Driver of Energetic Electron Precipitation in the Vicinity of Ganymede

The driver of energetic electron precipitation into Ganymede's atmosphere has been an outstanding open problem. During the Juno flyby of Ganymede on 7 June 2021, Juno observed significant downward‐going electron fluxes inside the bounce loss cone of Ganymede's polar magnetosphere. Concurrently, Juno detected intense whistler‐mode waves, both in the quasi‐parallel and highly oblique directions with respect to the magnetic field line. We use quasi‐linear model to quantify energetic electron precipitation driven by quasi‐parallel and very oblique whistler‐mode waves, respectively, in the vicinity of Ganymede. The data‐model comparison indicates that in Ganymede's lower‐latitude (higher‐latitude) polar region, quasi‐parallel whistler‐mode waves play a dominant role in precipitating higher‐energy electrons above ∼100s eV (∼1 keV), whereas highly oblique waves are important for precipitating lower‐energy electrons below 100s eV (∼1 keV). Our result provides new evidence of whistler‐mode waves as a potential primary driver of precipitating energetic electrons into Ganymede's atmosphere.

convection time of a flux tube across Ganymede may explain the energy-dependent loss cone features (the level of filling in the downward direction decreases with increasing energy). Although this mechanism may operate for lower-energy electrons, additional mechanisms are needed to explain the partially full downward loss cone at higher-energy electrons, for which the bounce period is shorter than their convection time.  attributed this feature to energy-dependent pitch angle scattering when electrons bounce between Ganymede and their near-Jupiter mirror point. Using the general wave-particle scattering theory,  further estimated pitch angle diffusion coefficients (potentially responsible for the partially or fully filled loss cone), as well as their energy dependence, while the driver of causing this pitch angle scattering was not identified. Tripathi et al. (2014) evaluated pitch angle diffusion by parallel whistler-mode waves near Ganymede based on the Galileo spacecraft measurement and found that whistler-mode wave amplitude of ∼16 pT is required to match the observed and calculated pitch angle diffusion coefficients. However, the quantitative role of whistler-mode waves with various properties (e.g., parallel vs. oblique wave normal angle; low vs. high frequency) in precipitating electrons in a broad range of energies into Ganymede's atmosphere still needs further investigations.
In the present paper, we focus on understanding the features of energetic electrons and plasma waves near Ganymede, as well as the underlying mechanisms of causing energetic electron precipitation into Ganymede's atmosphere.

Juno Observations Near the Vicinity of Ganymede
On 7 June 2021, the Juno spacecraft (Bolton & Juno Science Team, 2010) traveled near Ganymede (Hansen et al., 2022) and crossed Ganymede's magnetosphere (with at least one magnetic footpoint on Ganymede) near the Jovian equatorial plane (see Figure S1 in Supporting Information S1). Figure 1 shows an overview of plasma waves observed by the Waves instrument (Kurth et al., 2017) and electron distributions measured by the Jupiter Energetic-particle Detector Instrument (JEDI; Mauk et al., 2017) and Jovian Auroral Distributions Experiment (JADE; McComas et al., 2017), as Juno moved from the Jovian closed magnetic field lines (green lines in Figure  S1 in Supporting Information S1) to the regions where at least one magnetic footpoint is connected to Ganymede (red or blue lines in Figure S1 in Supporting Information S1). At ∼16:45 UT, a substantial change in electron distributions was detected with reduced electron fluxes at higher energies ( Figure 1c) and increased fluxes at lower energies (Figure 1d), as well as the changing shape of field-aligned local pitch angle distributions to more isotropic ones. These features indicate that Juno crossed the boundary between the Jovian closed magnetic field lines and Ganymede's magnetotail/wake region . Subsequently, Juno moved from the magnetotail/wake region (from ∼16:45 UT to 16:50 UT; Clark et al., 2022;Kurth et al., 2022) to Ganymede's magnetosphere at ∼16:50 UT (marked by the red vertical line), remained in the magnetosphere until 17:00 UT Clark et al., 2022;Kurth et al., 2022). Inside Ganymede's magnetosphere, electromagnetic whistler-mode emissions (below the electron cyclotron frequency) were intense during almost the entire interval from 16:50 to 17:00 UT (Figure 1b; Kurth et al., 2022), whereas strong electrostatic electron cyclotron harmonic