Statistical Study on L-O Mode Saturn Kilometric Radiation

Junhao Pan, Siyuan Wu, Shengyi Ye, Georg Fischer, Laurent Lamy, Philippe

Zarka, Ulrich Taubenschuss

► To cite this version:

Junhao Pan, Siyuan Wu, Shengyi Ye, Georg Fischer, Laurent Lamy, et al. Statistical Study on L-O Mode Saturn Kilometric Radiation. Geophysical Research Letters, 2025, 52 (15), 10.1029/2025GL114876. [arXiv:2005.01148]

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
RESEARCH LETTER

10.1029/2025GL114876

**Key Points:**

* The first global occurrence, spectral flux distribution, and polarization features of left-hand (L-O) mode Saturn kilometric radiation (SKR) are obtained

* Low-frequency L-O mode emissions (<100 kHz) nearly vanish within the Enceladus plasma torus (3–5 Rs), while high-frequency emissions (>300 kHz) are routinely observed across this region

* The L-O mode SKR is predominantly highly circularly polarized at low latitudes and exhibits elliptical polarization at high latitudes

**Correspondence to:**

S. Ye,
yesy@sustech.edu.cn

**Citation:**

Pan, J., Wu, S., Ye, S., Fischer, G., Lamy, L., Zarka, P., & Taubenschuss, U. (2025). Statistical study on L-O mode Saturn kilometric radiation. *Geophysical Research Letters*, *52*, e2025GL114876.
https://doi.org/10.1029/2025GL114876

Received 15 JAN 2025
Accepted 10 JUL 2025

**Author Contributions:**

**Conceptualization:** Shengyi Ye

**Data curation:** Junhao Pan, Siyuan Wu

**Formal analysis:** Junhao Pan, Siyuan Wu

**Funding acquisition:** Shengyi Ye

**Investigation:** Junhao Pan

**Methodology:** Junhao Pan, Siyuan Wu

**Project administration:** Shengyi Ye

**Resources:** Shengyi Ye

**Software:** Junhao Pan, Siyuan Wu

**Supervision:** Shengyi Ye

**Validation:** Junhao Pan

**Visualization:** Junhao Pan

**Writing – original draft:** Junhao Pan

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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Statistical Study on L-O Mode Saturn Kilometric Radiation

Junhao Pan¹ Ⓓ, Siyuan Wu¹,² Ⓓ, Shengyi Ye¹ Ⓓ, Georg Fischer³ Ⓓ, Laurent Lamy⁴,⁵ Ⓓ, Philippe Zarka⁴ Ⓓ, and Ulrich Taubenschuss⁶ Ⓓ

¹Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, PR China, ²School of Physics & Astronomy, University of Southampton, Southampton, UK, ³Institute of Physics, University of Graz, Graz, Austria, ⁴LESIA, Observatoire de Paris, CNRS, Université PSL, Sorbonne Université, Université Paris Cité, CNRS, Meudon, France, ⁵Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France, ⁶Department of Space Physics, Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czechia

**Abstract** Based on the 13 years-long observation of Saturn kilometric radiation (SKR) by the Cassini/Radio and Plasma Wave Science instrument, this study derives statistics for left-hand (L-O) mode SKR emissions. These emissions span a frequency range from below 10 kHz to approximately 1,000 kHz, with spectral flux densities ranging between 10⁻²⁴ and 10⁻¹⁸ W/(m² Hz) consistent with, although fainter than, right-hand mode SKR. Predominantly observed within 20 Saturn radii, the occurrence rates of L-O mode SKR exhibit a preference below 20° in latitude, and a local time asymmetry with a higher occurrence rate on the dayside. Occurrence maps indicate that low-frequency (<100 kHz) L-O mode SKR may be obstructed by the Enceladus plasma torus due to the higher electron density, while high-frequency (>100 kHz) emissions can pass through unhindered. Additionally, a substantial proportion of high-latitude L-O mode emissions exhibit strong elliptical polarization, contrasting with predominantly circular polarization observed at low latitudes.

