Variability of Io's poynting flux: A parameter study using MHD simulations

Variability of Io ’s poynting flux: A parameter study using MHD simulations

A. Bl €ocker ^{a , *} , L. Roth ^a , N. Ivchenko ^a , V. Hue ^b

a

KTH Royal Institute of Technology, Space and Plasma Physics, School of Electrical Engineering, Stockholm, Sweden

b

Southwest Research Institute, San Antonio, TX, United States

A R T I C L E I N F O

Keywords:

Io

Sub-alfvenic plasma interaction Io footprint

MHD simulations Poynting flux

A B S T R A C T

Io ’s plasma interaction creates an electromagnetic coupling between Io and Jupiter through Alfven waves trig- gering the generation of auroral footprints in Jupiter ’s southern and northern hemispheres. The brightness of Io’s footprints undergoes periodic variations that are primarily modulated by Io’s local plasma interaction through the Poynting flux radiated away from the moon. The periodic pattern with two maxima near 110 ^∘ and 290 ^∘ Jovian longitude where Io crosses the dense plasma sheet is generally understood. However, some characteristics, like the 2–4 times stronger brightening of the southern footprint near Jovian longitude 110 ^∘ or the lack of response to Io ’s eclipse passage, are not fully understood. We systematically study variations in Io’s plasma interaction and the Poynting flux using a 3D magnetohydrodynamic model, performing a series of simulations with different upstream plasma conditions and models of Io’s atmosphere. Our results indicate that the strong Jovian magnetic field near 110 ^∘ plays a more important role than previously estimated for the strong brightening there. We find that the Poynting flux is not fully saturated for a wide range of possible atmospheric densities (6
10 ¹⁸ –6
10 ²¹ m ^2 ) and that density changes in the atmosphere by a factor of > 3, as possibly happening during Io’s eclipse passage, lead to a change of the Poynting flux by > 20%. Assuming that these expected changes in Poynting flux also apply to the footprints, the non-detection of a dimming in the footprint during the eclipse by Juno-UVS suggests that Io’s global atmospheric density decreases by a factor of < 2.5. We show that for smaller atmo- spheric scale heights (i.e. a more con fined atmosphere), changes in the atmospheric density have less effect on the Poynting flux. The missing response of the footprint to the eclipse hence might also be consistent with a density decrease by a factor of > 3, if the effective atmospheric scale height is small (< 120 km). Finally, we provide new analytical approximations that can be used for analyzing the effect of the local interaction responsible for the footprint variability in future studies.

1. Introduction

Jupiter ’s moon Io is embedded in a sub-Alfvenic flow of Jupiter’s corotating magnetospheric plasma, which constantly overtakes the moon and interacts with Io’s atmosphere. From this interaction, different wave modes are excited with the Alfven mode being an especially important mode as it can transport momentum and energy along the background magnetic field over large distances. The Alfven waves travel along the magnetic field lines north and south from Io. During their propagation, they experience filamentation and partial reflection at the density gra- dients between different plasma regions in the torus (e.g., Wright and Schwartz, 1989; Chust et al., 2005; Jacobsen et al., 2007; Hess et al., 2010). In the reference frame fixed with Io, the Alfven waves form the so-called Alfven wings which are tilted towards the downstream direc- tion of the plasma (e.g., Drell et al., 1965; Neubauer, 1980). Ionization

and collisions within Io ’s atmosphere modify the plasma environment and drive large currents through the moon’s ionosphere which are coupled to Jupiter ’s upper atmosphere by Alfven wing currents. In the far field, Alfven wing currents cause acceleration and precipitation of elec- trons in Jupiter’s ionosphere, leaving imprints in Jupiter’s southern and northern hemisphere in the form of auroral footprints (see reviews by Kivelson et al., 2004; Saur et al., 2004; Clarke et al., 2004).

The Io footprint was the first detected satellite footprint identified by its H ^þ ₃ emissions in the infrared (IR) by Connerney et al. (1993) and then confirmed in the Far ultraviolet (FUV) with HST observations (Prange et al., 1996; Clarke et al., 1996). Jupiter ’s UV aurora is the result of in- elastic collisions of magnetospheric energetic electrons with atmospheric molecular hydrogen (H 2 , H, and Lyman- α ) whereas the IR aurora is mostly due to thermal emissions from the H ^þ ₃ molecular ion that originate from higher altitudes (1000 km) compared to the UV (250 km) (Radioti

* Corresponding author.

E-mail address: aljonab@kth.se (A. Bl€ocker).

Contents lists available at ScienceDirect

Planetary and Space Science

journal homepage: www.elsevier.com/locate/pss

https://doi.org/10.1016/j.pss.2020.105058

Received 11 March 2020; Received in revised form 26 June 2020; Accepted 20 July 2020 Available online 8 August 2020

0032-0633/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/).

et al., 2013). Radioti et al. (2013) present a comparative study of the UV and IR images of Jupiter ’s auroral emissions obtained from HST and high performance ground-based telescope on one rare occurrence. They showed that the Io footprint and tail are co-located in UV and IR, but the variation of the footprint brightness compared to the main emission is significantly larger in the UV than in IR. Both UV and IR images show that the footprint consists of several individual spots and a fainter tail which are associated with the direct Io-Jupiter Alfven wing coupling, as well as reflection of traveling Alfven waves between Io and the Jovian atmo- sphere (e.g, Connerney et al., 1993; Connerney and Satoh, 2000; Clarke et al., 2002; Gerard et al., 2006; Mura et al., 2018). Investigations of the structure of the Io footprint suggest three Io footprint spots with an extended downstream tail (Clarke et al., 2002; Gerard et al., 2006;

Bonfond et al., 2008). Substructures in the Io footprint similar in appearance to a von Karman vortex street are seen in high-resolution IR images obtained with the Juno spacecraft (Mura et al., 2018). The brightest spot is called the Main-Alfven-Wing (MAW) spot and is gener- ated directly by the main Alfven wing. It coincides with the location where the moon ’s Alfven wing intersects Jupiter’s upper atmosphere.

Some of the Alfven waves are reflected at the torus boundary where a latitudinal density gradient exists. The reflected waves which escape the torus create the re flected Alfven wing spots (RAW). The reflection ge- ometry strongly depends on the upstream plasma density at Io and thus on Io’s location in the torus (Bonfond et al., 2008, e.g.). The trans- hemispheric electron beam spots (TEB) are generated by electrons accelerated away from Jupiter in one hemisphere and precipitating in the opposite hemisphere (e.g., Bonfond, 2012). The electron beams propa- gate from one hemisphere to the opposite without being affected by the density gradient at the torus boundary (Bonfond et al., 2008). The rela- tive distance between the three spots systematically changes with respect to the λ III longitude of Io. The brightness ratios between the spots signi ficantly vary and therefore relate the generation of the spots to different processes (Bonfond et al., 2013). The fainter tail extends as far as 100 ^∘ of longitude in the direction of the corotation (Clarke et al., 2002). Theoretical models of the Io footprint tail emission (e.g., Hill and Vasyliunas, 2002; Delamere and Bagenal, 2003; Su et al., 2003; Ergun et al., 2009; Matsuda et al., 2012) assume that the Io footprint tail is sustained by a quasi-steady current system which is created due to angular momentum transfer from Jupiter to the subcorotating plasma in Io’s wake. However, the study of Juno measurements through the Io tail by Szalay et al. (2018) suggests that a more broadband acceleration mechanism, such as Alfvenic acceleration (e.g., Jacobsen et al., 2007;

