Radial variations in the Io plasma torus during the Cassini era

Authors


Abstract

[1] A radial scan through the midnight sector of the Io plasma torus was made by the Cassini Ultraviolet Imaging Spectrograph on 14 January 2001, shortly after closest approach to Jupiter. From these data, Steffl et al. (2004a) derived electron temperature, plasma composition (ion mixing ratios), and electron column density as a function of radius from L = 6 to 9 as well as the total luminosity. We have advanced our homogeneous model of torus physical chemistry (Delamere and Bagenal, 2003) to include latitudinal and radial variations in a manner similar to the two-dimensional model by Schreier et al. (1998). The model variables include: (1) neutral source rate, (2) radial transport coefficient, (3) the hot electron fraction, (4) hot electron temperature, and (5) the neutral O/S ratio. The radial variation of parameters 1–4 are described by simple power laws, making a total of nine parameters. We have explored the sensitivity of the model results to variations in these parameters and compared the best fit with previous Voyager era models (Schreier et al., 1998), Galileo data (Crary et al., 1998), and Cassini observations (Steffl et al., 2004a). We find that radial variations during the Cassini era are consistent with a neutral source rate of 700–1200 kg/s, an integrated transport time from L = 6 to 9 of 100–200 days, and that the core electron temperature is largely determined by a spatially and temporally varying superthermal electron population.

1. Introduction

[2] The Io plasma torus is produced by the ionization of roughly 1 ton/s of neutral material from Io's atmosphere. In situ and remote observations of the torus have largely characterized the density, temperature and composition of the torus (see review by Thomas et al. [2004]). The issue of temporal variability of the Io plasma torus has been debated for many years [Mekler and Eviatar, 1980; Eviatar, 1987; Thomas et al., 2004]; however, recent observations of the torus made by the Ultraviolet Imaging Spectrograph (UVIS) on the Cassini spacecraft during the flyby of Jupiter (October 2000 to March 2001) have yielded new insights into the temporal variability of the torus using a homogeneous model for mass and energy flow through the torus [Delamere and Bagenal, 2003]. The combined data analysis efforts by Steffl et al. [2004b] and modeling by Delamere et al. [2004] suggest that a significant change in the neutral source occurred near the beginning of the Cassini observing period, decreasing from >1.8 tons/s to 0.7 tons/s. Concurrent iogenic dust measurements made during the Galileo G28 orbit by Krüger et al. [2003] suggest that the observations are consistent with signficant volcanic activity on Io. While much of the UVIS data does not have sufficient resolution to address the issue of spatial variations in the torus, a full radial scan through the midnight sector was made on 14 January 2001, shortly after closest approach. The observed radial variations are described by Steffl et al. [2004a] and provide electron temperature, plasma composition (ion mixing ratios), and electron column density as a function of radial distance from L = 6 to L = 9. We have advanced our homogeneous model to address radial variations in a manner similar to the two-dimensional model by Schreier et al. [1998]. The goal of this study is to model the radial variations of the torus during the Cassini era and to compare the results with previous models (e.g., Voyager era model by Schreier et al. [1998]).

[3] The torus plasma stems from two primary source regions: (1) ionization of Io's extended neutral clouds, and (2) ionization of material within 5 RIo of the satellite [Bagenal, 1997]. The contribution from the second region (local source) ranges between 20 and 50% of the canonical ton/s of new plasma based on estimates by Bagenal [1997] and Saur et al. [2003]. The plasma is then modified by the effects of physical chemistry as it is transported outward. Electron impact ionization is the primary source of new material (mass and energy) and populates the higher ionization states. Neutral-ion charge exchange modifies the energy flow and removes neutral material from the system and numerous ion-ion charge exchange reactions generally make modifications to torus composition and ion temperature. Efficient radiative loss from the core electron population rapidly cools the torus and the roughly 5–10 eV electron temperature is maintained by thermal input from the hotter ion population (∼70–100 eV) and the ubiquitous superthermal electron population (40–100 eV). A key observation seen in both the Voyager and Cassini data sets is the steady rise in the core electron temperature with radius [Sittler and Strobel, 1987; Steffl et al., 2004a, 2004b]. Schreier et al. [1998] describe three mechanisms for heating the electrons, namely: (1) an increase in thermal temperature of the ions resulting in heating via Coulomb collisions, (2) hot (∼10s of keV) ions of ring current origin diffusing inward and heating the electrons, and (3) an increasing flux of superthermal electrons. [Schreier et al., 1998] conclude that mechanism 2 is the most likely.

[4] Radial transport is understood to be driven by centrifugally driven interchange motions of magnetic flux tubes [Richardson and Siscoe, 1981; Siscoe and Summers, 1981]. The interchange rate is regulated by several factors including Jupiter's Pedersen conductivity [Hill, 1986], ring-current impoundment [Siscoe et al., 1981], and velocity shear impoundment [Pontius et al., 1998] (see discussion by Thomas et al. [2004]). The standard treatment of the transport physics is handled with a radial Fokker-Planck diffusion equation [Dungey, 1965], where the transport timescale is parameterized by a diffusion coefficient which varies as a power of L (i.e., DLL = DoLn). While the detailed physics of radial transport mechanisms are not fully understood, observational constraints suggest that the transport timescale is roughly 60 days (for ∼1 RJ).