**Plain Language Summary**
Saturn kilometric radiation (SKR) is a broadband radio emission produced in Saturn's magnetosphere, coming in two types: the stronger right-hand (R-X) mode and the weaker left-hand (L-O) mode. While the R-X mode has been well studied, the L-O mode was less understood until now. Using 13 years of Cassini data, scientists mapped out where L-O mode SKR occurs around Saturn, covering frequencies from 10 to 1 MHz. They found that lower-frequency waves (below 100 kHz) disappear inside the Enceladus plasma torus—a ring of charged particles between 3 and 5 Saturn radii—while higher-frequency waves (above 300 kHz) pass through easily. The study also showed that the polarization (the way the electric field of these radio waves vibrate) changes with latitude: they're elliptical at higher latitudes (above 30°) and become circular closer to the equator. These patterns reveal details about Saturn's magnetic environment, like how dense the charged particles are in the torus and how this density shifts with latitude. This work helps us better understand how SKR is created and how it can be used to study Saturn's magnetosphere from afar.

1. Introduction

Saturn kilometric radiation (SKR) represents the most powerful nonthermal radio emission emitted from the Saturnian magnetosphere. It ranges in frequency from a few kHz to ~1 MHz, with a peak intensity between 100 and 400 kHz (e.g., Lamy, 2017 and references therein). Saturn kilometric radiation was initially observed by the Planetary Radio Astronomy experiment instrument onboard Voyager 1 in 1980 (Kaiser et al., 1980). Extensive studies have shown that SKR consists of two distinct components: the free-space right-hand (R-X) extraordinary (R-X) mode and the left-hand ordinary (L-O) mode (Cecconi et al., 2006; Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008, 2011). Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al. (2008) first identified the marginally observed L-O mode emissions in averaged dynamic spectra, noting that these emissions exhibit circular polarization degrees as high as dominant R-X mode emissions but with opposite sign to the R-X mode emissions. L-O mode SKR was generally observed at slightly lower frequencies than the prominent R-X mode SKR, especially near perikrones. Its spectral flux density was found to be 2–4 orders of magnitude lower than those of the R-X mode emissions (Cecconi et al., 2009; Lamy et al., 2011, 2018).

Saturn kilometric radiation is generated by the precipitated auroral electrons through the cyclotron maser instability (Wu and Lee, 1979). Direction-finding analyses of case studies demonstrated that the source regions of the L-O mode SKR are co-located with the R-X mode emissions, which can be mapped to the UV aurora oval (Cecconi et al., 2009; Lamy et al., 2011, 2018). The beaming of L-O mode SKR roughly compares to the R-X
mode, being nearly perpendicular at the source. The polarization of both modes is also similar, evolving from nearly linear at the source to fully elliptically polarized at high-latitudes (~30–60°) and quasi-purely circularly polarized at low latitudes (<30°) (Fischer et al., 2009; Lamy et al., 2011). Beyond those efforts, a dedicated statistical study of L-O mode SKR emissions remained to be done. Due to the opposite magnetic field orientations in the two hemispheres, R-X mode emissions exhibit distinct circular polarizations expressed via the Stokes parameters V, with L-O circular polarization (Stokes V > 0) in the southern hemisphere and R-X circular polarization (Stokes V < 0) in the northern hemisphere. In contrast, the circular polarization sense of L-O mode from the northern hemisphere is left-handed, and it is right-handed from the southern hemisphere. This polarization pattern makes it easy to distinguish the L-O mode emissions (with opposite circular polarization to the dominant R-X mode emissions) at higher latitudes (e.g., >30°). However, below 30° in latitude SKR from both hemispheres can be observed (Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008; Nakamura et al., 2019) leading to emission patches of both circular polarization senses. It is thus necessary to know the SKR source position/hemisphere for each distinct emission patch, otherwise the emission mode cannot be determined from the sense of polarization.