Bonfond et al., 2009, 2017; Crary and Bagenal, 1997) likely play a sig- nificant role in the generation of the tail rather than the large-scale parallel potential structures accelerating electrons near the tail as sug- gested by the theoretical models. Mura et al. (2018) showed that the extended tail occasionally produces two parallel arcs probably triggered by the northern anomaly in the Jovian magnetic field. Numerous Hubble Space Telescope (HST) observations of the Io footprint revealed that the brightness and emitted power of the footprints vary over a planetary rotation (Gerard et al., 2006; Wannawichian et al., 2010; Bonfond et al., 2013). Furthermore, the data suggest that the footprint emitted power peaks when Io crosses the plasma sheet. Several processes were suggested to control the morphology and brightness of the footprint spots and tail:

Io ’s local plasma interaction as it controls the magnetic energy fluxes which are fed into the Alfven wings (Hess et al., 2010, 2013; Saur et al., 2013), reflection of Alfven waves at density gradients at the torus boundary (Gurnett and Goertz, 1981; Crary and Bagenal, 1997; Jacobsen et al., 2007; Payan et al., 2014), electron acceleration at high latitudes (Hess et al., 2010), and magnetic mirroring of the accelerated electrons between the acceleration region and Jupiter ’s atmosphere ( Hess et al., 2013). The processes are acting at the same time and in different parts of the coupling between Io and Jupiter’s atmosphere (Hess et al., 2013).

Some studies focused on the brightness variations of the Io footprint:

Bonfond et al. (2013) present measurements of the brightness and precipitated power for each individual spot, using Far UV observations

from 1997 to 2009 with the HST. The brightness of the spots follows a quasi-sinusoidal modulation with an amplitude of about 30% of the average and strongly varies over short timescales (2–4 min). For the derived maximum vertical brightness, they calculate precipitating elec- tron energy fluxes between 250 and 2000 mW/m ² for the MAW spot. The ratio between the precipitated and the emitted power lies around 20%.

Moreover, Bonfond et al. (2013) found an asymmetry between the northern and the southern spots ’ brightness. Emissions of the spots in the southern hemisphere are on average twice as bright as in the northern hemisphere. This asymmetry is still under investigation. The footprint emitted power and brightness peak near the plasma sheet crossing, i.e.

System-3 longitude ( λ III ) 110 ^∘ and 290 ^∘ , where Io ’s orbit intersects the plasma torus plane. While Io is at the same centrifugal latitude, i.e.

similarly in the center of the plasma torus, the brightness of the southern spot at λ III 110 ^ is much larger than at 290 ^∘ . Bonfond et al. (2013) conclude that the centrifugal latitude of Io is not the only parameter controlling the spots ’ brightness, but that other processes such as the modulations of the power transmission along the Alfven wing, of the power transfer to the precipitating electron, or the size of the loss cone also play a major role. Hess et al. (2013) developed a model for the power transfer between the local plasma interaction at Io and the UV emissions taking into account the acceleration mechanism and the Alfven wave propagation effects. With their model, they can explain the average brightness of the spots. But the model does not reproduce the peak of brightness for Io ’s λ III longitudes close to 110 ^∘ . They conclude that Alfven wave reflections, magnetic mirroring of the electrons, local plasma interaction at Io, and kinetic effects close to Jupiter act together and determine the brightness of the spots but they are not able to explain all the details of the variations of the footprint brightness with λ III longitude.

Io’s plasma interaction is strongly controlled by Io’s atmosphere. The global atmosphere is persistently maintained by strong volcanic outgas- sing and sublimation of SO 2 frost and is known to undergo seasonal changes (Tsang et al., 2012). The atmospheric column density changes with latitude, longitude, and also with time. Depending on the helio- centric distance of Io and the longitude at the time of observation, ob- servations of Io’s atmosphere suggest that Io’s equatorial dayside SO 2

column density ranges from 1
10 ²⁰ to 22
10 ²⁰ m ^2 (e.g., Jessup and Spencer, 2015; Lellouch et al., 2007; Tsang et al., 2012). The observa- tions also showed that the atmosphere collapses by a factor of 5  2 shortly after eclipse ingress (Tsang et al., 2016). Volcanic plumes locally enhance the atmospheric density. Several studies moreover suggest that Io’s atmospheric density is occasionally increased due to enhanced vol- canic activity. Such quite drastic increases were derived from changes in the neutral and plasma environment (Yoneda et al., 2015; Yoshioka et al., 2017; Tao et al., 2018).

Hue et al. (2019) investigated observations of Io’s footprint from the Ultraviolet Spectrograph (UVS) on Juno recorded over Io ’s complete orbit and as Io went into eclipse. In their study, they focused on two aspects: the variability of the emitted power of the footprint with λ III

longitude and a possible change in the emitted power with atmosphere collapse during the eclipse. The observed emitted power variation of the southern footprint with Jupiter’s rotation is consistent with the trends of previous HST observations. Although the observations could not spatially separate the different spots due to Juno ’s geometrical constraints, no significant change in the Poynting flux integrated over a region encom- passing the MAW, TEB, and RAW was observed as Io left and moved in eclipse. They suggest that the absence of a signi ficant effect on the emitted power of the southern footprint when Io is in eclipse could be due to a saturated state of Io’s plasma interaction which would reduce the effects of an atmosphere collapse on the total Alfvenic energy flux.

Alternatively, the collapse of Io ’s atmosphere in eclipse during UVS ob- servations was less pronounced than previously observed.

The phenomena contributing the most to the variability of the foot-

print brightness is Io ’s local plasma interaction which will be addressed

in this paper. Here, we study two aspects: the variability of the Poynting

flux due to the variability of 1) plasma conditions and 2) atmospheric

changes. So far, the variability of the local interaction and the resulting energy flux toward the footprint has only been considered in simplified analytical approximations. In order to thoroughly assess the changes in the local interaction as the likely dominant effect controlling the foot- print variations, we apply two different approaches, namely numerical model and analytic approximation, to calculate the relative changes in the Poynting flux. We use a numerical model which was successfully applied to study the effect of atmospheric asymmetries on Io ’s plasma interaction (Bl€ocker et al., 2018). The numerical model is a 3D magne- tohydrodynamical (MHD) model which self-consistently calculates the interaction with Io ’s atmosphere, and which was already applied to Europa (Bl€ocker et al., 2016). It provides information on e.g., how a spatially inhomogeneous atmosphere affects the plasma flow and mag- netic field in Io’s vicinity and therefore the Poynting flux. Moreover, we apply the analytic model of Saur et al. (2013) which provides a simpli fied expression for the total Poynting flux and can be regarded as upper limits for the Poynting fluxes deposited into Jupiter’s ionosphere. By per- forming a series of MHD simulations of Io ’s local plasma interaction with different upstream plasma conditions and models of Io’s atmosphere, we systematically analyze the variability of the Poynting flux from the moon.

The study is used to reliably quantify the effects of Io ’s variable atmo- sphere and the variations of the upstream plasma conditions over a planetary rotation on the brightness and total emitted power of the footprints, based on the latest models and measurements of the plasma and atmosphere. In particular, we address the following two questions in this paper: (1) How much of the variability in the footprint brightness is caused by the variability in local interaction and power generated at Io?

(2) What effect does the variability of Io ’s atmosphere have on the Poynting flux radiated away from the moon? We compare our simula- tions only with observations of the southern footprint. Our goal is to quantify the typical amplitudes of the variations of the Poynting flux due to the changes in Io’s plasma environment and its atmosphere, and to derive a better picture on how the variability of Io’s local plasma inter- action can affect the variability of the emitted power of Io ’s footprint. In our study, we do not investigate the total emitted power of the footprint.

