Effect of plasma torus density variations on the morphology and brightness of the Io footprint

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1 PUBLICATIONS Journal of Geophysical Research: Space Physics RESEARCH ARTICLE Key Points: Io plasma torus density variations change brightness of auroral footprint Large density enhancements may explain the Io footprint shutoff observed in 2007 Propagation of Alfven waves in plasma torus determines Io footprint brightness Correspondence to: A. P. Payan, Citation: Payan, A. P., A. Rajendar, C. S. Paty, and F. Crary (2014), Effect of plasma torus density variations on the morphology and brightness of the Io footprint, J. Geophys. Res. Space Physics, 119, , doi:. Received 6 AUG 2013 Accepted 4 MAY 2014 Accepted article online 8 MAY 2014 Published online 28 MAY 2014 Corrected 3 JUL 2014 This article was corrected on 3 JUL See the end of the full text for details. Effect of plasma torus density variations on the morphology and brightness of the Io footprint A. P. Payan 1, A. Rajendar 1, C. S. Paty 1, and F. Crary 2 1 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USA, 2 Laboratory of Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, USA Abstract We develop a 2-D-layered model of the Io plasma torus to study the apparent shutoff of the Io footprint in 2007, when it disappeared beneath a region of diffuse emissions, roughly coincident with a massive eruption of Tvashtar Paterae. First, we investigate the effects of Io s location in the plasma torus and validate our model results against Hubble UV observations of the Io footprint. We are able to qualitatively reproduce variations in the morphology of the footprint due to Io s changing latitudinal location with respect to the center of the plasma torus, capturing the bright leading spot and the dimmer tail. Then, we consider the effects of an increase in the local plasma density on the brightness and morphology of the Io footprint. Our results show a correlation between a local density increase in the plasma torus and the dimming of the Io footprint as observed in In particular, we find that a local density enhancement at Io of fivefold compared to the nominal value is sufficient to produce the observed shutoff of the footprint. 1. Introduction Driven by extreme tidal forcing, Io is the most volcanically active body in the Solar System, ejecting approximately a ton per second of neutral material that is ionized to form the Io plasma torus. Field-aligned currents transmit torque from the ionosphere to the magnetospheric plasma, thus forcing the plasma torus to corotate with Jupiter, moving substantially faster than the orbital speeds in this region. The plasma torus axis of symmetry is aligned with Jupiter s magnetic dipole which is tilted by 10 relative to its spin axis, while Io orbits in Jupiter s equatorial plane at a much slower Keplerian speed. Therefore, the Io plasma torus wobbles around the moon as it travels along its orbit. In the reference frame of the plasma torus, Io moves from the Southern edge of the torus to its Northern edge. In addition, the difference between corotation speed (~74 km/s) and Io s orbital speed (~17 km/s) results in a net flow of plasma over the satellite. This 57 km/s flow produces piled-up magnetic field lines upstream of Io and a wake of disturbed field lines and plasma downstream. The resultant interaction accelerates charged particles along the magnetic field lines connecting Io and Jupiter, thus producing the Io auroral footprint. Io s bright auroral footprint in Jupiter s ionosphere is located equatorward of the main auroral oval. While the main oval features move in approximate corotation, the footprint is relatively fixed to the longitude of Io [Connerney et al., 1993; Clarke et al., 1996; Prangé et al., 1996]. The exact position is 0 10 downstream of the mapping of an unperturbed field line connected to Io. A suggested cause for this offset is the propagation time of an Aflvénic disturbance from Io to Jupiter s atmosphere [Hess et al., 2010, and references therein]. The footprint comprises a bright spot and a dimmer tail stretching downstream of Io [Gérard et al., 2002]. Under certain circumstances, the Io footprint contains more complex features, such as a Trans-atmospheric Electron Beam (TEB) spot upstream of the Main Alfvén Wave (MAW) spot, and numerous discrete Reflected Alfvén Wing (RAW) spots in the tail separated by a few degrees in longitude [Bonfond et al., 2008, 2009; Bonfond, 2010]. The extent of the entire feature is between 2 and 10 in longitude and is typically both brighter and longer in Jupiter s southern hemisphere where instances of a leading spot are mostly observed. Variations in the morphology and extent of the Io footprint appear in part to be controlled by Io s position relative to the center of the plasma torus [Gérard et al., 2006; Bonfond et al., 2008; Serio and Clarke, 2008]. Observations in 2007 of Jupiter s far-uv aurora with the Hubble Space Telescope revealed an increased number of isolated auroral blobs associated with large injections of hot plasma between 9 and 27 R J, alongside a continuous expansion of the main auroral oval over several months. Most unusually, they also PAYAN ET AL American Geophysical Union. All Rights Reserved. 3641