[5] The first constraints on the timescales for radial transport were provided by analysis of the high-energy particle (∼MeV) data from the Pioneer 10 and 11 flybys [Thomsen et al., 1977a, 1977b]. Thomsen et al. [1977a] estimated that the upper limit for the diffusion coefficient, Do(L ∼ 6), is roughly 6 × 10−7 s−1 (t ∼ 20 days) with n = 2.3 ± 0.5. Analysis of the Voyager 1 and 2 data of >0.5 MeV ions by Armstrong et al. [1981] indicated a best value of n ∼ 7.5. On the basis of analysis of the Voyager I low-energy plasma data, the wide range in n deduced from the energetic particle data was attributed to a marked transition (discontinuity) between plasma transport rates inside and outside of Io's orbit [Bagenal et al., 1980; Richardson et al., 1980]. For the region outside of Io's orbit (the region of interest in this paper), Siscoe and Summers [1981] determined that the diffusion coefficient varies as L4+p, where the parameter p was in the range 2 ≤ p ≤ 4.

[6] The empirical torus model by Bagenal [1994] shows a “ramp” region between L = 7.5 and 8.0, where the slope of the flux tube content profile steepens. Siscoe et al. [1981] suggested that inward transport of radiation belt particles might be impounding the torus plasma. While this prompted various attempts to model the flux tube content profile with radial variations in the rate of diffusive transport [Herbert, 1996; P. L. Matheson and D. E. Shemansky, Chemistry and transport in the Io torus ramp, unpublished manuscript, 1993], it is not clear whether the Voyager ramp region might be due, at least in part, to the latitudinal excursion of the spacecraft or to temporal variability of the plasma production.

[7] In this paper we compare the radial profiles (L = 6 to 9) of mixing ratios of the five major ion species (S+, S++, S+++, O+, and O++) and the total torus extreme ultraviolet (EUV) luminosity (PEUV) provided by the Cassini UVIS analysis of Steffl et al. [2004b, 2004a] to our modeled profiles and luminosity. The model contains the following variables: (1) neutral source rate, (2) radial transport coefficient, (3) the hot electron fraction, (4) hot electron temperature, and (5) the neutral O/S ratio. The radial variation of variables 1–4 are described by simple power laws, making a total of nine parameters. Most importantly, we explore the sensitivity of model results to variations in these parameters and compare the models matching the Cassini data with previous models (e.g., Voyager era model by Schreier et al. [1998]).

2. Cassini Data Set

[8] During the Cassini spacecraft's Jupiter flyby (October 2000 to March 2001), the UVIS instrument produced an extensive data set of spectrally dispersed images of the Io plasma torus. The UVIS instrument consists of two independent, coaligned spectrographs (EUV 561–1181 Å; FUV 1115–1913 Å) having a point-source spectral resolution of 3 Å FWHM [McClintock et al., 1993; Esposito et al., 1998]. The major ion species present in the torus all have spectral features in the wavelength range covered by the EUV channel. The field of view of the EUV channel of the instrument was such that for the first and last 2 months of the Jupiter encounter, the entire torus could be observed simultaneously. During the approach phase of the encounter, the total EUV power radiated by the torus decreased by 25% [Steffl et al., 2004b]. UVIS continued to make observations of the Io torus during the months of December 2000 and January 2001, but the spacecraft's proximity to Jupiter precluded simultaneous measurement of the total radiated EUV power. When total power measurements resumed after closest approach, the torus EUV luminosity remained relatively constant. On the basis of the observed inbound and outbound luminosity, we estimate the total EUV power for the 14 January radial scan to be 1.45 ± 0.25 terawatts.

[9] The spectral analysis method described by Steffl et al. [2004a] was used to derive the ion composition and electron temperature of the torus plasma at the ansa. This model assumes a uniform torus along the line-of-sight and uses the CHIANTI database [Dere et al., 1997; Young et al., 2003] to determine radiative emission rates. The assumption of a uniform column through the torus does not significantly affect the results for radial distances greater than 6 RJ. Spectra from October and November can be found in the work of Steffl et al. [2004b]; spectra from January can be found in the work of Steffl et al. [2004a].

[10] Historically, it has been difficult to determine the relative abundance of O II and O III in the Io torus [e.g., see McGrath et al., 1993, and references therein]. The observational setup of UVIS on 14 January 2001 (i.e., the long axis of the UVIS entrance slit oriented approximately parallel to Jupiter's rotation axis with the field of view being scanned radially inward from 10 to 4 RJ) allowed the inclusion of the FUV channel in the analysis of the spectra. The observed brightness of the O III lines at 1661 and 1666, a wavelength region covered by the FUV channel, places a firm upper limit the amount of O III in the torus [Steffl et al., 2004b].

