter with active volcanoes and an atmosphere of which the
structure and variability is poorly understood. A fascinating object on its
own, neutral gas from Io also serves as the main source of plasma in Jupiter’s
magnetosphere. Improving our understanding of Io’s atmosphere will allow us to
better understand the precise link between Io’s neutral environment and the
plasma torus surrounding Jupiter. In this work we analyse data from the
historic Galileo spacecraft that encountered Io. Specifically, we analyse
regions close to Io where (normally abundant) energetic protons are
disappearing. We find that charge exchange between these particles and Io’s
atmosphere along with the effect of the electric and magnetic fields on the
paths of these particles can cause such decreases. Charge exchange with the
atmosphere is either a major or the dominant source of losses, depending on
the flyby altitude. The losses of the protons are related to Io’s atmosphere
and hint at an atmosphere that is more extended on Io’s day side (also the
downstream side from the plasma flow’s point of view), doesn’t collapse fully
on the night (upstream) side, and appears to be more extended than we assumed.

##  1 Introduction

Io is the most volcanically active body in our solar system due to the
periodic deformation of its interior by Jupiter’s tidal forces. A fascinating
object in its own right, Io is also considered to be the main source of plasma
in Jupiter’s magnetosphere. However, it is not understood how changes in the
Io plasma torus’ density exceeding 300% are related to Io [Roth . (2024)].
This is in part due to our limited understanding of Io’s atmospheric structure
and variability. Dropouts of energetic ions could provide us with a new
diagnostic of Io’s neutral environment. In this introduction we review
features of Io’s environment that are relevant to the high energy protons
around Io. A more detailed review of Io’s atmosphere and its plasma
environment can be found in Bagenal2020TheEuropa.

###  1.1 Io’s atmosphere and role in Jupiter’s magnetosphere

The SO2 frost sublimation (e.g. Ingersoll1985,Moreno1991,Doute2001), volcanic
plumes (e.g. Morabito1979,Spencer2000,Walker2010), atmospheric sputtering
(e.g. McGrath1987MagnetosphericAtmosphere,Pospieszalska1996) and physical
chemistry [Dols . (2008), Dols . (2012)] contribute to the formation of an
extended atmosphere of SO2, S and O around Io. Minor species are also present
such as SO [Lellouch . (1996)] and NaCl [Lellouch . (2003)]. The atmosphere
extends into Hill’s sphere ($\sim$6 Io radii RIo, 1821 km) as a corona, which
is mainly composed of S and O [Wolven . (2001)] and is thought to be produced
by atmospheric sputtering [McGrath Johnson (1987)] and physical chemistry
processes [Dols . (2008)].

The atmosphere of Io is thought to be asymmetrical along different axes (e.g.
Blocker2018MHDAtmosphere). Being sublimation dominated, the dayside is more
dense than the nightside (e.g. Tsang2016TheEclipse). It is thought that the
atmosphere could partially collapse on the nightside due to the condensation
of atmospheric SO2 in the cold night temperature. The atmospheric density at
the poles is thought to be only a few percent of the atmosphere at the
equator, due to the equatorial distribution of frost, the preferential heating
of the sub solar point and the location of some main volcanoes closer to the
equator (e.g. Strobel2001TheHydrogen,Spencer2005Mid-infraredAtmosphere). The
anti‐Jovian atmosphere is denser and latitudinally more extended than the
sub‐Jovian side (e.g. Feaga2009IosAtmosphere,Spencer2005Mid-
infraredAtmosphere,Moullet2010SimultaneousArray). Lastly the atmospheric
density varies longitudinally with a denser upstream than downstream
atmosphere (e.g. Saur2002InterpretationPasses). Major uncertainties remain in
our understanding of the radial profile, longitudinal asymmetries, minor
species, and how much the atmosphere collapses at night or in eclipse.

Some of the neutrals escape Io’s gravity field to form giant neutral clouds of
S and O (several Jupiter radii in size, 71492 km) that extend along Io’s
orbit. The neutral clouds at Io’s orbital velocity are continuously passed by
the plasma flow of the Io torus at a relative velocity $\sim$57km/s [Kivelson
. (2004)]. They experience charge exchange and electron-impact ionization,
which supply the torus with fresh plasma. The flux of plasma directly from Io
is about $\sim 300$ kg/s (e.g. Saur2003TheIo,Dols2008ATorus). The plasma torus
has an average electron density $\sim$2000 cm-3 and an average thermal
temperature $\sim$60-100 eV [Kivelson . (2004), Bagenal Dols (2020)].
Centrifugal forces lead the plasma to flow radially outwards along Jupiter’s
magnetic equator thereby forming a plasma sheet [Bagenal (1989)].

While circulating through the magnetosphere, charged particles are accelerated
to suprathermal energies [Paranicas . (2000)] and are able to diffuse back
radially inwards [Khurana . (2004)] towards Jupiter’s moons. These particles
are referred to as energetic particles in the rest of the text. In summary, Io
is exposed to a flow of corotating low energy plasma ($\sim$100 eV) and to a
population of energetic charged particles, including the energetic protons
($>100$ keV) on which this study focuses.

###  1.2 Energetic ions near Io

The Energetic Particle Detector (EPD) onboard Galileo [Williams . (1992)]
detected dropouts of energetic ions during close flybys of Io. In this work we
investigate specifically the cause of energetic proton losses. Several causes
of energetic ion depletion have previously been proposed for various moons:
impact of the energetic protons on the moon’s surface, deflection of the
protons by inhomogeneous electromagnetic fields, charge exchange of the
protons with atmospheric neutrals and wave particle interactions.

Energetic ions that impact the surface are absorbed and therefore result in a
depletion, such losses have been widely reported at Io [Selesnick Cohen
(2009)] and various moons of Jupiter and Saturn e.g.
Paranicas2000EnergeticEuropa,Kivelson2004MagnetosphericSatellites,Roussos2022ABelts,Kotova2015ModelingDione,Krupp2020Magnetospheric20052015.
Furthermore, a magnetic field gradient can restrict access of energetic ions
in certain regions and cause apparent losses. Such features have been reported
at Io [Selesnick Cohen (2009)] and other moons of Jupiter and Saturn e.g.
Paranicas2000EnergeticEuropa,Roussos2012EnergeticInteraction,Huybrighs2023. We
will refer to losses due to perturbed fields as “forbidden regions”.

When energetic protons charge exchange with atmospheric neutrals they turn
into energetic neutral atoms (ENA) which will result in a depletion of the
energetic protons. Atmospheric charge exchange has been investigated as a loss
process of energetic ions at moons of Jupiter and Saturn e.g.
Mitchell2005EnergeticMagnetosphere,Wulms2010EnergeticFields,Kotova2015ModelingDione,Addison2021InfluenceWeathering.
Specifically at Europa Huybrighs2020AnDepletions demonstrated, using a Monte
Carlo particle tracing code, that proton depletions (115-244 keV) measured
during the E26 Galileo flyby were affected, in addition to absorption by the
surface, by atmospheric charge exchange and inhomogeneous fields. This study
builds on the modelling efforts of Huybrighs2020AnDepletions.

Specifically at Io, ion dropouts during three close Galileo flybys (I27, I31
and I32) have been analysed by Selesnick2009ChargeIo. Using ion back-tracing
simulations they demonstrated that losses of energetic oxygen and sulfur ions
($>$5 MeV/nucleon) measured by Galileo’s Heavy Ion Counter (HIC) could be
attributed to absorption by the surface and the effect Io’s Alfvén wings.
Selesnick2009ChargeIo accounted for the Alfvén wings by using an idealized
analytical description, but did not account for other perturbations such as
magnetic field pile-up. The addition of the Alfvén wings provides a better
reproduction of the measured ion dropouts during polar flybys I31 and I32. At
certain segments of the flyby, the Alfvén wings deflect ions that would
otherwise collide with Io’s surface, while enhancing losses in other segments.
For flyby I27 the effect of the Alfvén wing appeared to be small.

Ion dropouts have also been reported away from Io, but near the Io orbit,
using Voyager 1, Voyager 2 and Galileo data [Armstrong . (1981), Cheng .
(19832), Williams . (1996), Mauk . (1998), Lagg . (1998)]. Specifically,
Cheng1983EnergeticOrbit and Lagg1998DeterminationMeasurements proposed charge
exchange with neutrals as a loss process for the energetic ions, More
recently, Mauk2022 argued, based on [Smith . (2019)], that near Io’s orbit
charge exchange with low energy ions would dominate over charge exchange with
neutrals. Mauk2022 also argues that near Io’s orbit charge exchange losses
dominate for protons (roughly below 200 keV) over losses from scattering.
Furthermore, they suggest that at energies above 300 keV the scattering
dominates over charge exchange.

Lastly, ion dropouts have also been measured along field lines connected to
Io, but not in a close flyby of Io. The JEDI instrument on Juno measured
losses of energetic protons with energies in the 10-800 keV range over a
region larger than Io along field lines connected with Io [Paranicas .
(2019)]. They attribute these losses to wave-particle interaction, building on
Nenon2018AOrbit which proposes that near Io ion cyclotron waves could resonate
with energetic protons and cause proton losses. Nenon2018AOrbit suggest that
protons at energies between about 0.3 and 4 MeV are affected by
electromagnetic ion cyclotron waves near Io’s L shells. However,
Paranicas2019IosData also suggests that below 100 keV, proton losses to charge
exchange may become significant due to the large charge exchange cross
section.

###  1.3 Scope of this study

In this study we investigate the cause of energetic proton losses measured
close to Io ($<2R_{Io}$) by the Energetic Particle Detector (EPD) on the
Galileo spacecraft. While the effect of charge exchange has been considered as
a loss process for Io’s orbital environment, previous studies investigating
particle losses near Io [Selesnick Cohen (2009)] have not yet considered the
effect of charge exchange with the atmosphere, and they employed a highly
simplified model of the perturbed fields. Therefore, we opt to include charge
exchange with Io’s asymmetrical atmosphere as a loss process as well as a
detailed MHD model of the perturbed fields. To investigate the cause of the
losses we employ a particle back-tracing model which we use to reproduce the
flux of energetic protons as measured by Galileo during three Io flybys (I24,
I27 and I31).

We consider this study in the first place as a feasibility study to
demonstrate the sensitivity of the proton dropouts to the atmospheric
structure and magnetic field configuration. Using previously validated models
of fields and atmosphere we will show that the models are not able to fully
reproduce the energetic proton dropouts and that the proton data can thus
provide new observational constraints to modelers. Our aim is to provide
hypotheses and directions to encourage further modelling studies that exploit
the additional constraint offered by the energetic ions to the fullest.

##  2 Method: Energetic Particle Detector (EPD) and data selection

The EPD telescope contains the Composition Measurement System (CMS) that uses
a time of flight mass spectrometer to separate protons from other ions. A
triple coincidence detection system is used in order to limit the effect of
noise by penetrating radiation [Williams . (1992)]. The EPD telescope can scan
the whole sky in $\sim$140 seconds using the combined motion of a rotating
platform that moves through 7 motor positions and the $\sim$20 seconds period
spacecraft spin. The EPD CMS channels have an opening angle of 18 degrees.
Further details are documented in the EPD user manual [Kollmann . (2022)].

We focus specifically on EPD measurements of energetic protons. Though Oxygen
and Sulfur ions fluxes have also been measured by EPD, there are large
uncertainties in the charge exchange cross section for those species.
Furthermore, protons have a single charge state, while (part of the) oxygen
and sulfur ions could have higher charge states [Clark . (2016), Nénon André
(2019)], which would introduce more free parameters in the analysis.

