Kivelson et al.: Interaction with the Jovian Magnetosphere 545

Europa’s Interaction with the Jovian Magnetosphere

Margaret G. Kivelson and Krishan K. Khurana University of California, Los Angeles

Martin Volwerk Österreichische Akademie der Wissenschaften

Europa is embedded in Jupiter’s magnetosphere where a rapidly flowing plasma interacts electromagnetically with the moon’s surface and its atmosphere. In this chapter, the phenom- enology of the interacting system is presented and interpreted using both qualitative and quan- titative arguments. Challenges in understanding the plasma environment arise partly because of the diverse scale-lengths that must be considered as well as the nonlinear nature of the in- teractions. The discussion that follows describes selected aspects of the interacting system. On the scale of gyroradii, we describe the effects of newly ionized particles on fields and flows and their relation to wave generation. On the scale of Europa radii, we discuss the structure of the local interaction. On the scale of the tens of Jupiter radii that separate Europa from Jupiter’s ionosphere, we describe the aurora generated near the magnetic footprint of Europa in Jupiter’s upper atmosphere. We end by stressing the relevance of plasma measurements to achievement of goals of a future Europa Orbiter mission.

1. INTRODUCTION ropa, the smallest of the Galilean moons, was found also to be a plasma source (Intriligator and Miller, 1982; Eviatar The Galilean moons, although small, play a distinctive and Paranicas, 2005; Russell et al., 1999), albeit a second- role in the history of solar system science. Galileo recog- ary one. However, Europa’s plasma environment received nized that their motions in periodic orbits around Jupiter comparatively little attention until it was established by were compelling analogs of planetary bodies in a heliocen- Galileo observations that its geologically young surface lies tric system (see chapter by Alexander et al.). The complex above what is probably a global ocean (Khurana et al., orbital interactions of the inner moons were found to ac- 1998). This discovery promoted the priority of Europa and count not only for orbital stability (e.g., Goldreich, 1965), its local plasma environment as targets for further planetary but also for enhanced tidal heating (Peale et al., 1979), exploration. Although only 3 of the 12 flybys of the Galileo which powers volcanic activity on Io and melting of the ice prime mission (1995 through 1997) passed close to Europa, beneath the surface of Europa. That fluid oceans could be the next phase of the mission, designated the Galileo Europa present beneath the icy crusts of the three outer moons was mission, devoted half of its 14 flyby opportunities to Eu- discussed (Lewis, 1971) decades before spacecraft obser- ropa. Table 1 summarizes various relevant features of Gali- vations provided support for (if not full confirmation of; see leo’s flyby trajectories (or “passes”) plotted in Fig. 1. The chapter by Khurana et al.) this speculation for some of the final stage of Galileo’s odyssey included a specially designed moons, in particular, Europa. pass in which magnetometer measurements found a pre- Concurrent with studies of the interior, the particle and dicted reversal of the orientation of the internal dipole mo- fields environments of the moons began to attract attention ment, thus confirming the presence of an inductive field at following the discovery of Io’s control of jovian decametric Europa (Kivelson et al., 2000). emissions (Bigg, 1964). Goldreich and Lyndon-Bell (1969) This chapter addresses the subject of Europa’s interac- recognized that an electromagnetic link between the moon tion with the particles and fields of the jovian magneto- and Jupiter’s ionosphere could explain the observations, a sphere. The topic presents a considerable challenge because suggestion that implied the presence of plasma along the the moon and its magnetized plasma environment interact Io magnetic flux tube. Somewhat later, the existence of an nonlinearly. Relevant to the interaction are matters as di- extended nebula around Io’s orbit, the Io torus, was estab- verse as the chemical composition of the surface from lished (Kupo et al., 1976; Mekler and Eviatar, 1977). Io soon which particles are sputtered, the properties of the energetic became the focus of in situ particle and field measurements particles responsible for the sputtering, the temporal and by Voyager 1, and the ionian source of heavy ion plasma spatial characteristics of the magnetospheric plasma near that shapes the structure of much of the magnetosphere was the orbit of Europa, properties of the magnetic field that recognized (Bagenal and Sullivan, 1981; Shemansky and confines the plasma, and the electromagnetic characteris- Smith, 1981; see also review by Thomas et al., 2004). Eu- tics of the moon and its ionosphere. Europa’s response to

545 546 Europa

TABLE 1. Characteristics of Galileo’s close passes by Europa (boldface emphasizes flybys with full fields and particles data with closest approach at altitudes below 2050 km).

Location of Radial Distance Local Time Closest Europa Europa East c/a Relative

Pass Date, Time from Jupiter (RJ) (Hours) Approach (km) Latitutde Longitude to Europa E4 12/19/96 06:52:58 9.4–9.5 16.6–17.0 688.1 –1.7 322.4 Oblique Wake E6 02/20/97 17:06:10 — — 582.3 –17.0 34.7 Recording Lost Except PWS E11 11/06/97 20:31:44 9.0–9.4 10.8–11.9 2039.3 25.7 218.7 Oblique Wake E12 12/16/97 12:03:20 9.4–9.6 14.5–14.8 196.0 –8.7 134.3 Upstream E14 03/29/98 13:21:05 9.4–9.6 14.3–14.7 1649.1 12.2 131.2 Upstream E15 05/31/98 21:12:56 9.4–9.6 9.9–10.3 2519.5 15.0 225.4 Wake E16 07/21/98 05:04:43 — — 1829.5 –25.6 133.6 Recording Lost E17 09/26/98 03:54:20 9.2–9.6 9.6–10.3 3587.4 –42.4 220.3 Wake E18 11/22/98 11:44:56 — — 2276.2 41.7 139.3 Recording Lost E19 02/01/99 02:19:50 9.2–9.4 9.7–10.0 1444.4 30.5 28.2 Upstream E26 01/03/00 17:59:43 9.2–9.7 2.8–3.1 348.4 –47.1 83.4 Upstream/Polar the currents linking it to the magnetospheric plasma in turn produces what can be thought of as a periodically varying modify the local properties of the plasma and magnetic field internal dipole moment with its axis in Europa’s equatorial (Kivelson, 2004; Kivelson et al., 2004). plane. This changing internal source contributes signifi- In the following sections we first summarize the prop- cantly to the total field near Europa (Neubauer, 1999). The erties of Jupiter’s magnetosphere in the vicinity of Europa, properties of the background plasma of the extended Io and provide a large scale (magnetohydrodynamic) perspec- torus are controlled by a combination of electromagnetic tive on the interaction between Europa, its ionosphere, and and centrifugal forces; at the orbit of Europa, the plasma its plasma environment. We then discuss the presence of density peaks between Jupiter’s magnetic equator and its pickup ions in the local plasma, the special role of ener- centrifugal equator and decreases markedly above and be- getic particles in the interaction and the modification of the low; because of the 10° tilt between Jupiter’s spin axis and interaction by the inductive magnetic field. The properties its magnetic dipole axis, plasma properties at Europa are of the inductive field itself are discussed in the chapter by strongly modulated as Jupiter rotates. The most complete Khurana et al. We consider special features of passes up- survey of plasma density near Europa (Fig. 3, taken from stream and downstream of the moon in the flowing plasma, Kurth et al., 2001) makes use of data from Galileo’s Plasma with particular emphasis on properties of the wake region. Wave System (PWS) (Gurnett et al., 1992). Power at fuh,e, Next we describe the link between Europa and the auroral the electron upper hybrid frequency, is roughly proportional footprint in Jupiter’s upper atmosphere. We close with a dis- to the square root of ne, the electron number density, with cussion of expectations for fields and particle measurements a weak dependence on |B|, the magnitude of the magnetic as a component of future exploration of the remarkable body field. The variation of density from pass to pass results that is the subject of this book. largely from the changing location of the Galileo passes relative to Jupiter’s magnetic equator, a point to which we 2. OVERVIEW OF FIELD AND PLASMA will return. CONDITIONS NEAR EUROPA’S ORBIT At Europa’s orbit, the plasma approximately corotates (meaning that it flows in the azimuthal direction at approxi- Europa’s orbit, at 9.38 RJ (RJ is the radius of Jupiter, mately Jupiter’s angular velocity) as a result of electromag- taken as 71,400 km) from the center of Jupiter and effec- netic coupling between the equatorial plasma and Jupiter’s tively in Jupiter’s equator, lies at the outer edge of the Io ionosphere. Near the equator at distances beyond ~1.4 RJ, plasma torus within the inner magnetosphere, a region where Keplerian speeds are slower than plasma rotational speeds, the magnetospheric magnetic field is quasidipolar. As Ju- so the rotating plasma overtakes bodies orbiting Jupiter. piter rotates, the 10° tilt of the dipole moment relative to Plasma flows onto Europa’s trailing hemisphere at a rela- the axis of rotation causes the magnetic equator to sweep tive speed of roughly 100 km s–1 as indicated in Table 2. up and down over Europa at Jupiter’s 11.23-h synodic pe- Slight variations of plasma parameters with local time are riod with respect to Europa. The changing latitude and vary- observed as Europa orbits Jupiter every 84 h but the domi- ing ambient magnetic field over a jovian rotation period are nant temporal variations are at the 11.23-h synodic period illustrated in Fig. 2. The time-varying component of the during which Jupiter’s magnetic equator nods up and down field (whose contribution is principally in the radial direc- over Europa as the planet rotates. Table 2 (extracted from tion relative to Jupiter) drives an inductive response within Kivelson et al., 2004) lists additional key features of the Europa (Zimmer et al., 2000; Schilling et a.l, 2008), which plasma environment near Europa with values given as av- Kivelson et al.: Interaction with the Jovian Magnetosphere 547