3. Model of Torus Chemistry and Emissions

[11] We have developed a homogeneous, time-dependent model of torus physical chemistry for the purpose of investigating the sensitivity of torus composition to the following parameters: neutral source rate (��n), O/S source ratio (O/S), convective transport loss (τ), hot electron fraction (feh), and hot electron temperature (Teh). A detailed description of the model is provided by Delamere and Bagenal [2003]. The model is based largely upon several earlier models [i.e., Shemansky, 1988; Barbosa, 1994; Schreier et al., 1998; Lichtenberg and Thomas, 2001] but uses the latest CHIANTI atomic physics database for computing radiative loss [Dere et al., 1997].

[12] The model calculates the time rate of change of mass and energy for both ions and the core electrons based on the determination of mass and energy sources and losses until a steady state solution is reached. The primary sources of mass and energy are electron impact ionization and charge exchange reactions involving neutral gas. Charge exchange reactions determine the allocation of energy among the ion species and their respective ionization states. Charge exchange reactions involving neutrals also contribute significantly to the energy budget due to the pickup energy of plasma into the corotating plasma torus (see Table 1 for reactions). The velocity distribution for each species is approximated as Maxwellian. The electrons have a nonthermal component and a “Kappa” distribution is known to best match torus observations [Meyer-Vernet et al., 1995]. We approximate this nonthermal distribution with two Maxwellians for the core and hot populations. The hot electrons, through Coulomb coupling with the core electrons, provide significant energy input into the torus (∼20–60%). Major losses of mass include radial transport and fast neutral escape due to charge exchange reactions with thermalized ions (Ti = 60–100 eV). Radiation in the UV and optical is the major energy sink as roughly 50% of the input energy is transferred from the ions to the electrons via Coulomb coupling. The combination of these sources and sinks of mass and energy lead to an equilibration timescale of roughly 60 days.

Table 1. Charge Exchange Reactions, L = 6.0, k0 [Smith and Strobel, 1985], k1k16 [McGrath and Johnson, 1989]
Reactionk, cm3s−1
S+ + S++ → S++ + S+k0 = 8.1 × 10−9
S + S+ → S+ + Sk1 = 2.4 × 10−8
S + S++ → S+ + S+k2 = 3 × 10−10
S + S++ → S++ + Sk3 = 7.8 × 10−9
S + S+++ → S+ + S++k4 = 1.32 × 10−8
O + O+ → O+ + Ok5 = 1.32 × 10−8
O + O++ → O+ + O+k6 = 5.2 × 10−10
O + O++ → O++ + Ok7 = 5.4 × 10−9
O + S+ → O+ + Sk8 = 6 × 10−11
S + O+ → S+ + Ok9 = 3.1 × 10−9
S + O++ → S+ + O+k10 = 2.34 × 10−8
S + O++ → S++ + O+ + ek11 = 1.62 × 10−8
O + S++ → O+ + S+k12 = 2.3 × 10−9
O++ + S+ → O+ + S++k13 = 1.4 × 10−9
O + S+++ → O+ + S++k14 = 1.92 × 10−8
O++ + S++ → O+ + S+++k15 = 9 × 10−10
S+++ + S+ → S++ + S++k16 = 3.6 × 10−10

3.1. Radial Transport

[13] Following Schreier et al. [1998], we use the radial Fokker-Planck equation to describe the radial diffusion in the torus. For each species, the radial transport equation is of the form

equation image

where Y is any quantity conserved as a flux tube moves under interchange motion, L is the radial coordinate, and DLL is the diffusion coefficient. For the case of mass, the conserved quantity is the total number of ions per unit magnetic flux, NL2, and for thermal energy density of an isotropic plasma, adiabatic changes (i.e., Tequation imageV−2/3) requires that Y = NL2TL8/3, where T is the ion temperature and where the volume of a dipole flux tube of constant flux varies as L4. We note that this form of the conserved thermal quantity assumes that the plasma is free to expand into the entire flux tube volume and does not consider the affects of centrifugal confinement. Richardson and Siscoe [1983] assume that the scale height of the torus is small compared to L such that the effective volume ∝ L3H (rather than L4), where H is the plasma scale height. The conserved thermal quantity is therefore Y = NL2TL2T1/3, where Hequation image. The centrifugal confinement reduces the volume to roughly 80% of the flux tube for H = 1 RJ. The two expressions can be considered limiting cases of hot [Schreier et al., 1998] and cold [Richardson and Siscoe, 1983] plasma. The obvious generalization would be an intermediate case (V. Vasyliunas, personal communication, 2005). We are adopting the Schreier et al. [1998] expression for the purpose of comparison, but note in advance that a model comparison of these two expressions yielded only small differences in the transport parameters.