Building on Huybrighs2021ReplyDepletions we focus specifically on two energy
channels, one channel (155-224 keV, TP1) that is sensitive to charge exchange
with Io’s atmosphere due to the relatively large charge exchange cross section
(see Figure 12) and a second channel (540-1250 keV, TP3) that is not sensitive
to charge exchange due to the strongly reduced charge exchange cross section.
The energy range for TP1 is a different energy range than originally defined
in Williams1992TheDetector due to ’dead’ layer formation [Lee-Payne . (2020)].
The effect of dead layer formation is not as pronounced for TP3, hence the
original range of 540-1250 keV is used for that channel.

The data from TP1 is especially well suited to the study of atmospheric charge
exchange, due to the relatively large charge exchange cross section of protons
on the atmosphere. SO2 is the dominant atmospheric component. To our
knowledge, there are no published values of charge exchange cross sections of
H+ on SO2. Consequently we use the cross section of H+ on O2 as a reasonable
approximation, with experimental data from [Basu . (1987)] extrapolated to the
higher energies of TP1 and TP3 (Figure 12) as in [Huybrighs . (2020)]. It is
well known that charge exchange cross sections drop dramatically for very high
energies [Lo . (1971)]. We contrast the TP1 channel with the TP3 channel,
rather than the intermediate TP2 channel for which data is also available,
because the charge exchange cross section in TP3 is so small that it is not
sensitive to atmospheric charge exchange. Therefore, if losses occur in TP1
but not in TP3, this would argue in favour of the losses being caused by
charge exchange. In addition, due to the low sensitivity to charge exchange,
the TP3 channel could allow us to better isolate apparent losses associated
with forbidden regions caused by perturbations in the electromagnetic fields
surrounding Io. A last argument for the use of the channels is that these
energies are small enough for gyration scales ($<$30 km for TP1 and $<$100 km
for TP3, see Figure 13) to be sensitive to inhomogeneous fields.

The three flybys that we focus on are I24, I27, and I31. See Table 1 for the
parameters of the closest approach and Figure 1 for a visualisation of the
geometry of the flybys. The different flybys will allows us to demonstrate
that the causes of the proton losses depend on the flyby altitude and
geometry. Furthermore, different flybys will reveal different asymmetries (or
lack thereof) in the atmosphere. Two of the notable differences between the
three flybys are the fact that I24 passes Io at a distance which is about
three times greater than I27 and I31, and that I24 and I27 are equatorial
flybys while I31 passes over Io’s north pole. Note that we do not include
flybys J0 and I32 in this study. For flyby J0 we were not able to reconstruct
the EPD pointing using the data in the PDS, for flyby I32 no high resolution
EPD data is available.

Although the EPD signal shows proton depletion far from Io (e.g.
Lagg1998DeterminationMeasurements), we focus here on the depletion features
that are unique to the environment close to Io within $\sim 2$RIo from the
surface, a region dominated by the SO2 atmosphere. In the chosen region the
interaction with Io’s surface, atmosphere and perturbed fields is most
apparent.

Table 1: Parameters for the Galileo flybys of Io studied in this paper. All parameters are given for the respective points of closest approach. Flyby name |  | Date time
---
(UT)
| Local time
---
(h)
| Altitude
---
(km)
|  Longitude ($\phi$)
---
($\degree$)
|  Latitude ($\theta$)
---
($\degree$)
I24 | 1999-10-11 04:33:03 | 10.7 | 611 | -134.13 | 4.51
I27 | 2000-02-22 13:46:42 | 8.91 | 198 | -112.54 | 18.54
I31 | 2001-08-06 04:59:21 | 4.33 | 193 | -81.71 | 77.49
Figure 1: Overview of the different Galileo flybys. The red dot marks the
point of closest approach, the blue line the flight path and $\psi$ indicates
the zenith angle. The black areas indicate Io’s night side. Note that on the
left we have a ‘top-down’ view, with the vertical axis along the y-axis
(towards Jupiter), while on the right we have an ‘edge-on’ view of Io with the
vertical direction along the z-axis (pointing towards the north of the
system). In all panels the horizontal axis points along the direction of the
plasma flow. For all of these flybys Galileo flew from the left to the right
of the panels.

##  3 Method: modelling

We simulate the flux of energetic protons using a back-tracing approach under
different cases, to determine the relative contribution of surface impact,
charge exchange with the atmosphere and the electromagnetic fields to the
measured proton losses. We will consider cases with charge exchange, without
charge exchange, without perturbed fields and with perturbed fields and
compare them with each other. We will also consider two different atmospheric
models, one model with asymmetries (day-night, upstream-downstream, Jupiter
facing) and one without, which will allow us to determine the sensitivity of
the proton losses to different atmospheric configurations.

###  3.1 Atmospheric models

In this work, we will focus on two models of the SO2 distribution around Io:
one radially symmetrical model (referred to as the ’symmetrical atmosphere’ in
the rest of the text) and one asymmetrical model that takes into account
longitudinal and latitudinal asymmetries (referred to as ’asymmetrical
atmosphere’ in the rest of the text), leaving to future work a more
comprehensive study of atmospheric and field perturbation models. A comparison
between the two models will reveal the sensitivity of the proton losses to
different atmospheric configurations. Profiles of the two atmospheric models
for the different flybys are plotted in Figure 2. The global distribution of
the asymmetrical atmosphere is visualised for the three flybys in Figure 3.

Figure 2: Number density of the two atmospheric models along the trajectories
of the three flybys (from top to bottom) I24, I27, and I31.

Figure 3: Visualisation of the longitude and latitude dependent atmospheric
model used in this study and presented in Blocker2018MHDAtmosphere. The I24,
I27, and I31 flybys are shown respectively from left to right. The day/night
hemispheres are indicated with the white and black sides respectively. The
closest approach is indicated with a red point. In section 3.1 we give a
description of the model. Note that for I31 an ’edge-on’ view of the system is
shown in order to better visualise the polar flyby and show the latitudinal
variation of the atmosphere model.

####  3.1.1 Symmetrical atmosphere

The first model that we consider is a one-dimensional, spherically symmetric
exponential model based on Saur2002InterpretationPasses. This model is
described by:

$n(r)=n_{0}\exp\frac{-z}{H},$ (1)

Where $n_{0}$ is the number density at the surface, $z$ is the altitude (given
by $r-R_{Io}$), and $H$ is the scale height. We used $n_{0}=10^{9}$ cm-3 and
$H=100$ km, giving a column density of $1\times 10^{16}$ cm-2. The SO2
vertical column density is not well determined. It varies between $1\times
10^{16}$ cm-2 and $15\times 10^{16}$ cm-2 depending on the location of the
observation and the method of observation [Bagenal Dols (2020)]. For our
symmetrical atmosphere we use an SO2 column density of $1\times 10^{16}$ cm-2
as usually inferred from plasma/atmosphere interaction modeling (e.g.
Blocker2018MHDAtmosphere).

####  3.1.2 Atmosphere with longitudinal and latitudinal asymmetries

Our second model is an SO2 atmosphere that presents latitudinal and
longitudinal variations based on Blocker2018MHDAtmosphere, which is visualised
in Figure 3. The latitudinal variation in this model is based on the analysis
of reflected solar Lyman $\alpha$ intensity data from the Hubble Space
Telescope (HST) by Strobel2001TheHydrogen. It is thought that this latitude
dependency coincides with the regions of active volcanism and stronger
sublimation of frost layers [<]e.g.¿[]Spencer2005Mid-infraredAtmosphere.
Described by:

$n(r,\theta,\phi)=(n_{pol}+n_{s}(\theta,\phi))\exp\left(\frac{-z}{H}\right)$
(2)

where $n_{pol}=0.02n_{0}$ and $n_{0}$ is the surface density at the equator.
We set $n_{0}=4\times 10^{8}$ cm-3 and $H=140$ km. These values are the same
as in atmosphere model 2 in Blocker2018MHDAtmosphere. The latitude and
longitude dependencies are included as three factors $\beta_{1}$, $\beta_{2}$,
and $\beta_{3}$:

$n_{s}(\theta,\phi)=(n_{0}-n_{pol})\exp\left(-\left(\frac{0.5\pi-\theta}{0.625rad}\right)^{2}\right)\beta_{1}\beta_{2}\beta_{3}$
(3)

$\beta_{1}$ is the day/night asymmetry. This asymmetry is thought to exist due
to the strong temperature dependence of sublimation and its role in supporting
the atmosphere. Using high-resolution spectra gathered by the Gemini
telescope, Tsang2016TheEclipse found a decrease in atmospheric column density
from the day-side to the night-side of factor five. This work is the basis
upon which the day-night asymmetry is modeled using:

$\beta_{1}(\theta,\phi)=\left(1+\frac{2}{3}\cos\left(\psi(\theta,\phi,\theta_{s},\phi_{s})\right)\right),$
(4)

where $\psi$ is the solar zenith angle. The local times used in order to
calculate the subsolar point, given by $\theta_{s}$ and $\phi_{s}$, can be
found in Table 1. $\beta_{2}$ adds the sub-/anti-Jovian asymmetry. An
asymmetry in the atmospheric structure of Io is supported by both HI
Lyman-$\alpha$ images from HST [Feaga . (2009)] and data from the
Submillimeter Array [Moullet . (2010)]. This is described using:

$\beta_{2}(\phi)=\left(1+\frac{3}{5}\sin\left(\phi-\frac{1}{2}\pi\right)\right).$
(5)

$\beta_{3}$ represents the downstream/upstream asymmetry. According to
Saur2002InterpretationPasses this asymmetry exists due to the drag force of
the flowing plasma on Io’s atmosphere. It is described using:

$\beta_{3}(\phi)=\left(1+\frac{1}{3}\sin(\phi-\pi)\right).$ (6)

The properties of the asymmetrical atmosphere assumed for each flyby are
summarized in Table 2.

###  3.2 Electromagnetic fields around Io

Table 2: Atmospheric Properties of Io’s Simulation Runs Model Scenario |  $n_{0}$ (cm-3) |  $H_{0}$ (km) | Asymmetrya
---|---|---|---
atm. model I24 | 4.0 $\times$ 108 | 140 | up-/downstream, anti-/sub-Jovian, day/night
atm. model I27 | 4.0 $\times$ 108 | 140 | up-/downstream, anti-/sub-Jovian, day/night
atm. model I31 | 2.0 $\times$ 108 | 100 | up-/downstream, anti-/sub-Jovian, day/night
aApplied longitudinal asymmetry in the atmospheric configuration.

In our simulations we will consider both homogeneous and inhomogeneous
electromagnetic fields. In the homogeneous electromagnetic fields, no
perturbations due to the interaction of Io and the plasma that is corotating
with Jupiter will occur. In the inhomogeneous fields the perturbations are
simulated using an MHD approach. By simulating the particle flux for both
cases we can determine the contribution of the perturbed fields to the
measured flux, e.g. by determining if forbidden fields cause any of the
measured proton losses. We will demonstrate in the next section that the
inhomogeneous fields (as opposed to the homogeneous fields) can have a strong
influence on the energetic charged particle depletion.

The homogeneous magnetic field B is obtained from the Galileo MAG data from Io
and does not take into account the tilt of the background field. The electric
field E is calculated using the relation
$\textbf{E}=-\textbf{v}\times\textbf{B}$, in which v is the velocity of the
corotational plasma. The values for B and v in the homogeneous case are the
same as the initial values used for the inhomogeneous case (see Table 3).

