Azimuthal Variation in the Io Plasma Torus Observed by the Hisaki Satellite From 2013 to 2016
Abstract
In the Jovian magnetosphere, sulfur and oxygen ions supplied by the satellite Io are distributed in the so-called Io plasma torus. The plasma torus is located in the inner area of the magnetosphere and the plasma in the torus corotates with the planet. The density and the temperature of the plasma in the torus have significant azimuthal variations. In this study, data from three-year observations obtained by the Hisaki satellite, from December 2013 to August 2016, were used to investigate statistically the azimuthal variations and to find out whether the variations were influenced by the increase in neutral particles from Io. The azimuthal variation was obtained from a time series of sulfur ion line ratios, which were sensitive to the electron temperature and the sulfur ion mixing ratio S3+/S+. The major characteristics of the azimuthal variation in the plasma parameters were consistent with the dual hot electron model, proposed to explain previous observations. On the other hand, the Hisaki data showed that the peak System III longitude in the S3+/S+ ratio was located not only around 0°–90°, as in previous observations, but also around 180°–270°. The rotation period, the System IV periodicity, was sometimes close to the Jovian rotation period. Persistent input of energy to electrons in a limited longitude range of the torus is associated with the shortening of the System IV period.
Key Points
- Persistent azimuthal variations in the Io plasma torus were confirmed from three years of Hisaki observations
- The characteristics of the azimuthal variation were consistent with the dual hot electron model but different behaviors were also found
- The System IV period decreased 3 times. Two of these decreases were associated with increased volcanic activity on Io
1 Introduction
Io is the innermost Jovian Galilean moon and the most active volcanic body in our solar system. It supplies neutral particles (primarily oxygen and sulfur atoms and their compounds) to the magnetosphere (e.g., Thomas et al., 2004). The neutrals are ionized by electron impact and charge exchange. The ions are picked up by the planetary magnetic field, accelerated to the local plasma convection velocity, and begin to corotate around Jupiter. The ions distribute around Jupiter, near the orbit of Io, to form the Io plasma torus (charge density ~2,000/cm3).
The Io plasma torus is known to have an azimuthally inhomogeneous structure with respect to various plasma parameters, such as electron density, ion composition, and temperatures of ion and electron populations, that are strongly coupled with energy flows among the ions and electrons in the torus (e.g., Schneider et al., 1997; Steffl et al., 2006, 2008, and references therein). The corotation of azimuthal inhomogeneities with Jupiter produces periodic variations in the plasma torus luminosity observed by ground- and space-based remote instruments (e.g., Schneider & Trauger, 1995; Steffl et al., 2006). Previous observations have shown that there are two kinds of periodicities: the rotation period of Jupiter, known as the System III rotation period, and slightly longer System IV period. The System III period is based on the occurrence period of the Jovian decametric (DAM) radio emission. The DAM emission period corresponds to the rotational period of the Jovian magnetic field, that is, 9 hr 55 m 29.6854 s (approximately 9.925 hr) (Higgins et al., 1997). Although the System IV period (Dessler, 1985) is similar to the System III period (it is 1.5–5.5% longer), it is recognized to be independent of System III. Long-term observation of the torus enabled the two periodicities to be distinguished (Roesler et al., 1984; Sandel & Dessler, 1988; Woodward et al., 1994). The amplitude of the azimuthal variation peaks when the two periods are aligned and shows a long-term change at a period of the beat between the System III and IV periodicities (Steffl et al., 2006). Previous observations of the azimuthal variation, reviewed in Steffl et al. (2006), showed that the System IV period ranges from 10.07 to 10.47 hr.
The mechanism for producing the System IV period is still an open issue. The periodicity of 10.07–10.47 hr corresponds to a subcorotation velocity of 1.1–3.9 km/s and is close to the deviation in the plasma velocity from the rigid corotation measured by the Doppler shift of the [SII] 671.7- and 673.1-nm emissions (Brown, 1994; Thomas et al., 2001). However, the System IV periodicity of the [SII] line intensity is almost independent of radial distance from Jupiter while the deviation in the plasma velocity is strongly dependent on the radial distance (Brown, 1995). Brown (1995) concluded that the System IV periodicity cannot be explained by the lag in the plasma speed but is a pattern of a density wave in the torus. Based on the current knowledge, it is understood that the origin of the System IV period should be independent of the radial distance and decoupled from the subcorotation of the plasma. Brown (1995) also found from a six-month [SII] observation that there were two significant periodicities in the torus: the System III periodicity and a period of 10.214 ± 0.006 hr (2.91% longer than the System III period).
Continuous observation of the plasma torus for 45 days by the Cassini Ultraviolet Imaging Spectrograph (UVIS) revealed the detailed relationship among azimuthal variations of the plasma parameters in the plasma torus (Steffl et al., 2004a, 2006). Steffl et al. (2006) found persistent azimuthal variability in the ion mixing ratio, electron temperature, and electron column density in the plasma torus. The azimuthal variations of the S3+ mixing ratio and electron temperatures are in phase with each other but 180° out of phase with the variations of the S+ mixing ratio. The relationship between the sulfur ion mixing ratios and the electron temperature is explained by the electron impact ionization of sulfur ions (Steffl et al., 2006). The azimuthal variability persisted during the Cassini observation period and the amplitude of both variations of S+ and S3+ mixing ratios showed dramatic change with time, with two maxima occurring on day of year 280 and 307 in 2000. Steffl et al. (2006) found that this long-term change was due to a beat of the System III and System IV periodicities and that the maximum S+ mixing ratio occurred when the System IV peak in the S+ mixing ratio overlapped the System III peak at around 210° (or overlapped the S3+ peak around the System III longitude at ~30°). However, only two samples of the peak System III longitude could be obtained from the 45-day-long Cassini/UVIS observation. In this paper, we will confirm the Cassini/UVIS findings in a statistical sense with the Hisaki satellite observations.