2 revealed the disappearance, or shutoff, of the Io footprint under a patch of diffuse emissions most probably remaining from an injection blob. During this observation, Io was located between S3 longitude 202 and 212, which corresponds to Io being positioned northward of the centerline of the plasma torus [Bonfond et al., 2012]. Earlier in 2007, observations of Io with the New Horizons spacecraft revealed a large volcanic eruption of the Tvashtar Paterae [Spencer et al., 2007], potentially resulting in a significant increase in the mass density of the plasma torus local to Io. Contemporary observations of Io and Jupiter further revealed an enhancement of Jupiter s sodium cloud [Yoneda et al., 2009] and the shutoff of Jupiter s hectometric (HOM) radio emissions [Yoneda et al., 2013]. Yoneda et al. [2010] further showed that a volcanically active period at Io increases the flux tube content of the plasma torus by 1.5 compared to quiet times, which corroborates a likely increase in the local plasma mass density. In order to explain the acceleration of charged particles along field lines from Io to Jupiter generating the Io footprint, two different physical mechanisms, the unipolar inductor and the Alfvén wing models, have been proposed. In the unipolar inductor model [Piddington and Drake, 1968; Goldreich and Lynden-Bell, 1969],the interaction between the plasma flow and Io s conductive ionosphere generates an electric field that drives currents flowing across Io from the sub-jovian to the anti-jovian side and closing through Jupiter s ionosphere along the field lines connecting Jupiter and Io. As per its assumption of a low-density plasma, the unipolar inductor model neglects the plasma inertia and therefore does not apply to the dense homogeneous plasma torus. In the Aflvén wing model [Drell et al., 1965; Goertz, 1980; Neubauer, 1980], the motion of Io s conductive ionosphere through the dense plasma torus generates perturbations in the Jovian magnetic field that propagate as Alfvén waves along the magnetic field lines, which in turn accelerate particles into Jupiter s ionosphere to create the Io footprint. In the Alfvén wing model, the dense plasma torus may be either homogeneous or inhomogeneous [Deift and Goertz, 1973], the wave regime may be linear or fully nonlinear, and the pickup processes generate currents that close either in Io s vicinity[goertz, 1980] or in its corotational wake [Southwood and Dunlop, 1984]. These two models are not mutually exclusive. For instance, Crary and Bagenal [1997] and later Saur [2004] described a hybrid model in which the unipolar inductor model dominates when Io is located near the edge of the plasma torus and the Alfvén wing model dominates when Io is near the center of the torus. In a more recent work, Jacobsen et al. [2007] developed a single-layer model of the Io plasma torus and used a nonlinear, three-dimensional and time-dependent MHD model to study the structure of the Io footprint. They examined how the strength and the degree of linearity of the local interaction near Io influences the reflection pattern of Alfvén waves both inside the plasma torus and at Jupiter s ionosphere based on a simplified magnetic field geometry. They further tracked field-aligned currents to investigate the resulting morphology of the Io footprint and suggested that the discrete nature of the Io footprint corresponds to a weaker interaction when Io is near the edges of the plasma torus, while a continuous and spread-out footprint is more representative of a stronger interaction when Io is at the center of the plasma torus. Here, we present a discrete two-dimensional multilayer model that qualitatively explains the change in brightness and morphology of the Io footprint depending on the position of Io in the plasma torus and use this model to examine the relationship between an increase in the plasma torus density and a dimming of the Io footprint. We thus determine the approximate plasma torus density enhancement required to sufficiently decrease the brightness of the Io footprint at Jupiter such that it shuts off. Such a local density increase may be due to large volcanic eruptions on Io, such as the 2007 event mentioned above. Compared to Jacobsen et al. [2007] who use the current density in