The inhomogeneous magnetic field is obtained using the MHD simulations of
Blocker2018MHDAtmosphere, consistent with the asymmetrical atmospheric
description proposed in Section 3.1. The unique feature of the
Blocker2018MHDAtmosphere MHD simulations is the absence of a prescribed
magnetic field induced in Io’s putative magma ocean, as initially proposed by
Khurana2011EvidenceInterior. Blocker2018MHDAtmosphere propose a convincing
match to the Galileo Magnetometer data with the simple assumption of an
asymmetrical atmosphere and no induced dipole. Quoting their paper, they claim
that “we find that the measured perturbations can be primarily caused by the
plasma interaction with the longitudinally asymmetric atmosphere. This implies
that a significant magnetic induction signal from a partially molten magma
ocean is not necessarily required to explain the Galileo magnetometer data.”
These simulated magnetic perturbations, consistent with the Galileo
observations, are used in our study of the proton losses. For further details
on the MHD simulation we refer the reader to the paper. We will demonstrate in
the next section that the inhomogeneous fields (as opposed to the homogeneous
fields) can have a strong influence on the energetic charged particle
depletion.

The MHD simulations are used to self-consistently model the plasma interaction
of Io’s atmosphere with the corotating plasma from Jupiter’s magnetosphere.
The applied MHD model has already been used to study Io’s plasma interaction
by Blocker2018MHDAtmosphere. The authors adjusted the model to Io’s plasma
interaction from the model which was developed for Ganymede’s plasma
interaction by Duling2014. A detailed description of the model is given in
Blocker2018MHDAtmosphere. The model solves a set of three-dimensional
equations consisting of the continuity equation, the momentum equation, the
induction equation, and an equation for the internal energy on a spherical
grid. It takes into account collisions between ions and neutrals, plasma
production and loss due to electron impact ionization and dissociative
recombination, and the ionospheric Hall effect. Io’s atmosphere is implemented
as a globally asymmetric static SO2 neutral atmosphere (see Equation 3) which
is described in detail in Section 3.1. The atmosphere description is
introduced in the MHD model in the terms of ion-neutral collisions, electron
impact ionization, and the ionospheric Hall effect. An overview of the
parameter settings for the initial and boundary conditions in this model is
given in Table 3.
Figure 4 shows the magnetic perturbations around Io for each Galileo flyby
addressed here. In the three panels we see a strong increase of the magnetic
field magnitude upstream of the moon due to the pile-up of the magnetic field
lines. The formation of the Alfvén wings is clearly visible in the reduced
plasma flow velocity (arrows in third plot) north and south of the moon. They
are bent back with respect to the unperturbed background magnetic field. The
plots in the equatorial plane (I24 and I27) show that the plasma flow is
diverted around the moon and accelerated at the flanks. Most of the plasma
flow into the ionosphere is reduced and is swept around the moon and the
wings. Upstream of the moon the plasma flow velocity is decreased and
downstream of the moon it increases again to the background value due to the
Lorentz force. The asymmetry of the plasma flow and the magnetic field between
the Jupiter-facing side and anti-Jupiter facing side shown in the first two
plots is due to the plasma interaction with an asymmetric atmosphere. The
comparison between the plasma flow between the I24 and I27 case shows that the
plasma flow upstream of the moon is slowed down more effectively for the I27
case than for the I24 case. This is an effect of the asymmetric atmosphere
(see Figure 3). The Galileo flyby I31 provided a close pass of the north polar
region as presented in the trajectory in the third panel of Figure 4. The
spacecraft crossed the northern Alfvén wing. Due to its close flyby to Io the
electromagnetic perturbations are not only affected by the Alfvénic
interaction but also by the ionospheric current system.

In Blocker2018MHDAtmosphere a comparison between the MHD model and the
measured components of the magnetic field are shown in Figure 7 for I24 (atm.
Model 2) and Figure 10 for I27. Atm. model 2 is not shown in the plots for
I27, but the results are similar as to atm. Model 3. For those flybys a
comparison is also made to electron density derived from Galileo PWS and
plasma velocity components from Galileo PLS (PWS data is shown in Figures 9
and 12). In D we provide the MHD simulations for I31, and a comparison with
the magnetic field data which were not provided in Blocker2018MHDAtmosphere.

Table 3: Initial and Boundary Condition Values and Calculated Parameters in the IPhiO System for Io’s Simulations Flyby | $\underline{B}_{0}$ | $\underline{v}_{0}$ | $\rho_{0}$ |  $\epsilon_{0}$a
---|---|---|---|---
| (nT) | (km/s) | (amu/m-3) | (nPa)
I24 | (310, 530, $-$1910) | (57, 0, 0) | 3.06 $\times$ 1010 | 21.3
I27 | (300, 510, $-$1890) | (57, 0, 0) | 2.05 $\times$ 1010 | 24.6
I31 | (250, $-$675, $-$1930) | (57, 0, 0) | 2.95 $\times$ 1010 | 29.9
a$\epsilon_{0}=3/2nk_{B}(T_{e}+T_{i,0})$ with $k_{B}T_{i,0}=50$eV for I24
[Frank Paterson (2000)], $k_{B}T_{i,0}=90$eV for I27 [Frank Paterson (2001)],
and $k_{B}T_{i,0}=75$eV otherwise [Kivelson . (2004)].

Figure 4: Visualisation of the magnetic field magnitude (color map) and the
plasma flow (arrows) produced by the MHD model as run by
Blocker2018MHDAtmosphere for flybys I24, I27, and I31. The first two panels
represent cuts at z=0 and the third panel is a cut at y=0. The day/night side
are indicated with the white and black sides respectively. The point of
closest approach is indicated with the red point. Note that for I31 an ‘edge-
on’ view of the system is displayed in order to better visualise the polar
flyby.

###  3.3 Particle tracing

Table 4: Parameter values used in the particle tracing simulations. Technical parameters particle tracing simulation | Value
---|---
Integration time step particle trajectory [s] | 0.001
Number of integration time steps per gyration | $\sim 32$
Maximum number of time steps per particle | 90000
Number of particles per spacecraft trajectory step | 100
Number of energy bins | 10
Spacecraft trajectory time step [s] | 0.6s
Physical parameters particle tracing simulation | Value
Surface density symmetrical atmosphere [cm-3] | 1 $\times$ 109
Scale height symmetrical atmosphere [km] | 100
Surface density asymmetrical atmospherea [cm-3] | 4.0 $\times$ 108
Scale height asymmetrical atmospherea [km] | 140
$\underline{B}_{0}$ [nT] | (0, 0, $-$2000)
$\underline{v}_{0}$ [km/s] | (60, 0, 0)
aIncludes following asymmetries: up-/downstream, anti-/sub-Jovian, day/night, see Section 3.1.2. |

We simulate the measured flux of energetic protons using a Monte Carlo
particle back-tracing code, developed from
Huybrighs2017OnMission,Huybrighs2020AnDepletions,Huybrighs2023. Particle
tracing has been employed previously at various Galilean moons to investigate
the ion dynamics as affected by field perturbations (e.g.
Selesnick2009ChargeIo,Poppe2018ThermalMagnetosphere,Liuzzo2019EnergeticCallistob,Breer2019EnergeticEuropa,Carnielli2019FirstIonosphere,Plainaki2020,Addison2022EffectIce,Nordheim2022MagnetosphericSurface,Huybrighs2023)
and atmospheric charge exchange (e.g.
Huybrighs2020AnDepletions,Addison2021InfluenceWeathering).

Because the energetic protons have no influence on the electromagnetic fields
they can be treated as test particles. In the simulation protons are traced
back in time from the EPD detector. For each particle it is determined if it
impacts and/or charge exchanges. If, at any point along the particle
trajectory, a surface impact ($r\leq R_{\text{Io}}$) or charge exchange with
the atmosphere occurs, the particle is considered lost. This analysis is
performed for many particles to determine the depletion as a fraction of the
(normalized) undisturbed flux. All the steps of this process, from initiating
the particle to the possible loss, are described in the following paragraphs.
The relevant input parameters are summarized in Table LABEL:tab_particle.

We take into account the energy distribution of the proton flux in the
simulation. Particles are initiated at a random energy within the energy range
of the TP1 or TP3 channel, using a Monte Carlo approach. Once the particles
are initiated they are binned according to their initial energy (10 bins) and
pitch angle (64 bins). The energetic proton flux decreases with increasing
proton energy, though less than an order of magnitude over both the TP1 or TP3
channels [Paranicas . (2003)]. We account for this decrease in flux with
increasing energy by weighting the particles according to the energy
distribution of the flux. Since we found in Huybrighs2020AnDepletions that the
simulation is not very sensitive to the specific drop off profile in one
energy channel, we have used the same relative change in flux ($\sim$40
percent decrease in flux from the beginning to the end of the energy channel)
as used in
Huybrighs2020AnDepletions,Huybrighs2021ReplyDepletions,Huybrighs2023 for
Europa in this study.

We use a leap frog numerical integration scheme of the Lorentz force to trace
the protons back in time [Huybrighs . (2017), Huybrighs . (2020), Huybrighs .
(2021), Huybrighs . (2023)]. We simulate the trajectories of energetic protons
under a homogeneous and an inhomogeneous electromagnetic field (the latter is
discussed in the next section). In the homogeneous case we neglect any
perturbations in the electromagnetic field resulting from the interaction of
the corotational plasma with Io. Despite that the situation with homogeneous
fields is not expected to occur at Io in reality, we consider including this
case relevant so that we can determine relative the contribution of the
inhomogeneous fields to the proton losses.

We neglect the pitch angle distribution of the protons, thus our pitch angle
distribution is uniform. The consequence of this simplification is that our
simulations will not be able to reproduce losses that are the result from
variations in the background pitch angle distribution. However, we consider
this approach suitable because our simulations will show that the deviations
from the background distribution are much more pronounced features than the
measured variations in the data upstream of Io.

In the simulation back-traced particles are assumed to contribute to a flux
decrease, if they impact on Io’s surface or charge exchange with neutrals from
its atmosphere. This is because when a back-traced particle that impacts Io or
charge exchanges, is traced forward it would have to originate from the
atmosphere or the surface, and neither of those are sources of energetic
protons. It is then assumed that the corresponding particle does not exist and
should thus count towards a loss of flux. Perturbed fields can form ’forbidden
regions’ which will lead simulated particles to impact on Io’s surface,
resulting in an apparent loss as measured by the instrument. In reality the
particle has effectively been deflected away from the ’forbidden region’. In
the simulation a particle is considered to have impacted Io’s surface when its
trajectory intersects the moon’s surface. If the energetic proton charge
exchanges, it is assumed to turn into an energetic neutral atom (ENA). ENAs
are not bound by the electromagnetic fields, and will escape from the system
at a high velocity, thereby contributing to the proton loss. The probability
of charge exchange with the atmospheric neutrals is determined using Equation
(7) from Birdsall1991:

$P=1-\exp(-n\sigma g\Delta t)$ (7)

Where $n$ is the local number density (of the atmosphere), $\sigma$ is the
energy dependent charge exchange cross-section, and $g$ is the velocity of the
ion relative to Io. For each time-step along the trajectory of the back-traced
particle, $P$ is calculated [Brieda (2011)]. Charge exchange is said to occur
if at any point along the trajectory a randomly generated number from a
uniform distribution between 0 and 1 is less than the calculated probability.
The collision cross section ($\sigma$) has to be determined empirically for
different particles. Note that because we use the charge exchange cross
section of protons on O2 as an approximation of protons on SO2, any neutral
SO2 densities derived from our particle tracing analysis are also an
approximation.