Steffl et al. (2008) proposed two azimuthally varying sources of hot electrons that corotate and subcorotate in the plasma torus. The two hot electron sources were incorporated into a physical chemistry model (Delamere & Bagenal, 2003) and the azimuthal variation of ion composition and the beat frequency modulation in the amplitude of the azimuthal variation observed by Cassini/UVIS were reproduced by the model. When the hot electrons were placed at the System III longitude of 290°, their model found the System III peak in the S+(S3+) mixing ratio at around 210° (30°). Hess, Delamere, et al. (2011) discussed the hot electron sources. They proposed that the hot electrons are powered by inward motion of an empty flux tube. Electrons are accelerated in an Alfvén current system (e.g., Hess et al., 2010), which is created by the moving flux tube. The efficiency of the electron acceleration is related to the strength of the magnetic field at a foot point above the ionosphere, which causes the System III modulation of the hot electrons. Using the VIPAL magnetic field model developed by Hess, Bonfond, et al. (2011), they found that the hot electrons were most abundant around the System III longitude of 280°.
Steffl et al. (2006) also found that the System IV period during Cassini's Jupiter approach phase (October–November 2000) was 10.07 hr, 1.5% longer than the System III period but 1.3% shorter than the System IV period of 10.214 hr defined by Brown (1995). Subsequent ground-based observations of [SII] 671.2 and 673.1 nm in December 2000 showed a System IV periodicity of 10.14 ± 0.11 hr (Nozawa et al., 2004), suggesting recovery of periodicity toward the Brown value of 10.214 hr. Steffl et al. proposed that the increase in the neutral source by a factor of 3–4 caused by an Io volcanic event that occurred in September 2000 (Delamere et al., 2004) was responsible for producing the shorter System IV periodicity. Because Cassini/UVIS observed the Io plasma torus only during the later phase of the volcanic event, a causal relationship between the increased neutral source and the response of the torus is still not clear.
In this paper, the data set of the Io plasma torus emissions obtained by the extreme ultraviolet spectrograph EXCEED (Extreme Ultraviolet Spectroscope for Exospheric Dynamics), onboard the Hisaki satellite, is used (section 2.1). Hisaki has conducted long-term monitoring of the Io plasma torus since December 2013 and captured responses of the Jovian magnetosphere to the increase in neutrals from Io in early 2015 (Kimura et al., 2018; Koga et al., 2018; Tao et al., 2018; Tsuchiya et al., 2018; Yoshikawa et al., 2017; Yoshioka et al., 2018). The purpose of this study is to survey azimuthal variations in the torus using the large Hisaki data set obtained from December 2013 to August 2016. This data set provides a unique opportunity to confirm in a statistical sense the Cassini/UVIS findings on the azimuthal variations and to find how the increase in neutral particles from Io affects the azimuthal variations.
Ratios of sulfur emission lines are used to investigate azimuthal variations of thermal electron temperature and the sulfur ion mixing ratio S3+/S+. We investigated the dependence of two line ratios: SIV65.7/SIV140.5 and SIV65.7/SII76.5 nm on thermal electron density, thermal electron temperature, and hot electron fraction. We found that SIV 65.7 /SIV 140.5 nm depended primarily on the thermal electron temperature and SIV 65.7/SII 76.5 nm depended on the ratio of sulfur ion densities with different charge states (S3+/S+) (section 2.2). The azimuthal variation of the Io plasma torus was obtained from a time series of the two line ratios (section 2.3). From the three years of Hisaki observation data, we confirm that persistent azimuthal variations appeared in the Io plasma torus throughout periods of analyses (sections 3.2, 3.3, 3.7, and 3.8). We mainly found two results: (1) most of characteristics of the azimuthal variation are consistent with the dual hot electron source model proposed by Steffl et al. (2008). On the other hand, the Hisaki data showed that the peak System III longitude in the S3+ mixing ratio is located not only at ~30° but also around the longitude shifted by ~180° (sections 3.5, 3.6, and 4.1). (2) The System IV period sometimes became very close to the System III period (section 3.4). The shortening of the System IV periodicity was associated with persistent input of energy to electrons in a limited longitude range of the torus. An increase in neutral particle density associated with Io's volcanic activity is a possible mechanism contributing to the input of energy (section 4.2).
2 Observation and Data Analysis
2.1 Observation of the Io Plasma Torus
The EXCEED instrument onboard the Hisaki satellite conducted observations of the Io plasma torus (Tsuchiya et al., 2010; Yamazaki et al., 2014; Yoshikawa et al., 2014; Yoshioka et al., 2013). EXCEED obtains spectrographic images in a wavelength range of 52–148 nm with a spectral resolution of ~1 nm using a dumbbell-shaped slit that has a field of view of ~360arcsec along the Jovian equatorial plane and 140 arcsec in the north-south direction. This allowed us to obtain not only spectral information (Hikida et al., 2018) but also the spatial distribution of the plasma torus. Table 1 presents a list of ion emission lines used in this study and wavelength and spatial ranges for integration to obtain time variation of each emission line. All emission lines are the result of excitation by electron impact and subsequent radiation. For this study, we used the level-2 spectrograph image from EXCEED with which detected photons were accumulated for 1 min (Kimura et al., 2019). The level-2 images obtained during one Hisaki orbital period around the Earth (~106 min) were further integrated. The actual integration time was at least half the orbital period because the target of observation was visible for approximately a half of the orbital period. To remove contamination due to penetration of high-energy particles into the detector, we omitted the level-2 images for which the average intensity in a fixed dark area of the detector exceeded 2.6 × 10−4 count·s−1·pixel−1. To remove contributions of foreground geocoronal emissions to OII 83.4 nm, the data integration was limited to when Hisaki was in the shadow of the Sun (local time range of the satellite from 20:00 to 04:00). If the integration time was <10 min during one orbital period, the data set was not used for this data analysis. The measurement uncertainties were evaluated based on counting statistics
, where N is the total number of photons integrated in given time, wavelength, and spatial ranges. The photon count rates were calibrated to the brightness of the standard spectrophotometric star GD71 in Rayleighs (R).