Fig. 1. Galileo flyby trajectories in the EphiO coordinate system with x along the direction of corotation, y radially in to Jupiter, and z parallel to Jupiter’s spin axis. To the left, flybys E4–E14. To the right, E15–E26. None of the trajectories crossed over the polar regions. 548 Europa

3. MODELS OF THE INTERACTION BETWEEN EUROPA AND THE LOCAL PLASMA ENVIRONMENT

3.1. Magnetohydrodynamic Descriptions

Large-scale features of the interaction between the Eu- ropa and its plasma environment are most readily under- stood by treating the ionized ambient gas as a magnetohy- drodynamic (MHD) fluid. MHD is applicable if the length and timescales relevant to the interaction are long compared with the lengths and periods characteristic of single-particle motion in the environment. The radius of Europa is on the order of 1500 km, 2 orders of magnitude larger than the 8– 12-km gyroradi of the thermal ions; the period of ion cy- clotron motion is on the order of 2 s, short compared with Fig. 2. Top: From the Khurana (1997) model, the radial the 30-s time for plasma to flow across the diameter of the (dashed), θ (dash-dot), azimuthal (dotted) components of the mag- moon. Several MHD simulations of the interaction are now netic field and its magnitude (solid). Bottom: The dipole latitude available (Kabin et al., 1999; Liu et al., 2000; Schilling et (solid) and the centrifugal latitude (dashed) of Europa vs. west longitude over one Jupiter rotation period. In this longitude sys- tem, Europa’s position moves from large to small values.

erages and ranges. Dominant torus ions are low-charge states of iogenic sulfur and oxygen with a mean ion mass of 18.5 mp (mp is the mass of a proton) and a mean charge of 1.5 e. Despite the systematic temporal variations of the ambient plasma near Europa at the synodic period, the parameters of the external plasma environment can be con- sidered as stationary on the timescales of tens of minutes required for plasma to flow across Europa and its disturbed surroundings. Magnetized plasmas interact with a moon in several ways. On a large scale, electrically conducting material within or near the moon diverts the flow and perturbs plasma and field properties. Consequently, measurements made at different locations relative to the moon’s equator and from upstream to downstream relative to the flowing magnetospheric plasma are expected to reveal different aspects of the interaction. Furthermore, the conducting re- gion near the moon may vary with solar illumination, im- plying that aspects of the interaction may change with the spacecraft-moon-Sun angle. Data were acquired at differ- ent locations relative to both the flow direction and the spacecraft-moon-Sun angle near closest approach (c/a) on several low-altitude Galileo flybys indicated by the small triangles in Fig. 4 and identified more precisely in Table 1. By convention, latitude is measured relative to an axis par- allel to Jupiter’s spin axis and Europa longitude is measured from the Jupiter-facing meridian plane; in this paper lon- gitude (phi) is positive in the righthand sense. Closest ap- proach was less than 1000 km on only three passes and less than 2050 km on six passes for which full fields and par- ticle data were acquired. Four of the five relatively close Fig. 3. The electron number density inferred from the upper hy- passes approached Europa closely on the side upstream in brid resonance line in the plasma wave spectra for all Europa fly- the flow (or equivalently, trailing relative to orbital motion). bys. From Kurth et al. (2001). Kivelson et al.: Interaction with the Jovian Magnetosphere 549

TABLE 2. Properties of Europa’s field and plasma environment.

Symbol (units) Parameter

Bo(nT), jovian magnetic field, av. min (max) 370 (460) –3 ne(elns cm ), eln. density, eq. av. (range) 200 (18–250) 〈Z〉, ion charge, eq. av. (lobe) 1.5 (1.5) 〈A〉, ion mass in mp, eq. av. (lobe) 18.5 (17) –3 ni(ions cm ), ion number density, av. (range) 130 (12–170) ρ –3 m(amu cm ), ion mass density, av. (range) 2500 (200–3000) kTi(eV), ion temperature, equator (range) 100 (50–400) kTe(eV), electron temperature 100 pi,th(nPa), pressure thermal plasma, eq. (range) 2.1 (0.10–11) pi,en(nPa), pressure of 20 keV–100 MeV ions 12 pe(nPa), pressure of “cold” and “hot” electrons 2.4 p(nPa), total pressure, eq. (max) 17 (26) –1 vcr(km s ), local corotation velocity 117 –1 vs(km s ), satellite orbital velocity 14 vϕ(km s–1) plasma azimuthal vel. (range) 90 (70–100) u(km s–1), plasma velocity relative to Europa av. (range) 76 (56–86) –1 vA(km s ), Alfvén speed, eq. (range) 160 (145–700) –1 cs(km s ), sound speed, eq. (range) 92 (76–330) 2 Bo/2µo(nPa), magnetic pressure, eq. (lobe) 54 (84) ρu2(nPa), ram pressure, eq. av. (max) 24 (38) ρu2(nPa), lobe ram pressure 2.5

4 14 12

11

26 19

Fig. 4. Location of Europa relative to Jupiter and the Sun for Galileo encounters approaching 2050 km or less above the surface. Numbers identify the Galileo orbit for each flyby. The arrow shows the sense of corotational plasma flow. Triangles identify the location of closest approach. 550 Europa

Fig. 5. See Plate 27. Observed and modeled magnetic field for the E4 flyby. Red = measurements of Kivelson et al. (1997); dashed black = modeled field with no internally induced field; Blue, green, and black = modeled field including induction in a 100-km-thick ocean lying beneath a crust of 25 km for ocean conductivities of 100, 250, and 500 mS m–1, respectively. From Schilling et al. (2007).

al., 2007, 2008). Only Schilling et al. (2007, 2008) model theory of perturbations of a magnetized fluid and the as- the time variation of the system and calculate the induced sumption that there is a region of electrical conductivity at field by introducing the concept of a “virtual plasma” in- and near Europa. In Europa’s frame, the flowing plasma ternal to Europa. It is difficult to assess how this approxi- imposes an electric field, E = –u × B, where u is the flow mate treatment of the induced field modifies the outcome speed relative to Europa and B is the magnetic field. Al- of the calculations, but the signatures along the E4 trajec- though there may be regions of ionospheric conductivity tory capture some key features of the measured magnetic close to the moon (Kliore et al., 1997), the dominant con- field (Kivelson et al., 1992) as seen in Fig. 5. ductivity arises from ionization of neutrals liberated by Common to the simulation results are aspects of the in- sputtering (see chapters by Johnson et al. and McGrath et teraction that can be deduced qualitatively from the linear al.). When a neutral particle is ionized in a flowing plasma, Kivelson et al.: Interaction with the Jovian Magnetosphere 551

the newly freed ion and electron are accelerated in oppo- the context of the Io interaction by Southwood et al. (1980) site directions by the flow electric field, creating a transient and by Neubauer (1980) and is illustrated in Fig. 6. In this current aligned with E. The conductivity, σ, can be inferred figure, one sees the field tilted by the interaction to form from σ = |j/E|. Interactions are mediated by the three basic the Alfvén wings, and one can also infer that a portion of wave modes of the system, two of which are compressional the upstream flow (and the flux tubes that thread this por- (fast and slow waves) and one (the intermediate or shear tion of the flow) flows around the moon instead of flowing Alfvén wave) noncompressional (e.g., Kivelson, 1995). onto it. From Table 2 it follows that, in Europa’s rest frame, the If an internal induced field is present, the symmetry of velocity of the magnetospheric plasma is slow compared the Alfvén wings in the direction radial to Jupiter is bro- with the nominal Alfvén speed and the fast magnetosonic ken; the Alfvén wings are displaced inward (toward Jupi- speed. This implies that no shock forms upstream of the ter) in one hemisphere and outward in the other (Neubauer, interaction region, but instead the incident flow is slowed 1999). Downstream of Europa, further Alfvénic perturba- by the action of fast magnetosonic signals. The slowing of tions act to restore the field to its unperturbed orientation. the flow builds up a wedge of magnetic and thermal pres- Interaction with the moon reduces the plasma pressure in sure upstream of the obstacle that diverts some of the inci- the downstream wake. The pressure is restored by compres- dent flow. The flow slows first where unperturbed stream- sional slow mode perturbations (in which thermal and mag- lines impact the moon. With the magnetic field frozen into netic pressure are in antiphase). the plasma, the slowing in one portion of the flux tube while The overall picture of the flow and field that we have remote regions continue in unperturbed motion imposes a described are clearly evident in Fig. 7, reproduced from the kink (or curl) in the background field, which implies that simulation of Schilling et al. (2008). In their simulation, the ∇ currents are present ( × B = µoj where j is the current den- flow is directed toward positive x and the uniform back- sity). The kink propagates both up and down the field at ground magnetic field is in the z direction. In Fig. 7a one the Alfvén speed, carried by an Alfvén wave, the only MHD sees the flow slowing (light color) as it approaches the wave mode that carries field-aligned current (j||). Thus, to moon. The diverted flow experiences a Bernoulli effect and lowest order, the plasma is modified by the presence of a speeds up along the flanks (dark color). For x > 1, there spherical obstacle not merely in the immediately surround- is a narrow region in the wake of the moon where plasma ing regions but along a pair of tilted cylinders extending to refilling flux tubes that have interacted with the moon is the north and south. The disturbed regions, bounded by compressed and flow is very slow. In Fig. 7b the Alfvén characteristics of the Alfvén wave, are referred to as Alfvén wing structure is apparent, with the perturbed flow region wings. If the plasma flow is perpendicular to the back- bent back along the flow direction as described. The flow θ ground field, B, the angle, A, by which the characteristics is extremely slow not only in the z = 0 plane but in other are rotated from plus or minus the background field can be planes at constant z (not shown) where the plasma diverts expressed in terms of the Alfvén Mach number of the flow, around a region whose center shifts toward x > 0 as z in- θ –1 MA, as A = tan MA (Neubauer, 1980; Southwood et al., creases. Thus it is not only the moon that perturbs the flow, 1980). MA = u/vA is defined in terms of u and vA = B/ but also its associated pair of tilted Alfvén wing cylinders. ρ 1/2 ρ (µo ) , the Alfvén speed; here is the mass density. The Figure 7c shows the pileup of field in the upstream region general structure of the interaction region was described in of slowed flow. This represents the effect of the fast mode perturbation described. Also evident in Fig. 7c is the change of field orientation imposed by the Alfvén waves whose characteristics bound the Alfvén wings. The upstream field can be significantly tilted relative to the flow, and this implies that the flow has a component along the background field as well as across the field, which introduces some north-south asymmetry into the solutions. The assumption common to all simulations available is that the background magnetic field is uniform on the scale on the order of a few RE (1 RE = the radius of Europa, 1560 km) near Europa. This approximation is good at the 10% level.