We neglect the following loss processes: charge exchange with the low energy
ions, energy loss due to Coulomb collisions with ions and electrons, and wave
particle interaction. Mauk2022 suggest that charge exchange with the low
energy ions could dominate over charge exchange with neutrals near Io’s orbit.
However, in this study we are dealing with the environment very close to Io
($\sim 2$RIo) where the neutral density of the atmosphere is orders of
magnitude larger than the ion density ($\sim$2000 cm-3; Bagenal2020TheEuropa).
Furthermore, the charge exchange cross section of the energetic protons on the
low energy ions is two orders of magnitude smaller than the cross section of
energetic protons and the neutrals (see Table 9 in [Mauk . (2022)]). We
therefore expect charge exchange with the low energy plasma to be only a minor
effect compared to charge exchange with the neutral environment close to Io.

We also assume that the effect of Coulomb collisions as a loss process is
negligible. Coulomb collisions could result in energy losses of energetic
protons, which would result in apparent losses of the protons. However,
Nenon2018AOrbit has shown that for energies of 0.1 MeV the loss rates due to
charge exchange with neutrals of the Io and Europa torus are orders of
magnitude larger than the losses due to Coulomb collisions. They specifically
modelled Coulomb collisions with bound electrons of the neutral particles of
the Jovian hydrogen corona and Io and Europa gas torus, with bound electrons
of the cold plasma ions and with free electrons of the cold plasma of the
inner magnetosphere of Jupiter. We also neglect Coulomb collisions as a loss
process for the TP3 channel, if Coulomb losses with the particle environment
(which at the distances of this work is dominated by the atmospheric density)
were a major loss process in this channel for the data segments we considered,
then we would expect to see a correlation between the density of the
atmosphere and the dropout, which is not what we observe for TP3.

We also neglect wave particle interaction as a loss process that plays a major
role in the proton loss features we observe within $\sim 2$RIo. We build on
Mauk2022 which argues that near Io’s orbit charge exchange losses dominate for
protons (roughly below 200 keV). As we will demonstrate later, the depletion
features at 540-1250 keV can be explained by the field configuration,
indicating that also at these higher energies wave particle interactions do
not play a major role in proton depletion within $\sim 2$RIo.

We ignore the possibility of protons re-entering the simulation box after
exiting, because the bounce periods are larger than the time it takes the
corotation to cover the spatial scales of the relevant proton loss features.
Therefore, we consider it unlikely that losses occurring closer to upstream
would create the measured losses further downstream by modifying the proton
distributions. See C for a more detailed discussion.

Considering the complexity of the processes leading to proton depletion in
Io’s atmosphere (electric and magnetic field perturbation, neutral density
etc.) the atmospheric density cannot be directly inferred from the
measurements. Thus, we analyze the data with a forward modeling approach,
prescribing an atmospheric distribution and electric and magnetic field
perturbations around Io to compute the proton depletion and compare it to the
Galileo data.

##  4 Results

###  4.1 Measured energetic proton depletions during flybys I24, I27, and I31

In Figure 5 we show the measured energetic proton flux (solid orange line) for
the three flybys in the TP1 and the TP3 channel. The vertical red dashed line
indicates the point of closest approach for each flyby and the grey dashed
line indicates the radial distance to Io. The flux in these plots has been
normalized to the mean of two cycles of the instrument from the start of the
flyby segment. This allows for comparison with the particle tracing code which
expresses depletion numbers in percentages. The periodic variation of the flux
measurements is due to the rotation and scanning motion of the spacecraft (as
mentioned above, this takes about 140 s).

We observe that the region over which depletions occur along the spacecraft
trajectory is larger in the TP1 channel than the TP3 channel for I27 and I31.
Furthermore, for flyby I24 no depletion is observed in the TP3 channel (b) at
all. This decrease in size or disappearance of the depletion region in TP3 is
suggestive of charge exchange playing a major role in the depletion because
the charge exchange cross section decreases significantly from the TP1 to the
TP3 channel (see Figure 12). For I24 in TP1 the depletion region is
symmetrical with the distance to Io, while in I27 and I31 the symmetry breaks
down. During both I27 and I31 (TP1) the depletion region is more extended on
the day/downstream side (right side in panels a c and e). For TP3 I24 does not
show a trend of depletion. The extent of the depletion region in I27 and I31
(TP3) is roughly symmetrical with respect to the distance to Io. However,
during I31 there is a complicated structure, with a near complete depletion
occurring after the closest approach from 05:02 to 05:04 that does not occur
post closest approach.

Note that we do not attribute the measured depletions to the gyroradius
effect. That is, the effect where particles impact on Io’s surface because
they encounter it during their gyromotion along the field line. Figure 13
shows that the gyroradius of the respective protons is smaller than the
closest approach altitude, even during the closer flyby I27. Furthermore, the
gyroradii shown in Figure 13 are for the upstream conditions, and represent a
lower estimate. Near Io the magnitude of the field will increase due to
magnetic pile up, therefore the gyroradius will be even smaller near Io.

An artifact that introduces nonphysical dropouts can occur in the EPD data,
when measurements are taken on motor position 7 [Jia . (2021), Huybrighs .
(2021)]. For flybys I24 and I27 this artifact does not occur because the EPD
was kept in a fixed motor position, which is different from motor 7. For the
data segment of I24 and I27, considered in this study, the motor position is
fixed to position number 4. During I31 motor position 7 is one of the motor
positions that is scanned, however we find that the EPD data gathered, when
the motor is in position 7, does not appear to fall outside of the general
trend. We conclude that the data artifact will not affect the conclusions of
this study, because we focus on the general trend and structure of the
depletion rather than depletion features measured at single motor positions.

Figure 5: The normalized energetic proton flux as detected by the EPD is shown
using the solid orange line for the three Io flybys I24 (a and b), I27 (c and
d), and I31 (e and f). The TP1 (155-224 keV) flux is shown in the left side
panels (a, c, and e) and the TP3 flux (540-1250 keV) in the right side panels
(b, d, and f). The point of closest approach is marked with a vertical red
dashed line. Note the periodic variation in the flux due to the rotation and
scanning motion of the spacecraft. The dotted grey line shows the distance to
Io in RIo (axis on the right side).

###  4.2 Data-simulation comparison

Figure 6: Normalized energetic proton flux as detected by EPD in the TP1
channel (155-224 keV) (orange solid line) compared to the depletion as
predicted in the particle back-tracing simulations for the three Io flybys I24
(a and b), I27 (c and d), and I31 (e and f). The simulations results where no
atmospheric charge exchange was taken into account are shown in black.
Simulations that consider charge exchange with the symmetrical atmospheric
model are shown in dark blue and those considering the asymmetrical model are
shown in light blue. The left side panels (a, c, and e) show the results when
assuming homogeneous electromagnetic fields, and the right side panels (b, d,
and f) show the results when perturbed electromagnetic fields are taken into
account. The dotted grey line shows the distance to Io in RIo (axis on the
right side). Vertical green and pink lines in the right column correspond to
the starting point of particle trajectories shown in Figure 8. Vertical green
and pink lines in the left column correspond to individual particles
trajectories plotted in Figures 9, 10 and 11.

In Figure 6 the results are shown for the back-tracing simulations for the TP1
energy channel (155-224 keV). In the plots on the left of the figure (a, c,
and e) the results are shown for the homogeneous fields, while the right side
(b, d, and f) shows the results for the inhomogeneous fields. The first row (a
and b) shows the results for I24, the second row (c and d) for I27, and the
third row (e and f) for I31. In each plot, the EPD measurement is shown in
orange. The depletion predicted while assuming no atmospheric interactions is
shown in black, and the simulations considering charge exchange with the
atmosphere are shown in dark blue for the symmetrical atmosphere and light
blue for the asymmetrical atmosphere. In Figure 7 simulation results for the
TP3 energy channel (540-1250 keV) are shown. The same colors and labels are
used as in Figure 6.

Figure 7: Normalized energetic proton flux as detected by the EPD in the TP3
channel (540-1250 keV) (orange solid line) compared to the depletion as
predicted in the particle back-tracing simulations for the three Io flybys I24
(a and b), I27 (c and d), and I31 (e and f). Note that the simulations without
charge exchange and with charge exchange fall together exactly, because the
effect of charge exchange is negligible. The left side panels (a, c, and e)
show the results when assuming homogeneous electromagnetic fields, and the
right side panels (b, d, and f) show the results when assume perturbed
electromagnetic fields. The dotted grey line shows the distance to Io in RIo
(axis on the right side).

We will argue that at 155-224 keV charge exchange is the dominant loss process
(I24) or a main loss process combined with surface absorption (I27 and I31).
The measured losses are also sensitive to the description of the
electromagnetic field (I27 and I31). Due to the collision cross section
decreasing exponentially with energy, the likelihood of charge exchange
occurring with high energy particles is smaller than for lower energy
particles. Therefore the 540-1250 keV (TP3) simulation results do not show any
significant difference when atmospheric charge exchange in included, all the
solutions are overlapping each other (black, dark blue en light blue line). We
will argue that 540-1250 keV protons during I24 are not affected by Io and
that inhomogeneous electromagnetic fields are responsible for the proton
depletion observed during the two closer flybys I27 and I31. Due to I31’s
polar trajectory surface absorption is also an important loss process during
that flyby.

####  4.2.1 Flyby I24

Panels a and b in Figure 6 show the results for flyby I24 (155-224 keV, TP1).
If atmospheric charge exchange is not taken into account (black line), no
depletion at all is predicted for I24 for either the homogeneous fields (a) or
the MHD fields (b). This indicates that neither impact on the surface or the
configuration of the electromagnetic fields can explain the proton losses
during flyby I24.

The asymmetrical atmospheric model (light blue) partially reaches the
approximate depth of the depletion. We interpret the partial agreement as an
indication that charge exchange with the atmosphere is likely the main cause
of the observed depletion region and therefore the dominant loss process at
155-224 keV during this flyby. However, the simulated depletion does not reach
the depth of the depletion consistently. Instead we observe that the simulated
flux periodically returns to the unperturbed level, whereas the data does not.
This periodic discrepancy will be discussed further in Section 4.3.

For the symmetrical atmospheric model (dark blue line), we see depletion of no
more than about 10% around the point of closest approach (red dashed line)
when assuming homogeneous electromagnetic fields (a). The difference with the
symmetrical atmosphere is that the density at the altitude of the I24 flyby is
higher due to a higher scale height (Figure 2). When also including the MHD
fields (b), we see a slight increase in depletion up to about 20%. Though the
MHD simulations have not been run self-consistently with the symmetrical
atmosphere, it also appears unlikely that a combination of this particular
symmetrical atmosphere and perturbed fields will explain the depth of the
proton loss. Overall, we conclude that it is unlikely that charge exchange
with this symmetrical atmosphere can explain the observed proton losses. While
perturbed fields (panel b) slightly modify the depletion pattern for both
atmospheric models, we conclude that the overall effect of the perturbed
fields on the proton losses for this flyby is minor.