the Jovian ionosphere as a proxy to study the morphology of the Io footprint, the two-layered model considered in this paper specifically represents the dispersion of energy transported by Alfvén waves inside the plasma torus. Our model of the Io footprint thus produces results that are more analogous to the observed auroral intensity. Furthermore, it provides a structure of the Io footprint that is physically consistent with the hypothesis put forth by Bonfond et al. [2008]. Indeed, the two-layered model presented here is the first to consistently address how Io s location in the plasma torus affects the relative brightness and longitudinal structure (including extent) of the Io footprint and the first to examine a local density increase in the plasma torus as a potential mechanism to shutoff the Io footprint (as observed in 2007). 2. Methodology We have created a model of the Io plasma torus to study the influence of the location of Io within the torus and the variation of plasma density on the brightness and morphology of the Io footprint. The torus PAYAN ET AL American Geophysical Union. All Rights Reserved. 3642

3 Figure 1. Model of the Io torus. The plasma torus is represented as a two-dimensional flat ribbon, composed of two layers of uniform density and of identical vertical extent. three-dimensional structure is represented as a two-dimensional flat ribbon obtained from a field-aligned cut through the torus, as shown in Figure 1. We then treat this surface as a two-dimensional plane for the longitudinal extent over which the footprint is generated. In the model, the torus is composed of two discrete layers of uniform density determined from the global variation of density in the plasma torus, obtained from the most abundant species [Bagenal, 1994]. The resulting densities in the inner layer, the outer layer, and outside of the plasma torus are determined to be ρ 1 = 60,000 amu/cm 3, ρ 2 = 13,000 amu/cm 3, and ρ out = 50 amu/cm 3, respectively. These densities are considered nominal. The height of the inner layer from the torus centerline is determined from the latitudinal wobbling of the plasma torus around Io (6.4 ) [Gledhill, 1967; Bonfond et al., 2012] and from the approximate e-folding values of the overall mass density profile of the most abundant species in the plasma torus [Bagenal, 1994]. This corresponds to z = ± 0.75 R J in Figure 1. In this context, the vertical extent of the outer layer is also taken to be 0.75 R J from the edge of the inner layer and thus extends from z = ± 0.75 to ± 1.5 R J. The region outside the torus extends from 1.5 R J up to the Jovian ionosphere, 4.5 R J away, and is assigned the much lower plasma density of 50 amu/cm 3. In the model, the vertical location of Io is varied with respect to the centerline of the ribbon to represent the changing position of Io in the plasma torus due to the wobble, and the density of the inner layer is increased to represent a local density enhancement due to volcanic eruptions. According to Yoneda et al. [2010], an increase in volcanic activity at Io results not only in an increase in the brightness scale height and in the brightness of the [SII] nm emission line from the Io plasma torus related to the sulfur ion chemistry but also, and most importantly, in an increase in the flux tube content and thus in the local density. Therefore, following a volcanic event on Io, the flux tube content of the plasma torus is not constant. This is why only the inner layer density has been increased in our model. This choice is further motivated by the need to model the temporally and spatially localized density increase in the plasma torus due to the enhanced volcanic activity on Io observed by Spencer et al. [2007] shortly before Bonfond et al. PAYAN ET AL American Geophysical Union. All Rights Reserved. 3643

4 Table 1. Nominal Values for the Densities, Alfvén Speeds, and Alfvén Waves Swept Back Angles in Each Layer and Outside of the Plasma Torus Inner Layer (1) Outer Layer (2) Outside of Torus (Out) ρ i (amu) 60,000 13, ρ i (kg/m 3 ) V Ai (km/s) ,020 θ i (deg) [2012] observed the disappearance of the Io footprint under a diffuse patch of auroral emissions at Jupiter. It is worth noticing that increasing the ratio of ρ 1 and ρ 2 is, by definition, changing the scale height of the torus. However, the fresh plasma would be more anisotropic and therefore more equatorially confined. It is assumed that as the corotating plasma in the torus impinges on Io, MHD waves are swept back by an angle θ A given by equation (1) [Gurnett and Goertz, 1981; Bagenal, 1983]: tanðθ A Þ ¼ V flow =V Ai (1) where V flow is the difference between corotation speed of the plasma and orbital speed of Io (V flow =V corotation V Io =74 17 = 57 km/s) and V Ai is the Alfvén speed in