2. Poynting flux: Analytical and numerical calculations

The moon and its atmosphere can be considered as an obstacle to Jupiter’s magnetospheric plasma flow. Io’s plasma interaction modifies the electric and magnetic field in Io’s vicinity and generates waves. The magnitude and the direction of the energy flux in electromagnetic waves is described by the Poynting vector. The Poynting vector is calculated by

S ¼ E
B μ 0

(1)

where μ 0 is the magnetic permeability of free space. The calculation of S requires information about the magnetic field B and the electric field E in Io’s Alfven wings. In the ideal MHD framework, the electric field can be expressed as E ¼ v
B with the relative plasma velocity v. Since B and v in the Alfven wings are altered by the plasma conditions in Io’s vicinity and the atmospheric properties of the moon, their correct determination is challenging. In order to calculate B and v, we apply two different ap- proaches: a numerical model and an analytic approximation derived by Saur et al. (2013). The numerical model self-consistently calculates the plasma interaction with Io’s atmosphere which allows the adjustment of Io’s atmospheric properties in order to study the effect of the atmosphere on the Poynting flux. The analytic approximation is based on an idealized model of the sub-Alfvenic interaction and uses parametrizations of the interaction strength and of the extension of Io’s interaction region to take into account the in fluence of Io’s atmosphere.

2.1. Numerical model for Io’s plasma interaction

The model for the simulations of Io ’s plasma interaction is described

in detail in Bl€ocker et al. (2018). This numerical 3D model solves a set of MHD equations that account for collisions between ions and neutrals, plasma production and loss due to electron impact ionization and dissociative recombination, and the ionospheric Hall effect. In particular, we use the magnetic field and the velocity field at the end of each simulation, when approximately steady state solution in Io’s vicinity is reached, in order to calculate the Poynting flux. Basic plasma parameters of the numerical model which were used in the simulations presented in this paper are summarized in Table 1. We apply both the Cartesian and the spherical coordinate system centered at Io for the description of Io’s atmospheric properties and plasma conditions. The Cartesian system is the IPHIO system with the z axis being parallel to Jupiter ’s spin axis, the positive y axis facing Jupiter, and the x axis being along the flow direc- tion of the corotational plasma. The spherical system is described by the radius r, the colatitude θ measured from the positive z axis, and the longitude φ measured from the positive y axis in the direction of the negative x axis.

In our model, we assume that the atmosphere solely consists of SO 2

and adopt the same analytic expression for the number density of Io’s atmosphere as in Bl€ocker et al. (2018). The numerical model has the advantage over the analytic model that we are able to describe the at- mospheric distribution in three dimensions. In the simulations, we apply a latitudinaly asymmetric atmosphere given by

n A ðr; θ; φÞ ¼
n pol þ n s 

exp





 h H 0



(2)

with the low surface number density at the poles n pol ¼ 0:02 n 0 , the scale height H 0 , and altitude h ¼ r  R Io (with Io ’s radius R Io ¼ 1821 km) above the surface. The surface number density is described as

n s ðθÞ ¼
n 0  n pol

 exp





 0:5 π  θ 0:625rad

 2 

(3)

where n 0 is the surface number density at the equatorial latitude. We refer to this latitudinaly asymmetric atmosphere as “equatorial atmo- sphere ” in this paper. The latitudinal variations of the SO 2 surface number density were derived by Strobel and Wolven (2001) from Lyman- α observations (their equation (9)) and applied by Bl€ocker et al.

(2018).

We perform simulations with different setups which are summarized in Table 2. In the first model scenario S1 (see Table 2), we investigate the in fluence of variations of Io’s upstream plasma conditions on the Poynting flux over a planetary rotation. Therefore, we consider the new model of the magnetic field for Jupiter’s internal field “JRM09” derived from Juno’s first orbits (Connerney et al., 2018) and the “CAN” current sheet model (Connerney et al., 1981). The variations of the magnitude of the background magnetic field with λ III longitude are shown in Fig. 1a.

For the variations of the upstream plasma density, we implement the model from Bagenal and Delamere (2011) shown in Fig. 1b. We perform simulations for λ III from 0 ^∘ to 350 ^∘ with a 50 ^∘ interval. Each simulation provides the magnetic field and velocity field for a particular λ III longi- tude which we use to calculate the Poynting flux. In the model scenarios S2, we focus on Io’s atmosphere. We vary the surface number density by a factor of about 3 and keep the scale height constant so that the equatorial

Table 1

Parameters used in the numerical model.

Parameter Value

Plasma velocity (IPhiO) v (57, 0, 0) km/s

Ion temperature k

T

75 eV

Electron temperature k

T

5 eV

Mass of magnetospheric plasma ions m

19 amu

Singly charged ions produced in the ionosphere m

64 amu

Effective ion charge of z

1.3

Parameters are taken from Kivelson et al. (2004).

column density varies also by a factor of about 3. The minimum column density value is 6 :3
10 ¹⁸ m ^2 and the maximum column density value is 6:3
10 ²¹ m ^2 (see model scenario S2a in Table 2). We also test how longitudinal asymmetries in Io’s atmosphere influence the Poynting flux (model scenario S2b). Therefore, we include a dayside/nightside asym- metry in Io’s atmosphere with a decrease in the atmospheric surface number density from the day to the night side hemisphere by a factor of five based on the results of Tsang et al. (2016). Therefore, we multiply the surface number density (equation (3)) by the factor β given by βðθ; φÞ ¼

 1 þ 2

3 cosð ψ ðθ; φÞÞ



(4)

where ψ is the solar zenith angle. Io ’s atmosphere consists predominately of SO 2 and might be in vapor pressure equilibrium. If Io’s surface SO 2

frost is no longer heated by the sun (in eclipse), the surface temperature decreases and the atmosphere collapses onto the surface (Saur and Strobel, 2004; Tsang et al., 2016). In case of a volcanically dominated atmosphere, the atmosphere does not collapse. Tsang et al. (2016) showed that the atmosphere at ingress longitudes is mostly sublimation-driven and mostly volcanically-driven at egress longitudes because of the distribution of volcanic hotspots on Io. However, it is still uncertain how Io ’s atmosphere looks like in eclipse. The distinction be- tween the sublimation-dominated (hydrostatic) and volcanic (plume-- like) atmospheres is crucial as the associated vertical structures are very different, with dynamical, thermal, and compositional implications (Lellouch et al., 2007). In model scenario S2c, we vary the atmospheric scale height of an equatorial atmosphere between 60, 120 and 240 km in order to study the in fluence of the variation of the scale height on the Poynting flux. The minimum scale height of 60 km has been chosen to resolve the density structure in the numerical grid. There are different studies suggesting the scale height of Io’s atmosphere. The hydrostatic scale height near the surface of Io ’s SO 2 atmosphere is about 10 km and increases with altitude due to plasma heating (Walker et al., 2012). Roth et al. (2014) fitted their phenomenological model to UV observations of Io ’s aurora and found that most of the radiation is emitted within 100 km above the surface and the best-fit suggests an emission scale height of only about 10 km. Saur et al. (2002) argued that the atmosphere is compressed and the atmospheric scale height is decreased on the up- stream side due to the drag force on the neutral atmosphere produced by the plasma flow past Io’s atmosphere. They proposed a scale height which varies between 50 and 110 km with longitude. Walker et al.

(2012) performed global atmospheric simulations of Io ’s sublimation-driven atmosphere out of eclipse and in eclipse taking flow

dynamics into account. They showed that although the atmosphere is collapsed in eclipse, the exobase height (between 160 km and 180 km) in the region between λ III ¼ 270 ^∘ and 360 ^∘ remains relatively unchanged mostly due to large thermal inertia. An overview of different atmosphere models including studies of the extended corona used in modeling of Io ’s plasma interaction is given in Dols et al. (2012). In the model scenarios S3, we investigate the mutual effects of an equatorial atmosphere and plasma conditions on the Poynting flux with the numerical model. For the simulations of model scenarios S1, S2a, S2c, and S3 we apply the equa- torial atmosphere and for the simulations of model scenario S2b we apply the equatorial atmosphere with a longitudinal asymmetry given by equation (4).