waves (above electron cyclotron frequency) were mostly observed from 16:50:00 to 16:51:30 UT. Moreover, sudden decreases in electron fluxes over a broad energy range measured by JEDI from 30 keV to ∼1 MeV ( Figure 1c; Clark et al., 2022) and JADE from 100 eV to ∼30 keV (Figure 1d; Allegrini et al., 2022) were detected in the magnetosphere compared to those in the magnetotail/wake region. The electron local pitch angle distributions were field-aligned in the region dominated by the Jovian closed magnetic field (before ∼16:45 UT), exhibited a mixed distribution in the magnetotail/wake region (from 16:45 UT to 16:50 UT), and were mostly pancake but asymmetric in the region dominated by Ganymede's magnetic field lines (after ∼16:50 UT). In Figures 1e-1j, the white dashed lines with black dots represent the local bounce loss cone with the downward (upward) direction near 0° (180°). The bounce loss cone of Ganymede is the pitch angle value for the electrons that mirror at Ganymede's surface, estimated using a centered dipole magnetic field model of Ganymede's magnetosphere (with the equatorial magnetic field intensity of 719 nT) based on Kivelson et al. (2002), but neglecting the small tilt between the dipole moment and the anti-parallel direction from Ganymede's spin axis. Inside Ganymede's magnetosphere (marked by the green horizontal bar on the top part of Figure 1), the majority of electrons with pitch angles smaller than the local loss cone are lost to Ganymede's surface. However, outside Ganymede's magnetosphere (the regions except for the green horizontal bar), electrons with pitch angles smaller than the loss cone of Jupiter (400 km above the 1-bar level) are lost to Jupiter's atmosphere. From 16:50 UT to 16:56 UT (between the red and blue vertical lines), precipitating electron fluxes were relatively small at high energies (above tens of keV) with slightly higher downward-going electron fluxes than upward-going ones. It is noteworthy that due to the limited coverage in pitch angle for the JADE measurements, it is difficult to obtain precipitating electron fluxes from ∼16:46 UT to 16:53 UT at energies below ∼30 keV. However, starting from ∼16:53 UT, when precipitating electron measurements were available from JADE, downward-going electron fluxes were evidently higher than the upward-going ones. Between 16:56 UT (blue vertical line) and 17:01 UT (green vertical line), a clear asymmetry in pitch angle distribution was observed with almost full downward loss cone compared to the upward one. In particular, after ∼16:56 UT the downward bounce loss cone remained almost full even for higher-energy electrons (above tens of keV), which may indicate energy-dependent pitch angle scattering (e.g., Tripathi et al., 2014;.

Time 1 Time 2
Magnetosphere Magnetotail/Wake Jupiter Jupiter Figure 2 shows the plasma wave observations in more detail, as also described by Kurth et al. (2022). Inside Ganymede's magnetosphere (after ∼16:50 UT), intense whistler-mode waves were observed in both electric ( Figure 2a) and magnetic wave power ( Figure 2b). Interestingly, these whistler-mode waves exhibit two distinct modes, as can be inferred from the ratio between the wave electric and magnetic fields (E w /cB w ; Figure 2c), where c is the speed of light, E w is the y component of the wave electric field, and B w is the z component of the wave magnetic field in spacecraft coordinates (Kurth et al., 2017). E w /cB w is expected to be close to or smaller than 1 for electromagnetic waves with small or intermediate wave normal angles, but large for electrostatic or highly oblique electromagnetic waves. The higher frequency component (>∼1 kHz) was highly oblique, but the lower frequency component (<∼1 kHz) was quasi-parallel. We calculated the magnetic amplitude of these two components of whistler-mode waves based on the Juno observation (Figure 2d), which indicates large amplitudes (up to a few hundred pT) for the quasi-parallel waves and modest amplitudes (up to tens of pT) for the oblique waves. The total electron density was inferred from the upper hybrid resonant frequency line ( Figure 2a) and is shown in Figure 2e (black line). It is interesting to note that the electron density smoothly increased (up to ∼15 cm −3 ) until 16:57 UT, after which it suddenly increased by a factor of ∼2 and remained elevated for ∼1 min, albeit with large fluctuations. This remarkable feature suggests that Juno crossed two different regions in Ganymede's magnetosphere Kurth et al., 2022). Therefore, we mark the region over 16:57-17:00 UT with horizontal black dashed lines in the colored blocks shown in the top row in Figure 2.