Ion Species | Emission Line | Wavelength (Integration) | Spatial Range (Integration) |
---|---|---|---|
S+ | SII 76.5 nm | 75.5–77.5 nm | 3.5–7.5 RJ (both dawnside and duskside separately) |
S2+ | SIII 68.0 nm | 67.0–69.0 nm | |
S3+ | SIV 65.7 nm | 64.7 – 66.7 nm | |
SIV 140.5 nm | 138.5–142.5 nm | ||
O+ | OII 83.4 nm | 82.4–84.4 nm |
Three periods of Io plasma torus observations, used in this study, are shown in Table 2 (seasons A, B, and C). Ground-based observations of iogenic sodium emissions showed that the brightness was almost constant with only some small enhancements detected in seasons A and C but increased significantly in season B from the middle of January to March 2015 (Yoneda et al., 2015; Figure S3), suggesting that there was an increase in volcanic activity. Infrared (IR) monitoring of Io during season B was sparse (de Pater et al., 2016; de Kleer & de Pater, 2016), but it is suggested that Pillan Patera and Kurdalagon Patera could be candidate sources of the active plumes during this period (Tsuchiya et al., 2018). de Kleer and de Pater (2017) showed that the brightness of Loki Patera increased around January and April 2016 (in season C), although the sodium emission did not show significant variation. The Hisaki data obtained from 2013 to 2016 were useful in investigating the effect of the increased supply of neutral particles from Io's volcanic activity on the azimuthal variation of the Io plasma torus.
2.2 Sulfur Emission Line Ratios: Proxies of Temperature and Composition

Figures 1a–1c show model SIV 65.7/SIV 140.5-nm line ratios as a function of thermal electron temperature, thermal electron density, and hot electron fraction. The CHIANTI atomic database version 8.0 (Del Zanna et al., 2015; Dere et al., 1997) was used to derive the dependencies on the electron parameters. Figures 1b and 1c show that the line ratio is independent of the thermal electron density but is strongly dependent on the thermal electron temperature and somewhat less so on the hot electron fraction. Note, the color bar in Figure 1c shows a much smaller range of line ratios than Figure 1b, emphasizing the weak dependence on the hot electron fraction. Figure 1a also shows that the dependence on thermal electron temperature is stronger than that on the hot electron fraction. From hereon we call this ratio (SIV 65.7/SIV 140.5 nm) the “temperature ratio”.

Figures 1d–1f show dependence of the SIV 65.7/SII 76.5-nm ratio on the electron parameters. Note that a full-scale range of Figures 1d–1f is only ±13% of the midvalue (0.69). Figure 1e shows that the line ratio is almost independent of both electron density and temperature if the electron temperature is greater than 3.7 eV. Figure 1f shows that the ratio has a weak inverse dependence on the hot electron fraction. Figure 1d also shows that the ratio has weak dependence on both thermal electron temperature and hot electron fraction. The SIV 65.7/SII 76.5-nm ratio has only weak dependences on electron density, thermal electron temperature, and hot electron fraction; in other words, the ratio depends primarily on the ion mixing ratio S3+/S+. From hereon we call this ratio (SIV 65.7/SII 76.5 nm) the “composition ratio”.
2.3 Rotational Modulation Analysis

Six free parameters in equation 2 (I0, I1, IIII, IIo, ϕ1, and ϕ2) and their uncertainties are determined by a least squares fit (Press et al., 1992). Each uncertainty corresponds to the one-dimensional confidence interval bounded by ∆χ2 = 1.0, where ∆χ2 is the residual of the χ2 value from the minimum χ2 (i.e., the χ2 with the best fit parameters). In this study, a five-day data window was used to obtain a robust fit to both 10- and 42-hr periodicities. The data window was shifted every day to find time variations of the six parameters. The maximum number of data points for the five days was ~68 (5 days/106 min). For the occasions where the number of points in a five-day interval was <25, the interval was omitted from the analysis. We also discarded the fitting results when the χ2 value exceeded 500. An example of the sinusoidal fit to the plasma torus light curves is shown in Figure S1 in the supporting information.
3 Results
In this section, initially we present the behavior of the ion emission intensities, then move to the rotational modulation in temperature ratio and composition ratio. We found that the behavior of the rotational modulation which appeared in the ion emission intensities was very complex because the variation in ion emission intensities might be result of multiple effects from azimuthal inhomogeneity and local time dependence of the plasma parameters (section 3.1). Subsequently, we show that variations in temperature ratio and composition ratio under the typical plasma torus condition (sections 3.2 and 3.3). We used these ratios as proxies for the azimuthal variations of the thermal electron temperature and sulfur ion mixing ratio in the torus (sections 3.4–3.8).