[14] For the diffusion coefficient we assume a power law of the form DLL = K (L/Lo)m, where Lo = 6.0. Density is updated in the equatorial plane subject to the latitude-averaging scheme described below and the equatorial densities are converted to total flux tube content (NL2) by determining the variation in number density along the magnetic field. The distribution of plasma along the magnetic field can be determined by considering the balance between plasma pressure, centrifugal force, and the ambipolar electric field on a dipole magnetic field line. Specification of density at a given point on the magnetic field, So, determines the density at all other points, S, according to

equation image

where Ω is the angular velocity of the corotating plasma, ρ is the perpendicular distance to the spin axis, and Φ is the ambipolar potential [Bagenal and Sullivan, 1981]. The total flux tube content for a dipole field is given by

equation image

An iterative scheme is used to convert between the updated flux tube mass content and the equatorial densities. We assume isotropic Maxwellian particle distributions so that the temperature of each species is constant along the magnetic field and the effects of thermal anisotropy are ignored.

[15] The transport equation is subject to boundary conditions. At L = 6.0 we use ∂(NL2)/∂L = 0 to determine mass flux across in the inner simulation domain boundary, and for large L (i.e., >30) we require that NL2 = 0. To justify our inner boundary condition, we note that Io resides at L = 5.9 and steep (positive) gradients in flux tube content occur inside of the ribbon region at L = 5.7. The Voyager analysis of Bagenal [1994] shows a fairly flat profile in flux tube content between L = 5.7 and 6.0 with small-scale variations not resolved on our 0.25 RJ model grid. For the energy update we fix the temperature on the inner boundary (L = 6.0) to 60 eV and for large L the temperature is fixed at 100 eV (consistent with Voyager ion temperatures in the plasma sheet). Chemistry is only calculated for L = 6.0 to L = 11.0 using the latitudinally averaged chemistry model for each radial grid cell (0.25 RJ grid resolution).

3.2. Latitudinal Averaging

[16] The rapid rotation of Jupiter and its magnetic field tightly confines torus plasma to the centrifugal equator. To calculate the torus chemistry, we assume that mass and energy flow are largely determined by plasma density in the centrifugal equator plane. The scale heights of the different ion species are comparable (1–2 RJ); however, the neutral clouds are largely confined to the orbital plane of Io with a much smaller scale height [Smyth and Marconi, 2000]. Therefore the ion/neutral chemistry in the torus could be significantly influenced by the latitudinal distribution of ions and neutrals.

[17] Io moves ∼7° in latitude with respect to the centrifugal equator plane of the plasma torus (i.e., above and below the torus) in the 13 hours of Jupiter's rotation (and System III longitude) in Io's reference frame. We assume that the neutral clouds are tightly confined to Io's orbital plane and likewise are subject to significant latitudinal excursions (directly correlated with longitude) with respect to the plasma. To approximate the longitudinally varying neutral source, we fixed the neutral cloud offset to 3.5° in latitude with a fixed scale height of 0.1RJ. We argue that it is reasonable to assume longitudinal symmetry because the chemistry timescales are significantly longer than the System III period and thus small deviations from rigid corotation (∼ few km/s) will smear out longitudinal variations [Brown, 1994; Steffl et al., 2005]. The total neutral source rate was converted to an equatorial volumetric quantity for each grid cell by multiplying the source rate by an approximate volume, VzδA = (π1/2Hn)π [(L + dL/2)2 − (LdL/2)2], where Hn is the neutral scale height (assumed identical for S and O).

[18] For a rapidly rotating magnetosphere with dipolar magnetic field, the density of a single ion species plasma has a Gaussian distribution about the centrifugal equator with the same scale height for ions and electrons. With multiple ion species one can approximate the distribution of their densities using separate Gaussians with separate scale heights. The difference between this Gaussian approximation and a self-consistent treatment of a multiple species plasma is minor (within ±1 RJ). Furthermore, since most chemical reactions depend on the product of two densities, the contribution of high-latitude densities has very little effect. The separate Gaussian approximation facilitates simple analytical expressions for determining flux tube averaged quantities. In addition, all distributions are treated as simple Maxwellians so that the temperature for any given species is constant along the magnetic field line. The density of the hot electron component is assumed to be constant along the magnetic field. Figure 1 illustrates the distribution of plasma along the magnetic field with respect to the centrifugal equator plane. The dark solid lines show the O and S neutral distributions for the limiting case where Io makes its largest excursion from the centrifugal equator plane of the plasma torus (i.e., λIII ∼ 20° or 200°).

Figure 1.

Sample flux tube distribution with offset neutral clouds (dark solid lines). In this example the neutrals are offset by 7° with a 0.1 RJ scale height. The density of the oxygen neutral cloud is typically 4–5× greater than the neutral sulfur cloud.

[19] In the Gaussian approximation the total number of ions of each species on a given flux tube will be defined as

equation image

where Hequation image is the plasma scale height, Ω is the angular frequency of Jupiter's rotation (1.76 × 10−4 rad/s) and n(0) is the density in the centrifugal equator plane, and Zi is the ion charge number. Given the flux tube total, N, the density in the equator plane is

equation image

Now consider a reaction involving two ion species. The total flux tube integrated source rate for species γ due to a reaction between species α and β is

equation image

where k is the reaction rate coefficient and H′ = equation image. The updated equatorial density for species γ over a time interval, δt, is

equation image

[20] Chemistry involving ion/neutral reactions can be calculated in a similar manner; however, in this case the neutral clouds lie in Io's orbital plane rather than the centrifugal equator plane of the plasma torus. Thus the spatial location of the neutral distribution is a function of System III. The location of the neutral cloud can be treated as a simple offset, zo, from the centrifugal equator plane which we take to be a constant value of 3.5° in this initial azimuthally symmetric model. So

equation image

where a = (Hi2 + Hn2)/(Hi2Hn2), b = −2zo/Hn2, and c = zo2/Hn2.