At 540-1250 keV (TP3), Figure 7, even though there is a variability of the
measured proton flux, there appears to be no correlation between the measured
proton flux and the distance to Io. We consider it likely that the proton flux
at 540-1250 keV during this flyby is not affected by Io. Indeed, the
simulations demonstrate that neither surface impact, charge exchange or
perturbed fields are expected to have any effect during this flyby. The lack
of depletions in the TP3 channel, and the partial agreement between the
simulated and measured depletions in the lower energy TP1 channel argues in
favour of charge exchange being the dominant loss process at the TP1 energies
(155-224 keV).

####  4.2.2 Flyby I27

In the simulation results for flyby I27 (155-224 keV, TP1), no depletion is
seen in the homogeneous fields plot (black line in panel c in Figure 6) when
neglecting atmospheric charge exchange. However, with the inhomogeneous fields
and no charge exchange (black line, panel d) we do see a strong periodic
depletion between the 13:45:00 and 13:49:00, but no depletion predicted
outside of this area. We attribute these depletions to the electromagnetic
fields used in case d, which guide the particles to Io’s surface in the back-
tracing sense due to a tilt in the magnetic field that is neglected in the
homogeneous case. An example of such a particle trajectory is shown in Figure
8. In forward sense this particle does not exist, because Io’s surface does
not emit energetic protons. The periodic losses in the black line in panel d
can thus be considered as a ’shadowing’ by Io’s surface which absorbs the ions
and that occurs specifically under this field configuration.

Figure 8: Particle trajectories during flyby I27 with homogeneous fields
(left), and perturbed and tilted fields (right). The green particle is not
considered lost, it neither impacts on Io’s surface or charge exchanges. On
the left the pink particle is lost because it charge exchanges with the
atmosphere, however on the right its trajectory is guided towards the surface
and impacts. In the background of the right panel the magnitude of the
perturbed electromagnetic fields has been plotted. Note also that the
gyromotion of the particle has been plotted. The panels on the left and right
correspond, respectively, to the lines with the same color on the left of the
closest approach in panels ’c’ and ’d’ in Figure 6.

With atmospheric charge exchange taken into account the simulations show
deeper depletions compared to I24 in the case with atmospheric charge
exchange. We attribute this difference to the lower altitude of the closest
approach (see Table 1) and the corresponding higher atmospheric densities for
both atmospheric models. We also observe that the difference in depth of
depletion between the two models is smaller than for I24. Towards the
extremities of the flyby the asymmetrical model still exceeds the simulated
depletion depth for the symmetrical model, due to higher densities at higher
altitudes in the asymmetrical model (see Figure 2). Near closest approach the
density of the symmetrical model is comparable to that in the asymmetrical
model, and the depth of depletion in the symmetrical case is also comparable
to the asymmetrical case. Just as for flyby I24 we observe that the simulated
flux periodically returns to the unperturbed level, whereas the data does not.
This periodic discrepancy will be discussed further in Section 4.3.

The extent of the loss region in the case with only the perturbed fields is
smaller than the loss region in the data. For both atmospheric models the loss
region with atmospheric charge exchange extends beyond the region in which
losses occur associated with the choice of fields (black line, d), indicating
that both charge exchange and an appropriate description of the fields are
needed to explain the loss region.

At 540-1250 keV (TP3) proton depletion is visible in the EPD data around the
point of closest approach (13:47:00). The predicted depletion for the
homogeneous fields (c) is negligible. However, for the case with inhomogeneous
and tilted fields (d) a series of depletions are predicted. We find that the
simulation reproduces the general structure of depletion features well, with
the depth of the depletion being reproduced, as well as the increase in flux
between each depletion. From this general agreement we conclude that an
appropriate choice of electromagnetic field can explain the majority of the
depletion features during I27 at 540-1250 keV.

####  4.2.3 Flyby I31

I31 results are shown in panels e and f in Figure 6. Without taking
atmospheric charge exchange into account (black lines) strong and periodic
depletions are predicted for the homogeneous fields. This is due to the fact
that I31 is a polar flyby (see Figure 1). Charged particles move along the
magnetic field lines, which are approximately parallel to Io’s rotation axis.
Therefore, when Galileo (along with the EPD) flies over the northern pole of
Io, Io is placed directly in the path of charged particles moving (in forward
sense) from south to north which blocks their path to the EPD (see Figure 11,
left column). When assuming inhomogeneous fields (f), the depletion is
localised closer around the point of closest approach between 04:57:00 and
05:03:00. We attribute this difference to deflection of energetic ions away
from the surface by the inhomogeneous fields. However the simulations with the
inhomogeneous fields are not able to explain the extent of the depletion
region along the flyby.

When including the symmetrical (in dark blue) and asymmetrical (in light blue)
atmospheric models we see that the extent of the depletion region is better
reproduced. However, just as for flyby I24 and I27 we observe that the
simulated flux periodically returns to the unperturbed level, whereas the data
does not. This periodic discrepancy will be discussed further in Section 4.3.

Whereas for flyby I24 the depletion region correlates roughly with the radial
distance to Io, for the downstream side of the I31 this correlation breaks
down as an extended depletion region is visible, both in the data and the
simulation with the asymmetrical atmosphere. It appears that the simulated
dropout is sensitive to the enhanced atmosphere on the dayside/downstream side
of Io. Figure 2 shows that the density along the trajectory is symmetrical
with respect to the closest approach, however the simulated proton loss is
not. The proton loss is thus not fully determined by the density at the
trajectory, but also by density structures elsewhere. We emphasize that charge
exchange simulation is not exclusively sensitive to the atmospheric density
along the spacecraft trajectory, but the density along the entire particle
trajectory.

At 540-1250 keV (TP3) we observe that, just as for the TP1 channel, depletions
are expected to occur even in the absence of perturbed fields (e). The
periodicity is due to the spin of Galileo and EPD looking into directions for
which Io blocks the field of view and prevents particles from reaching the
detector.

We observe that by introducing perturbed fields the complete depletion $\sim$2
mins around the closest approach is reproduced. This implies that in the back-
tracking simulation all ions impact Io’s surface in this region. We consider
this a ’forbidden field’ region, wherein the specific configuration of the
field prevents access of protons. However, large discrepancies between the
simulated and measured proton loss occur elsewhere along the flyby. The
predicted extent of the depletion regions is reduced in the inhomogeneous case
as compared to the homogeneous case. For the homogeneous fields we see
depletion between 04:55:30 and 05:04:30, while for the inhomogeneous fields
the depletion is concentrated between 04:57:00 and 05:03:00. Which is shorter
than the time during which depletions are observed in the measurement. A
periodic depletion is seen in the measurement, around 04:56:00, but is not
reproduced. A near complete region of depletion occurs from 05:01:00 to
05:04:30, which is poorly reproduced by the simulation. Our simulations for
I27 show that at these high energies the bulk of the depletion feature can be
explained solely by an appropriate choice of electromagnetic field. Therefore,
we attribute the discrepancies between the simulated proton flux and the
measurement to discrepancies between the simulated magnetic field and the real
configuration.

###  4.3 Periodic discrepancy between data and model at 155-224 keV

As described in the previous sections a periodic discrepancy occurs between
the simulated losses and the measured loss at 155-224 keV (TP1). While the
simulated flux periodically returns to the unperturbed level, the data does
not. We attribute this periodicity to the approximately 20 second spin of the
Galileo spacecraft, which makes EPD scan different directions. Meaning that in
certain directions the losses are predicted better than in others. We further
interpret this periodic discrepancy as an indication that our atmospheric
model can be improved in the directions where we underpredict the loss, in
particular by increasing the scale height of the atmosphere.

Firstly, we point out that the periodic matching and mismatching of the data
by the model does not occur at 540-1250 keV (TP3) and is therefore an energy
dependent effect. In fact, the overall agreement between the simulation with
perturbed fields and the data is notably better at 540-1250 keV (where charge
exchange is negligible) than for the simulations at lower energies (155-224
keV) without charge exchange. Considering that atmospheric charge exchange is
more likely to occur in the lower energy range than the higher energy range.
The fact that the model more accurately reproduces the data in the higher
energy regime compared to the lower energy regime suggests that the model is
not sufficiently capturing the entirety of the charge exchange occurring at
Io. This implies that if the atmospheric model is improved, charge exchange at
lower energies would be enhanced and the depletion features at 155-224keV will
be better reproduced.

Next we will discuss the discrepancy for flyby I24 as an example. Because
charge exchange is the dominant loss process during this flyby, the
interpretation of the discrepancy is simpler. During the entire duration of
I24 a periodic matching and mismatching of the depth of the depletion
associated with the asymmetrical model occurs. In Figure 9 we show particle
trajectories for four points along the trajectory where the depletion reaches
approximately the depth of the data (pink trajectory), and where it does not
(green trajectory). The trajectories corresponding to points where the depth
of depletion is underestimated have a smaller gyroradius, or equivalently,
higher speed parallel to the magnetic field. The trajectories corresponding to
those points where the depth of the depletion is approximately attained, have
larger gyroradius, or equivalently lower speed parallel to the magnetic field.

The periodicity in the simulation (light blue line, Figure 6, panel a) has
three dips within 20 seconds (the spin of the spacecraft). This is because
during a full rotation of 20 seconds the detector viewing direction changes
from perpendicular to the field line (larger gyroradius, large dip #1), to
parallel (smaller gyroradius, no or small dip), perpendicular again but in
opposite direction (larger gyroradius, large dip #2), parallel again but in
opposite direction (smaller gyroradius, no or small dip) and back to the
initial viewing angle (larger gyroradius, equivalent to large dip #1).

Next we discuss flyby I27, during which a different pattern of agreement
between the data and the model than for I24 occurs. At the extremities of the
I27 the depletion pattern is similar to I24: i.e. three approximately equal
dips are visible every 20 seconds, with an underprediction of the measured
depletion in between the dips (e.g. near the pink and green line on the right
side of panel c in Figure 6). However, near the closest approach the pattern
of depletion becomes different. Within the 20 second spin we see an
underprediction of the depletion (green line on the left of the closest
approach), a deep depletion that matches the data (purple line) and an
undeprediction again. Thus, compared to I24, or the extremities of I27, we see
only one deep dip per spin. In fact, what is different is that in the closer
part of I27 within each 20 second cycle there is one of the two more field
aligned directions (e.g. purple line left of the closest approach in in Figure
6, panel c) along which the depletion is now also approximately reproduced.
Combined with the directions perpendicular to the field that were already
depleted (previously referred to as deep dips #1 and #2) this depleted and
field aligned direction forms the single deep dip we observe during one spin.
The other field aligned direction (e.g. green line left of the closest
approach, Figure 6 left column, panel c) still underpredicts the loss. In I24,
or at the extremities of I27 (e.g. purple and green line right of the closest
approach in Figure 6, panel c), both of the field aligned directions produce
the losses about equally poorly. Corresponding particle trajectories are shown
in Figure 10. The field aligned direction which is depleted in the closer part
of I27 corresponds to the direction southward of the trajectory. Considering
that the I27 flyby is located north of Io’s equator, particles going in these
directions appear to have a higher chance of charge exchanging, even when they
are more field aligned and have smaller gyroradii. We argue that this is
because they traverse a larger section of the low altitude and therefore
denser atmosphere, which results in a higher chance of charge exchange.

The underprediction in the northward field aligned directions appears to hold
even in the case with the inhomogeneous fields (Figure 6, panel d). In the
northward directions (e.g. closest to the green line on the left of panel c)
the effect of the field configuration seems negligible. However, the southward
field aligned directions (e.g. closest to the pink line on the left of panel
c) is fully depleted in panel d. This means that we likely cannot derive any
direct information about the atmospheric losses in those directions, since
they are already fully saturated even without atmospheric charge exchange.