3.2. Ion Pickup

Fig. 6. Structure of the interaction region near a conducting The conductivity of the moon’s environment is critical moon. On the left, in the plane containing the field and the un- in controlling the streamlines of the flow onto and around perturbed flow velocity. On the right, a cut through the center of the moon in the plane normal to the unperturbed flow. In this the surface. Electric currents can flow in Europa’s iono- schematic, Jupiter is to the right and only flux tubes lying between sphere, whose properties vary with solar illumination and the two dark curves with arrows showing the direction of field- with the plasma properties of the surroundings. Europa’s aligned current flow actually encounter the moon. Other flux tubes surface and transient atmosphere are continually bombarded drape around it. Adapted from Southwood et al. (1980). by magnetospheric charged particles that sputter neutrals 552 Europa

tor ~20 (~60). When first ionized, the ions are, on average, at rest relative to Europa. They must be accelerated to full corotation, a process that creates a drag on the magnetic field lines in addition to the drag of the conducting body and its ionosphere. As mentioned previously, the drag is greatest at the location on the field line where the flux tubes pass closest to Europa. The differential slowing of differ- ent points along a field line bends the field as shown Fig. 7b. The bend-back displays itself through a rotation of the field from the z into the x direction. The amount of bend-back is related to the amount of ionization occurring near the moon, which, in turn, varies with the moon’s distance from the center of the jovian plasma torus. The kinked field acts to reaccelerate the plasma through the magnetic curvature force. Instead of describing the curvature of flux tubes, one can describe the phenomenology in terms of the currents gen- erated. Newly liberated charged particles are accelerated by the electric field of the flowing plasma in which they are embedded. The new ions, referred to as “pickup ions,” cre- ate a pickup current density, jpu, given by ρ jpu = eni L = miniu/B (1) . Here e is the magnitude of the electron charge, ni is the ρ number density of new ions introduced per second, L = umi/ eB, is the ion Larmor radius of a typical ion of mass mi in a magnetic field, B, and u is the flow speed. The require- ment that current density be divergenceless (∇ · j = 0) re- quires the pickup current to close through field-aligned currents (flowing toward Europa’s orbit on the side closer to Jupiter and away from it on the other side). The pairs of field-aligned currents produce magnetic perturbations that bend the field below the moon toward the flow direction and above the moon toward the opposite direction (–u), thus producing the previously described Alfvén wing structure. In this description, it is the Lorentz force, jpu × B, rather than a curvature force that accelerates the slowed plasma. In a later section, we show examples of passes on which the magnetic perturbations are consistent with generation by pickup currents for reasonable estimates of the quanti- ties that appear in equation (1). It is now clear that coupling between the local region and the more distant parts of the flux tube is central to im- posing the form of the field and the flow near Europa. In Fig. 7. See Plate 28. The flow speed (a) in the x–y plane, (b) in turn, the flow patterns in the vicinity of the moon are con- the x–z plane, and (c) the magnetic field in the x–z plane. Dashed trolled by the combined effects of the conductivity in the lines represent boundaries of the northern and southern Alfvén wings. From the MHD simulation of Schilling et al. (2008). immediate neighborhood of the moon and properties of the background plasma. Neubauer (1998) showed that the con- ductivity of the ionosphere and of the pickup ions can be from the surface (see chapter by Johnson et al.). Those lumped together by defining a generalized Pedersen con- Σ neutrals are widely distributed near Europa. The neutrals ductance, for which we use the symbol P and, for the serve as a source of new ions as discussed relative to inter- purpose of estimates, assume to be constant over a radial δ δ actions near Io by Goertz (1980). Table 3 of Luna et al. distance (1 + ) RE around Europa, where an increment (2005) analyzes the processes that produce ions near Eu- accounts for the region of strong pickup. ropa. Electron impact dominates, with a production rate ex- In order to understand surface sputtering, one needs to ceeding that of charge-exchange (photoionization) by a fac- consider the flux tubes that actually encounter the moon and Kivelson et al.: Interaction with the Jovian Magnetosphere 553

give energetic particles access to the surface. Not all the flux tubes in the unperturbed plasma on streamlines directed δ toward the 2(1 + ) RE width of the conducting region near Europa actually intercept that cross section because stream- lines diverge as shown in Fig. 7a. The fraction (1 – f) of the upstream fluid that flows into the region of width 2(1 + δ ) RE depends on the Alfvén conductance of the unperturbed Σ –1/2 plasma, A = (µovA) (Neubauer, 1980; Southwood et al., Σ 1980) and on P according to the relation Σ Σ Σ f = P/( P + 2 A)(2) where f is the fraction of the incident flow that avoids the Σ Σ obstacle. In the limit P >> A, none of the upstream flow reaches the surface, whereas all of the flow reaches the surface if the local conductance vanishes. In Europa’s case, Σ Σ both P and A are in the range of a few to tens of Siemens –1 Σ ≈ (1 S = 1 amp volt ), whereas A 6S using the nominal vA from Table 2, so some of the flow is diverted but some reaches the surface. The values of both conductances Fig. 8. Lines of equal electric potential or streamlines of elec- change with Europa’s position in the torus because both tron flow. The spacing between the lines is proportional to the flow increase as the plasma density increases. Streamlines ob- speed. About 20% of the upstream plasma encounters Europa in tained from simulations can, in principle, provide insight this model, and the flow speed drops to about 25% of the inci- into the way in which the response varies as local condi- dent flow speed. From Saur et al. (1998). tions change, but it is important to remember that the spe- cifics of the solutions are extremely sensitive to assumed one may imagine that any particle that reaches Europa’s internal boundary conditions. Conclusions extracted from surface is lost. In this case, connection with Europa imme- simulations are instructive but should be viewed with abun- diately removes all the particles arriving from the opposite dant skepticism. hemisphere. To the north of Europa, particles that are mov- ing downward are absorbed, whereas those moving upward 3.3. Beyond Magnetohydrodynamics continue unaffected, are reflected at a mirror point, and move downward, after which they are absorbed. Thus af- Close to the moon, corrections for multifluid phenomena ter half a bounce period, most of the particles initially on a are relevant in understanding some features of the interac- flux tube linked to Europa are gone. The bounce period is tion and various models have examined the interaction using energy dependent but scales as (W/m)1/2, where W is the approaches that deal with the complexity of the plasma and particle thermal energy and m is its mass. Imagine that the its interaction with Europa’s atmosphere while accepting a bulk of the plasma mirrors within, let us say, 2.5 RJ of the non-self-consistent treatment of the perturbations of the equator. Then the relevant timescale for emptying the flux magnetic field (e.g., Saur et al., 1998). Streamlines from tube is this solution appear in Fig. 8. As in the MHD treatment, the ≈ 1/2 1/2 conductivity of the region surrounding Europa impedes or Tb 5RJ/(W/m) = 30s[m(me)/W(keV)] diverts the plasma flow, allowing only about 20% of the upstream plasma to reach the surface of Europa. The di- This implies that the flux tube is depleted of keV electrons version of the flow was clearly observed on Galileo passes well before it reaches the downstream side of the polar cap. upstream and on the flanks of the interaction region (Pater- Protons of similar energy persist in the flux tube 40 times son et al., 1999). longer and heavy ions continue to reach the surface even Other aspects of the interaction are illustrated in Fig. 8. longer. Thus, it is easy to accept the conclusion of Paranicas The streamlines twist inward toward Jupiter as they move et al. (2002) that ion bombardment is relatively uniform across the polar cap, a consequence of the Hall conductance across the surface of Europa but electron sputtering is lo- of the ionosphere. Flux tubes that encounter Europa are calized to Europa’s trailing hemisphere (upstream in the slowed in their flow (to about 25% of the unperturbed flow flow). (More precise analysis takes into account the fact that speed), but continue to drift on average in the direction of drift paths of energetic particles are modified by gradients the corotation flow. Let us assume that the flow speed is in the locally perturbed magnetic configuration, as well as reduced to 10 km s–1, implying that it takes on the order of finite gyroradius effects.) The bombardment of Europa by 5 min for a flux tube to flow across the polar cap. Within the energetic particles lost from the plasma has consequences the flux tubes that pass through Europa, the plasma char- for the structure of surface ice (Paranicas et al., 2000, 2001, acteristics are markedly modified. In the simplest picture, 2002; see also chapter by Paranicas et al.). 554 Europa