medium i of density ρ i. V Ai is p calculated from the well-known relationship V Ai ¼ B= ffiffiffiffiffiffiffiffi μ 0 ρ i [Bazer and Hurley, 1963; Crary and Bagenal, 1997], where the local magnetic field strength B is taken to be the field strength at Io s location (B = B surface / (L shell _ Io ) 3 = /(6) 3 = T) and μ 0 is the permeability constant (μ 0 = Hm 1 ). Table 1 summarizes the characteristics of all the plasma torus layers for the nominal case. It is further assumed that only two Alfvén wavefronts are launched at the leading edge of Io in the upward and downward directions (cf. Figure 1). Upon encountering a density discontinuity within the torus, where the magnetic field lines are substantially distorted, the Alfvén waves are assumed to undergo partial reflection and transmission (refraction) [Ferraro, 1954; Stein, 1971; Goertz, 1980]. We then follow these wavefronts inside the plasma torus to determine the longitude with respect to Io at which Alfvén waves exit the torus and the proportion of the initial energy carried by these exiting wavefronts. For the reflected wavefront, the angle of reflection θ r is assumed to be equal to the angle of incidence θ i. The fraction of energy transported by the reflected wavefront, denoted E r, is obtained from the incident energy E i according to E r = C r _ ab E i, where C r_ab is the coefficient of reflection at the boundary between medium a and mediun b, calculated in equation (2) [Wright, 1987]: ð C r_ab ¼ V Aa V Ab Þ 2 ðv Aa þ V Ab Þ 2 (2) In equation (2), V Aa is the Alfvén speed in medium a of density ρ a and V Ab is the Alfvén speed in medium b of density ρ b. For the transmitted wavefront, the angle of transmission θ t is calculated from θ i according to the modified Snell s Law in equation (3) [Bazer and Hurley, 1963; Stein, 1971]: sinðθ t Þ ¼ V Aa sinðθ i Þ (3) V Ab In equation (3), V Aa is the Alfvén speed in medium a of density ρ a and V Ab is the Alfvén speed in medium b of density ρ b. The dissipation of the Alfvén waves as they propagate inside the torus is neglected, so that the fraction of energy transported by the transmitted wavefront at is given by E t =(1 C r _ ab )E i = C t _ ab E i, where C t_ab is the coefficient of transmission between medium a and mediun b, calculated in equation (4) [Wright, 1987]: C t ¼ 4V Aa V Ab ðv Aa þ V Ab Þ 2 (4) For the nominal case, C r_12 = 0.13 and Ct _12 = 0.86 (between the inner and the outer layers of the plasma torus), C r_2out = 0.78 and Ct _2out = 0.22 (between the outer layer and the outside of the plasma torus). PAYAN ET AL American Geophysical Union. All Rights Reserved. 3644

5 Table 2. Relative Energy (Expressed as a Percentage of the Initial Directed Wave Energy) of the Main Spot and of the First Three Trailing Spots of the Io Footprint in Jupiter s Northern Ionosphere Latitudinal Position of Io in the Plasma Torus (deg) Relative Energy (%) Main Spot Second Spot Third Spot Fourth Spot Once the Aflvén waves leave the torus, thus entering a region of negligible distortion of the magnetic field, it is assumed that they propagate along the field lines and accelerate charged particles into the ionosphere of Jupiter to produce the Io footprint, as per the Alfvén wing model. Since the Alfvén speed outside of the torus is very large (>6000 km/s), V A1 V A2 in equation (3), and therefore, θ t 0. Similarly, the kev electrons speed outside the torus is very large. Therefore, both the Alfvén waves and the charged particle accelerations they produce are field aligned. In this context, it is assumed that the Io footprint features are created at the longitudes where the Alfvén waves exit the plasma torus. Also, we assume that the intensity of each feature is positively correlated with the energy transported by the escaping wavefronts [Gérard et al., 2006]. While only two wavefronts are launched at Io, a new pair of reflected and transmitted wavefronts is created at each density discontinuity inside the plasma torus. All the escaping wavefronts are tracked by our model, resulting in the footprint being created by hundreds of separate Alfvén wavefronts impinging on Jupiter s ionosphere. We assume that the auroral spots composing the Io auroral footprint are created by the most energetic wavefronts. Because of the large number of wavefronts that arrive in close proximity on Jupiter s ionosphere, we model the intensity of each auroral spot by integrating the energies carried by all wavefronts longitudinally located within 1 of the corresponding most energetic wavefront. This is similar to the observations of the Io footprint by the Hubble Space Telescope, which are limited by its resolution (between 0.2 and 0.8 as per Gérard et al. [2006]). As a result, the individual spots comprising our modeled auroral footprint are