Lastly, we discuss the periodic discrepancy for flyby I31. In Figure 11 we
show particle trajectories for four points along the I31 trajectory where the
depletion reaches approximately the depth of the data (pink trajectory), and
one where it does not (green trajectory). First considering the two
trajectories in the left column of Figure 11. The direction in which the
simulation matches the depth of depletion (pink) corresponds to a direction
that intersects with the surface. As discussed in the previous section such a
particle is considered lost. The green trajectory is essentially moving in the
opposite direction and does not intersect the surface, implying that the loss
process associated with this direction has to be different from surface
impact. In the right panel the pink trajectory (depth of depletion reproduced)
does not intersect the surface, rather the cause of the depletion is charge
exchange. As for I24 and I27 it appears that both atmospheric models
underestimate the losses in the more field aligned directions that do not
encounter the denser part of the atmosphere. The conclusions for the ’green’
particles hold even when including perturbed fields, at those points the
depletion seems unaffected by the perturbed fields (black line).

However, we also observe that during the two minutes around the closest
approach the cyclical mismatch disappears in the case with the inhomogeneous
fields. This suggest that at least part of the mismatch could be attributed to
a mismatch between the simulated field and the real configuration.
Nonetheless, the simulations suggest that the role of the electromagnetic
field in producing the losses only matters in a segment along the trajectory
that is more confined than where atmospheric charge exchange plays a role.
Suggesting that both charge exchange and field perturbations are required to
reproduce the observed loss.

In conclusion, we find that the periodic discrepancy can be attributed to the
properties of the atmospheric model. Directions in which the depletion is
underpredicted correspond to ions that have small gyroradii and are travelling
away from Io or the denser part of its atmosphere. Losses along these
directions thus contain more information about possible charge exchange at
larger distances from Io. We will discuss the implications of this finding
further in Section 5.4.

Figure 9: Particle trajectories during flyby I24. Green particles are
particles that are not lost in the simulation, pink ones are lost by charge
exchange. Note also that the gyromotion of the particle has been plotted.
Green particles correspond to smaller gyroradii, while pink particles
correspond to larger gyroradii. Furthermore, pink particles corresponding to
times along the trajectory where the simulation matches the depth of the
dropout in the data approximately, green ones correspond to points where the
loss is underpredicted. The corresponding points along the trajectory are
indicated in Figure 6 panel ’a’, left column on the left side of the closest
approach, right column on the right side.

Figure 10: Particle trajectories during flyby I27. The green trajectories are
particles that are not lost, while the pink trajectories are particles that
are lost by charge exchange. Note also that the gyromotion of the particle has
been plotted. Furthermore, pink particles correspond to points along the
trajectory for which the depth of the depletion is approximately recreated,
while it is underestimated for the points corresponding to the green
trajectories. The points along the trajectory corresponding to these particles
is indicated in Figure 6 panel ’c’, left column on the left side of the
closest approach, right column on the right side.

Figure 11: Particle trajectories during flyby I31. The left column shows a
particle that is lost by impact on Io’s surface (pink) and a particle that is
not lost (green). The right column shows a particle that is lost by charge
exchange with the neutral atmosphere (pink) and a particle that is not lost
(green). Note also that the gyromotion of the particle has been plotted.
Furthermore, the pink particles correspond to points along the trajectory at
which the depth of depletion is approximately reproduced, while the green ones
correspond to points where the depletion is underpredicted. The points along
the trajectory corresponding to these particles are indicated in Figure 6
panel ’e’, left column on the left side of the closest approach, right column
on the right side.

##  5 Discussion

###  5.1 Atmospheric charge exchange is a major or dominant loss process
during flybys within $\sim 2$RIo

In this section we argue that atmospheric charge exchange is a necessary
factor in order to explain the energetic proton depletion seen in the TP1 data
during the Galileo flybys of Io. In fact, we suggest that near Io atmospheric
charge exchange is the dominant loss process for flybys of 600 km altitude,
while in closer flybys of 200km the electromagnetic field configuration and
surface absorption also play a role in the measured proton depletion. In this
sense the environment closest to Io is different than the environment along
Io’s orbit, but not close to Io, wherein charge exchange with the low energy
plasma is thought to be the dominant loss process [Mauk . (2022)]. Table
LABEL:tab_summary summarises the effects contributing to the proton loss and
the derived atmospheric properties.

Table 5: Overview of the effects contributing to the proton losses and derived atmospheric properties, derived from the data-model comparison for the TP1 channel (155-224 keV). Relevant loss processes | I24 | I27 | I31
---|---|---|---
Surface absorption | No | Yes | Yes
Charge exchange | Yes | Yes | Yes
Forbidden fields | No | No | Yes
Atmospheric property |  |  |
Day/downstream extension | No | Yes | Yes
Full collapse on nightside | No | No | No
Global extended component | Yes | Yes | Yes

As discussed in Section 4.1, at higher energies (540-1250 keV, TP3) the
depletion region decreases in size along the flyby (I27 and I31) or disappears
altogether (I24). This energy dependent size of the depletion region itself is
already a strong indication for a role of charge exchange with the atmosphere
as a loss process. Furthermore, the simulation results discussed in the
previous section indicate that the inclusion of atmospheric charge exchange
leads to deeper energetic proton depletion for all flybys in all cases,
including those with homogeneous electromagnetic fields, with perturbed fields
and for both atmospheric models, in the energy range of the TP1 channel of the
EPD (155-224 keV), thereby further supporting our hypothesis regarding the
role of charge exchange.

The effect of charge exchange is most apparent for flyby I24, for which we
argue that charge exchange is the dominant loss process of energetic protons.
Our simulations can reproduce the extent of the depletion region, as well as
attain the depth of observed depletion, while neither perturbed fields or
impact of the surface play a significant role during this flyby. Furthermore,
the lack of any depletion in the TP3 channel is fully consistent with the
energy dependent charge exchange cross section.

For flyby I27 the picture is more complex, as both electromagnetic fields
which guide particles to the surface and charge exchange play a role in the
formation of the depletion features, according to the simulations. The role of
electromagnetic fields is confined to the region closest to Io, while the
effect of charge exchange extends further. Furthermore, the depletion region
in TP1 extends well beyond the depletion region in TP3, which is fully
consistent with the energy dependence of charge exchange. We conclude that
during I27 charge exchange is the major loss process during most of the flyby
segment.

For flyby I31 the picture is different due to the polar geometry of the flyby.
Here surface impact, perturbed fields and charge exchange play a role in the
formation of the depletion features. However, also here the depletion region
in TP1 extends well beyond the depletion region in TP3, which is fully
consistent with the energy dependence of charge exchange. We conclude that
during I31 charge exchange is a major loss process, becoming the dominant
process on the outbound part of the trajectory which is on Io’s
dayside/downstream side.

Nearest Io during I27 and I31 we observe that situations occur where half of
the spin cycle or the entire cycle is fully depleted due to perturbed fields.
The corresponding directions are difficult to interpret in terms of charge
exchange, considering that any atmospheric model would fit them. Furthermore,
the directions along the trajectory nearest Io where fields have no effect are
aimed away from Io, thus this limits the sensitivity of the analysis in
interpreting the density of Io’s atmosphere, nearest to Io.

Previously Huybrighs2020AnDepletions,Huybrighs2021ReplyDepletions have
established that field perturbations and atmospheric charge exchange are
required to explain particle dropouts measured during the E26 flyby of Europa
(closest approach 350 km), in addition to losses by particles impacting on
Europa’s surface. Whereas the same processes take place at Io, we point out
that the relative importance of atmospheric charge exchange is much larger at
Io, due to its substantially denser neutral environment. This is true for all
flybys considered in this study, from the lower altitude flybys I27 (closest
approach at 198 km) and I31 (closest approach at 193 km) as well as for the
higher altitude flyby I24 (closest approach at 611 km).

###  5.2 Proton losses are sensitive to the electromagnetic field
configuration within $\sim 0.5$ RIo

Here we argue that an appropriate choice of electromagnetic field is also
necessary to explain the proton depletion seen at 155-224 keV (TP1), together
with charge exchange and surface impact, and at 540-1250 keV (TP3) together
with surface impact, in flybys closer to the surface such as I27 (198 km) and
I31 (193 km). At higher altitudes, such as flyby I24 (611 km), the choice of
field configuration does not appear to cause losses. Losses due to the field
configuration are caused when the field guides protons to the surface and
makes the impact. Perturbations in the electromagnetic field can also form
’forbidden regions’ to which the access of the energetic proton is restricted
(I31).

During flyby I27 (closest approach at 198 km), the field configuration causes
losses, up to 100%, near the point of closest approach of Io in both TP1 and
TP3 (Figures 6 and 4 in panel d, black curve). This is in contrast to flyby
I24 (closest approach 611 km), which has a qualitatively similar geometry with
respect to the upstream flow and Io as I27 (see Figure 1), however the choice
of fields has no major effect on this flyby. Thus, due to the higher altitude
the electromagnetic fields are unable to make the back-traced particles
intersect with Io’s surface.

It should be noted that for flyby I31, the perturbed fields also reduce the
range along the trajectory within which the depletion occurs. This is due to
the fact that the fields bend the trajectories of the charged particles around
Io, allowing a greater number of particles to pass from the south to north
side of the moon than if homogeneous fields are assumed.

Even though the fields on their own do not cause proton losses during flyby
I24, they do have a (minor) effect on the proton losses due to charge
exchange. The simulated depletion pattern for I24 with atmospheric charge
exchange and homogeneous fields (Figure 6, panel a) differs from the depletion
pattern calculated with atmospheric charge exchange and perturbed fields
(panel b in the same figure) in both shape and depth. With the inclusion of
the perturbed fields points of maximum depletion are deeper by about 10%. This
implies that even if the field configuration does not lead to charged particle
depletion directly, it does affect the depletion caused by the atmospheric
charge exchange. Hence, we argue that perturbed fields are also an
influential, though minor, factor in the charged particle depletion seen in
TP1 during flyby I24.

###  5.3 Evidence for an extended atmosphere on the downstream/dayside, lack
of evidence for full atmospheric collapse on upstream/nightside

Here we argue for the existence of an extended downstream/dayside atmosphere
during flybys I27 and I31, as well as the lack of evidence for complete
atmospheric collapse on the upstream/nightside, based on the energetic proton
measurements.

Figure 5 reveals some evidence for an asymmetry during flyby I27. By visual
inspection it can be determined that the trend of the loss in TP1 (155-224
keV) strongly correlates with the radial distance on the outbound (right side)
part of the trajectory, while the trend of the loss on the inbound (left side)
of the figure is lagging the trend of the radial distance. Considering the
evidence for atmospheric charge exchange is the main loss process, during most
of the segment, this suggests that the atmosphere is less expanded on the
nightside than on the dayside.

Flyby I31 crosses from the night side into the dayside over Io’s pole (see
Figure 1), as well as from the upstream to the downstream plasma environment.
Figure 6 shows that the measured depletion region during I31 extends further
on the dayside/downstream region than on the nightside region/upstream. Thus,
the energetic protons measurements are indicative of a dayside/upstream
asymmetry in the proton losses. The simulation with the asymmetrical
atmosphere (see Section 3.1), which incorporates a day-night asymmetry as well
as an upstream-downstream asymmetry, demonstrates that the extended depletion
from approximately 05:04:30, corresponding to the dayside, is caused by
atmospheric charge exchange alone. Whereas the radially symmetrical atmosphere
is unable to reproduce the extended loss on the dayside. Therefore we
interpret the extended loss region on the dayside as an indication of an
extended atmosphere on the downstream/dayside.