Based on the measured ambient magnetic field intensity, we further calculated the ratio between the electron plasma frequency and electron cyclotron frequency (blue line in Figure 2e). It is noteworthy that the whistler-mode wave spectra changed at ∼16:57 UT with quasi-parallel wave power extending to even lower frequencies (below tens of Hz). Simultaneously, the oblique wave intensity decreased after ∼16:57 UT. Therefore, we chose two time snapshots to model energetic electron precipitation driven by whistler-mode waves: Time 1 (2) before (after) the change in wave spectra in the lower (higher) latitude of Ganymede's polar region. Since whistler-mode waves  f pe /f ce indicated two distinct components, we quantified the effects of quasi-parallel and highly oblique whistler-mode waves separately.
It is important to note that several studies suggested that Juno did not cross the closed field lines during this flyby and remained in the open field line region with one footpoint on Ganymede and the other on Jupiter Clark et al., 2022;Duling et al., 2022), although we may not completely exclude the possibility that Juno briefly crossed the closed field line region (e.g., Romanelli et al., 2022). In our modeling, we assume that Juno remained in the open field line region and electrons moved along the magnetic field line with one footpoint on Ganymede and the other on Jupiter.

Modeling of Energetic Electron Precipitation Driven by Whistler-Mode Waves
We model energetic electron precipitation due to interactions with whistler-mode waves based on the quasi-linear theory, which is commonly used in previous studies to evaluate the effects of plasma waves on energetic particles (e.g., Schulz & Lanzerotti, 1974;Thorne et al., 2010). The model used for Ganymede's magnetic field environment is a simple intrinsic dipole field (Kivelson et al., 2002) superimposed on the ambient Jovian magnetic field (JRM09+CON2020; Connerney et al., 2018Connerney et al., , 2020. The total electron density used in the model is based on the Juno observation (Figure 2e) from the magnetic footpoint on Ganymede to Jovian magnetic equator and an empirical density model (Dougherty et al., 2017) from Jovian magnetic equator to the magnetic footpoint on Jupiter. Whistler-mode waves are assumed to be present along the magnetic field line ( Figure S1b in Supporting Information S1) from Ganymede's surface to 50° of magnetic latitude in the Jovian JRM09+CON2020 coordinate.
To model electron precipitation driven by whistler-mode waves through pitch angle scattering and acceleration, we solve the two-dimensional Fokker-Planck equation along the field line with one foot on Ganymede and the other on Jupiter . Note that since electrons bounce in a closed magnetic field line, the Fokker-Planck simulation approach is valid. The detailed description of the Fokker-Planck simulations is provided in Text S1 in Supporting Information S1. The modeled pitch angle distribution inside the loss cone is compared to the energy-dependent loss cone filling of electrons observed by Juno, as discussed below. Figure 3 shows the modeling results of energetic electron precipitation driven by whistler-mode waves, as well as the associated wave and plasma parameters that were used as model inputs. This modeling result is shown at Time 1, when Juno traveled to the lower latitude of Ganymede's polar region. Whistler-mode wave spectra (Figure 3a) indicate that the magnetic wave amplitude of quasi-parallel waves at several hundred Hz (∼73.3 pT) is larger than that of oblique waves (17.4 pT). The detailed information of the wave normal distribution of quasi-parallel and highly oblique whistler-mode waves is described in Text S2 in Supporting Information S1. Bounce-averaged diffusion coefficients in equatorial pitch angle (<D αα > in Figure 3d), momentum (<D pp > in Figure 3e), and mixed terms (|<D αp >| in Figure 3f) were calculated for the sum of quasi-parallel and oblique waves. <D αα > shows large values over a broad range of energies from tens of eV to several hundred keV, whereas large <D pp > values are observed mostly below a few keV near the bounce loss cone. Figure 3b shows the bounce-averaged diffusion coefficients (<D αα > and <D pp >) at the bounce loss cone for the quasi-parallel (blue) and highly oblique whistler-mode waves (red) separately. Moreover, the total <D αα > of quasi-parallel and highly oblique waves (black solid line) and the strong diffusion limit (D SD ; black dotted line) are overplotted for direct comparison. The strong diffusion limit is calculated as = 2 2 LC , where LC is the equatorial pitch angle of bounce loss cone and is the electron bounce period between Ganymede and near-Jupiter mirror point in the northern hemisphere. <D αα > is predominantly contributed from the quasi-parallel waves at electron energies above several hundred eV, whereas highly oblique waves play a dominant role in both <D αα > and <D pp > at energies below several hundred eV. It is interesting to note