[21] For ion/electron chemistry the condition of quasi-neutrality gives

equation image

where H′ = (Hβ2 + Hα2)/(Hβ2Hα2) and Zα is the charge number. The hot electron chemistry is simply determined by

equation image

where feh is the hot electron fraction in the centrifugal equator plane, and ne(0) is the electron density determined by the quasi-neutrality condition.

[22] It is relatively simple to calculate the mass flow through the torus when the Gaussian approximation is used for determining the latitudinally averaged chemistry. Energy flow calculations are somewhat more complicated. The basic problem for calculating energy flow is that the change in energy (due to chemical reactions, radiation, collisions, etc.) for a given species is a function of z; therefore the best approach should provide a flux tube weighted average for the temperature updates. For instance, the Coulomb collision rates are functions of density for both species, so the energy change due to Coulomb interactions is of the form

equation image

where να/β is the thermal equilibration rate between species α and β and the flux tube averaged contribution is determined by evaluating

equation image

Radiation can be handled in a similar manner where the radiation contribution from each species is calculated along the magnetic field and the latitudinally averaged rates are given by

equation image

where ρα,λ are the radiative rate coefficients of species α at wavelength λ. We then compare the flux tube averaged composition with those derived from the Cassini UVIS data [Steffl et al., 2004b].

4. Results and Discussion

[23] The coupled radial transport of mass and energy has nine parameters: hot electron fraction (feh), hot electron temperature (Teh), neutral source (��n), transport coefficient (DLL) and respective power laws, and the O/S neutral source ratio. A six-dimensional parameter space search using the downhill simplex method of Nelder and Mead [1965] was used to find the set of model input parameters that provided the best model fit to the observed radial Cassini profiles (specifically, the mixing ratios of major ion species and total EUV power radiated). Preliminary results were fairly insensitive to the hot electron temperature and the O/S ratio, so these parameters remained fixed during subsequent parameter searches. We adopted an expression for the hot electron temperature of the form 42 eV (L/Lo)5.5, where Lo = 6 and O/S was fixed at 1.8. The increase in the hot electron temperature with radius was motivated by the Sittler and Strobel [1987] analysis of the Voyager I electron data which showed a 500 eV superthermal tail, but we note that the results are insensitive to the exact radial dependence of the hot electron temperature as the ionization rates are weakly dependent on temperature above 100 eV. We constrained the parameter search with the end points (L = 6 and 9) of the radial profiles of the five major ion species and the total EUV power radiated from Steffl et al. [2004a]. Given that we are modeling the radiated power between L = 6 to 9 and that a significant fraction (i.e., 20%) of the total power radiated originates inside of L = 6 (i.e., near Io), we approximated this additional radiation in the L = 5.75 to 6.0 interval as equal to the modeled value in the L = 6 to 6.25 interval. On the basis of the time history of the observed power radiated (total power is not available during the period of closest approach, including the 14 January radial scan) we constrained our fits using 1.4 ± 0.25 terawatts based on interpolation of the October–April torus EUV luminosity profile. Improved fits were obtained by including mid points (i.e. L = 7.0) for the S+ and S+++ profiles as constraints.

[24] Figures 2 to 4 show the best fit model results to the Cassini UVIS radial profiles and the sensitivity of the best fit to variations in the radial power law dependence of transport time, hot electron fraction, and neutral source. In this simple model we have not attempted to address small-scale radial variations seen in the data (i.e., bump between L = 7.5 and 8.0). These sensitivity studies represent a small subset of the total nine-dimensional parameter space but represent the most important parameters for determining the radial profiles. Sensitivity to variations of parameters at L = 6.0 are similar to our previous sensitivity studies presented by Delamere and Bagenal [2003] and Delamere et al. [2004] for the homogenous model. In Figure 2 we show in the top left panel the integrated transport time for diffusion coefficients of the form DLL(Lo)(L/Lo) with α = 3.6, 4.6, and 5.6. Following Cheng [1986] and Schreier et al. [1998], an estimate of the radial transport timescale, τ, can made by integrating the radial transport equation,

equation image

For comparison we show the Schreier et al. [1998] results as plus symbols. For our best fit, the integrated transport time from L = 6 to L = 9 is roughly 140 days, though the modeled times ranging between 100 and 200 days are all consistent with the data. The total power radiated for the respective short, best fit, and long transport times is 1.1, 1.4, and 1.7 terawatts.

Figure 2.