We use a spherical grid and the model domain extends to 25 R Io from the moon’s center in the radial direction. The spherical grid consists of 240
120
120 cells. The angular resolution of the grid in θ and φ is equidistant with △θ ¼ 1:5 ^∘ and △φ ¼ 3 ^∘ . The radial resolution in- creases by a factor of 1.016 from cell to cell from the inner boundary (surface of Io) to the outer boundary. The resolution at Io’s surface is 16 km. The simulation is performed until the Alfven wings reach the outer boundary. The unperturbed plasma flow at 57 km/s requires a typical time of 64 s to cross Io’s diameter. The Alfven velocity varies in the simulations with the initial conditions for the background magnetic field and the plasma density (see Table 2). With Alven velocities between 120 km/s and 490 km/s the Alfven wave needs between 93 s and 380 s to reach the outer boundary. We apply the same boundary conditions as used in Bl€ocker et al. (2018) where the moon ’s spherically-symmetric surface is plasma-absorbing and possesses a negligible electrical con- ductivity. Boundary conditions for the magnetic field have been derived by Duling et al. (2014) ensuring that there is no radial electric current penetrating the isolating surface. The inner and outer boundary values for the simulations performed in this study are presented in Tables 1 and 2. We use the magnetic field and the velocity field from the simulations to calculate the total Poynting flux S k anti-parallel to the background magnetic field B 0 over the plane perpendicular to B ₀ in a cross section through the Alfven wing. The considered plane is chosen to be suffi- ciently far away from the moon (3 Io radii) in order to exclude the effect of other wave modes, i.e., the fast and slow mode. We calculate the Poynting vector in a reference frame moving with the ambient magnetic field, i.e. the relative velocity is v ¼ v’  v 0 where v 0 is the unperturbed plasma velocity and v ’ is the velocity in the rest frame of the moon.

2.2. Analytic model of the poynting flux

Saur et al. (2013) derived an analytic expression for the Poynting flux Table 2

Initial and boundary condition values in the IPhiO system and atmospheric density and scale height for Io ’s simulations.

Model Scenarios B

n

N

H

(nT) (10

cm

) (10

m

) (km)

S1: Variation with λ

long. see Fig. 1a) see Fig. 1b) 2.0 120

S2a: Var. atm. density 1900 1.9 0.063; 0.2; 0.63; 120

2.0; 6.3; 20; 63

S2b: Var. day/night asym. 1900 1.9 3.35

120

S2c: Var. atm. scale height 1900 1.9 0.2; 2.0; 20; 60; 120; 240

S3a: Var. Plasma cond. 1600;  1750; 0.5; 1.5; 0.2 120

1900;  2050; 2.5; 3.5;

 2200 4.5

S3b: Var. Plasma cond. 1600;  1750;- 0.5; 1.5; 2.0 120

1900;  2050; 2.5; 3.5;

 2200 4.5

S3c: Var. Plasma cond. 1600;  1750; 0.5; 1.5; 20.0 120

1900;  2050; 2.5; 3.5;

 2200 4.5

a B _0;x and B _0;y are zero for scenarios S2 and S3. B ₀ for S1 was calculated with JRM09 þ current sheet model.

b Upstream plasma density.

c Maximum column density at the equator.

d Simulations were performed with 4 different dayside/nightside asymmetries.

in sub-Alfvenic plasma interaction within the framework of MHD. The model is based on approximations for Io ’s plasma interaction and the conclusions derived from the model are based on parametrization of the plasma conditions. Saur et al. (2013) find that the Poynting flux radiated away from Io can be written as (their equation (54))

S ¼ 2 π R ² _eff ð α M A B 0 cosθÞ ² μ 0

v A (5)

where R eff is the radius of the interaction region, B 0 is the strength of the background magnetic field, v A is the Alfven velocity, α is the interaction strength, M A is the Mach number, and θ 2 ½0; π  is the angular deviation of the plasma flow from the perpendicular to B 0 . θ is zero when the incident plasma flow is perpendicular to B 0 . The interaction strength is a measure of the relative strength of the sub-Alfvenic interaction and de- pends on the atmospheric density and the plasma conditions. When the plasma interaction is saturated, meaning that the plasma flow past Io’s atmosphere is completely deflected around Io, the maximum value of α ¼ 1 is reached. When there is no plasma interaction, then α ¼ 0. The interaction strength α can be approximated by (Neubauer, 1998; Saur et al., 1999)

α ¼ Σ P

Σ P þ 2Σ A (6)

where Σ A is the Alfven conductance. Σ P is the integrated local Pedersen conductivity along the magnetic field lines through Io’s ionosphere and depends on the neutral density and the plasma properties. The conduc- tance can not be directly measured and has to be modeled (e.g., Saur et al., 1999, 2002; Kivelson et al., 2004). A denser neutral atmosphere leads to an increase in the ionospheric conductivity and therefore an increase in α . A dependence between the interaction strength and the column density is displayed in Fig. 4 of Saur et al. (2003) calculated with their 3D plasma model. Hue et al. (2019) approximated α ^{from Fig. 4 of} Saur et al. (2003) by

α ¼ 1  α ref

 N col

N ref

 γ

(7)

for an atmospheric column density N col > N ref ¼ 1:8
10 ¹⁸ m ^2 with

γ ¼ 0:57 and α ref ¼ 0:75. In this paper, the interaction with a global

atmosphere with a constant scale height of 100 km and an average torus

electron density of 3600 cm ^3 was assumed. For the analytic model, we

assume an average mass for the magnetospheric plasma of m i ¼ 19 amu

Fig. 1. Variations of plasma conditions and the total

Poynting flux S k with Io’s λ III W-longitude. a) Back-

ground magnetic field at Io calculated with JRM09

model and the current sheet model (Connerney et al.,

1981, 2018). b) Plasma number density at Io from the

torus model of Bagenal and Delamere (2011). c)

Poynting flux calculated with the numerical model for

an equatorial atmosphere with a column density of

N col ;eq ¼ 2
10 ²⁰ m ^2 (model scenario S1, see

Table 2) are shown by blue squares. Analytic model

results calculated with equations (5) and (7) are

shown by the black line for N col ¼ 2
10 ²⁰ m ^2 . The

cyan dashed and solid lines show the Poynting flux

calculated with equation (5) and different constant α ^.

(For interpretation of the references to colour in this

figure legend, the reader is referred to the Web version

of this article.)

(Kivelson et al., 2004) and an effective radius for the interaction region of R eff ¼ 1:3 R Io (Saur et al., 2013).

The Hall current does not directly affect the Poynting flux but the Hall conductance influences the electromagnetic fields in the Alfven wings.

Saur et al. (1999) showed that the Hall conductance in the vicinity of Io is comparable to the Pedersen conductance, and that the ionospheric Hall effect strongly twists the direction of the electron flow in Io’s ionosphere and rotates the electromagnetic field in Io’s Alfven wings. The Hall conductance ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Σ H increases the interaction strength through α ¼

Σ

þðΣ

þ2Σ

Þ

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Σ

Σ

þðΣ

þ2Σ

Þ

p (calculated with equation (A10) from Saur et al.

(1999)). Assuming Σ A ¼ 4:4 S, Σ H ¼ 100 S, and Σ P ¼ 200 S (Kivelson et al., 2004) the ionospheric Hall effect has a negligible in fluence (1%) on the Poynting flux.