In analysis of particle access to Europa’s surface, one Pass E12 is more complicated. Downstream of Europa, additional matter should be considered. In addition to the the field is again well represented by the Khurana (1997) flux tube content and the flow patterns, the geometry of the model, and the electron density decreases to a nominal intersection between the flux tube and the surface also af- 100 cm–3, which appears to be typical of measurements fect the flux per unit area on different parts of Europa’s sur- remote from closest approach on several of the passes (Kurth face. None of the Galileo passes crossed the polar regions, et al., 2001; Paterson et al., 1999). However, in the upstream so one must rely on inference and theory to describe par- portion of the pass, the electron density is exceptionally ticle access to different parts of the surface. One thing is high (~900 cm–3). The very high density can be attributed clear: For a uniform field aligned with Europa’s spin axis, in part to Europa’s location between the centrifugal and flux tubes of unit magnetic flux have constant cross-sec- magnetic equators, where the background density is high- tion areas, but the areas on Europa’s surface intercepted by est. The magnetic field is also unusually large; somewhat the flux tubes vary with latitude (λ) as 1 + cosλ. This im- upstream of Europa the field magnitude reaches 825 nT, a plies that flux tubes carrying constant electron flux deliver level almost double the nominal background. As local fewer electrons per unit area to the near-equatorial surface pickup would slow the flow and correspondingly increase than to the polar regions. This effect contributes to the varia- the magnitude of the magnetic field, it seems probable that tion of sputtering across the surface of Europa. In particu- local ionization contributes significantly to the anomalously lar, sputtering by electrons is thereby somewhat reduced in high electron density and that ionization becomes increas- the upstream, low-latitude regions where the flux tubes are ingly significant as the trajectory moves closer to Europa still full of energetic electrons, although the compression (see Fig. 3). of the field in the upstream region counters the geometric The combination of high density and large B can arise effect. The regions of most intense sputtering should not if ion pickup rates are high. Let us assume that the mass vary significantly as the magnetospheric field rocks back and average charge of the ions added locally is the same as and forth over a synodic jovian rotation period because the that of the background (Table 2), implying that the ion num- variations of the external field are largely nullified by the ber density is 0.7 ne. Here we distinguish between pickup, internally induced field. which adds ions to the plasma, and charge exchange, which does not. Like pickup, which adds new ions that must be 4. UPSTREAM accelerated, charge exchange slows the flow because it re- places a moving ion with an ion at rest and this replace- Table 1 lists several upstream Galileo passes (E12, E14, ment ion must be accelerated to the bulk flow speed. It does E19) with their trajectories illustrated in Fig. 1. The E12 not change the ion density because one ion is lost for each pass is of special interest because it encountered Europa ion added. All of the processes increase the field magnitude. when it was located near the (N–S) center of the torus. On Each ion added to the flow acquires a thermal speed and a this pass, the plasma density was substantially larger than gyrocenter speed equal to that of the background plasma. on other passes (see Fig. 3, noting that the scale shifts for At Europa’s orbit, the nominal thermal speed exceeds the –3 different passes and that ne on E12 exceeds 900 cm shortly flow speed, so pickup cools the plasma. As the flow slows, before closest approach, whereas it remains below 200 cm–3 the field magnitude increases. Energy conservation requires on the other two passes). Figure 9 shows the magnetic field the flow kinetic energy of the bulk plasma to decrease by 2 signature for these upstream passes: E12 (closest approach miu for each new ion added, so the bulk flow speed de- 196 km), E14 (closest approach 1649 km), and E19 (clos- creases. (Here we ignore contributions to plasma accelera- est approach 1444 km). The magnetic field perturbations tion imposed by currents connecting the equatorial plasma within ~3 RE of Europa differ markedly on these passes. to Jupiter over times relevant to the interaction.) On passes E14 and E19 in regions beyond ~4 RE from Upstream of Europa on E12, the field magnitude is mod- Europa, the magnetic field is well described by the Khurana ulated by nearly periodic (~3 min) structures in which the (1997) model. [Other models such as those of Khurana and field magnitude decreases and then increases abruptly (Rus- Schwarzl (2005) and Alexeev and Belenkaya (2005) do not sell, 2005). Although it is not possible to establish whether noticably modify field values in the inner magnetosphere.] these variations are spatial or temporal structures, the forms The electron density, on the order of 100 cm–3 or less and have the appearance of periodic pressure pulses propagat- close to constant from Fig. 3, is also nominal. Near closest ing upstream with a steep forward edge followed by a re- approach, on E19 the density rises to ~200 cm–3, suggest- laxation. Pressure pulses would slow the flow and account ing that local effects roughly double the density. At the same for the increases of field magnitude. Localized slowing time the increase of field magnitude to a maximum of bends the field and the curvature exerts a force like that of 481 nT (or 32 nT above the model background field) is a bow string under tension. The curvature force reacceler- consistent with some slowing of the flow. Similar changes ates the plasma and reduces the field magnitude. The 3-min of field magnitude upstream of Europa, consistent with recurrence of the pulses has no evident relation to natural increased density, are observed on E14 although no asso- periods of the interaction and remains a puzzle. ciated density increase is identified by the PWS measure- Although some of the periodic field increases that were ments (Fig. 3). measured upstream of Europa on E12 are pulse-like, the Kivelson et al.: Interaction with the Jovian Magnetosphere 555 . (d) E19 upstream flybys of Europa, very near the center of the plasma sheet. Solid lines = data, dashed = data, near the center of plasma sheet. Solid lines very E19 upstream flybys of Europa, (c) E14, and (b) E12, (a) 1997). A shock-like structure in the field magnitude at 11:51 UT on Dec. 16, 1997 is shown expanded in expanded magnitude at 11:51 UT on Dec. 16, 1997 is shown A shock-like structure in the field 1997). Khurana, Magnetic field (EphiB coordinates) for Galileo’s for Galileo’s (EphiB coordinates) Magnetic field lines = model background ( lines Fig. 9. Fig. 556 Europa sudden increase of field magnitude at 11:51 UT is suffi- dense plasma encountered on this pass, it is also possible that ciently abrupt that it may be a shock. The jump occurs in illumination of the atmosphere on Europa’s upstream side ~4 s, consistent with a thickness of a few ion gyroradii. As- also contributes (see chapter by McGrath et al.). suming that the background plasma has cooled through pickup and that the thermal velocity is small, one can set 5. THE WAKE REGION the fast magnetosonic speed to the Alfvén speed (vA), –3 which, with B = 480 nT, ni = 600 cm , and mi = 20 mp (mp A wake develops downstream of an obstacle in a flow- is the mass of a proton), is 96 km s–1. The field magnitude ing fluid, whether hydrodynamic or magnetohydrodynamic. at 11:51 UT exceeds background by only ~20%, implying One of the earliest scientific sketches of such a region in a that the flow has not yet slowed substantially (there are no fluid flow was made by Leonardo da Vinci (see Fig. 10). published flow estimates for this pass). Table 1 provides a Europa’s wake lies on its leading side, ahead of the moon range of 56–86 km s–1 for u, but the ranges of Table 1 are in its orbital motion, as described above. In this section we not limits as evident from the fact that the E12 electron discuss wake structure and describe some features of the density of 900 cm–3 falls well outside the listed range of wake region, including flux tubes with anomalous plasma 18–250 cm–3. It is then possible to suppose that the excep- content, pickup ions, and nonuniform distribution of ener- tionally high densities of this pass reduced the Alfvén speed getic ions. below the flow speed in portions of the region upstream of Five Galileo passes crossed the Europa wake but full Europa. When this happened, the pressure pulses steepened particles and fields data are available for only four of them. to form weak shocks behind which the flow slowed, caus- The E4, E11, E15, and E17 flybys encountered Europa in ing the field to build up further before reacceleration of the differing locations in the torus (see Fig. 2). Passes E4 and flow decreased it once again. E11 occurred when Europa was at relatively high magnetic The exceptionally high plasma density within a few RE latitude, moving toward the (N–S) center of the torus for of Europa on E12 calls for a local source of pickup ions. E4 and exiting it for E11. For E15 (and E17) Europa was Recognizing that pickup slows the flow and increases the in (or relatively near) the center of the plasma torus. This field magnitude, one can confirm that this interpretation is means that plasma responses sensitive to ambient plasma self-consistent. We estimate jpu by assuming that the rate conditions may differ from pass to pass. of addition of new ions near Europa is 10% of that near Io, Before examining the wake data, we introduce the co- –1 3 i.e., ~100 kg s in a volume on the order of (3 RE) . If the ordinate systems used, acknowledging that only those pickup current flows across a surface of extent ~2 RE along immersed deeply in the study of magnetic fields become the upstream flow, then from equation (1) and Ampere’s greatly enamored of coordinate systems. One can separate law, the expected change of B, ΔB, is ~600 nT, roughly in out some of the effects of the tilt of the background field the range observed. Although it seems probable that the by an appropriate choice of coordinates. Two systems use- exceptionally large pickup rate is caused by the unusually ful for the analysis of the field observed near Europa (Kivel-