3.1 Rotational Modulation Analysis for Ion Emission Intensities in Season B
Figures 2 and 3 show results of the rotational modulation analysis of the ion emission intensities (SII 76.5 nm, SIII 68.0 nm, SIV 65.7 nm, and OII 83.4 nm) for the duskside and dawnside of the Io plasma torus, respectively, during season B. Figures 2a and 3a show the mean intensities of ion emission lines (I0). A decrease in the brightness ratio of SIV to SII and an increase in SIII and OII intensities are two indicators of the plasma torus response to an increase in neutrals. In the dawnside, for example, the intensities of SII 76.5 nm and SIV 65.7 nm were almost the same (~50 R) until the middle of January (~day of year 19). After day of year 19, the SII intensity increased to ~120 R while the SIV intensity slightly decreased to ~40 R (Tsuchiya et al., 2018; Yoshikawa et al., 2017). Then, the ratio of SIV to SII decreased. SIII 68.0 nm and OII 83.4 nm also increased during the same period from ~150 to ~200 and ~100 to ~ 150 R, respectively. It is suggested that these variations were caused by an increase in the neutral particle density (O and S atoms) in the plasma torus. The increase in the neutral particle density caused the decrease in S3+ through charge exchange (S3++O → S2++O+), and the increase in S+ due to electron impact ionization (S → S++e) (Delamere et al., 2005). The brightness of SIII and OII, whose emitters (S2+ and O+, respectively) are the main constituents of the plasma torus, increased from the beginning of February to the middle of March, suggesting that the mass production rate in the plasma torus enhanced during this period. Yoshioka et al. (2018) estimated the neutral source and plasma production rates in the plasma torus with a spectrum diagnosis analysis and a physical chemistry model and found that they increased approximately by factor of 4.5.


Figures 2b, 2c, 3b, and 3c show the amplitude of the rotational modulation and the System III longitude when the intensity of the rotational modulation was at the maximum. In a similar manner, Figures 2d, 2e, 3d, and 3e show the amplitude of the Io orbital period modulation and the Io phase angle when the intensity was at the maximum, respectively. Throughout the period shown in the figures, the amplitude of the Io orbital period modulation (IIo/I0) was generally smaller than 0.15 and the Io phase angle at the maximum brightness was distributed around 0° on the dawnside (Figure 3e) and 180° on the duskside (Figure 2e) for all emission lines. We will discuss an origin of this feature in section 3.2. The rotational modulation showed complex behaviors. Before March 2015, the amplitude of the rotational modulation (IIII/I0) was smaller than 0.15 but it grew from March 2015 and approximately doubled. The source of the increase in the rotational modulation is consistent with increases in hot electron density in a limited longitude range and will be discussed in section 4.1 in detail. On the duskside, the peak longitude for all four emission lines moved from 0° to 540° during January 2015. This yields a mean longitude drift rate of 540°/month or ~18°/day. If one assumes that the rotational modulation is caused by rotation of the azimuthal variation in the ion brightness, the positive longitude drift indicates that the rotation period is slower than the System III rotation period because the longitude increases with time as Jupiter rotates. However, longitude drift rates were not always the same among ion emission lines (e.g., in December 2014 and March 2015, the longitudes of different emission lines did not align with each other), and the drift rate on the dawnside was different from that on the duskside. The rotational modulation in the ion intensities shown in Figures 2 and 3 cannot be explained by the simple rotation of an azimuthally inhomogeneous structure of brightness. It may be a result of the multiple effects from azimuthal inhomogeneity and local time dependence of the plasma parameters (e.g., Schneider & Trauger, 1995; Smyth et al., 2011; Steffl et al., 2006) and the azimuthal plasma speed in the plasma torus (Brown, 1995; Thomas et al., 2001).
3.2 Rotational Modulation Analysis of the composition ratio in Season B
In this section, we show variations in the composition ratio during season B. Figure 4a shows dawnside ion emission intensities, averaged over the five-day window (the same as Figure 3a). Figure 4b shows the mean ratio for the dusk (red) and dawn (black). The ratio decreased from the end of January to the end of March. As described in section 3.1, the decrease is interpreted as an increase in the neutral particle density. A red bar in Figure 3b indicates a period when the ratio was smaller than 0.75. This is similar to the period of the sodium enhancement which is shown by a blue bar. Subsequently, the ratio recovered and further increased by the end of April 2015. This recovery coincided with the increase in the thermal electron temperature (shown in section 3.3), which was consistent with the increase in the sulfur ion charge state. Figures 4c and 4d show the amplitude of the azimuthal variation and the System III longitude at the peak ratio, respectively. The amplitude shows significant time variation with a time scale of 10–20 days. This corresponds to a beat modulation between the System III and System IV periodicities (Steffl et al., 2006). The amplitude of the beat modulation was smaller than 0.2 until February, increasing to 0.4 in March. The beat modulation is described in detail in section 3.6. The drift rate of peak longitudes was variable in time (ranging from 4° to 18°/day), but had similar drift rates in both the dawnside and duskside. This is consistent with the subcorotation of an azimuthal inhomogeneity around Jupiter.

Figures 4e and 4f show the amplitude modulation associated with Io's orbital period and Io's phase angle at the peak ratio, respectively. The relative amplitude is distributed approximately in range of 0.05–0.1. The peak Io phase angle for the dawnside and duskside is stable and well constrained (small uncertainty). The similar phase dependence is also observed in the ion intensities as shown in Figures 2e and 3e. Tsuchiya et al. (2015) showed that hot electrons that were heated around Io are transported downstream by the azimuthal plasma flow. The hot electrons quickly lose their energy through Coulomb interaction with ambient thermal electrons with a time scale less than 10 hr (Suzuki et al., 2018; Volwerk et al., 1997). As a result, the hot electron fraction increased downstream of the satellite (Tsuchiya et al., 2015, Figure 3). Because of the longitude inhomogeneity of hot electron fraction, the ion brightness on the dawnside (or duskside) increases when the Io phase angle is around 0° (180°). In the same manner, the composition ratio decreases on the dawnside (or duskside) when the Io phase angle is around 0° (180°). Increases in the composition ratio occur on the opposite side of the torus: the ratio increases on the dawnside (duskside) when the Io phase angle is around 180° (0°). This is consistent with the results shown in Figure 4f.