3. Results and discussion

In this section we present the calculations of the Poynting flux from the results of the numerical model. We begin with the investigations of the Poynting flux variations over a planetary rotation and compare them to the analytic model calculations and Io footprint emitted power EP derived from Juno-UVS observations (Hue et al., 2019). Note that the derived EP of the footprint by Hue et al. (2019) includes the MAW, TEB and RAW spots. Particularly, we aim to understand how the relative changes of the Poynting flux are connected to the emitted power varia- tions of the Io footprint. Due to the sparse coverage of the Juno-UVS data in terms of λ III for the northern footprint we do not investigate the modulation of the northern footprint and compare our model results only to the modulation of the EP of the southern footprint. Then, we investi- gate what effect the variability of Io ’s atmospheric density and the magnetospheric plasma properties have on the Poynting flux.

3.1. Modulation by the plasma environment

3.1.1. Periodic modulation with λ III longitude

The upstream plasma density and magnetic field environment change with Io ’s location inside the torus (see Fig. 1a and b). Systematically varying the upstream plasma conditions with Io’s location inside the torus, we calculate the changes in the Poynting flux. The blue squares in Fig. 1c display the calculated Poynting flux from the interaction with an equatorial atmosphere which has a column density of 2
10 ²⁰ m ^2 . The variations in the Poynting flux are structured similarly to the variations in the plasma density with the λ III longitude. A global and a local maxima are recognizable close to the plasma sheet crossings at around λ III ¼ 100 ^∘ and λ III ¼ 300 ^∘ , respectively. The variations in the magnetic field magnitude (Fig. 1a) introduce the asymmetry of the double-peak feature in the evolution of the Poynting flux with changing λ III . The Poynting flux at the local minimum at 200 ^∘ is about 3% larger than at the global minimum at 0 ^∘ . The evolution of the Poynting flux with λ III longitude shows a maximal increase by 59% at the global maximum ( λ III ¼ 100 ^∘ ) with respect to the global minimum (λ III ¼ 0 ^∘ ).

3.1.2. Comparison of analytic and numerical models

In Fig. 1c), we show the Poynting flux calculated with the analytic approximation given by equations (5) and (7) for N col ¼ 2
10 ²⁰ m ^2 (black line). The parametrized equation (7) is based on modeled plasma interaction with a radially symmetric atmosphere. We refer to the radi- ally symmetric atmosphere as “global atmosphere” in this paper. The analytic calculation of the Poynting flux is underestimated by the nu- merical results mostly due to applied different atmospheric distributions in the models. The plasma interaction in the analytic description is close to saturation for the case where α ¼ 0:95 (see equation (7)). We fitted the interaction strength α shown by the cyan lines in Fig. 1c to the numerical model results for the Poynting flux (blue squares). In the area around the minimum jB 0 j between λ III ¼ 250 ^∘ and 340 ^∘ , the interaction strength α is smaller, so that a larger fraction of plasma can enter Io ’s atmosphere

shown by the solid cyan line. The Poynting flux is larger by about 54% at λ III ¼ 100 ^∘ and by about 39% at λ III ¼ 300 ^∘ with respect to the Poynting flux at λ III ¼ 0 ^∘ in the analytic approximation. The numerical model re- sults show an increase in the Poynting flux by about 59% at λ III ¼ 100 ^∘ and by about 28% at λ III ¼ 300 ^∘ with respect to the Poynting flux at λ III ¼ 0 ^∘ . This implies that, the magnetic field strength modulation has a stronger effect on the Poynting flux modulation than approximated by the analytic model. Furthermore, Saur et al. (2013) showed that the Poynting flux also depends on the angle θ between the upstreaming plasma flow and the background magnetic field due to the cross-product of E and B in equation (1). For Io ’s vicinity, the plasma flow is almost perpendicular to the background magnetic field. The maximal deviation of the incident plasma flow from being perpendicular to B 0 occurs at about λ III ¼ 110 ^∘ with θ ¼ 12 ^∘ which reduces the Poynting flux in this region by about 4% according to equation (5).

For an equatorial atmosphere, most of the plasma interaction appears in the equatorial latitudes which leads to a strong deceleration of the upstreaming plasma in this region. At the poles, the atmosphere is very thin so the deceleration of the plasma flow is diminished. The atmo- spheric gas content in an equatorial atmosphere is smaller ( 50%) than in a global atmosphere with the same equatorial column density. Because the factor α is a measure of sub-Alfvenic interaction strength, it can be calculated with the normalized difference in velocity in the orbital di- rection inside the Alfven wing. The equatorial atmosphere distribution produces an inhomogeneous plasma flow velocity inside the Alfven wings (see Fig. 3c of Bl€ocker et al., 2018). Therefore, the interaction strength varies inside the Alfven wing while the interaction region re- mains of the same radius as in the case of a global atmosphere. The interaction strength α in the cross-section of the northern Alfven wing (with radius 1 R Io ) for the equatorial atmosphere with N col;eq ¼ 2
10 ²⁰ m ^2 varies between 0.94 and 0.67 with an average value of 0.89.

Therefore, significant differences in the Poynting fluxes are visible in Fig. 1c between the equatorial atmosphere from the numerical model and the global atmosphere from the analytic model (black line).

3.1.3. Comparison of numerical results and Juno-UVS observations The emitted power (green triangles) derived from UVS observations and the Poynting flux (blue squares) calculated with the numerical model shown in Fig. 2 are normalized for a better comparison of the relative changes. The increase of the emitted power by about 154% from λ III ¼ 0 ^∘ to λ III ¼ 100 ^∘ is considerably stronger than the increase of the modeled Poynting flux by about 59%. Therefore, a much stronger local increase in the plasma density, magnetic field and/or torus plasma flow velocity at λ III ¼ 100 ^∘ would be needed to explain the factor of about 2.5 amplitude variation seen in the Juno-UVS data with the modeled Poynting flux, if we assume that the observed variation is solely caused by the local plasma interaction with Io ’s atmosphere.

From HST observations of the southern footprint, it was shown that the footprint is about 40% brighter at the crossing at 110 ^∘ than at 290 ^∘ (Bonfond et al., 2013; Wannawichian et al., 2010). The Poynting flux calculated from numerical model results at λ III ¼ 100 ^∘ is about 24%

larger than at λ III ¼ 300 ^∘ . Io is moving from the southern to the northern

edge of the torus and crosses the plasma sheet at λ III ¼ 110 ^∘ . Then, Io

moves from the northern to the southern edge and crosses the plasma

sheet at 290 ^∘ . The difference between the two maxima at the plasma

sheet crossing is large. The only well-known asymmetry in the magnetic

field causes only a weaker asymmetry in the simulation results than

observed. The stronger observed brightening of the footprint at λ III ¼

110 ^∘ compared to the one at λ III ¼ 290 ^∘ can have three reasons: (1) the

asymmetry in the magnetic field has even more influence on the local

plasma interaction than derived from our numerical model results; (2) an

asymmetry in the plasma density between λ III ¼ 110 ^∘ and λ III ¼ 290 ^∘

exists in addition to the magnetic field asymmetry; (3) the brightness

difference between λ III ¼ 110 ^∘ and λ III ¼ 290 ^∘ is not created by the local

plasma interaction, but by processes at high latitudes along the fluxtube.