in fact composed of multiple spots in very close proximity to one another. This allows for the variabilities in spots brightnesses summarized in Tables 2 and 3 and illustrated in Figure 2. Finally, we would like to emphasize that our study does not completely model the bouncing wave scenario described in Bonfond et al. [2008] in which it does not take into account any reflection of the escaping Alfvén waves on Jupiter s ionosphere. Therefore, our two-layer model does not reproduce the TEB mentioned in Bonfond et al. [2008] and does not consider any reflections or refractions of this TEB inside the plasma torus. Instead, it focuses on the representation of the MAW and the RAW described in Bonfond et al. [2008]. In this work, we are only concerned with the longitudinal distribution of energy escaping the plasma torus as Alfvén waves generated at Io reflect and refract inside the plasma torus. We examine changes in the resulting energy distribution as they relate to the position of Io in the plasma torus and the local plasma density. 3. Results The main goal of the paper is to study the effects of a local plasma density increase at Io on the brightness of the Io footprint, potentially following a major volcanic eruption on Io. In order to do so, it is first necessary to Table 3. Relative Energy (Expressed as a Percentage of the Initial Directed Wave Energy) of the Main Spot and of the First Three Trailing Spots of the Io Footprint in Jupiter s Southern Ionosphere Latitudinal Position of Io in the Plasma Torus (deg) Relative Energy (%) Main Spot Second Spot Third Spot Fourth Spot PAYAN ET AL American Geophysical Union. All Rights Reserved. 3645

6 ε ε ε ε ε Figure 2. Bubble plot of the relative energy (expressed as a percentage of the initial directed wave energy) escaping the Io plasma torus toward Jupiter s northern and southern ionospheres as a function of longitude for various positions of Io above the centerline of the plasma torus, characterized by the corresponding latitudinal position. The area of each bubble represents the relative energy of the corresponding auroral spot. The reader should be aware when reading this plot to not interpret the area of the bubbles as the actual latitudinal/longitudinal extent of the emission. The longitudinal scale is defined such that 0 corresponds to the position of Io. The inserts to the left and right of the bubble plot show processed observations from the Hubble Space Telescope of the Io footprint in Jupiter s northern and southern hemispheres, respectively, for various latitudinal positions of Io above the centerline of the plasma torus (HST observations first published in this projection in Bonfond et al. [2008]). assess the ability of the model to correctly predict the morphology and brightness of the Io footprint for various positions of Io in the plasma torus. The reflection and refraction model within the two-dimensional-layered torus model was applied to different positions of Io with respect to the centerline of the plasma torus, and the resulting Io footprints were compared to the corresponding published observations. The bubble plot in Figure 2 pictorially represents the resulting morphology and brightness of the Io footprint in both the northern and southern hemispheres of Jupiter for 11 latitudinal positions of Io in the inner layer and north of the centerline of the plasma torus. The bubble plot representation has been chosen to illustrate the discrete nature of the brightest features in Io footprint as obtained from our multilayer model; a continuous density gradient model would partially diffuse these predicted structures in the footprint. The area of the bubbles represents the relative wave energy escaping the torus at various longitudes with respect to the initial directed wave energy launched at Io. Tables 2 and 3 summarize the relative energy of the main spot and of the first three secondary spots in the northern and southern hemispheres of Jupiter, respectively. The structure of the footprint is obtained by calculating the relative energy escaping the plasma torus for the various positions of Io with respect to its centerline for the cases above and by representing it as a function of longitude on Jupiter s ionosphere. The morphology of the resulting footprint on both the northern and southern Jovian hemispheres is compared with processed observations from the Hubble Space Telescope depicted in Bonfond et al. [2008, Figure 3]. Figure 2 shows that as the latitudinal position of Io above the centerline of the plasma torus increases, the longitudinal extent of the Io footprint and the interspot distances increase in both the northern and southern hemispheres. In the northern hemisphere, the position of the MAW spot shifts toward smaller longitudes (closer to