3.3 Rotational Modulation Analysis of the temperature ratio in Season B
In this section, we show that variations in temperature ratio behaved consistently with the thermal electron temperature. Figure 5 shows the results of the rotational modulation analysis for the temperature ratio. Figure 5b shows that the mean ratios are distributed between 0.35 and 0.62. The dependence of the ratio on the electron temperature, shown in Figure 1b, indicates that this ratio range yields a thermal electron temperature range between 4.2 and 5.7 eV, which is consistent with the thermal electron temperature range in the plasma torus (6–7 RJ) reported previously (e.g., Bagenal, 1994; Steffl et al., 2004b; Yoshioka et al., 2014). The mean ratios were larger for the duskside (red) than for the dawnside (black), which is consistent with the difference in the thermal electron temperature that is caused by a large-scale dawn-dusk electric field (Barbosa & Kivelson, 1983; Ip & Goertz, 1983; Murakami et al., 2016). Figures 5c and 5d show the azimuthal variation of the ratio. The longitudes in both the dawnside and the duskside varied similarly. Figures 5e and 5f show the amplitude modulation associated with the Io orbital period. Figure 5e shows that almost all the normalized amplitude is distributed between 0.0 and 0.05, and Figure 5f shows that the uncertainties in the peak phase angle are large, which reflects the weak dependence of the temperature ratio on the hot electron fraction. This ratio is a proxy for the thermal electron temperature in the torus.

3.4 System IV Periodicity

Figure 6 shows the drift of the peak System III longitude of the composition ratio (Figures 6a, 6c, and 6e) and the System IV period derived by fitting the drift with a linear function (Figures 6b, 6d, and 6f). We selected a time window for the linear fit when the drift rate of the peak System III longitude was stable and the amplitude of the azimuthal variation (IIII/I0) was larger than 0.03 for more than five days. The drift of the peak longitude in seasons A and C will be presented in sections 3.7 and 3.8 in detail. The vertical bar on each data point in Figures 6b, 6d, and 6f indicates an uncertainty of the rotation period estimated using a least squares fit and a horizontal bar represents the time span used to derive the rotation period. The mean rotation period during the three-year Hisaki observation is 10.07 ± 0.07 hr.

The rotation period decreased 3 times: February 2014 (season A), March–April 2015 (season B), and May–June 2016 (season C). The mean and the shortest System IV period in each season are summarized in the bottom part of Figure 6.
In season B, the rotation period decreased to 9.94–9.98 hr from late March to April in 2015. The decrease in the rotation period (the green bar in Figure 4c) was delayed by approximately two months after the start of the Io plasma torus response to the volcanic activity (the red bar in Figure 4b). The green bar indicates a period when the System IV period was shorter than 10.07 hr (the shortest period identified by previous studies). On the other hand, the decrease in the rotation period occurred concurrently with the increase in the thermal electron temperature (from March to April as shown in Figure 5b). Similar but weaker characteristics were also indicated in season C (see section 3.8). A couple points in Figure 6f show the rotation period decreased to 10.03 hr in May–June 2016. In season A, there is a suggestion that the rotation period decreased to 10.01 hr in February 2014, although there is only a single point in Figure 6b and no significant volcanic activity on Io had been reported in early 2014. We also note that there are times when the System IV period is noticeably longer than 10.07 hr, particularly in season A.
3.5 Phase Difference Between Thermal Electron Temperature (Temp) and Sulfur Ion Mixing (Comp) Ratios
The Cassini/UVIS observation showed that the azimuthal variations of S3+ mixing ratio and the electron temperature were more or less in phase with each other (Steffl et al., 2006). In this section, we examine the relationship between S3+/S+ and the thermal electron temperature in the Hisaki observations. In Figure 7, the azimuthal variations derived from the composition ratio (red) and the temperature ratio (black) in season B are compared. Figures 7a–7c and 7d–7f show the results obtained for the dawnside and duskside, respectively. The peak longitude of both ratios varied in a similar manner (Figures 7b and 7e). Figures 7c and 7f show the differences between the two peak longitudes. The peak longitude of the temperature ratio preceded that of the temperature ratio by 0°–90°. The difference between the peak longitudes was sometimes negative or >90° when the amplitude of the azimuthal variation was small. Because the uncertainty of the peak longitude becomes relatively large when the amplitude is small, the reliability of these values is low. From more detailed analysis (Figure S2), we found that 70% of the data points for the three seasons are distributed from 0° and 45° (Figures S2v and S2h). This indicates that the peak thermal electron temperature tends to precede the peak S3+ abundance range by 0°–45°.

3.6 Source System III Longitude of the Hot Electrons
The beat frequency modulations of the System III and System IV periods are visible in the amplitude of the azimuthal variations shown in Figure 7. The amplitude of the azimuthal variation shows a maximum when the azimuthal inhomogeneities rotating with the System III and System IV periods are aligned. The System III longitude at which the beat modulation is maximum reflects the source longitude of the hot electrons (Hess, Delamere, et al., 2011; Steffl et al., 2008). In this section, we examine distribution of the source longitude with the Hisaki observations.
Red hollow diamonds in Figures 7a, 7b, 7d, and 7e indicate the amplitude and longitude when the amplitude of the composition ratio was at a local maximum. The local maximum is determined if all four criteria described below are satisfied: (1) the amplitude (IIII/I0) is larger than 0.05, (2) the value is the maximum in a 11-day window (±5 days), (3) the amplitude value tends to increase toward and decrease away from the maximum value within the window, and (4) a time interval of the missing data should be less than five days in the window. The window size of 11 days was chosen to be shorter than the beat period. From Figure 6, the longest System IV periodicity was 10.24 hr. This gives the beat periodicity of 13 days. The missing data could cause an error in the System III longitude because the longitude drifts with time. The error in the longitude will be 31° when the System IV period is 10.07 hr (the mean periodicity from the Hisaki observation) and the interval of data missing is five days. The same peak search procedure has also been carried out for the temperature ratio and local maxima are shown by blue hollow diamonds. After the middle of February 2015, most of the peak longitudes were distributed in the 0°–90° range (blue shaded area in the figure), indicating that S3+ was abundant in this longitude range, which is consistent with the Cassini data. During the period between two beat modulation maxima, the peak longitude drifted ~360° around Jupiter. This is also typical of the beat modulation observed by Cassini (Steffl et al., 2006). The beat modulation sometimes did not accompany a drift of the peak longitude but was stable in time (e.g., early April 2015). This suggests that the amplitude of the azimuthal variation rotating with the System III period was larger than that of the System IV period and the azimuthal variation was fixed with the System III coordinate, consistent with Steffl et al. (2008). On one occasion the peak longitude drift even showed a negative drift (e.g., late April 2015), indicating a rotation rate faster than that of the System III period. However, this does not reflect the actual rotation of the azimuthal variation and is discussed in section 4.2.