Wannawichian et al. (2013) applied an empirical model for the density structure of Io’s plasma torus. The model is based on in-situ data and theory of the torus structure, and varies with dipole L shell, magnetic latitude, magnetic longitude, and local time. Although temporal electron density variations by a factor of 3–5 in the plasma torus were observed (e.g., Thomas et al., 2007; Steffl et al., 2008; Wannawichian et al., 2013) the general modulation of the Io footprint brightness with λ III longitude

remained unchanged, which indicates that the brightness strongly de- pends on Io’s location inside the torus and not on the temporal factors, e.g., local time, observational epoch (Wannawichian et al., 2013). With the quantitative models of electron density and the generated power near Io, Wannawichian et al. (2013) model the observed footprint brightness variations. They find that the longitudinal changes in plasma conditions which are needed to create variations in the electrodynamic interaction comparable to the observed modulation of the footprint emissions would require an unrealistically cold plasma torus with a torus density scale height of 0.35 Jupiter radii and a corresponding ion temperature of 6 eV so that the plasma is confined to the region close to magnetic equator and Io moves through strong density gradients during a Jupiter rotation.

Bonfond et al. (2013) suggested that the asymmetry of the two maxima at Fig. 2. Normalized emitted power (EP) of the south- ern Io footprint derived from Juno-UVS observations (Hue et al., 2019) is shown by the green triangles (normalized with EP ¼ 10:7 GW). Data points above 20 GW were neglected. The variation of the normal- ized Poynting flux calculated with the numerical model is shown by the blue squares (normalized with S _k ¼ 800 GW). For a more detailed presentation of the measurements, see Fig. 3 in Hue et al. (2019). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3. Poynting flux for an atmospheric column density N col;eq at the equator and an atmospheric scale height of 120 km for the upstream plasma conditions B 0 ¼ 1900 nT and n ¼ 1920 cm ^3 derived from the numerical model are shown by the blue squares. S _k is normalized with S _k;min ¼ 200 GW. The black line shows the Poynting flux calculated with the analytic approximation (equation (5)). The cyan line shows the Poynting flux calculated with the simplified an- alytic expression (9) derived from the numerical model results (blue squares).

The red squares show the modeled Poynting flux from plasma interaction with atmospheres with scale heights of 60 km and 240 km (discussed in Section 3.2.2). Green triangles show the results from the numerical model with H 0 ¼ 120 km and different plasma number densities: n ¼ 500 cm ^3 and n ¼ 4500cm ^3 (discussed in Section 3.2.5). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4. The magnitude of the plasma flow velocity calculated with the numer-

ical model is shown along the y axis which is directed towards Jupiter. The inner

boundary (Io ’s surface) is located at y ¼ 1 R Io . The plasma interaction with

Io’s atmosphere of different densities and H 0 ¼ 120 km leads to different ex-

tensions of the interaction region (solid lines). The plasma velocity of the un-

perturbed flow is displayed by the dashed black line. The blue dash-dotted and

dashed lines show the perturbed plasma flow velocity due to the interaction

with atmospheres of N col ;eq ¼ 2
10 ²¹ m ^2 and scale heights of 60 km and 240

km, respectively. (For interpretation of the references to colour in this figure

legend, the reader is referred to the Web version of this article.)

the plasma sheet crossing might not only be in fluenced by Io’s centrifugal latitude at the torus but also by the modulations of power transmission along the wing, by power transfer and by the size of the loss cone.

The modeled Poynting flux for N col;eq ¼ 2
10 ²⁰ m ^2 lies in the range of 680 –1080 GW (blue squares) whereas the electron precipitated power for the MAW spot derived from a set of HST observations in Far-UV domain from 1997 to 2009 lies in the range of 20–250 GW (Bonfond et al., 2013). This means that sometimes more than 20% of the total Poynting flux in Io’s Alfven wave can be transferred to the accelerated electrons to create the MAW spot. The rest of the energy is used for the Alfven wave reflection at the torus boundary, partially spread to other auroral features like the downstream tail, and converted into another form of energy (see, e.g., Chust et al., 2005; Jacobsen et al., 2007; Hess et al., 2010, 2013; Saur et al., 2013).

Bonfond et al. (2013) analyzed the HST FUV observations of the northern MAW spot at λ III ¼ 110 ^∘  280 ^∘ and showed that the northern MAW spot is about two times dimmer than the southern MAW spot. The asymmetry between the northern and southern footprints was also observed in the IR images obtained by Juno (Mura et al., 2018) and by Juno-UVS mostly at λ III ¼ 0 ^∘  30 ^∘ and 90 ^∘  130 ^∘ . Since the plasma interaction is symmetric with respect to Io ’s northern and southern hemispheres, the brightness and the emitted power of the northern and southern footprints would be the same if Io’s plasma interaction would be the only parameter controlling the properties of the footprints. Bonfond et al. (2013) suggested that the brighter southern MAW could be related to the weaker surface magnetic field and a more open loss cone for this longitude range. However, this loss cone effect is not expected to have such a strong in fluence on the brightness difference between the north- ern and southern footprints (Bonfond et al., 2013; Hess et al., 2013).

3.2. Modulation by Io ’s atmosphere

Changes in Io’s atmospheric density influence the plasma interaction by modifying the ionospheric Pedersen and Hall conductances. We test how the change in atmospheric density during the eclipse could affect the Poynting flux and the footprint brightness. We perform simulations with locally varying column densities, varying atmospheric scale heights, and fixed plasma upstream conditions (see Table 2 scenarios S2a and S2c).

Our goal is to provide information on how entering/exiting the eclipse could affect the emitted power of the Io footprint. Furthermore, we investigate the in fluence of longitudinal asymmetries in Io’s atmosphere (Table 2 model scenario S2b) and atmospheric inhomogeneities on the Poynting flux. In the end of this Section, we discuss the mutual effects of changes of the atmospheric density and upstream plasma conditions on the Poynting flux (Table 2 model scenarios S3).

3.2.1. Variations of the atmospheric surface density

The variations of the Poynting flux with different column densities for standard plasma conditions (B z ¼  1900 nT, n ¼ 1920cm ^3 ) are shown by the blue squares in Fig. 3. The different column densities are imple- mented by varying the number density while keeping the scale height constant. The total Poynting flux varies by a factor of about three from a thinner atmosphere with N col;eq ¼ 6
10 ¹⁸ m ^2 to a denser one with N _col;eq ¼ 6
10 ²¹ m ^2 for standard plasma conditions. The Poynting flux in the analytic approximation (black line) is higher than the Poynting flux from the numerical model (blue squares) until it is almost saturated for column densities N col > 6
10 ²⁰ m ^2 . The Poynting flux calculated with the numerical model does not indicate saturation and is overall more affected by variations of the neutral number density than in the analytic model. The model results differ because of two reasons: the first one is that we apply an equatorial atmosphere and vary the equatorial column density whereas the analytic model assumes a global atmosphere with a global atmospheric column density. Hence, the column densities relate to different global abundances and are not directly comparable. The second reason is that, in the analytic model, a constant effective radius of the

interaction region R eff is used. In the analytic model Io ’s plasma inter- action is saturated for N _col;eq  6
10 ²¹ m ^2 ( α  1 according to equa- tion (7)) in an interaction region with a constant radius. On the contrary, the numerical model self-consistently calculates the plasma flow velocity and determines the radius of the interaction region. The numerical re- sults show that the effective radius of the interaction region increases with increasing column density. In Fig. 4, we display the plasma flow velocity along the positive y axis for three different column densities (solid lines) and estimate the interaction region from the intersection point of the perturbed and unperturbed flow (black dashed line). Close to the moon’s surface (y ¼ 1 R Io ), the velocity is strongly decreased. The area where the plasma flow velocity decreases becomes larger with increasing atmospheric density. Outside this area, the plasma flow is accelerated and reaches velocities above the magnetospheric plasma velocity shown by the dashed black line because most of the plasma is directed around the moon. The dependence of the interaction region R eff ;num on the column density can be approximated by

R eff;num ¼ 1:1  N col;eq

6
10 ¹⁸ m ^2



(8)

for 6
10 ²¹ m ^2 > N col;eq > 6
10 ¹⁸ m ^2 and H 0 ¼ 120 km based on our model results. We can then approximate the Poynting flux for the upstream plasma conditions B 0 ¼ 1900 nT and n ¼ 1920 cm ^3 derived from the numerical model similar to equation (5) by the simpli fied expression:

S num ¼ 2 π R ² eff;num

ð α num M A B 0 Þ ² μ 0

v A (9)

where α num ¼ 1  0:6



N

6
10

 0:4

. The interaction strength was derived in analogy to equation (7). In our case the interaction strength is varying more with N _col;eq as in the case suggested by Hue et al. (2019) (see equation (7)). In this paper, we provide an alternative scaling for the interaction strength and interaction region as a function of the column density. The results calculated with equation (9) are shown by the cyan line in Fig. 3 and fit the numerical model results (blue squares).