Fig. 10. A sketch from Leonardo da Vinci showing the water flow around and in the wake of an obstacle. Kivelson et al.: Interaction with the Jovian Magnetosphere 557

son et al., 1992) are both Europa-centered, with x along yEphiB). However, the passes plotted in Fig. 11 show distinct the background flow. In the EphiO coordinate system, z is asymmetry of the magnetic signatures across the wake. What aligned with Europa’s spin axis, yˆ = zˆ × xˆ is positive toward are the processes that introduce asymmetry across the flow Jupiter, and the background field has nonvanishing x and direction? One must distinguish between intrinsic asymme- y components. In the EphiB coordinate system, yˆ = (–B/ try and asymmetry because the spacecraft trajectories are B) × xˆ (again positive toward Jupiter), zˆ = xˆ × yˆ, and the not parallel to the yEphiB axis. This means that any analysis field lies in the x–z plane. When this latter system is used should be based on actual trajectories applied to models of to analyze data near Europa it is referenced to the field the underlying asymmetry. orientation at closest approach. Thus, the y component of Neubauer (1999) showed that an inductive field such as the field vanishes at closest approach and remains relatively that identified at Europa (Kivelson et al., 1999; Zimmer et small in the near vicinity of Europa. However, a finite al., 2000) displaces and shrinks the Alfvén wing and modi- x component along the flow is not removed and can be on fies the wake symmetry as illustrated in Fig. 12. Recogniz- the order of 20% of the field magnitude. ing that an inductive response acts to exclude the time-vary- The magnetic field data for the wake crossings are shown ing part of the magnetospheric magnetic field from the in Fig. 11 in EphiB coordinates. In the panels, the geomet- interior of Europa, the fractional reduction in scale of the ric wake limits are shown. The geometric wake extends over Alfvén wing and/or of the wake in the y direction (S) can be ≤ ≤ the region –1 y 1 RE. In the EphiB system, one might estimated as anticipate symmetry about y = 0, so departures from such B symmetry are of interest and the data are not symmetric S ≈ z (3) about the wake center. Part of the asymmetry must result |B| from the changes in downstream distance as Galileo crossed where Bz is measured in the EphiO coordinate system. In- the wake (see Fig. 1). Other contributions to the asymme- deed, this estimate, as well as the predicted displacements of try of the wake are discussed below. Alfvén-wing-related structures, has been verified in Galileo Characteristic of the wake region is the “bend-back” of observations (Volwerk et al., 2007) for a number of passes the magnetic field associated with the Alfvén wing, de- including E17 (see Fig. 11). scribed in section 3. Much of the bendback arises through Additional asymmetries in the radial direction can be interaction with pickup currents whose magnitudes decrease introduced through ionospheric effects. In an analysis of the as Europa moves away from the center of the torus. Be- Io interaction, Saur et al. (1999) showed that the Hall con- cause of the north-south symmetry of the Alfvén wings, the ductance of the ionosphere twists the electric field from bend-back is most evident on wake passes at |zEphiB| > 1 RE radially outward toward the direction of corotation through as, for example, in Fig. 11d. Different degrees of bend-back an angle in the data shown in Fig. 11 are plausibly accounted for by Σ a combination of the different values of |zEphiB| and the dif- θ H twist = Σ Σ (4) ferent plasma density and associated pickup densities as- P + 2 A sociated with the location of Europa relative to the dense Σ center of the plasma torus. The E4 and E11 passes occurred in terms of H, the Hall conductance of Io’s ionosphere, and well away from the center of the torus. Bend-back is diffi- the Pedersen and Alfvén conductances previously defined. cult to assess for E4, which entered the wake region at small Correspondingly, the flow velocity (E × B)/B2 twists from |zEphiB|. The signature is further obscured by the significant azimuthal toward Jupiter through the same angle. inductive field signature, but it appears to be small except Europa was located at the center of the plasma torus for over a very narrow region in the center of the wake. On the E15 pass. At this location, the induced field should have E11, the wake crossing was relatively distant but the nega- been very small so asymmetry of the wake signature must tive excursion of the Bx component near the central por- have resulted from other mechanisms such as the twisted tion of the wake is consistent with weak bend-back. Bend- electric field that we have discussed above (Saur et al., back produces a negative perturbation in Bx for zEphiB > 0 1999) or asymmetries of energetic particle fluxes (discussed θ and a positive perturbation in Bx for zEphiB < 0. Thus, the below). In order to estimate twist, values of the Pederson, perturbations of Bx in the geometric wake on passes E15 Hall, and Alfvén conductances are needed. Saur et al. (1998, and E17, which encountered Europa relatively near the cen- Figs. 5 and 6) find that the Pederson conductivity dominates Σ ≈ Σ ≈ ter of the torus at zEphiB > 0 and < 0, respectively, appear the Hall conductivity, with typical values H 1 s and P Σ to arise from bend-back. 10 S. A can be obtained from measurements. A character- –1 istic value of vA is ~160 km s (Table 2), which implies an θ ≈ 5.1. Wake Asymmetry Alfvén conductance of approximately 5 S. Thus, twist 0.05 rad (= 3°) rotated from radially outward into the plasma The interaction of Europa with the jovian magnetosphere flow direction. According to the predictions of equation (4), produces naturally an upstream-downstream asymmetry as the ions should be only slightly deflected by this twist angle evident from the MHD analysis, but to lowest order one in the direction away from Jupiter. Such a small deviation might expect symmetry across the flow direction (i.e., in in thermal and pickup plasma density cannot be inferred 558 Europa 7 with 24-s samples) are plotted as solid lines. = 0.

1) lies between the gray markers and a solid line shows y and a solid line shows 1) lies between the gray markers ≤ y ≤ The magnetic field data for Galileo’s wake crossings E4, E11, E15, and E17 in EPhiB coordinates. Data (0.33-s samples except E1 crossings E4, wake data for Galileo’s The magnetic field Fig. 11. The background magnetic is plotted with a dashed line. The wake (–1 wake The magnetic is plotted with a dashed line.The background Kivelson et al.: Interaction with the Jovian Magnetosphere 559

Fig. 12. Schematics of Alfvén wings and associated current systems showing how induction effects introduce asymmetries by shift- ing the northern and southern wings in opposite directions and simultaneously reducing their cross section areas. The successive im- ages represent forms associated with a rotation period from north through the equator to south and return. (Here the field rotations approximate those at Callisto. The rotation angles would be smaller at Europa.) From Fig. 7 of Neubauer (1999).

from the data, but the estimated conductances could be asymmetry of the chemistry of the surface imposed by the incorrect, implying that larger twists may be imposed. How- reimplanted ions (see chapter by Carlson et al.). ever, although flow paths across the polar cap are modi- The issue of wake asymmetry has been discussed in con- fied by the Hall conductance, Fig. 8 shows that near the z = nection with simulations of the Europa interaction. Kabin 0 plane, the wake is little skewed. et al. (1999, their Fig. 10) modeled the interaction for the Some of the wake asymmetry may arise because the fate conditions of the E4 flyby. Liu et al. (2000) also modeled of heavy ions newly picked up in the flowing plasma differs the E4 flyby. This pass was not ideal for tests of asymme- on the two sides of Europa. The corotation electric field in tries because it occurred relatively far above the center of Europa’s frame accelerates newly ionized positive ions out- the torus and thus contains a strong inductive signature. ward from Jupiter. Consequently, some of the ions picked Kabin et al. (1999) had to assume that the incident velocity up on the subjovian side immediately impact Europa’s sur- deviated by 20º from azimuthal in order to obtain reason- face and are lost to the plasma, thus reducing the total mass able agreement with the observations; Paterson et al. (1999) loading on that side. On the antijovian side, outward accel- reported that flows deviated from corotation during the E4 eration does not lead to impact. encounter with Europa. Prior to closest approach, the flow The ion loss through impact on the surface can be mod- deviated inward toward Jupiter (as inferred by Kabin et al., eled using a uniform, vertical magnetic field directed in the 1999) but was unsteady in direction. Thus, the expected negative z direction as appropriate for passes near the center orientation of the wake is somewhat uncertain in the simu- of the plasma torus. We assume that pickup of ions occurs lations and it seems possible that features other than the in a small region around Europa, with the rate of pickup flow direction may cause a rotation of the wake. decreasing with radial distance from the moon from n0 at N. Schilling (personal communication, 2008) observes 1.01 RE to 0.06 n0 in 10 concentric rings with widths of a gradient (in y) of the wake density at y = 0.5 RE, in simu- 0.01 RE. The magnetic field strength is 400 nT, and the lations of the E12 flyby for which Europa was located very pickup ions have mass 32 amu. The corotation electric field near the center of the plasma torus. Because Schilling uses accelerates the particles away from Jupiter, and the fresh an MHD code that does not include finite gyroradius ef- ions gyrate around the magnetic field with gyroradii (85 km) fects and the inductive field is small at the epoch of this determined by the pickup velocity, which is assumed to flyby, it seems possible that the wake asymmetry in his be 100 km s–1. The total pickup density in this two-dimen- simulation is a response to the Hall conductance (Saur et sional model is calculated in 0.25 × 0.25 RE bins across the al., 1999). However, Fig. 8 shows that although flow paths wake. The pickup density, plotted in Fig. 13, develops a across the polar cap are modified by the Hall conductance, clear asymmetry in the wake because of losses on the sub- near the z = 0 plane the wake is little skewed so the source jovian side. Near y = 0.6 RE there is a strong gradient in of the density asymmetry in the simulation is uncertain. density in y. Pass E15 near the center of the plasma torus (where induction does not introduce asymmetry) and rela- 5.2. Clues to Pickup Ion Composition from tively close to Europa’s equator (0.56 RE < zEphiB < 0.78 RE Waves in the Wake across the geometric wake) shows systematic negative Bx, consistent with bend-back that ends abruptly at yEphiB ~ Interestingly, on passes E11 and E15 the magnetic field 0.5 RE. It is possible that the change relates to the orbit, but fluctuates considerably through most of the geometrical if pickup ions dominate the plasma density in the wake wake, whereas on pass E4, high-frequency fluctuations region, the sharp rotation may be related to the density appear only in a limited region around y = 0. Data from gradient we propose from the model of Fig. 13. The model the E17 pass were acquired at a time resolution (24 s) that also suggests that one should look for a subjovian/antijovian is too low to resolve the high-frequency perturbations. Nu- 560 Europa