The R-X mode emissions generally dominate the SKR spectrum. The weaker L-O mode emission is typically obscured by R-X mode emission. However, it turned out to be easily detectable at the lower edge (i.e., at lower frequencies) of the R-X mode SKR emissions on the wave spectrogram, either statistically or during perikrones. This particularity was proposed to result from different refraction conditions along the raypath of low-frequency R-X/L-O mode emissions near their source region (Lamy et al., 2018). Indeed, R-X mode emissions should experience significant refraction as they are generated with wave frequency much closer to their cut-off frequency. In contrast, the co-generated L-O mode emissions should bear less refraction due to the lower $f_{pe}$ in the source region. This differential refraction makes L-O mode more easily detectable in the regions where R-X mode is refracted out, as also proposed to explain the observations of the auroral kilometric radiation at Earth (Mellot et al., 1984). The L-O mode emissions are also often observed at the margins of the equatorial shadow zone during Cassini's equator crossing (Lamy, Zarka, Cecconi, Hess, & Prangé, 2008). However, a dedicated study is still needed to understand this observation feature.

## 2. Data and Methodology

The wave electric field spectrograms used in this work are from the Cassini Radio and Plasma Wave Science (RPWS) High Frequency Receiver (Gurnett et al., 2004). We analyze the wave electric field spectrograms between 3.5 and 1,100 kHz, spanning from 2004 DOY 001 (day of year) when Cassini was approaching Saturn at a distance of 0.58 astronomical unit (AU) to 2017 DOY 258 when Cassini burned up in Saturn's atmosphere. The wave Stokes parameters used are derived through goniopolarimetric inversion of auto and cross-correlations of RPWS antenna signals (Cecconi & Zarka, 2005). To obtain the wave incoming directions (defined by two angles, colatitude ($\theta$) and azimuth ($\varphi$)) and the Stokes parameters (S the Poynting flux, $Q$ and $U$ the normalized linear polarization parameters and $V$ the normalized circular polarization degree), the inversion process generally requires pre-assumptions on two of the parameters due to the measurement's limitation when RPWS is operating in the 2-antenna mode, which returns 4 measured values from one antenna pair:

1. Assume that the emissions originate from the center of Saturn; this inversion gives the wave polarization features but not the wave incoming direction. It produces the so-called n3d level data (Cecconi et al., 2017b).

2. Assume that the emissions are purely circularly polarized, with linear polarization parameters $Q = U = 0$; this inversion gives the wave circular polarization and the wave in-coming directions but not the linear polarization. It produces the n3e level data, referred to as direction-finding data below (Cecconi et al., 2017c).

To identify the L-O mode emissions observed in the equatorial region, we use the wave incoming direction (under the assumption of no linear polarization) combined with the sign of circular polarization to distinguish the L-O mode emissions as previously done in Cecconi et al. (2009). The determined wave incoming directions from the n3e data set are redefined according to the source apparent altitude $z$ in the projection frame: the x-axis points from the center of Saturn toward the Cassini spacecraft, the z-axis is perpendicular to x-axis such as the north pole direction of Saturn lies in the x-z plane, and the y-axis completes the orthogonal triad. Source with $z > 1$ Rs are mapped to the northern hemisphere, while $z < -1$ Rs mapped to the southern hemisphere. The method is the same as used in Figures 2 and 3 of Cecconi et al. (2009).
To identify L-O mode emissions, we first preprocess the wave intensity and polarization spectrograms to eliminate the unwanted signals by using the emission event lists, such as Saturn narrowband emissions (Wu et al., 2021), Saturn Anomalous Myriametric emissions (Wu, Ye, Fischer, Jackman, et al., 2022), and Saturn electron cyclotron harmonics (Long et al., 2021). Then we apply a data-cleaning process by removing emissions that are weak (intensity <25 dB, background intensity around $10^{-17}$ V$^2$m$^{-2}$ Hz$^{-1}$) and unpolarized (Stokes I-VI < 0.2) in both the electric field spectrogram and wave polarization data. Next, we apply a 2D median filter with a 3 × 3 window in the time-frequency plane to eliminate isolated pixels. Measurements of circular polarization are primarily influenced by both the signal-to-noise ratio (SNR) and the geometric alignment between the wave direction and the antenna plane, which is defined by the effective axes of the RPWS dipole Ex and monopole Ew (Fischer et al., 2007; Gurnett et al., 2004). Higher SNR correlates with higher circular polarization. Thus, Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al. (2008) defined the polarization selection range for SKR as 0.2 < |VI| < 1.1. L-O mode SKR is categorized using two identification criteria based on spacecraft latitudes:

1. At high latitudes (latitude above 25°), we retain data points with circular polarizations exceeding 0.2 in the northern hemisphere and below -0.2 in the southern hemisphere.