Before the middle of February 2015, the Hisaki data showed that there were two different behaviors of the beat modulation that had not been observed by Cassini/UVIS. (1) In Figure 7b, five beat modulations were identified on the dawnside in composition ratio (red hollow diamond nos. 1–5) before the middle of February. Three events (nos. 1, 3, 4) were found in the longitude sector from 180° to 270° (orange shaded area in the figure) that were shifted from those found after the middle of February by 180°. (2) At the beginning of January 2015 (between red diamond no. 2 and no. 3 in Figure 7b), the peak longitude drifted less than 180° during the time interval of the two beat modulation maxima. Similar behavior was also seen for the temperature ratio (indicated by the blue hollow diamonds in Figures 7a and 7b). A good example is found in late January: the peak longitude drifted only ~180° during the interval of the two beat modulations (between blue diamond no. 4 and no. 5). These behaviors suggest that sometimes the azimuthal variation has not only a single-peaked structure, but also a double-peaked one. Figure 8 shows a histogram of the peak System III longitude of the composition ratio derived from the Hisaki observation for three seasons. The peak longitude is in a range of 0°–90°. While the statistics are limited, the plot shows an intriguing trend to be explored with future data.

3.7 Azimuthal Variation in Season A
Figure 9 is a summary of the rotational modulation analysis for season A for the duskside of the torus. The results obtained for the dawnside were similar. The beat frequency modulation is presented in Figure 9d. Only two maxima were identified, in December 2013 and February 2014 around the System III longitude of 170° and 0°, respectively. The peak longitude of the temperature ratio (black symbols in Figure 9e) preceded that of the composition ratio (red symbols), which is consistent with the result in season B.

The rotation period of the plasma torus decreased from as high as ~10.2 hr (late January) to 10.01 hr (late February). Figure 9a shows that the intensity of SII 76.5 nm slightly increased with respect to that of SIV 65.7 nm after February 2014. This suggests an increase in the neutral particle density in the plasma torus. However, there is no evidence for an increased volcanic activity on Io: both the sodium nebula and the oxygen neutral cloud emissions were almost stable during this period (Koga et al., 2018; Yoneda et al., 2015) and the ion brightnesses and the line ratios do not show significant time variations (Figures 9a–9c).
3.8 Azimuthal Variation in Season C
Figure 10 shows the results of the rotational modulation analysis for season C during the duskside. Again, similar results were obtained for the dawnside. The Hisaki data presented in Figures 10a and 10c suggests modest neutral particle increase in the plasma torus in 2016: from late January to late February, from late April to May, and from late July to August. The first and second responses of the plasma torus roughly correlate with the activity of Loki Patera. The paper by de Kleer and de Pater (2017) modeled IR radiative intensity from Loki Patera. The two orange bars in Figure 10c indicate periods when the intensity exceeded 100 GW·μm·sr (from a model with modified thermal property of lava, see blue thin solid line in their Figure 3). The decreases in the composition ratio (red bars in Figure 10c) may be related to volcanism at Loki Patera. The response to the third event, which occurred in August 2016, resembled the response to a volcanic event in season B. We have not yet identified a candidate source region.

From both Hisaki and ground-based observations obtained during seasons B and C, it appears that the amount of gas escaping from Io does not have a simple correlation with the IR radiant flux from the surface. During the eruption of Lokipatera, the maximum IR radiant flux in the 3.8 mm-band was observed to be 147 ± 22 GW/sr/mm on 22 January, 2016 (de Kleer & de Pater et al., 2017). However, the putative response of the plasma torus to the Loki eruption was less than the changes observed during either the Pillan or Kurdalagon eruptions in season B. Pillan patera was observed to have a peak IR flux of 80 ± 16 GW/sr/mm on 18 February, 2015 (de Pater et al., 2016), while Kurdalagon patera was observed to have a peak IR flux of 68 ± 11 GW/sr/mm on 5 April, 2015 (de Kleer & de Pater et al., 2016). One possible caveat is that the frequency of observations during 2015 was considerably lower and the true peak in radiant flux might has been missed.
The beat frequency modulation in season C is similar to that in season B. The peak longitude of the temperature ratio preceded that of the composition ratio, which is consistent with the data from seasons A and B. Figure 10e shows that, before the middle of March 2016, the System III longitudes at which the beat modulation was greatest were distributed not only in the longitude ranges of 0°–90° but in the range of 180°–270°. On the other hand, the peak longitudes were concentrated between 0° and 90° following the end of March.
Figure 6f shows that the rotation period became shorter than 10.07 hr on three occasions (indicated by three green bars in Figure 10d). During these times, the thermal electron temperature (Figure 10b) increased (middle of May to the beginning of June) or peaked (end of February and middle of August). However, a relationship between the decrease in the rotation period and the increase in the thermal electron temperature in season C was not as clear as the relationship seen in season B. The shortening of the System IV period was delayed by one to two months after the increase in the IR intensity (orange bar) and the decrease in composition ratio (red bar).