Fig. 13. See Plate 29. A simple model of the ion pickup around Europa, showing an abrupt decrease in density near y = 0.6. Den- sity units are arbitrary. merical modeling of the interaction of Europa and the jovian Ion cyclotron waves grow off the free energy in aniso- magnetosphere by Schilling et al. (2007, 2008), whose sim- tropic distributions of positive ions and are typically left- ulation assume E4 conditions, has shown that the enhanced hand polarized at frequencies below the ion gyrofrequency. density downstream of the moon is concentrated in a small Thus, wave analysis provides a tool for identifying the ions region of the wake. It is probable that the newly picked-up generating the waves. The magnetic field data are trans- ions are concentrated in this dense plasma region and that formed to a mean field aligned (MFA) coordinate system, it corresponds to the interval near the center of the wake where the mean field is determined by a low-pass filter (for where the field magnitude dips and high-frequency fluctua- periods longer than 5 min). From the transverse components tions are found. (Bν and Bρ) the lefthanded and righthanded polarized com- Newly picked-up ions form a ring distribution, i.e., par- ponents (BR = Bν + iBρ, BL = Bν – iBρ) are obtained and ticle velocities are distributed in a torus around the field power spectra can be produced separately for the two po- direction in velocity space. The Galileo plasma analyzer larizations. In Fig. 14 the dynamic spectra are shown for (PLS) observed such distributions both in heavy ions (prob- the lefthand and righthand polarized components of the ably oxygen) and lower-mass ions (probably protons) on wave power in the frequency band f < 0.5 Hz. The gyrof- passes E4 and E6 (Paterson et al., 1999). Similar velocity requencies of heavy ions and molecular ions in the back- space distributions were identified near Io (Frank and Pater- ground field of ~400 nT fall in this range (0.375 for O+ or ++ + + son, 2000, 2001). Such anisotropic distributions may be S , 0.1875 for S , and 0.0938 for SO2). inherently unstable to the generation of ion cyclotron waves. The ion source near Europa is an extended cloud of The magnetic perturbations produced by such waves have neutrals sputtered from the surface or the atmosphere. A been used to characterize the mass per unit charge of pickup number of elements have been identified on and around ions near Europa (Volwerk et al., 2001) and near Io (Hud- Europa. The Galileo Near-Infrared Mapping Spectrometer dleston et al., 1997, 1998). (NIMS) suggests that Mg is present on the surface (McCord Kivelson et al.: Interaction with the Jovian Magnetosphere 561

Fig. 14. See Plate 30. Dynamic spectra of the lefthand (top three panels) and righthand (lower three panels) polarized components of the magnetic field for E4, E11, and E15. + + + The white solid traces show the cyclotron frequencies for Na (A = 23), O2 (A = 32), K + + (A = 40), Cl (A = 35), and SO2 (A = 64). Vertical lines delimit the geometric wake.

et al., 1998; see chapter by Carlson et al.). Brown and Hill of these elements are possible constituents of the local (1996) observed a neutral Na cloud and Brown (2001) re- plasma. Further details on the properties of Europa’s atmo- ported that K was present in Europa’s atmosphere. Kargel sphere are provided by the chapter by McGrath et al. (1991) and Kargel et al. (2000) suggested that Cl would The power in the spectra of Fig. 14 is intermittently large be present on the surface and Küppers and Schneider (2000) at frequencies consistent with generation by ions of the found spectroscopic evidence supporting this proposal. Ions heavy elements suggested above. We assume that the back- 562 Europa

α ground plasma contains only low-energy particles of the with nα(ne) the density of -ions (electrons), qα(e) the same mass per unit charge as the newly ionized ions. For charge on an α-ion (electron), mα the mass of an α-ion, and this condition, waves grow fastest at frequencies just be- B the magnitude of the magnetic field. The introduction of low the ion cyclotron frequency of the pickup ions (Hud- a trace element in a plasma creates a crossover frequency. dleston et al., 1997). White lines have been added to the In a two-component plasma in which the fractional density dynamic spectra to identify the cyclotron frequencies of of the trace species (subscript o) is N, one finds + + + + Na (23 amu), O2 (32 amu), Cl (35 amu), K (39 amu), and SO+ (64 amu). There exist two stable isotopes of Cl at 35 2 2 N 1 – N ω and 37 amu; the trace in Fig. 14 relates to the 35-amu iso- + = 1, where z = X , κ Ω tope. Although some wave power extends through the full 1 – z 1 – z o (7) range of the spectrum, the most intense emission bands are Ω 2 and κ = o found near the cyclotron frequencies of the heaviest ions. Ω Spectral power is significantly larger in the lefthand polar- 1 ized component than in the righthand polarized component over much of the interval plotted. The wave power is most Solving for z, one finds intense in the spectrograms in and near the geometric wake for E11 and E15 but for E4 the wave power is less clearly 1 – κ z = 1 + N (8) limited to the wake region and may have multiple sources. κ The wave power is not continuous across the wake (Vol- werk et al., 2001). In the passes illustrated in Fig. 14, the In the multicomponent plasma, if N is small the crossover power is most intense in regions with depressed |B| (see frequencies are close to the gyrofrequencies of the trace ele- Fig. 11) where the plasma pressure, and possibly the den- ments, in this case Cl, Na, and K. Waves traveling through sity, are higher than in the surroundings. Volwerk et al. used a medium in which there are gradients in composition and/ ω spectral analysis to establish the propagation direction of or magnetic field strength can cross X and reverse polar- + the O2 cyclotron waves and found that during the intervals ization. Petkaki and Dougherty (2001) observed this phe- of enhanced power the waves appeared to originate near nomenon in Jupiter’s middle magnetosphere. the surface of the moon. Tracing the wave paths back from 5.2.2. Negatively charged chlorine. Chlorine has a par- successive locations along Galileo’s orbit (see their Fig. 7), ticularly strong electron affinity: –3.5 × 105 J mol–1, which they found that only the regions of intense emissions could suggests that Cl– can be stable for a finite time in Europa’s be mapped back along ray paths to what is plausibly a sig- exosphere and wake region. For example, in the Earth’s D nificant pickup region. layer at 70 km altitude, Cl is the most abundant negative Ion cyclotron waves are typically lefthand polarized. ion (Turco, 1977; Kopp and Fritzenwaller, 1997). The chem- Figure 14 enables us to compare the power in lefthand and istry in the Earth’s D layer is driven by HCl, which could righthand polarized waves. Although power in the lefthand conceivably also be present in the europan atmosphere and polarized waves is larger in most of the frequency-time ionosphere. Negatively charged ions gyrate in the righthand range shown, there are intervals where the righthand po- sense around the magnetic field. Chlorine has been identi- larized wave is dominant. This happens in E11 at the Cl fied in the torus by Russell and Kivelson (2001) in the mag- cyclotron frequency between 20:65 and 20:70 UT, where netometer data near Io. Fegley and Zolotov (2000) suggested the power in the righthand component is much stronger than from looking at the chemistry of Io’s volcanic gases that that in the lefthand component. Righthand polarization can negatively charged Cl is a component of the torus. The pick- be caused by pickup of negatively charged chlorine Cl– but up of both Cl+ and Cl– would account for the polarization it is also possible to generate righthand polarized waves in reversals that are observed, with the most of the wave power a multicomponent plasma passing through the crossover polarized in the lefthand sense in regions dominated by Cl+ frequency. We examine these two possibilities starting with but with a reversal of polarization where Cl– dominates. the latter. Either mechanism described above can account for 5.2.1. The crossover frequency. In a multicomponent polarization reversals near the gyrofrequency of Cl. Fig- ω plasma one defines the crossover frequency X (see, e.g., ure 15 shows details of the polarization reversals. On the Melrose, 1986, chapter 12.3; Petkaki and Dougherty, 2001) E11 pass, the polarization becomes relatively linear through from the relation the polarization reversals (Fig. 15, left column), but on E15 (Fig. 15, right column) the waves remain circularly polar- Nα ized. These features are consistent with transitions across ∑ = 1 (5) ω Ω 2 α 1 – ( X/ α) the crossover frequency. However, polarization reversals are absent for emissions near the gyrofrequencies of other trace where Nα is the fractional ion density of species α and Ωα elements such as Na and K. Noting that Cl differs from the is the gyrofrequency given by other trace ions in its strong affinity for negatively charged ions and that reversed polarization is observed only near nαqα qαB Nα =,Ωα = (6) the gyrofrequency of Cl ions, we think it most likely that ene mα Kivelson et al.: Interaction with the Jovian Magnetosphere 563

Fig. 15. Hodograms of the magnetic field for E11 (left) and E15 (right) for two short intervals where there are several reversals of the polarization direction of the waves. The data are band-passed filtered around the gyrofrequency of singly charged chlorine.