The atmosphere is expected to be denser on the dayside due to enhanced
sublimation (e.g. Tsang2016TheEclipse). It is also thought to have a higher
scale height on the downstream side (e.g. Saur2002InterpretationPasses).
Because the downstream and dayside coincide during I24 and I27 we cannot
distinguish between these two possible physical explanations for the extension
on the downstream/dayside.

For flyby I24 the trend of the loss follows the radial distance closely, we
conclude that there is no clear sign of an atmospheric asymmetry in this
flyby. The lack of a strong asymmetry does not necessarily imply that no
asymmetry exists. We propose that it is the specific geometry of the I31
flyby, polar from the upstream/nightside to the downstream/dayside, that is
most favourable to reveal the presence of asymmetries between the
upstream/nightside and the downstream/dayside as compared to the other two.
However, since I24 and I27 have similar geometries with the
downstream/dayside, but different altitudes, it appears that the visibility of
the asymmetry between the upstream/nightside and the downstream/dayside could
be limited to lower altitudes.

We note that even though the atmosphere on the upstream/nightside extends
less, there is still some loss on the upstream/nightside. From the proton
measurements there is thus no evidence that the atmosphere is fully collapsed
on the upstream/nightside.

Additional measurements, in particular those on the dayside when the dayside
and the upstream side are not coinciding, could provide clarity on the role of
enhanced sublimation in the formation of Io’s extended atmosphere on the
dayside, additional flybys on the Jovian side could reveal the Jovian/anti-
Jovian asymmetry.

###  5.4 Evidence for a global extended atmospheric component

In Section 4.3 we argued that for each of the three flybys there are viewing
directions for which we underpredict the proton losses, that is where the
modelled loss returns to unperturbed level whereas the data does not. We
observe for the three flybys that the directions in which we underpredict the
depth of the depletion corresponds to more field aligned particles that have a
higher parallel velocity and thus smaller gyroradius. (An exception occurs
when those particles pass through the denser part of the atmosphere closer to
Io or the extended atmosphere on the upstream/dayside where they are
depleted.) In contrast, the directions where the depth of depletion matches
the data approximately correspond to particles that are less field aligned and
have larger gyroradii. We suggest that a more extended atmosphere could
compensate for the lack of depletion in the field aligned directions
corresponding to smaller gyroradii, while retaining the relative agreement in
other directions.

The protons with the larger gyroradius spend more time in the high density
part of the atmosphere (due to a lower velocity parallel to the magnetic
field) and thus have a higher chance of charge-exchanging in this region than
a particle with the same total energy that has a smaller gyroradius and higher
parallel velocity. If an additional extended atmospheric component were to be
included, the larger gyroradius particles would still charge exchange at a
similar position along their trajectory in back-tracing sense (since they are
most sensitive to the denser part). The smaller gyroradius particles, which
would have had a low chance of charge exchange in the dense part of the
atmosphere, would get a higher chance of charge exchanging if there were an
extended atmosphere that is of a larger physical scale. In this sense an
extended atmosphere could increase the depletion for smaller gyroradius
particles while having less effect on the larger gyroradius particles. Indeed,
during I27 we observe that field aligned directions could be depleted when the
densities are increased. At the pink marker during I27 (Figure 6, left side,
panel c) the direction corresponds to particles that are closer to field
aligned (see Figure 10), indeed the depletion at this point is reasonably well
reproduced. On the other hand, at the green marker (left side) in the same
figure, the field depletion is underpredicted. The difference between the two
is that the pink marker travels through the densest part of the atmosphere,
that is located at lower altitudes.

Additional simulations for a wide range of atmospheric properties are needed
to constrain the properties of the extended atmosphere, we leave such a
comprehensive enterprise as a subject for a future study. However, we do
consider it likely that the missing atmospheric component extends beyond 2 Io
radii, based on the fact that we observe the periodic discrepancy between the
data and simulations throughout all flyby segments we considered.

The presence of such an extended atmosphere is supported by remote and in-situ
observations of Io. Using the Hubble Space Telescope imaging spectrograph,
[Wolven . (2001)] detected Far Ultraviolet (FUV) emissions of O and S neutral
atoms extending to at least 10 RIo around Io. Based on the direction of the
instrument aperture, it can be inferred that these emissions are probably
spherically distributed. Assuming nominal torus values for the electron
density and temperature, Wolven et al. infer an Oxygen density $\sim$ 1-2
$10^{5}$ cm-3 at 2 RIo. The charge exchange cross sections of protons on O
follow the same trend as H on O2, but have somewhat lower values [Basu .
(1987)]. We therefore consider charge exchange with the S and O corona as a
possible explanation. Follow-up studies should consider a multi-species
atmospheric model that includes the O and S corona and appropriate cross-
sections.

Along most flybys of Io, Galileo observed Electro-Magnetic Ion Cyclotron
(EMIC) waves at frequencies close to the SO${}_{2}^{+}$ and SO+
gyrofrequencies [Huddleston . (1998), Russell Kivelson (2000), Russell .
(2001), Blanco-Cano . (2001)]. Such EMIC emissions are produced when neutrals
are freshly ionized, forming a typical PickUp ring-distribution in phase
space. These EMIC emissions were observed mainly downstream of Io and
sometimes far from the moon: along the J0 flyby in Io’s wake, EMIC waves were
observed extending to $\sim$ 6-20 RIo in the inbound-outbound directions of
the Galileo trajectory. These EMIC detections suggest the presence of a
tenuous corona of SO2 and SO extending far from Io, mainly in the downstream
direction. Under simplifying assumptions, Huddleston1997 infer a lower limit
of the SO2 density $\sim$ 10 cm-3 at 4 RIo but this estimate is very model-
dependent. Although EMIC waves were also observed, at the S+ gyrofrequencies,
such waves are usually damped by the torus thermal species and more difficult
to observe. Based on Galileo PLS measurements of the plasma density and
temperature along the I32 flyby, Dols2012AsymmetryFlybys propose the presence
of SO2 and SO coronae extending far downstream of Io and that such downstream
coronae could be produced by SO2 resonant charge exchange in Io’s atmosphere.
On the contrary, our proton absorption data indicates an extended atmosphere
both on the inbound (upstream) and outbound (downstream) parts of the
spacecraft trajectories. In summary, there is observational evidence that Io’s
atmosphere is very extended, which might explain some of the discrepancies
between the observations and the simulations discussed above.

Above we argue that the more field aligned particles are more sensitive to an
extended atmospheric component, unless they pass through a denser part of the
lower altitude atmosphere and are already depleted there. However, above a few
1000 km altitude the density of the atmosphere no longer exceeds that of the
plasma torus ($\sim 2000$ cm-3) and charge exchange losses with the torus
become more important. We don’t consider charge exchange with the low energy
torus ions as a likely cause of the depletion features that we have attributed
to a possible extended atmospheric component. The features that we focus on in
this work only occur within 2 RIo and are therefore likely an aspect of the
interaction with Io’s local environment.

###  5.5 Energetic particle data as an unexploited constraint on the
electromagnetic field and atmosphere configuration at Io

Our results show that the apparent proton losses during the flybys of Io are
sensitive to both the electromagnetic field configuration and the atmospheric
properties, because of neutral-ion charge exchange. These data thus provide an
additional unexploited avenue to constrain the electromagnetic field and
atmosphere structure around Io. A comprehensive parameter study to investigate
the effect of the atmospheric and field properties on the proton flux forms
the next logical step. Such studies should eventually take into account
constraints provided by all Galileo datasets, including magnetic field (MAG),
low energy plasma (PLS), plasma waves (PWS) and energetic ions (EPD). A multi-
species atmospheric model or induced dipole, such as in
Dols2012AsymmetryFlybys, should also be considered. However such a
comprehensive endeavour is computationally intensive and we therefore consider
it outside of the scope of this study. Instead this study aims to provide
hypotheses and directions to guide such future modelling efforts.

Thanks to the fact that the TP3 channel of the EPD is sensitive to the field
configuration but not sensitive to depletion through atmospheric charge
exchange, data from this channel may be used as an initial constraint on the
perturbed field model around Io. Once constraints are placed on what type of
electromagnetic fields are present around Io, these may then be used in
combination with atmospheric models to place constraints on the atmospheric
structure of Io by looking at the depletion in the TP1 channel of the EPD.

When comparing atmospheric models, it is of great use to have different flight
geometries. Flybys that have a point of closest approach similar to that of
I24 (611 km) allow us to fit atmospheric models with less influence on the
depletion by the electromagnetic fields. Furthermore, when combining these
observations with lower flybys at the same latitude (such as I27), information
can be gained on the vertical structure of the atmosphere allowing us to fit
surface density and scale height accordingly. Polar flybys, such as I31, could
be used for the testing of different longitudinally dependent models.

The Galileo data is of high value in this context, and will retain this value
in the absence of a dedicated Io mission. The next missions destined for the
Jupiter system, JUICE and Europa Clipper, are not scheduled to encounter Io
from close by. However, the energetic particle data set has been expanded by
two flybys by Juno with their closest approach at approximately 1500 km. Juno
caries the energetic particle detector JEDI [Mauk . (2017)] which would be
able to measure the proton flux.

Interpretation of the ion measurements is hampered by a lack of appropriate
charge exchange cross sections. Here we used the cross section of H+ on O2 as
a proxy for SO2. This assumption leads to an underestimation of the charge
exchange cross section, which makes it more difficult to accurately estimate
the absolute values of atmospheric densities. However, our conclusions on the
atmospheric configuration depend on relative differences between inbound and
outbound segments of the trajectory, as well as relative differences between
viewing directions that already represent the depletion well and those that
don’t, we therefore consider that these conclusions will hold, even for
somewhat different charge exchange cross sections. Further laboratory studies
could confirm our assumptions about the cross sections at higher energies as
well as provide species specific cross sections, in particular cross sections
for S and O ions are lacking.

###  5.6 Io’s role as a proton radiation belt sink in Jupiter’s magnetosphere

Nenon2018AOrbit has modelled Jovian trapped protons with kinetic energies
higher than 1 MeV. In the Nenon2018AOrbit model Io is considered as an inert
absorber of protons. This work shows that the electromagnetic field
configuration is important in determining the exact size of Io as a sink. For
example, we have shown that from approximately equatorial flybys of 200 km
(e.g. I27) protons can be guided to the surface and impact. On the other hand,
the particle tracing simulations presented in this work show that near Io the
energetic protons of energies above $\sim 100$ keV can also be partly
deflected by the perturbed fields (e.g. flyby I31). Thus when treating Io as
an inert body the losses at these energies could also be overestimated.
Furthermore, Nenon2018AOrbit does not take into account charge exchange with
Io’s atmosphere. Indeed, our simulations show that at energies of 1 MeV the
effect of charge exchange will be minor. However, at lower energies where
charge exchange is more efficient (e.g. below 224 keV) charge exchange will
increase the size of Io as a proton sink in Jupiter’s magnetosphere, causing
charge exchange losses up to at least 1 Io radius away.