the longitudinal position of Io), while in the southern hemisphere, it shifts to larger longitudes (away from the longitudinal position of Io). This is consistent with the morphology of the Io footprint depicted in Bonfond et al. [2008, Figure 3] when one neglects the presence of the leading spot. Additionally, as per Bonfond et al. [2008], the TEB is created in the northern Jovian hemisphere as the upward-directed MAW impacts on Jupiter s ionosphere. The downward-directed TEB then directly propagates to the southern Jovian hemisphere where it creates the Io footprint leading spot at about the longitudinal position of Io [cf. Bonfond et al., 2008, Figure 4]. Therefore, in the southern Jovian hemisphere, the Io footprint leading spot should be located at ~0 longitude in our Figure 2, which is upstream of the corresponding MAW spot. Although our model does not include the mechanisms responsible for the creation of the leading spot in the Io footprint, Figure 2 shows that as the latitudinal position of Io above the centerline of the plasma torus exceeds 4, the shift in the longitudinal location of the southern MAW spot leaves space for the leading spot. Once again, this is consistent with the PAYAN ET AL American Geophysical Union. All Rights Reserved. 3646

7 Figure 3. Modeled emitted power of the Main Alfvén Wave (MAW) spot as observed by HST in Jupiter s northern hemisphere for several observation campaigns of the Io footprint (adapted from modeled power calculations in Bonfond et al. [2013]). The observation campaigns are color coded and described in the legend at the bottom of the figure. The added information concerns the power reduction required to observe a dimming of the Io footprint from nominal observations (depicted in orange). The green square highlights the data corresponding to the dimming of the Io footprint as observed in 2007, while the purple square highlights the data corresponding to nominal observations of the Io footprint. The minimum modeled power for the nominal observations lies at 6.5 GW, while the maximum modeled power corresponding to the dimming of the Io footprint lies at 4.7 GW. location of the leading spot in the southern Io footprint depicted in Bonfond et al. [2008] for latitudinal positions of Io in the plasma torus exceeding 4. To summarize, we have shown that the model captures both the geometry of the footprint (MAW spot and several fainter RAW spots) as well as its longitudinal extent as it relates to the latitudinal position of Io in the plasma torus. The two-layer model may now be used to predict the effect of a local density increase around Io (i.e., density enhancement of the central layer of our model) on the brightness and the morphology of the Io footprint when Io is above the centerline of the plasma torus (~215 S3 longitude) to correlate with the observation of Figure 4. Energy of the main Io footprint s spot as a percentage of the initial directed wave energy. The dimming of the Northern Io footprint by about 67% from its nominal brightness requires a fivefold density increase in the plasma torus local to Io, as depicted by the blue rectangle. PAYAN ET AL American Geophysical Union. All Rights Reserved. 3647

8 the Io footprint dimming in 2007 (Bonfond et al. [2013]). As mentioned earlier, this event is contemporary to a large volcanic eruption of the Tvashtar Paterae [Spencer et al., 2007], potentially resulting in a significant increase in the mass density of the plasma torus local to Io. This volcanic eruption led to both an enhancement of Jupiter s sodium cloud [Yoneda et al., 2009] and the shutoff of Jupiter s hectometric (HOM) radio emissions [Yoneda et al., 2013]. In such a case, Yoneda et al. [2010] argued that a volcanically active period at Io increases the flux tube content of the plasma torus by 1.5 compared to quiet times. To obtain the local density increase required to make the Io footprint fainter than the background emission, we determined the emitted power reduction corresponding to a dimming of the Io footprint compared to a nominal observation of the Io footprint brightness. We considered 2007 observations and studied the case where the lowest power emitted by the MAW spot during nominal observations is 6.5 GW, while the highest power emitted by the MAW spot as the footprint shut off is 4.7 GW. This corresponds to a reduction of the emitted power by about 67%. For this case, we found that the local density at Io must be increased fivefold relative to its nominal value in the inner layer to produce the corresponding ~67% reduction in the relative energy transported by the MAW. This is depicted in Figure 3. The MAW spot does not involve multiple wavefronts overlapping each other, so the corresponding energy is simply the product of the two transmission