the polarization reversal indicates that there is a significant The EPD flux drops when Galileo was near and within trace population of negative Cl ions. the geometrical wake (bounded by the vertical lines in Fig. 16). However, losses differ from one channel to an- 5.3. Energetic Particles in the Wake other. It would be expected that the most energetic particles would be absorbed most effectively by the moon. Electrons The losses of energetic particles in flux tubes flowing should disappear first; a weaker signature would be ex- over Europa’s polar cap were discussed in sections 3.3 and pected for ions. For losses depending on the gyroradius of 5.1, where it was noted that the bounce times for electrons the particles; the signature in the ion flux might be larger and very energetic ions are sufficiently short that one can than in the electron flux. expect that flux tubes will be partially emptied as they flow The analysis of wake signatures is complicated by chang- across the moon. The signature of the loss should be evi- ing values of zEphiB and downtail distance as the spacecraft dent in the energetic particle detector (EPD) data (Williams crosses the wake. Decreases of energetic particle fluxes tend et al., 1992). In Fig. 16, the data for the following EPD to appear abruptly when the wake entry is relatively close channels are shown: F2 electron channel at 304–527 keV; to Europa, but gradients become less steep with increasing F3 electron channel at 527–844 keV; A5 total ion channel distance down the wake. Specifically, the plots reveal some (H, He, O, S, etc.) for protons at 515–825 keV (higher for of the following behavior. other species); and O2 a “pure” oxygen channel (with some E4: The flux of perpendicular electrons decreases S contamination) at 26–51 keV per nucleon. The data abruptly near closest approach, before Galileo enters shown in Fig. 16 apply to different ranges of pitch angles, the wake. The decrease occurs in a region where α: per-pendicular with 85° ≤ α ≤ 95°, and (anti)parallel the total electron density (lowest panel in Fig. 16) with (160° ≤ α ≤ 180°) 0° ≤ α ≤ 20°. increases. After the spacecraft enters the wake, it 564 Europa 95°, ≤

α el fluxes

≤ for perpendicular (85° cal lines delimit the geometric wake as defined in the text. as defined cal lines delimit the geometric wake 180°, right panels) pitch angles for the F2, F3, A5, and O2 channels of the EPD. In the (anti)parallel panels the (anti)parall A5, and O2 channels of the EPD. In (anti)parallel F3, 180°, right panels) pitch angles for the F2, ≤

α

≤ 20°, 160° ≤

α

≤ , EPD data, and PWS (inferred) electron density for E4, E11, and E15. The energetic particle signatures are plotted separately signatures particle , and PWS (inferred) E4, E11,The energetic EPD data, electron density for and E15. x See Plate 31. B left panels) and (anti)parallel (0° Fig. 16. Fig. are indicated with (red dots) blue plusses. The bottom panel shows the electron density inferred from the PWS instrument. Verti are the electron density inferred from the PWS instrument. indicated with (red dots) blue plusses. The bottom panel shows Kivelson et al.: Interaction with the Jovian Magnetosphere 565

moves significantly down the wake (toward large x, can be understood as the effect of passage over an absorb- see auxiliary data in Fig. 11); and the electron flux ing body. Above the interaction region, ions coming from slowly increases to preencounter levels. The (anti)par- positive z would not show an absorption effect, whereas allel electron count rates change less abruptly, but ions coming from negative z would have been absorbed as the flux of these electrons also recovers slowly. Per- the flux tubes crossed the moon and would remain depleted pendicular ion losses are evident on the Jupiter-fac- in the plasma for some distance downstream of the moon. ing side of Europa prior to Galileo’s entry into the wake. In the same region, losses are minimal in the 5.4. Anomalous Flux Tubes (anti)parallel fluxes, consistent with the loss being related to finite ion gyroradius effects discussed in In the previous section, we alluded to ion pickup in the section 5.1. vicinity of Io. Pickup ions can significantly increase the E11: The flux signatures are relatively featureless, local mass density and provide the free energy that drives consistent with the relatively modest variations of the flux tube interchange (Kivelson et al., 1997; Thorne et al, magnetic field in the wake crossing. The flyby took 1997; Bolton et al., 1997). The interchange process occurs place further downstream of Europa and at a higher spontaneously in a rapidly rotating magnetosphere where zEphiB than the E4 and E15 flybys. In the perpendicu- flux tubes with large integral mass density (flux tube con- lar electron data there is a slow drop of counts, start- tent) move outward, changing places with flux tubes that ing at the geometrical wake, and continuing over the have a lower flux tube content. Signatures similar to those whole wake, with a minimum outside the geometri- identified at Io have been found downstream of Europa at cal wake. the antijovian boundary of the wake (Volwerk et al., 2001). E15: The perpendicular electron counts decrease Figure 17 shows a short interval of magnetic field data slowly but recover quickly on the Jupiter-facing side acquired close to the exit through the antijovian side of the of the wake as do the (anti)parallel electrons. The ion geometrical wake (y = –1 RE) on the E4 pass. At about count rates do not change markedly. Only the anti- 07:06 UT there is a strong, short-duration (5 s) decrease of parallel counts in channel A5 show a slight drop in the magnetic field strength with simultaneous signatures in counts near the center of the wake. Bx and By. The perturbation is not a localized rotation of It may be significant that the rapid decrease of flux in the magnetic field. The sharply bounded field decrease is several channels on the E4 pass and the rapid increase of primarily a change of field magnitude. Assuming perpen- flux outbound on the E15 pass, at different downstream dis- dicular pressure balance, the localized decrease of magnetic tances, both occur on the side of the wake closest to Jupiter pressure can be interpreted as evidence that a narrow flux (y > 0). The effect has not been interpreted in the published tube contains plasma of higher thermal pressure than that literature. However, one can consider processes known to act in surrounding flux tubes. This is different from the situa- on energetic particles, asking which might increase fluxes tion at Io where the short duration anomalies were abrupt on the Jupiter-facing side of the wake region. Pitch-angle field magnitude increases that were interpreted as an in- scattering (Paranicas et al., 2000) does not lead to inward ward-moving depleted flux tubes. Here the signature can displacement of flux tubes. Gradient-curvature drift of ener- be interpreted as that of an outward-moving, newly loaded getic particles in the perturbed magnetic geometry sur- flux tube with thermal pressure higher than that of the sur- rounding Europa could produce asymmetry favoring inward roundings. The decrease of the field magnitude at 07:06 UT displacement of the energetic electron wake [see for ex- is close to that measured in the center of the E4 wake in ample, the Thorne et al. (1999) analysis of drift paths of Fig. 11. Thus, it is plausible that the source of the dense highly relativistic electrons for a magnetized Io], but the flux tube is the high-density region at the wake center where signature at Europa appears at relatively low energies for Paterson et al. (1999) report a peak density of 70 cm–3, the which magnetic drift perturbations are small. The inter- largest observed during the flyby. The density increase was change process, observed in the Io plasma torus (Bolton et followed by an increase of temperature (106 K in the back- al., 1997; Kivelson et al., 1997; Thorne et al., 1997) leads ground plasma). It should be noted that the magnetic field to inward displacement of flux tubes differing from those depressions last less than the 1-min resolution of the plasma in the surroundings by having energy density dominated by density and temperature measurements. Pressure balance re- Δ Δρ ≅ energetic particles and number density correspondingly quires that B B = µo . With the ambient field B 420 nT reduced. Although further analysis is called for, it is pos- and the field perturbation ΔB ≅ 30 nT, the change in mag- sible that interchange also can account for the inward dis- netic pressure is 10 nPa. Taking values just prior to the den- placement of the energetic electron wake. sity spike in the wake center (n = 20 cm–3, and T = 2 × 106K) Another feature of the data in Fig. 16 calls for interpre- from Paterson et al. (1999), we calculate p = nkT = 0.6 nPa. tation. Fluxes in the A5 channel on the E15 pass differ for This implies that there must be a significant contribution upward- and downward-moving ions. The antiparallel ion of suprathermal particles that provide the additional pres- flux (red dots) dips in the center of the wake whereas the sure in the center of the wake that excludes a portion of the parallel ion flux (blue plusses) does not change. With Bz < ambient field. 0, the antiparallel particles are moving toward positive z. Let us suppose that part of the pressure within the wake ≈ With Galileo at zEphiO 1 RE, the dip in antiparallel ion flux arises from a localized increase in the pickup rate with re- 566 Europa

Fig. 17. E4 magnetometer data December 19, 1996: Top: From 0705 to 0711 UT. The shaded areas show possible flux tube interchange. Bottom: One minute of data (0705:50 to 0706:50) expanded. spect to the background rate in the bulk plasma. [Even in exceed the background temperature. The change of perpen- the background plasma, pickup ions contribute to the re- dicular pressure from the addition of pickup ions would be Δ Δ 2 Δ 2 γ2 Δ ported temperature (Paterson et al., 1999).] Assume that p⊥ = n(miu /2) = n(miuco-rot /2 ) = B B/µo = 10 nPa. ions are picked up in a background flow at some fraction of Solving for the density enhancement, one finds Δn(cm–3) = –1 γ γ ≤ γ 2 local corotation speed, say u(km s ) = 100 , with 1. 1180/mi(AMU) where mi(AMU) is the mass of the For γ ≥ 1/3, the thermal energy of the pickup ions would pickup ion in AMU. For nominal mass 20 ions, Δn ≈ 60/ Kivelson et al.: Interaction with the Jovian Magnetosphere 567

Fig. 18. Three images of the northern polar aurora. Hubble Space Telescope images have been summed and enhanced in contrast in order to display the faint emissions from the tail leading the brighter emission at the footprint of Europa. From Grodent et al. (2006).