3.2.2. Variations of the atmospheric scale height

The red squares in Fig. 3 display the modeled Poynting flux for different column densities with atmospheric scale heights H 0 ¼ 60 km and 240 km, respectively. Fig. 3 shows that, for dilute atmospheres (N col ;eq ¼ 2
10 ¹⁹ m ^2 ), the variation of the atmospheric scale height does not have a large effect on the Poynting flux, whereas for higher column densities (N _col;eq ¼ 2
10 ²⁰ m ^2 and 2
10 ²¹ m ^2 ), the effect is signi ficant. The Poynting flux is two times higher for an atmosphere with a global scale height of 240 km and N _col;eq ¼ 2
10 ²¹ m ^2 than for 60 km with the same column density. According to our numerical model results, the decrease in Poynting flux with decreasing column density is enhanced with increasing scale height. For H 0 ¼ 240 km (H 0 ¼ 60 km), the Poynting flux is decreased by about 73% (57%) for a decrease in the column density from 2
10 ²¹ m ^2 to 2
10 ¹⁹ m ^2 . In Fig. 4, we display the interaction region for a scale height of 60 km (blue dash-dotted line) and 240 km (blue dashed line). For a scale height of 60 km, the atmo- sphere and therefore the interaction region is concentrated close to the moon. For an atmosphere with a higher scale height (240 km), the at- mosphere is distributed in a larger region so that the interaction region is larger and the gradient in the plasma flow velocity is smoother. Assuming a decrease in the column density from 2
10 ²⁰ m ^2 to 2
10 ¹⁹ m ^2 , we expect a decrease in the Poynting flux by 30% (55%) for an atmospheric scale height of 60 km (240 km).

3.2.3. Effects of atmospheric asymmetries

We consider 4 cases (see Table 2 scenario S2b) where the subsolar

point ( θ s ; φ s ) is on the upstream side ( θ s ¼ 90 ^∘ ; φ s ¼ 90 ^∘ ), on the down- stream side ( θ s ¼ 90 ^∘ ;φ s ¼ 270 ^∘ ), on the Jovian side ( θ s ¼ 90 ^∘ ;φ s ¼ 0 ^∘ ), and on the anti-Jovian side (θ s ¼ 90 ^∘ ;φ s ¼ 180 ^∘ ). The comparison of the four cases with the case of the plasma interaction with a longitudinally symmetric atmosphere (Table 2 scenario S2a) with N _eq;col ¼ 2
10 ²⁰ m ^2 shows no significant changes. The Poynting flux from the interaction with an atmosphere concentrated on the Jovian side (anti-Jovian side) is about 3% (2%) lower than with a longitudinally symmetric atmosphere.

When investigating the effect of a changing atmosphere due to vol- canic eruptions, we add localized enhancements to the global atmo- sphere density. Dense atmospheric inhomogeneities are described in the model by equation (14) in Bl€ocker et al. (2018). We calculated the Poynting flux radiated away from Io due to the interaction with an at- mosphere with the Tvashtar plume and with the Pele plume, and found an increase in the Poynting flux by about 2% due to the atmospheric inhomogeneity. In summary, our results show that longitudinal asym- metries and inhomogeneities in the atmosphere do not strongly affect the Poynting flux and that the global atmospheric abundance predominantly determines the strength of the interaction.

3.2.4. Eclipse case

In Fig. 5, we show the relative decrease in the Poynting flux when Io enters the eclipse derived from the results of our numerical model similar to Fig. 8 of Hue et al. (2019). The decrease in the Poynting flux △S k in Io ’s Alfven wing is calculated by △S k ¼ ^S

S ^S

with S o being the Poynting flux out of eclipse and S i the Poynting flux in eclipse. The x and y axes display the equatorial column density outside and during the eclipse, respectively. The atmospheric scale height is constant (H 0 ¼ 120 km) for all model scenarios shown in Fig. 5. We expect, e.g., a decrease in the Poynting flux by 10% for a decrease of the column density from 1
10 ²¹ to 5
10 ²⁰ m ^2 in eclipse. Tsang et al. (2016) derived a decrease in the column density from 2
10 ²⁰ m ^2 to 5
10 ¹⁹ m ^2 from observations of Io ’s atmosphere shortly after eclipse ingress. According to Fig. 5, this decrease in the column density implies a decrease in the Poynting flux by

about 20%. However, a response of the footprint to the eclipse in the emitted power derived from Juno-UVS observations by Hue et al. (2019) was not detected. The proposed explanation for that non-detection was that Io’s atmosphere is dense enough to produce a saturated interaction when Io is in eclipse and when Io is out of eclipse. In Section 3.2.1, we showed that saturation of the Poynting flux is not reached for the tested range of possible column densities with increasing atmospheric surface densities while keeping the scale height constant at 120 km. The un- certainty associated with the Juno-UVS observations presented by Hue et al. (2019) can be approximated as 10%. This implies that the variations of the atmospheric column density during the eclipse lie between the dashed diagonal line and the 0.1 contour line. This results in a maximum possible decrease in the column density according to Fig. 5 by a factor of 2.5 (from 5
10 ²¹ m ^2 to 2
10 ²⁰ m ^2 ) and is not consistent with the observations from Tsang et al. (2016) under the assumption of an un- changed scale height and that the source of the brightness variation is solely caused by the local plasma interaction. Note that, we analyzed simple cases where we assumed that only the surface number density decreases during eclipse and the scale height is kept constant. In reality, the atmospheric scale height might drop as well due to temperature changes, which might have an in fluence on the Poynting flux. Due to little information about a possible change of the atmospheric scale height in eclipse, we have focused only on the change of Poynting flux with the atmospheric column density by varying the neutral number density. The effect of the change of the atmospheric scale height on the Poynting flux is discussed in Section 3.2.2..

Fig. 5. This contour plot displays the relative decrease in the Poynting flux △S k

during the eclipse. The upper left triangle is empty because we assume that there is no increase in the column density during the eclipse. The x and y axes display the equatorial column density outside and during the eclipse, respectively. Blue lines show contours of decrease for the upstream plasma conditions B 0 ¼ 1900 nT and n ¼ 1920 cm ^3 (Model scenario S2a) and for an atmospheric scale height of 120 km. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Figure 6. Contour plots are showing the total Poynting flux as a function of the

upstreaming plasma density and Jupiter ’s background magnetic field calculated

from the numerical model in a cut through the Alfv en wing. The Poynting flux is

calculated from plasma interaction with Io ’s atmosphere for three different

column densities and is normalized by a) S _k;min ¼ 200 GW, b) S k;min ¼ 400 GW,

c) S _k;min ¼ 645 GW.