coefficients through the inside and outside boundaries of the plasma torus. As the density in the inner layer increases, the Alfvén speed in the inner layer (V A1 ) decreases. The density in the outer layer remains constant, and thus, the Alfvén speed in the outer layer (V A2 ) remains unchanged. Consequently, according to equation (4), the transmission coefficient through the inside boundary between the inner and outer layers of the plasma torus (Ct _12 ) decreases, while the transmission coefficient through the outside boundary between the outer layer and the outside of the plasma torus (Ct _2out ) does not change. Therefore, the product of the two transmission coefficients, which is also the energy of the MAW spot, decreases as shown in equation (5): Energy MAW ¼ C t_12 C t_2out ¼ 4B= p ffiffiffiffiffiffiffiffiffi μ 0 ρ 1 p B= ffiffiffiffiffiffiffiffiffi μ 0 ρ 1 þ V A2 V A2 2 4V A2 V Aout ðv A2 þ V Aout Þ 2 (5) The decrease in energy of the MAW spot as the density in the inner layer of the plasma torus increases is depicted in Figure 4. We found that the relative energy of the MAW spot first decreases by half (from ~19% to ~10%) as the density in the inner layer is multiplied by up to 10 compared to its nominal value. For larger increases in the local density at Io (from 10 to ~30 ), the resulting relative energy of the MAW spot is also reduced by half (~10% to ~6%) but the decrease in energy is spread over a larger range of density increase and tends to flatten out. As a consequence, changes in density less than tenfold have a large effect on the relative Aflvén wave energy escaping the torus, and thus on the brightness of the Io footprint. It should be noted that the values of the emitted power of the MAW spot provided by Bonfond et al. [2013] on which this study is based are modeled values, obtained from data gathered over several observation campaigns. This produces some inherent uncertainty in the emitted power reduction factors calculated above and thus in the resulting density increases required to shut off the Io footprint. However, our model accurately and self-consistently predicts the morphology and intensity of the Io footprint, and the density enhancements we obtain to explain the footprint shutoff are consistent with previous observations of torus variability from volcanic activity on Io. Delamere et al. [2004] showed that an observed 3 order of magnitude increase in the Io dust emission [Krüger et al., 2003] was coincident with an enhanced UV emission from the Io plasma torus and determined that this required ~3 enhancement in the neutral gas production from Ionian volcanic activity. It is thus reasonable that the large 2007 eruption of Tvashtar Paterae could produce a substantial enhancement of neutral gas production and thus a sufficient increase in plasma torus density to shut off the Io footprint. 4. Conclusions We have investigated the change in brightness and morphology of the Io auroral footprint depending on the relative location of Io inside the plasma torus and the local plasma density. To do so, we have created a twodimensional model of the torus. The model features two discrete density layers representative of the Io plasma torus structure. Using this geometry, we track the Alfvén waves generated at Io as they propagate PAYAN ET AL American Geophysical Union. All Rights Reserved. 3648

9 through the plasma torus and experience reflections and refractions at density discontinuities. From the longitudinal locations of the Alfvén waves escaping the torus and the energy carried by these wavefronts, we determine the structure of the Io footprint. Despite its simplifications, our model predicts a footprint morphology and brightness consistent with UV observations of Jupiter for various positions of Io in the plasma torus. By altering the density of the central layer of our torus model, we have also shown that it is possible for a local density increase in the plasma torus to produce a dimming and potential shutoff of the Io footprint. In particular, we have determined that a local density enhancement at Io of 5 would decrease the energy of the main Alfvén wave spot to a point where the Io footprint becomes undistinguishable from the diffuse auroral background emissions. This is consistent with observed torus variability due to enhanced Ionian volcanic activity. 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10 Erratum In the originally published version of this article, an instance of text was incorrectly typeset. The following has since been corrected and this version may be considered the authoritative version of record. In section 3, the sentence This is depicted in Figure 4. has been changed to This is depicted in Figure 3. PAYAN ET AL American Geophysical Union. All Rights Reserved.