The extended loss region around Io could be measured along the field lines
connected to the loss region. Indeed losses of energetic protons with energies
in the 10-800 keV range over a region larger than Io have been measured by
Juno along field lines connected with Io [Paranicas . (2019)]. Whereas
Paranicas2019IosData focuses on wave particle interactions as a source of
loss, this work illustrates that charge exchange (at energies below 224 keV)
and the electromagnetic field configuration near Io will also play a role in
the proton depletion. In fact, we suggest that the field configuration is a
more important effect than losses due to wave particle interaction because our
simulations at 540-1250 keV (TP3), have a good qualitative agreement with the
measured loss regions, without the need of invoking wave-particle
interactions.

In conclusion, we propose that the losses due to charge exchange near Io and
apparent losses due to perturbed fields will also help explain losses observed
along field lines connected to Io and its immediate environment.

###  5.7 Io’s atmosphere is a source of 150 $>$ keV ENAs

Previously Futaana2015Low-energyTori have demonstrated that low-energy S and O
energetic neutral atoms (referred to as LENA by the authors), of 460eV and
920eV respectively, resulting from the charge exchange of $<$1 keV plasma from
the plasma torus with Io’s neutral particle environment are detectable by the
Jovian Neutrals Analyzer (JNA) instrument on the JUpiter ICy moon Explorer
(JUICE).

High energy ($>$10 keV) ENA emissions were first reported by Kirsch1981 based
on Voyager 1 LECP measurements. However, the mass or charge state could not be
determined. Later, Krimigis2002 reported ENA emissions, possibly 50-80 keV
hydrogen atoms, from Jupiter, based on Cassini INCA measurements.
Subsequently, Mauk2003 attributed the origin of the ENA emissions to Jupiter’s
atmosphere and a possible neutral cloud slightly outside of the orbit of
Europa. The emissions were not attributed to Io’s torus or Io itself.

This study suggests that energetic protons with energies exceeding 155 keV
will charge exchange with Io’s atmosphere, and produce ENAs of $\sim 150$ keV
energies. When the energetic protons become Energetic Neutral Atoms (ENA) they
are no longer bound by the electromagnetic field and will escape at high
energies that are similar to their energies before neutralisation
[<]e.g.¿[]Rees1989PhysicsAtmosphere. While the proton flux at $\sim$ 100 keV
is about two orders of magnitude less at Io than at Europa, the total mass of
Io’s atmosphere is 100 times that of Europa [Bagenal Dols (2020)]. Therefore,
we recommend that future studies on the interpretation of ENA imaging of
Jupiter’s magnetosphere also consider Io as a possible source of $\sim$100 keV
ENAs.

These $\sim$100 keV ENAs could be detected by the Jovian Energetic Neutral and
Ions (JENI) detector part of the Particle Environment Package (PEP) on the
JUICE mission [Barabash . (2013)]. Variations of keV ENA flux at Io could
provide information about variations in the energetic proton flux and
variations in the neutral environment of Io. While the LENAs will reach JUICE
within a few hours [Futaana . (2015)], the ENAs could reach JUICE in a
Ganymede orbit within just a few minutes, thereby providing a more
instantaneous assessment of the neutral-ion interaction at Io.

###  5.8 Energetic ion detectors on future missions to Io

Proposals are put forward for new dedicated missions to Io
[<]e.g.¿[]McEwen2021FutureIo. This study demonstrates the added value of
including an energetic ion detector to investigate the electromagnetic field
configuration and atmospheric structure around Io. While a magnetometer or
neutral mass spectrometer only measures the field and atmospheric density
along the flyby, the energetic ions are sensitive to the wider environment of
Io. Their flux dropouts will thus provide information about the field
configuration outside of the flyby trajectory. Thus, we recommend to include
an energetic particle detector on future missions to Io.

A combination of lower and higher altitude flybys would be beneficial for
isolating the relative importance of electromagnetic field perturbations and
atmospheric charge exchange on the resulting proton loss. Flybys at different
longitudes, latitudes and local times could help disentangle the atmospheric
asymmetries.

##  6 Conclusion

In this work we used particle back-tracing in order to simulate the energetic
proton losses measured in channels TP1 (155-224 keV) and TP3 (540-1250 keV) of
the EPD during Galileo flybys of Io I24, I27 and I31. The three sources of
depletion taken into account in the simulations are: absorption by the
surface, atmospheric charge exchange, and perturbed fields creating ‘forbidden
regions’. From these simulations we conclude the following:

  * •

Atmospheric charge exchange is a major loss process of energetic protons in
the TP1 channel of the EPD during Galileo flybys I27, and I31 (closest
approach near 200km); and the dominant process during I24 (closest approach at
611 km).

  * •

The electromagnetic fields can also play a role in the proton losses in the
energy range of TP1 and TP3, in particular within $\sim$0.5 RIo during flybys
I27 and I31. This region is more confined than the region over which we expect
charge exchange losses ($\sim$2 RIo).

  * •

A combination of atmospheric charge exchange and an appropriate description of
the electromagnetic field is necessary to fully describe the energetic proton
depletion seen in the TP1 channel of the EPD during all Galileo flybys I24,
I27, and I31.

  * •

Proton losses are not only sensitive to atmospheric densities or field
perturbations along the trajectory, but to the entire region traversed by the
energetic ions and thus offer more global information than other in-situ
measurements.

None of our models are able to fully reproduce all properties of the proton
loss observed in the data. However, from partial agreements and discrepancies
we find that the losses in the TP1 channel (155-224 keV) suggest several
properties of the structure of Io’s atmosphere:

  * •

A longitudinal asymmetry with an extended atmosphere on the day/downstream
side, which is apparent for lower flybys near 200 km, but not at higher
altitudes at 600km on the night/upstream side.

  * •

There is no evidence for full atmospheric collapse on the night/upstream side

  * •

Underpredictions of the proton losses in more field aligned directions hint at
the existence of a global extended atmosphere $>1$ Io radii.

These findings open up a new set of data to be used in order to constrain
atmospheric models of Io and the electromagnetic fields around Io. Future work
should involve fitting a range of self-consistent atmospheric and
electromagnetic field models to the EPD data set using this back-tracing
method to establish confidence in our interpretation and to constrain the
properties of the extended atmospheric component hinted at in our results.
Improved understanding of the charge exchange cross section, including those
for other energetic ions species (S, O), would greatly benefit the
interpretation of the data. Lastly, we emphasize the importance of energetic
ion detectors on future missions to Io. Having energetic particle data sets
for a variety of flyby geometries would further increase the reliability of
the constraints on the fields and atmosphere.

##  Appendix A Charge exchange cross section

The charge exchange cross section of H+ on O2 that is used in the simulations
is shown in Figure 12, together with the energy range of the TP1 and TP3
channels of the EPD instrument.

Figure 12: Charge exchange cross section of H+ on O2 as a function of energy
from Basu1987LinearObservations (red dots) and a fit to the data (blue line).
TP1 (green band) covers an energy range from 115 to 244 keV and TP3 (orange
band) covers a range from 540 to 12500 keV. The mean cross section values of
the two channels are indicated using the solid black line for TP1 and the
dashed black line for TP3.

##  Appendix B Proton gyroradius

The proton gyroradius as a function of pitch angle and energy range of the TP1
and TP3 channels of EPD are shown in Figure 13.

Figure 13: Gyroradius as a function of pitch angle and the energy range of the
TP1 channel (left) and TP3 (right). The magnetic field is the background field
assumed in the simulations for I27 in Blocker2018MHDAtmosphere. Also indicated
are the radius of Io and the altitude of the closest approach.

##  Appendix C Proton bounce period

The proton bounce period as a function of pitch angle and the energy range of
the TP1 and TP3 channels of EPD is shown in Figure 14. Considering a
corotation velocity of 57 km/s, and an Io radius of 1821 km it would take
about 128 seconds for the corotation to cover the entire length of the
simulation box. Particles with a bounce period shorter than this occurring at
the upstream edge of the simulation could in principle re-enter at the
downstream edge. Meaning that any losses occurring at the upstream side could
affect the ion distribution on the downstream edge, which is not accounted for
in the simulation. We consider this not a major concern for the TP1 simulation
since the bounce period of particles generally exceeds this limit. For the TP3
channel the bounce period becomes smaller, however the apparent region of
proton losses associated with Io also becomes smaller than 1 Io radius. A
lower limit of 63 seconds is applicable, which is still exceeded by the bounce
periods. It is thus not likely in TP3 either that the distribution of the
protons is affected by losses occurring along the flyby in such a way that it
would cause the depletion features.

Figure 14: Bounce period as a function of pitch angle and energy range of the
TP1 channel (left) and TP3 (right). The bounce period is calculated using
Equation 2.2 from Baumjohann1997.

##  Appendix D MHD simulation for flyby I31

Figure 15 provides a comparison between the measured (black lines) and
simulated magnetic field (blue lines) for flyby I31. The I31 Galileo flyby was
a close encounter above the north polar region, reaching its nearest point to
Io at a distance of 194 km above its surface. The trajectory intersected the
northern Alfvén wing, evident in the significant magnetic field disturbance,
especially in Bx resulting from the bending of the wing. Given the
spacecraft’s close proximity to Io, variations in the magnetic field
attributable to the ionospheric current system may also be evident in the
magnetic field data. The MHD model reproduces the general structure of the
magnetic field perturbation. However, Bz is overestimated by the MHD model and
the disturbance is displaced further towards the upstream side of the
trajectory. The modeled By component exhibits only weak perturbations inside
the Alfvén wing (beetween 04:54 UT and 05:04 UT). Measured small-scale
perturbations during the wing crossing are obvious in the MAG data, implying
that the atmosphere is probably not as smooth as it is described in our model.
The magnetic field could also be affected by intense wave emissions generating
small-scale fluctuations. Further investigations on the effect of different
local atmospheric asymmetries (e.g., volcanic plumes) in the atmosphere on the
plasma interaction during I31 could provide a better fit to the variations of
the magnetic field during the wing crossing.

Figure 15: Magnetic field components along the I31 flyby trajectory in the
IPHIO coordinate system. Comparison between the Galileo MAG data (black lines)
and the results obtained from the MHD model (blue lines). The dashed vertical
line displays the closest approach at 04:59 UT. The dashed nearly horizontal
line shows the background magnetic field. Simulations were obtained using the
model from Blocker2018MHDAtmosphere. Horizontal axis labels from top to
bottom: time (UT), x (RIo), y (RIo), z (RIo)

.

###### Acknowledgements.

HH is supported by a DIAS Research Fellowship in Astrophysics. CPA van Buchem
was supported by the ESA-Leiden University MSc program. HH was supported by an
ESA research fellowship. HH gratefully acknowledges financial support from
Khalifa University’s Space and Planetary Science Center (Abu Dhabi, UAE) under
Grant no. KU-SPSC-8474000336. We also acknowledge: Andreas Lagg for the EPD
data software, the 2019 and 2020 workshops on ’Outer planet moon-magnetosphere
interactions’ in fostering collaborations that contributed greatly to this
work and the International Space Science Institute (ISSI) visiting scientist
program. This study has been partially performed in the context of the
activities of the ISSI International Team 515. CMJ’s work at DIAS is supported
by Science Foundation Ireland Grant 18/FRL/6199. V. Dols is supported by the
NASA System Workings 2020-0139 Grant 80NSSC22K0109 and also supported at the
University of Colorado as a part of NASA’s Juno mission supported by NASA
through contract 699050X with the Southwest Research Institute

## Open Research

EPD data are available through NASA’s Planetary Data System (PDS) [PDS
(2022)]. Simulation results are archived in Huybrighs2024_data.

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