4 Discussion
4.1 Comparison With the Dual Hot Electron Model
The dual hot electron model of the Io plasma torus was proposed by Steffl et al. (2008) and Hess, Delamere, et al. (2011) to explain the azimuthal variation observed by Cassini/UVIS. The model incorporates two types of azimuthal, single-peaked, hot electron sources with different rotation periods (i.e. the System III and System IV periods) into a physical chemistry model. The System IV hot electrons slowly subcorotate in the plasma torus on a time scale comparable to the chemical time scale in the plasma torus (~10 days) and produce azimuthal variations in the thermal electron temperature and ion composition. On the basis of this model and the Cassini/UVIS observations, we expect four characteristics, described below, to be observed in the plasma torus. (1) The azimuthal variations in longitude slowly drift relative to the System III longitude and (2) the amplitude of an azimuthal variation varies with a beat period between the System III and System IV periods. These characteristics were seen in the Hisaki observation data. (3) The model predicts that the azimuthal variation of the S+ mixing ratio is approximately out of phase with the S3+ mixing ratio. Although the Hisaki observations presented in this paper did not distinguish the S+ and S3+ mixing ratios, SIV65.7/SII76.5 nm “composition ratio” showed clear azimuthal variation. The amplitude of the azimuthal variation sometimes reached up to 40% (March 2015 and May 2016). (4) Steffl et al. (2008) and Hess, Delamere, et al. (2011) incorporated the hot electron population that peaked around the System III longitude of 280° into the torus chemistry model. They found that the excess of the hot electron population extended downstream due to the subcorotation of plasma and that the peak longitude where S3+ is abundant would occur around the System III longitude ~30° (shifted forward by ~100°). This prediction was seen in the Cassini/UVIS data (Steffl et al., 2006; phase difference between Te and the S3+ mixing ratio shown in their Figure 3). The Hisaki data showed that the peak longitudes of the thermal electron temperature preceded those of the S3+/S+ ratio by 0°–45°. The thermal electron temperature increases due to the Coulomb interaction with the hot electrons. A time scale of the interaction between hot (~100 eV) and thermal electrons (~5 eV) is a few hours (e.g., Yoshioka et al., 2014) while the ionization of sulfur ions (S+ → S2+ → S3+) takes several tens of days to hundreds of days (Delamere et al., 2005; Steffl et al., 2008). Because of these time scale differences, the peak longitude of the thermal electron temperature is expected to be between the longitude of the source of the hot electrons and the peak longitude where S3+ is most abundant. Based on these considerations, the results from the Hisaki data are explained by the competing effects of subcorotation of hot electrons and chemical reactions in the plasma torus and are qualitatively consistent with the prediction of the model. From the observational evidence described above, the dual hot electron model seems to be applicable to the Io plasma torus for the Hisaki observation periods.
On the other hand, the Hisaki observations showed two characteristics that cannot be explained by the dual hot electron model: (1) while the S3+-abundant System III longitude was primarily found in the range of 0°–90°, another S3+ abundant longitude occurred in the range of 180°–270° during volcanically quiet periods. This secondary longitude is not included in the model proposed by Hess, Delamere, et al. (2011). (2) The Hisaki data showed that the System III longitude sector in which the S3+/S+ ratio or the thermal electron temperature increased sometimes occurred twice during one revolution of the peak longitude drift. This suggests that the azimuthal variation contains not just a single-peak component but also second-peak component. A possible origin of the double-peak component was investigated by Copper et al. (2016) and Steffl et al. (2008). They considered the effect of the offset between the centrifugal and rotational equators (“Basic azimuthal model” in their paper). The plasma torus and extended neutral cloud are spread vertically around the centrifugal and rotational equators, respectively. The centrifugal and rotational equators intersect at the System III longitudes of 110° and 290°. Due to an increased source rate of S+ through electron impact ionization of sulfur atoms and an increased loss rate of S3+ through a charge exchange reaction in these longitudes, the double-peaked azimuthal variation of S3+/S+ was produced at the System III longitudes around 40° and 220° (Steffl et al., 2008, Figure 3). These longitudes are consistent with the Hisaki observations (0°–90° and 180°–270°), but Steffl et al. (2008) showed that the amplitude of the double-peaked variation of S3+/S+ was very small (only ~1%). For the next step in the analysis of the Hisaki data, we plan to include a 5-hr (half of a Jovian rotation) periodic component in equation 2 and search for double-peaked variations of plasma parameters in the Io plasma torus.
4.2 Time Variation in the System IV Periodicity
The Hisaki data showed that the amplitude of the azimuthal variation of the composition ratio was usually <0.2 (December 2013 to January 2014, April 2014, December 2014 to February 2015, January–March 2016, July–August 2016) but increased up to 0.3–0.4 during the shortening of the System IV period (February 2014, March–April 2015, and May–June 2016). Increase in the azimuthal amplitude means that azimuthal variations associated with System III, System IV, or both increased. Because the peak longitude continued to drift with time during the periods of the increasing azimuthal amplitude, the amplitude of the azimuthal amplitude of System IV was consistently greater than that of System III during these periods.
During the periods March–April 2015 and May–June 2016, the System IV rotation period decreased following increased volcanic activity on Io. The increases in the azimuthal amplitude tend to occur concurrently with the increase in the thermal electron temperature (Figures 5b and 10b). These facts suggest that the decrease of the System IV period is associated with input of energy to electrons over a limited longitude range of the Io plasma torus. Because the equilibration time for the hot and thermal electrons in the plasma torus (approximately hours) is very short compared to the beat modulation period (from a few weeks to a month), persistent input of energy is needed to maintain large-amplitude azimuthal variations in the plasma torus. Although determining the amount of input energy and energy sources is outside of the scope of this paper, possible sources of the energy input to the thermal electrons in the torus are hot electrons included in the inward moving flux tubes (Kimura et al., 2018; Yoshikawa et al., 2017; Yoshioka et al., 2014; Yoshioka et al., 2017), local heating processes in the moving flux tubes (Frank & Peterson, 2000; Hess, Delamere, et al., 2011), and energy coupling with picked up ions (Barbosa et al., 1983).