that the total <D αα > exceeds the strong diffusion limit at energies below several keV, indicating efficient pitch angle scattering due to whistler-mode waves at lower energies. Moreover, for oblique waves <D pp > is even larger than <D αα > at energies below ∼100 eV, indicative of strong energy diffusion. Figure 3c shows the observed electron pitch angle distribution at Time 1, demonstrating larger electron fluxes in the downward direction than upward ones. The observed electron pitch angle distribution is also shown with color-coded solid lines at various energies overplotted with the modeled electron pitch angle distribution (dotted lines only shown inside the downward loss cone) for the quasi-parallel waves (Figure 3g), oblique waves (Figure 3h), and full waves including both quasi-parallel and oblique waves (Figure 3i), respectively. The comparison between the observed and modeled electron pitch angle distribution indicates that quasi-parallel waves alone play an important role in scattering electrons between several hundred eV and tens of keV, leading to the observed electron precipitation (Figure 3g), although they play a minor role in pitch angle scattering lower-energy electrons (below several hundred eV). However, the oblique waves are effective in scattering lower-energy electrons (below several hundred eV) leading to an almost flat pitch angle distribution inside the loss cone, due to the combination of efficient pitch angle scattering and energy diffusion (Figures 3b, 3d, and 3e). The full waves by including both quasi-parallel and oblique waves lead to efficient electron precipitation over a broad energy range from tens of eV to tens of keV, most consistent with the observations. However, the modeled result still underestimates electron precipitation at higher energies (above tens of keV), suggesting that an additional mechanism is needed to explain this discrepancy.  Figures 1 and 2). (a) Magnetic wave spectra of the observed whistler-mode waves for the quasi-parallel (blue) and oblique components (red). (b) Bounce-averaged pitch angle diffusion coefficients at the bounce loss cone for the entire whistler-mode waves (black solid line), quasi-parallel waves (blue solid line), and oblique waves (red solid line); bounce-averaged momentum diffusion coefficients at the bounce loss cone for the quasi-parallel waves (blue dashed line) and oblique waves (red dashed line); and the strong diffusion limit (black dotted line). (c) Electron flux as a function of local pitch angle and energy, where the black dashed lines represent the bounce loss cone of Ganymede. (d) Bounce-averaged electron pitch angle diffusion coefficients (<D αα >), (e) momentum diffusion coefficients (<D pp >), and (f) mixed terms (|<D αp >|) as a function of equatorial pitch angle and energy. (g) Observed electron pitch angle distribution (solid lines) and modeled electron pitch and distribution (dotted lines) only shown inside the downward loss cone, color-coded for various energies of electrons which interact with quasi-parallel whistler-mode waves. (h) The same format as panel (g) but for oblique waves. (i) The same format as panel (g) but for the full waves (sum of quasi-parallel and oblique waves). Figure 4 shows the modeled electron precipitation with the same format as Figure 3 but during Time 2, when Juno was in Ganymede's higher-latitude polar region. As discussed earlier, the whistler-mode wave spectra suddenly changed near 16:57 UT with much stronger quasi-parallel waves (∼275 pT) at lower frequencies extending down to tens of Hz (Figure 4a), while the oblique wave amplitude (11.6 pT) was slightly weaker than that during Time 1 (Figure 3a). Bounce-averaged diffusion coefficients (Figures 4b and 4d-4f) show that <D αα > due to quasi-parallel waves is large at energies above ∼1 keV, whereas both <D αα > and <D pp > due to oblique waves are large, exceeding the strong diffusion limit, for lower-energy electrons (∼tens of eV to 1 keV). The local electron pitch angle distribution demonstrates an almost flat profile inside the downward loss cone (Figures 4c  and 4g-4i) over a broad range of energies from ∼30 eV to a few hundred keV, indicating stronger electron precipitation compared to that during Time 1. The comparison between the model and observation indicates that the quasi-parallel waves play a dominant role in precipitating higher-energy electrons above ∼1 keV (Figure 4g), whereas the oblique waves mostly contribute to precipitating lower-energy electrons below ∼1 keV (Figure 4h). It is interesting to note that the oblique waves were able to reproduce the overfilling loss cone feature that was observed with stronger electron flux inside the downward loss cone (than outside of it) for lower-energy electrons below ∼1 keV. The combined effects of quasi-parallel and oblique whistler-mode waves lead to effective pitch angle scattering over a broad energy range (from 10s eV to a few hundred keV), remarkably consistent with the observation (Figure 4i).