Sensitivity of radial profiles to variations in transport rate. The top left panel shows the integrated transport time for three cases (DLL = 4.2 × 10−7 (L/6)4.6, 4.2 × 10−7(L/6)5.6, and 4.2 × 10−7(L/6)3.6 s−1) as well as the results of Schreier et al. [1998] (plus symbols). The remaining panels compare the mixing ratios of the model (lines) with the Cassini data (cross symbols).

[25] In Figure 3 we show in the top left panel the core electron temperature as a function of radius and compare with the Cassini-derived result of Steffl et al. [2004a]. The total power radiated for the low, best fit, and high cases is 1.3, 1.4, and 1.6 terawatts, and we thus conclude that the model is consistent with the data for these hot electron profiles. With the exception of the Cassini-derived electron temperature beyond L = 8.5 (see discussion below regarding radial variations in the hot electron fraction), the modeled core electron temperatures are consistent with the data.

Figure 3.

Sensitivity of radial profiles to variations in hot electron fraction. The top left panel shows the core electron temperature for three cases (feh = 2.5 × 10−3(L/6)4.4, 2.5 × 10−3(L/6)5.4, and 2.5 × 10−3(L/6)3.4) as well as the Cassini results of Steffl et al. [2004a] (plus symbols). The remaining panels compare the mixing ratios of the model (lines) with the Cassini data (cross symbols).

[26] Figure 4 compares the sensitivity of the radial profiles to variations in the extended neutral source. The best fit uses a fairly steep power law of the form ��n(Lo)(L/Lo)−α with α = 12. For the considerably higher power, α = 20, the results do not change significantly, indicating that the radial profiles are strongly determined by chemistry near L = 6. In the case of a strong extended source (α = 4) the results change considerably and do not match the data. The total mass loading rates and radiated power for the respective low, best fit, and high power of L cases are 2100, 900, and 700 kg/s and 4.2, 1.4, and 1.0 terawatts. Clearly, the radiated power provides an important constraint in fitting the neutral source parameters and we conclude that a mass loading rate of 700–1200 kg/s matches the data.

Figure 4.

Sensitivity of radial profiles to variations in neutral source. The top left panel shows the neutral source strength, ��n, for three cases (��n = 6.8 × 1027(L/6)−12, 6.8 × 1027(L/6)−20, and 6.8 × 1027(L/6)−4 s−1). The remaining panels compare the mixing ratios of the model (lines) with the Cassini data (cross symbols).

[27] Figure 5 shows the latitudinally integrated O and S neutral column densities for the α = 12 (solid lines) and α = 20 (dotted lines) cases shown in Figure 4. These profiles compare favorably with the Voyager-based neutral cloud models of Smyth and Marconi [2003] at L = 6; however, our best fit profiles require substantially higher neutral density in the extended clouds. Our α = 20 case is the best match to the Smyth and Marconi [2003] model but the total power radiated is significantly lower than the Cassini observations, illustrating once again the importance of the radiated power constraint. Given the time-variable nature of the neutral source during the Cassini observing period, it is worth considering the possibility that the radial profiles contain a residual imprint of the inferred enhanced neutral source associated with the September 2000 dust outburst [Delamere et al., 2004; Krüger et al., 2003]. The integrated transport time of >100 days from L = 6 to 9 is comparable to the 100+ days since the beginning of the Cassini observing period and the inferred dust outburst. The model results are steady-state solutions for a known time variable problem and the time variable nature of the coupled interaction between neutral clouds and the plasma torus is left for future study.

Figure 5.

Modeled neutral cloud column density as a function of radius. The solid lines are the average column density of the respective O and S neutral clouds for the best fit case, (L/6)−12, and the dotted lines for the (L/6)−20 case. Both neutral cloud profiles generate radial profiles that are consistent with the Cassini data.

[28] Figure 6 compares the modeled NL2 profiles with the total flux tube content from the Voyager era [Bagenal, 1994] and Galileo era [Crary et al., 1998]. The total flux tube content for our Cassini model is roughly 50% higher than the Voyager era and comparable to the Galileo era. The primary difference is in the higher S++ densities observed during the Cassini era. As expected, the short lifetime of S+ due to electron impact ionization leads to a rapid decrease in S+ while the higher ionization states increase initially with radius. The slopes for the Voyager and Cassini total NL2 profiles are initially similar, but our model does not attempt to reproduce the so-called Voyager ramp region. We feel that the Cassini radial profiles do not provide definitive evidence for such a ramp region. Although the Cassini radial profiles do show fluctuations outside of L = 7.0, these variations could be explained with a variety of mechanisms including a fluctuating hot electron population or possibly a residual imprint of the time varying neutral source. We note that it is difficult to radially propagate a coherent compositional variation because the chemistry effectively smears it out; however, we cannot dismiss the possibility that the enhanced flux tube content and extended neutral clouds from the Cassini model reflect residual plasma at large L (i.e., L > 8) associated with the September 2000 dust outburst.

Figure 6.

Comparison of total flux tube content for the Cassini model (solid line) with the total flux content from the Voyager era [Bagenal, 1994] and the Galileo era [Crary et al., 1998].