3.2.5. Mutual effects of atmosphere and plasma conditions

In this section, we focus on the dependence of the Poynting flux on plasma conditions for different atmospheric surface number densities with a constant scale height, as well as its dependence on atmospheric surface number densities for different plasma properties. In Fig. 3 (green triangles), we display numerical model results of the simulations with two different plasma densities (500 cm ^3 and 4500 cm ^3 ) for different atmospheric surface densities. The decrease in the Poynting flux associ- ated with a decrease in the column density from 2
10 ²¹ m ^2 to 2
10 ²⁰ m ^2 is almost constant by 36% for the three plasma densities 500 cm ^3 ( filled green triangles), 1920 cm ^3 (blue squares), and 4500 cm ^3 (green triangles). The decrease in the Poynting flux associated with a decrease in the column density from 2
10 ²⁰ m ^2 to 2
10 ¹⁹ m ^2 depends on the plasma density and is largest for n ¼ 500 cm ^3 with 52%.

For n ¼ 4500 cm ^3 , the Poynting flux decreases by 35%. The strongest effect of plasma density variations is visible for a dilute atmosphere with N _col;eq ¼ 2
10 ¹⁹ m ^2 . A decrease in the plasma density from 4500 cm ^3 to 500 cm ^3 results in a decrease in the Poynting flux by 74%, whereas for N col;eq >2
10 ²⁰ m ^2 , the decrease is about 65%. The results indicate that the Poynting flux experiences strong variations due to variations of the atmospheric surface density with N col;eq <2
10 ²⁰ m ^2 in a low plasma density environment (n ¼ 500 cm ^3 ).

In Fig. 6, we show contour plots of the Poynting flux as a function of the magnetospheric plasma density and the background magnetic field for three different column densities. The Poynting flux experiences the strongest variations due to varying plasma conditions for an atmosphere with a small column density of N col;eq ¼ 2
10 ¹⁹ m ^2 (see Fig. 6a). The interaction strength of an atmosphere with a small atmospheric column density is small in the interaction region and variations of the upstream plasma conditions have a stronger effect on the Poynting flux. The model results shown in Fig. 6 indicate that, to achieve a relative change of the Poynting flux by a factor of 2.5 as observed by UVS for the southern footprint from λ III ¼ 0 ^∘ to λ III ¼ 100 ^∘ (see Section 3.1.3 and Fig. 2), local variations of the plasma density from n ¼ 500 cm ^3 to n ¼ 3100 cm ^3 for B 0 ¼ 1900 nT and N col;eq ¼ 2
10 ²⁰ m ^2 (see Fig. 6b) are needed. For a dilute atmosphere with N col;eq ¼ 2
10 ¹⁹ m ^2 (see Fig. 6a), smaller variations of the plasma density from n ¼ 500 cm ^3 to n ¼ 1800 cm ^3 for B 0 ¼ 1900 nT are needed to produce a change of the Poynting flux by a factor of 2.5 in amplitude. Variations of the plasma density have stronger influence on the Poynting flux variations than the magnetic field in the ranges of n and B 0 studied in this paper. Changes of the background magnetic field from B 0 ¼ 1600 nT to B 0 ¼ 2200 nT affect the Poynting flux by a maximum factor of 1.4 mostly in regions with upstream den- sities > 2000 cm ^3 . The model of Smyth et al. (2011) showed that, for the 1995 Galileo J0 epoch, such strong local variations of the electron den- sity with Io ’s λ III longitude as shown in Fig. 6 are possible. The combi- nation of a dilute atmosphere and strong variations of the plasma density in the vicinity of Io could provide the relative changes of the Poynting flux that can be fitted to the general trend of the Io footprint emitted power with λ III longitude. However, Smyth et al. (2011) showed that the global maximum of the electron density lies near λ III ¼ 290 ^∘ and not at λ III ¼ 110 ^∘ . An on average higher torus density at λ III ¼ 290 ^∘ than at λ III ¼ 110 ^∘ was also observed by Steffl et al. (2008); Hess et al. (2011).

4. Summary and conclusions

In this study, we apply a 3D MHD code to self-consistently model the plasma interaction with Io ’s atmosphere and to understand how varia- tions in Io ’s plasma environment and Io’s atmosphere affect the Poynting flux radiated away from Io. Our purpose is to relate these changes to observed variations of the emitted power at Io ’s footprints. We compare the modeled variations of the total Poynting flux with the relative vari- ations of the emitted power of the southern footprint derived from Juno- UVS observations (Hue et al., 2019). Furthermore, we compare our model results of the Poynting flux with theoretical investigations from

Saur et al. (2013). We also provide a simpli fied expression for the total Poynting flux for averaged plasma conditions derived from our numerical model for an equatorial atmosphere with atmospheric scale height of 120 km based on the equations from Saur et al. (2013). Our main con- clusions are the following:

 The numerical model results suggest that the magnetic field strength at Io plays a more important role for the observed difference of the footprint maxima during the two plasma sheet crossings at λ III ¼ 110 ^∘ and λ III ¼ 290 ^∘ than suggested by previous theoretical investigations (Saur et al., 2013).

 The observed difference in the southern footprint brightness between the plasma sheet crossings at λ III ¼ 110 ^∘ and λ III ¼ 290 ^∘ is still a factor of 1.6 larger than the difference in our model results. To achieve the observed difference in the modeled Poynting flux, a higher plasma density, a stronger magnetic field or a higher plasma flow velocity near λ III ¼ 110 ^∘ would be needed.

 The global atmospheric properties such as the total gas content or the atmospheric scale height essentially affect the Poynting flux. Plasma interaction with an atmosphere with a scale height of 60 km results in weaker variations of the Poynting flux with changing atmospheric column densities than an extended atmosphere. We also show that the Poynting flux is not fully saturated for a wide range of possible at- mospheric densities.

 A decrease in the column density from 2
10 ²⁰ m ^2 to 5
10 ¹⁹ m ^2 in eclipse as suggested by Tsang et al. (2016) would imply a decrease in the Poynting flux by about 20% according to our model results. The decrease in the Poynting flux might be lower if assuming a smaller scale height (< 120 km). The non-detection of a response to eclipse seen in the Juno-UVS observations (Hue et al., 2019) indicate that the decrease in the column density in eclipse during Juno-UVS observa- tions might be lower (by a factor of < 2.5) than suggested by Tsang et al. (2016), assuming the change in Io’s power supply due to eclipse is not canceled or counterbalanced by energy transmission processes.

 Variations in the upstream plasma conditions primarily affect the Poynting flux of the interaction with dilute atmospheres (N _col;eq < 2
10 ²⁰ m ^2 ).

 Volcanic plumes, longitudinal asymmetries in Io’s atmosphere, and magnetic induction from a possible subsurface magma ocean have negligible effects on the Poynting flux.

Note that we ignore the effects of the Alfven wave transmission, fil- amentation, reflection and the efficiency of the electron acceleration process in our study. All these effects might contribute to the variation of Io footprint brightness but these effects are beyond the scope of this paper. Our study provides a better understanding of Io’s plasma inter- action in Jupiter ’s magnetosphere. Investigation of the electromagnetic connection between Io and Jupiter is of great importance as Io’s plasma interaction also serves as a role model for studies of exoplanet environ- ments. Aurorae have been observed at the end of the stellar main sequence and were speculated to be due to similar effects as in the Io- Jupiter system (Hallinan et al., 2015). The electromagnetic connection can also be used in the search for exomoons around giant planets in exoplanetary systems (Noyola et al., 2014).

CRediT authorship contribution statement

A. Bl€ocker: Conceptualization, Methodology, Visualization, Soft- ware, Writing - original draft. L. Roth: Conceptualization, Writing - re- view & editing. N. Ivchenko: Conceptualization, Writing - review &

editing. V. Hue: Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial

interests or personal relationships that could have appeared to in fluence