Summary and Discussion
During the flyby of Ganymede on 7 June 2021, Juno crossed Ganymede's polar magnetosphere (with one magnetic footpoint on Ganymede and the other on Jupiter) and observed evident loss cone features in association with intense whistler-mode waves. Using the Juno observations and quasi-linear modeling, we performed a quantitative analysis to determine the primary driver of causing energetic electron precipitation into Ganymede's atmosphere. The principal findings are summarized below.
1. In the vicinity of Ganymede, the local electron pitch angle distribution exhibited an asymmetric distribution with the downward electron fluxes larger than the upward ones, indicative of the evident loss cone feature. The amount of filling in the downward direction was energy-dependent (decreasing with increasing energy). 2. In association with enhanced precipitating electron fluxes, whistler-mode waves were detected in two distinct modes: quasi-parallel waves at lower frequencies up to a few hundred pT, and very oblique waves at higher frequencies up to tens of pT. 3. In Ganymede's lower-latitude polar region (Time 1 in Figures 1 and 2) where energetic electron precipitation was modest, quasi-parallel whistler-mode waves play a dominant role in precipitating electrons from several hundred eV to tens of keV through pitch angle scattering, while oblique waves are important for precipitating electrons from tens of eV to hundreds of eV. However, the modeled result underestimates electron precipitation at energies above tens of keV, which needs an additional explanation. 4. In Ganymede's higher-latitude polar region (Time 2 in Figures 1 and 2) where energetic electron precipitation was strong, the associated quasi-parallel whistler-mode waves were stronger and wave power extended to lower frequencies. The comparison between the observed and modeled electron distribution indicates that the quasi-parallel waves play a dominant role in precipitating higher-energy electrons above ∼1 keV, whereas the oblique waves mostly contribute to precipitation of lower-energy electrons below ∼1 keV.
It is noteworthy that whistler-mode waves are assumed to be present with the constant wave amplitude along the magnetic field line from Ganymede's surface to 50° of Jovian magnetic latitude. Although it is shown that whistler-mode wave amplitude significantly increases near the vicinity of Ganymede and Europa (Shprits et al., 2018), how the whistler-mode wave intensity varies along the field line connecting Jupiter and Ganymede is currently unknown. However, based on the statistical distribution of whistler-mode waves using Juno data (e.g., Li et al., 2020;Menietti et al., 2021), whistler-mode wave intensity tends to remain in the similar level from the equator to higher latitudes. Therefore, the assumption used in the present study may be fairly reasonable. Nevertheless, further investigations using more plasma wave data and ray tracing modeling are required to improve our understanding of wave distribution along the magnetic field line connecting Ganymede and Jupiter.
Regarding the underestimated electron precipitation at higher energies in Ganymede's lower-latitude polar region (at Time 1), it is possible that quasi-linear modeling underestimates energetic electron precipitation, especially for large amplitude and/or oblique whistler-mode waves (e.g., Bortnik et al., 2008;Gan et al., 2022;Hsieh et al., 2022;Zhang et al., 2022), or electrons are further scattered into the loss cone or accelerated when they bounce between Ganymede and their near-Jupiter mirror point through additional nonlinear waves or turbulence (e.g., Sulaiman et al., 2022). However, these effects are beyond the scope of the present paper and left for further investigations.
In summary, our study provides new direct evidence that whistler-mode waves potentially play a dominant role in energetic electron precipitation into Ganymede's atmosphere over a broad range of energies from 30 eV to several hundred keV. Since electron precipitation into the atmosphere is known to generate aurora (e.g., Li et al., 2017Li et al., , 2021, we suggest that some of the diffuse aurora observed near Ganymede  may be related to the pitch angle scattering driven by whistler-mode waves. However, the quantitative evaluation of Ganymede's aurora driven by whistler-mode waves is beyond the scope of the present study and is left as a future investigation.

Data Availability Statement
We