[29] Figure 7 shows the radial variation in the modeled ion temperature. At L = 6, the average ion temperature is roughly 100 eV. The initial increase is due to pick up from an extended neutral source. The solid lines in the top left corner show the pickup temperatures for S and O as a function of radius (i.e., the relative velocity of the corotating plasma with respect to the local Keplerian velocity). Without an additional energy source, the ions cool adiabatically as the plasma is transported radially outward. The modeled ion temperatures are somewhat higher than those determined for the Voyager (60 eV) and Galileo (<60 eV) eras [Crary et al., 1998]. Note that this model temperature is really an average energy and the 100 eV value from the model is consistent with Voyager measurements of 60 eV core ion temperature averaged with ∼20% hot (∼500 eV) ions [Bagenal, 1994].

Figure 7.

Model ion temperature versus radial distance. The pickup temperature for S and O are indicated by the solid lines.

[30] Figure 8 shows the mass source and loss timescales for each species as a function of radius for the best fit case. The source/loss timescale for species α interacting with species β (i.e., ionization or charge exchange) is given by knβ, where k is the reaction rate coefficient. The charge exchange reactions are labeled k0–k16 and are identified in Table 1. Electron impact ionization is labeled “EI” and impact ionization by the hot electron component is labeled “HEI.” The solid lines show the integrated transport time for each species which differ in accordance with variations in the NL2 profiles for each species. The peak in the NL2 profiles for O++ and S+++ result in a peak in the integrated transport time at L = 7, indicating that the primary source of these higher ionization states is located radially outward from the primary Io mass loading region near L = 6. These figures illustrate the relative importance of chemistry versus transport as a function of radius. Much of the chemistry is only important near L = 6 with the exception of electron impact ionization of S, S+, and O+. Chemistry involving S+++ and O++ becomes important between L = 7 and 8 where the transport timescales effectively become very long as d(NL2)/dL = 0. Charge exchange losses for S+++, particularly k14, are important throughout our radial interval.

Figure 8.

Timescales for transport and chemistry. The integrated transport time for each species is indicated by the solid lines. Chemistry timescales are indicated by the symbols and the various reactions are identified on the left. Electron impact ionization is labeled “EI” and hot electron impact ionization is labeled “HEI.” The charge exchange reactions k0–k16 are given in Table 1.

[31] We provide an initial assessment of the affect of Europa's oxygen source on the radial profiles. Estimates of Europa's oxygen source have been provided by Schreier et al. [1993], Saur et al. [1998], and Mauk et al. [2004] based on Voyager plasma measurements, observations of Europa's atmosphere, and results of Galileo ENA (energetic neutral atom) imaging, respectively. These studies all indicate an oxygen neutral source of roughly 2 × 1027 s−1. As a limiting case, we introduce the entire Europa oxygen source in the interval L = 9.0 to 9.25. Figure 9 compares our best fit Io-only radial profile with the Europa + Io oxygen source. The primary difference is an increased abundance of O+ and a decreased abundance of S+++. However, these differences are still contained within the error bars of the Cassini analysis and we cannot conclude that the signature of an Europa oxygen source is seen in the Cassini data. The final four data points for the O+ abundance do increase, but we cannot conclude whether this is due to Europa or due to other factors including time variations in hot electrons and/or Io's neutral source. Charge exchange between Europa's neutral hydrogen clouds and O+ (not included in our model) will further decrease the O+ abundance. On the basis of the rate coefficients of Kingdon and Ferland [1996] (for <1 eV plasma) we do not expect the additional O+ loss (due to H charge exchange) to significantly alter the Europa + Io radial profiles. Charge exchange between hydrogen and sulfur ions is expected to be insignificant. So, we conclude that even a substantial cloud of neutral hydrogen does not make a significant effect on the plasma chemistry. Figure 10, however, shows significant modification to the radial ion temperature profiles due to the pickup of europagenic oxygen.

Figure 9.

Radial profiles with Europa oxygen source.

Figure 10.

Ion temperature profiles with Europa oxygen source.

[32] Finally, Schreier et al. [1998] reported three mechanisms for heating electrons from 3.6 eV to 5 eV to provide the Voyager-observed electron temperature and torus emissions: (1) an increase in the temperature of thermal ions, (2) hot ions diffusing inward, and (3) a flux of superthermal electrons. Mechanism 2 was most strongly supported by the Schreier et al. [1998] model. We argue that superthermal electrons are the most likely candidate. First, measurements of the hot ion populations made by the Galileo EPD (Energetic Particle Detector) [Mauk et al., 2004] show that hot (20 keV) inward diffusing ion densities peak near Eurora's orbit at <1 cm−3 and decline to insignificant levels inside of L = 7.5. Our model requires a 20 keV hot ion population of roughly 10 cm−3 to significantly alter (i.e., 1–2 eV) the electron temperature. For the densities observed by Mauk et al. [2004], the heating is insignificant. Second, the Voyager I electron measurements reported by Sittler and Strobel [1987] showed a superthermal electron component (∼500 eV) and the measured fraction of hot electrons is consistent with the required abundance for our model (∼<0.01).