γ2. Thus, the change of field magnitude is consistent with tor and ionosphere flow not only in the immediate vicinity the high ion density in the wake if relatively heavy ions are of Europa but also develop throughout the pickup cloud that picked up in the wake in a nearly corotational flow. Paterson surrounds it. The auroral tail extends over a distance that et al. observed flow only slightly below corotation across maps to more than 70 Europa diameters, or more than 3 RJ. the entire wake region. Alfvén wing theory (Neubauer, 1980; Southwood et al., From this analysis, one is led to suppose that the field 1980; Goertz, 1980) provides the basis for understanding depression observed at 07:06 UT, similar in magnitude to how the flow perturbations arising in near-equatorial regions that observed in the center of the wake, is produced by a through the interaction with a conducting moon (or a pickup flux tube of small cross section that has been transported cloud) drive currents that couple to Jupiter’s ionosphere. outward from the plasma wake. We do not understand why Field-aligned currents arise not only in the vicinity of the interchange at Io appears to require small depleted flux moon, but can also develop in the moon’s wake where the tubes moving inward in a background of filled flux tubes flow is slowed below corotation. It is the latter effect that assumed to be moving slowly outward, whereas the signa- accounts for the emissions seen to extend along the mapped ture at Europa appears closer to the reverse. footprint of Europa’s orbit. Estimates of the length of the auroral tail for the case of Io are given by Southwood and 6. EUROPA’S SIGNATURES IN Dunlop (1984), and parallel arguments can be applied to THE JOVIAN AURORA Europa’s tail. The field-aligned currents that couple the equator with the ionosphere are carried principally by elec- Elsewhere in this chapter, we have discussed how local trons, which are far more mobile than ions. Details of the interactions generate magnetic perturbations, including physics controlling the currents that link the Galilean moons Alfvénic disturbances that carry field-aligned currents. Such and the aurora have been considered mainly in the context disturbances generated near Europa and other Galilean of the Io interaction (e.g., Delamere et al., 2003), but the moons propagate along magnetic field lines from the equa- considerations that apply to Io are relevant as well to Eu- tor to Jupiter’s ionosphere where auroral emissions are ropa. One critical issue is the distribution of plasma along observed near the magnetic footprints of Io, Europa, and the flux tubes linking the two regions. Although in the ter- Ganymede (Clarke et al., 1998, 2002). The auroral emis- restrial magnetosphere charged particle motion from the sions associated with Io are most intense near its magnetic equator into ever stronger magnetic fields is affected prin- footprint and the bright spot tails off into a lengthy tail of cipally by the magnetic mirror force, in the jovian system reduced intensity along the magnetic mapping of Io’s orbit inertial forces must also be taken into account. In regions (ahead of Io in the sense of planetary rotation). More re- near the equator centrifugal forces acting on the rotating cently it has been discovered (Grodent et al., 2006) that plasma impede plasma motion away from the magnetic Europa’s footprint (a localized bright spot near the loca- equator. Similarly, near Jupiter’s ionosphere gravitational tion in Jupiter’s ionosphere magnetically conjugate to Eu- forces act to concentrate plasma at low altitudes. The plasma ropa) is accompanied by a shorter tail of faint auroral emis- density is likely to become very small in regions of a flux sions along the magnetic locus of Europa’s orbit (Fig. 18). tube somewhere between the equator and the ionosphere. The scale of Europa’s localized ionospheric footprint maps Nonetheless, mechanisms must exist to carry the electric to an interaction region on the order of 15 Europa diam- currents that couple the two regions, even through regions eters near the equator, requiring that currents between equa- where the plasma density is low. It is then plausible to ex- 568 Europa pect a field-aligned electric field to develop in order to ac- nal structure inevitably demands that we learn a great deal celerate the small number of electrons present in the inter- about its interaction with the magnetospheric plasma of mediate low-plasma-density region and thereby close the Jupiter. current loop. Electrons accelerated by the field-aligned elec- Fields and particles instruments will provide the data tric field not only carry current, but also excite the neutrals needed to improve our knowledge of the inductive field of the upper atmosphere, which in turn emit the auroral while also adding to our understanding of surface compo- radiation. Using spectroscopic analysis of the auroral emis- sition by providing fingerprints of pickup ions, seeking evi- sions, Dols et al. (2000) established that the Io footprint dence of electron beams and clarifying their sources and signature requires precipitation of electrons with tens of keV identifying the aspects of the interaction that control wake energy. The Europa footprint also emits in the extreme ul- structure and wave dissipation. Correlations of local mea- traviolet (Clarke et al., 2002) supporting the view that there surements with Hubble-type images should enable us to must be field-aligned potential drops on the order of tens understand the currents linking Europa with the aurora. A of kV on field lines linking Europa to Jupiter’s ionosphere. magnetometer supplemented by a plasma instrument will Recent analysis of auroral signatures at Io’s footprint has characterize flow patterns and their variation with magnetic identified two different excitation mechanisms that must be latitude. An orbiter regularly probing high europan latitude acting to produce the brightest spots observed in the aurora will provide the data that we lack today on how plasma (Bonfond et al., 2008). Some emissions are found at loca- convects across the polar cap, how quickly flux tubes lose tions interpreted as being slightly ahead (in the sense of particles of different energies after they first encounter the rotation) of the mapped location of Io’s footprint. The dis- body, and just where those particles are absorbed on the placement from the actual magnetic footprint occurs be- surface. This information should be of great value in estab- cause the signal propagates from equator to ionosphere lishing sputtering rates to characterize Europa as a plasma at a finite speed within a flowing plasma. However, Bon- source; it should enable us to investigate the role of ener- fond et al. also observed emissions at locations closer to getic particle bombardment in causing surface discolora- the mapped footprint of Io that can link to regions coupled tion (Khurana et al., 2007; see chapter by Carlson et al.), to Io only through signals propagating along the field at thus enabling us to untangle intrinsic and extrinsic modifi- speeds well in excess of typical wave speeds. Electrons of cation. The data from repeated orbits will be acquired at a greater than or equal to tens of keV energy travel at speeds considerable range of jovian magnetic latitudes, providing that are factors of hundreds faster than the Alfvén speed a range of high and low external plasma density environ- and can carry signals between Jupiter’s northern and south- ments that will enable us to see how the response varies ern ionosphere in tens of seconds. Thus, it seems that beams with such local parameters as Alfvén Mach number and of energetic electrons, possibly similar to those observed sound speed. We will find out how ion pickup rates vary on Galileo’s first pass by Io (Williams et al., 1999; Frank with jovian magnetic latitude. A sensitive, high-time-reso- et al., 1999), generate the additional puzzling bright spots. lution magnetometer will be able to identify ion cyclotron There is good reason to assume that the mechanism that waves associated with pickup ions of different mass per unit creates the beams at Io is at work near Europa as well, form- charge, giving evidence of surface composition and the ing electron beams that have not yet been observed. presence and distribution of minor constituents on the sur- face. Prior to entry into a capture orbit, Europa’s wake could 7. FOR THE FUTURE be probed at different downstream distances in order to un- derstand the processes that reaccelerate the plasma slowed One cannot write about Europa in 2008 without think- by its interaction with Europa. ing about possible future missions to this fascinating solar We all remember Arthur C. Clarke’s words: “All these system body. Studies of Europa missions have been pur- worlds are yours, except Europa. Attempt no landing there...” sued vigorously on both sides of the Atlantic Ocean (Solar (Clarke, 1968), but he never asked us not to go into orbit System Exploration Survey, 2003; Bignami et al., 2005), around it. Let us hope that a return to Europa comes soon and, assuming that technological issues are resolved and and gives us answers to our questions. costs are controlled, it seems likely that the next decade will witness the fruition of the planning, the launch of a Europa Acknowledgments. The authors would like to thank C. Parani- Orbiter. 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(1997); dashed black = modeled field with no internally induced field; Blue, green, and black = mod- eled field including induction in a 100-km-thick ocean lying beneath a crust of 25 km for ocean con- ductivities of 100, 250, and 500 mS/m, respectively. From Schilling et al. (2007).

Accompanies chapter by Kivelson et al. (pp. 545–570). Plate 28. The flow speed (a) in the x–y plane, (b) in the x–z plane, and (c) the magnetic field in the x–z plane. Dashed lines represent boundaries of the northern and southern Alfvén wings. From the MHD simulation of Schilling et al. (2008).

Accompanies chapter by Kivelson et al. (pp. 545–570). Plate 29. A simple model of the ion pickup around Europa, showing an abrupt decrease in density near y = 0.6. Density units are arbitrary.

Accompanies chapter by Kivelson et al. (pp. 545–570). Plate 30. Dynamic spectra of the lefthand (top three panels) and righthand (lower three panels) polarized components of the magnetic field for E4, E11, and E15. The white solid + + + + traces show the cyclotron frequencies for Na (A = 23), O2 (A = 32), K (A = 40), Cl + (A = 35), and SO2 (A = 64). Vertical lines delimit the geometric wake.

Accompanies chapter by Kivelson et al. (pp. 545–570). ≤ α ≤ Plate 31. Bx, EPD data, and PWS (inferred) electron density for E4, E11, and E15. The energetic particle signatures are plotted separately for perpendicular (85° 95°, left panels) and (anti)parallel (0° ≤ α ≤ 20°, 160° ≤ α ≤ 180°, right panels) pitch angles for the F2, F3, A5, and O2 channels of the EPD. In the (anti)parallel panels the (anti)parallel fluxes are indicated with (red dots) blue plusses. The bottom panel shows the electron density inferred from the PWS instrument. Vertical lines delimit the geometric wake as defined in the text.

Accompanies chapter by Kivelson et al. (pp. 545–570).