The decrease in the rotation period observed in February 2014 occurred during a quiet period of volcanic activity. This suggests that an increase in volcanic activity is not required to shorten the System IV period. Figure 9 shows that the shortening of the System IV period occurred when the composition ratio decreased. Assuming that an increase in neutral particles supplied to the torus resulted in the decrease in the composition ratio (see section 3.1), the plasma in the torus is slowed down through the pickup process and an electrical current is generated (Vasyliunas, 2016). The current is closed with the Pedersen current in the Jovian ionosphere through field aligned currents (e.g., Pontius & Hill, 1982). This current system could enforce azimuthal flow and compensate the delay of plasma flow from corotation. Shortening the System IV period could also occur if the ionospheric Pedersen conductivity at the magnetic field footprint of Io plasma torus increases. Modeling studies are needed to quantitatively evaluate these hypotheses.
The time variation in the peak longitude sometimes showed phase jumps and negative drift, as described in section 3.6. The Hisaki data showed that a phase jump occurred when the amplitude of the azimuthal variation showed a minimum and was very close to zero (see the middle of January 2015 in Figure 4d and the middle of May 2016 in Figure 10e for examples of the phase jump). This could be one characteristic predicted by the dual hot electron model. Steffl et al. (2008) showed that the rotation period of ion composition varied with time depending on the relative phase difference between two hot electron sources. The rotation period of ion composition increased when the azimuthal patterns of the two hot electron sources were nearly out of phase and the amplitude of the azimuthal variation was at minimum. The negative drift of the peak longitude was sometimes observed (e.g., at the end of April 2015 shown in Figure 4d, the beginning of January 2014 shown in Figure 9e, and the beginning of July 2016 shown in Figure 10e). However, this does not indicate that the rotation rate was faster than the System III period. Instead, this could be explained by the phase jump. The negative drift occurred when the amplitude of the azimuthal variation showed minima. If the difference in longitude before and after the phase jump exceeds 180°, the longitude drift rate, which is derived from five-day data, cannot track the real longitude variation and shows an apparent negative drift.
5 Summary
- Based on the CHIANTI atomic database version 8.0, we examined the dependences of two line-intensity ratios, SIV65.7/SII76.5 nm (“composition ratio”) and SIV65.7/SIV140.5 nm (“temperature ratio”), on thermal electron density, thermal electron temperature, and hot electron fraction under typical Io plasma torus conditions. As the name suggests, the temperature ratio depends primarily on the thermal electron temperature and has a weak dependence on the hot electron fraction. Likewise, the composition ratio depends primarily on the density ratio of S3+ to S+ and has a weak inverse dependence on the hot electron fraction.
- Using these two line ratios, we confirmed significant and persistent azimuthal variations in the Io plasma torus over three years. The mean rotation rate of the azimuthal patterns during the three years of Hisaki observations was found to be 10.07 ± 0.07 hr, ~1.5% slower than the System III period.
- The azimuthal variation of the S3+/S+ mixing ratio, as inferred by our “composition ratio”, is nearly in phase with that of the thermal electron temperature, as inferred by our “temperature ratio”. This is consistent with the prediction of the dual hot electron model (Hess, Delamere, et al., 2011; Steffl et al., 2008). The peak longitude of the electron temperature tends to precede that of the higher sulfur ion charge state (S3+/S+) by 0°–45°, which is explained by the competing effect of the subcorotation of hot electrons and chemical reactions in the torus.
- The beat frequency modulation of the System III and System IV periods was confirmed by the Hisaki observations. S3+ was abundant and the thermal electron temperature increased in the 0°–90° and the 180°–270° System III longitude sectors. During an interval when the System IV period shortened, S3+ and the thermal electron temperature increased only in the 0°–90°sector. The amplitude of the azimuthal variation occasionally showed two minima during one beat modulation period. These results suggest that the azimuthal variation of the hot electrons contains not only a single-peak component in longitude but also a double-peak component that is fixed in the System III coordinates.
- The rotation period of the Io plasma torus sometimes decreased from the mean periodicity of 10.07 hr. The period fell to 9.93–9.97 hr in March–April 2015 and to 10.03 hr in May–June 2016. The decreases in the rotation period in 2015 and 2016 were coincident with increases in Io's volcanic activity. Both decreases occurred when the thermal electron temperature in the plasma torus increased. On the other hand, the decrease in the rotation period in February 2014 occurred when there was no increase in Io's volcanic activity and no observed increase in the thermal electron temperature.
- The observed decreases in the rotation period associated with Io's volcanic activity are related to an increase in the thermal electron temperature rather than to a total ion mass in the plasma torus.
Acknowledgments
This study has been done as a Master thesis study by RA. This work was supported by JSPS KAKENHI grants JP26400476, JP16K05567, and JP17H02965, and by JSPS and MAEDI under the Japan-France Integral Action Program (SAKURA). We acknowledge the contribution of the International Space Sciences Institute (ISSI) in Bern, Switzerland, for hosting and funding the ISSI international team on “The influence of Io on Jupiter's magnetosphere” (ID388). We thank the HISAKI NASA/PSP members for the useful discussions. The HISAKI data sets are archived in the ISAS/JAXA Data Archives and Transmission System (DARTS). The level-2 data set used in this study is open to public from the DARTS website (https://www.darts.isas.jaxa.jp/pub/hisaki/euv/). The information about the level-2 data analysis and calibration are described at http://c.gp.tohoku.ac.jp/hisaki/.