[33] Figure 11 compares the Voyager core electron temperature and hot electron fraction with our Cassini model and shows not only a comparable abundance but also a similar radial dependence. Both Voyager and Cassini observations show an increase in core electron temperature with radius and significant variation in core electron temperature for L > 7.5. To illustrate the sensitivity of the core electron temperature to the hot electron fraction, we have added perturbations to the hot electron fraction for our best fit Cassini profiles. For the Voyager case we used a Gaussian perturbation centered at L = 8.0 to approximate the bump seen in the Voyager analysis of Sittler and Strobel [1987] and for the Cassini case we added a step function at L = 8.5. Both cases yield the observed radial profiles for core electron temperature. The hot electron fraction in our Cassini model is consistently higher than the Voyager data, but this might be expected for a two-Maxwellian treatment of what is probably closer to a “Kappa” distribution [Meyer-Vernet et al., 1995] where the affect on composition of the midrange temperatures (i.e., 30–70 eV) may be more significant than a single superthermal 500 eV tail. Electron impact ionization rates are roughly independent of temperature above 100 eV and thus composition may be strongly dependent on an accurate description of the midrange Kappa electrons. The apparent radial variation in the electron profiles between the Voyager and Cassini eras suggest, perhaps, additional evidence of temporal variability. Possible physical mechanisms that result in a greater abundance of hot electrons may include enhanced radial transport and/or variations in the neutral source. We note that the Voyager hot electron enhancement coincides with the so-called ramp region in the NL2 profiles, suggesting a possible connection between time-variable radial transport and hot electron abundance. A similar ramp region could exist for the Cassini era, but the model and data cannot confirm this. A more detailed analysis of the superthermal electron population is left for future study.

Figure 11.

Comparison of the core electron temperature and the hot electron fraction as a function of radius for the Voyager analysis of Sittler and Strobel [1987] (solid lines), Cassini model (dashed line), and a Voyager model (dot-dashed lines). The plus symbols are the core electron temperatures derived from Cassini UVIS by Steffl et al. [2004a].

5. Conclusions

[34] On 14 January 2001, the Cassini UVIS instrument made a radial scan of the Io plasma torus. Plasma composition for the five major ion species as a function of radius as well as total torus luminosity were provided by Steffl et al. [2004a]. Using a steady-state, two-dimensional model of plasma transport and chemistry, we have modeled the Cassini radial composition profiles and total luminosity. The model is subject to five primary parameters: hot electron fraction, hot electron temperature, neutral source rate, transport coefficient, and the neutral O/S ratio. Simple power laws for the radial variation of the hot electron fraction, hot electron temperature, neutral source rate, and transport coefficients complete our nine-dimensional parameter space. A comprehensive search of a six-dimensional parameter space (fixed O/S ratio and hot electron temperature profile) yielded the following best fit parameters: DLL(L) = 4.2 × 10−7(L/6)4.6 s−1, &#55349;&#56494;n(L) = 6.8 × 1027(L/6)−12 s−1, and feh(L) = 2.5 × 10−3(L/6)4.4. These best fit parameters yield an integrated transport time from L = 6 to 9 of 140 days, a total neutral source supply rate of roughly 900 kg/s, and a total luminosity of 1.4 terawatts.

[35] The major findings of this paper are summarized below.

[36] 1. The integrated transport timescale for plasma diffusing from L = 6 to L = 9 ranges between 100 and 200 days, slightly longer than the diffusion timescales of Schreier et al. [1998] (∼100 days).

[37] 2. Chemistry is largely determined inward of L = 6.5. The transport rate is fast compared to collision and Coulomb coupling timescales for L > 6.5.

[38] 3. The core electron temperature is highly sensitive to the specification of the hot electron fraction due to efficient thermal coupling between hot and cold electrons. The hot electron fraction increases with radius and shows significant spatial variability. Comparison with the Voyager era profiles of Sittler and Strobel [1987] suggests possible temporal variability.

[39] 4. Observed hot ion densities [Mauk et al., 2004] (>20 keV) are not sufficient to heat the core electron population. The increase in the electron temperature with radius is likely due to thermal coupling with an increasingly abundant hot electron population as seen in the Voyager results of Sittler and Strobel [1987].

[40] 5. A neutral source of roughly 1 ton/s is necessary to provided the total radiated power observed by Cassini UVIS (1.45 ± 0.25 × 1012 W).

[41] 6. A preliminary assessment of Europa's neutral source suggests that the radial profiles of composition are relatively insensitive to the additional oxygen and hydrogen at Europa because of the rapid radial transport beyond ∼9RJ. However, the additional mass loading at Europa will significantly alter the ion temperature profiles.

Acknowledgments

[42] Peter Delamere and Fran Bagenal are supported by NASA grants NAG5-12994 and NNG04GQ85G. Andrew Steffl's analysis of the Cassini UVIS data is supported under contract JPL 961196.

[43] Arthur Richmond thanks Aharon Eviatar and Edward C. Sittler for their assistance in evaluating this paper.

Ancillary