2. For low latitude observations, we utilize the direction-finding data to discern the wave's source hemisphere and identify L-O mode SKR from both hemispheres according to their circular polarization (i.e., left-handed from the North and right-handed from the South).

To mitigate contamination from residual of the narrowband emissions and other noise, we manually check and delete the erroneous detections. In high-latitude observations, the circular polarization sign derived from 2-antenna inversions may contain errors due to varying antenna configurations relative to nearby sources. The elevation angle (beta) of the SKR source above or below the antenna plane is a crucial geometric factor. We only include data with beta >20° to ensure accurate polarization and direction-finding results (Cecconi & Zarka, 2005). Ambiguous intervals are excluded as done similarly in O'Dwyer et al. (2023). Our algorithm ultimately detected 854.54 hr (≈35.6 Earth days) of L-O mode SKR out of nearly 14 years' observation. Intensities were distance-normalized to 1 AU and transposed into spectral flux density in W/(m$^2$ Hz) following Zarka et al. (2004). Two selected examples are displayed in Figure 1.

The first event depicted in Figures 1a–1g shows the RPWS observations from UT 19:00, 2006-09-25 to UT 03:00, 2006-09-26. The selected L-O mode emissions are shown in Figure 1b for clarity. Compared to the surrounding R-X mode emissions in Figure 1a, the L-O mode emissions exhibit weaker spectral flux densities. The selected emissions in blue and red (Panel (d)) correspond to the L-O mode circular polarization features from the south and north hemispheres, respectively. Observations in Figures 1a–1g represent typical L-O mode SKR observations, detected at the lower edge of the R-X mode emissions as previously reported (Cecconi et al., 2009; Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008).

Figures 1f and 1g indicate that the first event exhibits relatively low linear polarization and shows a trend of evolving polarization degree as the spacecraft approaches the equator. This will be discussed in Section 5.

The second case in Figures 1h–1n was observed while the Cassini spacecraft was positioned at 2.4–3.6° north of the equator, enabling simultaneous observation of SKR from both hemispheres. At approximately 06:00 in Figure 1j, the emissions in L-O mode at frequencies of 40–50 kHz constitute only a minor fraction, due to insufficient number of direction-finding data points. This phenomenon is characterized by the complex circular polarization in Figure 1j. The direction-finding data in Figure 1l gives the source hemisphere of these emissions, suggesting that Cassini observed both R-X and L-O mode emissions from both hemispheres during this interval. The identified emissions in Panel (m) exhibit low linear polarization.

Weak L-O mode SKR are impossible to detect due to the overlap of much stronger R-X mode SKR in the same time-frequency area. Therefore, all upcoming detection times or occurrence probabilities of L-O mode SKR should be considered as minimum values. Nevertheless, the long observation time of almost 14 years suggests that it is useful to establish statistical characteristics and distributions as done in the next three sections.

### 3. Statistical Characteristics of the L-O Mode Emission

We first explore the statistics of the identified L-O mode emissions as shown in Figure 2. The observed L-O mode emissions cover a frequency range from a few kHz to ~1 MHz, which is similar to that covered by R-X mode emissions (Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008). However, the frequency distribution
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Two examples of the identified left-hand (L-O) mode Saturn kilometric radiation. Panels (a–g) depict the first case, where (a, b) display wave electric field spectrograms, with (b) showing the selected L-O mode emissions. Panels (c–d) gives the circular polarization degree with Panel (d) displaying the selected L-O mode cases. Panel (e) gives the source hemisphere from the direction-finding data with dark blue representing emissions from the northern hemisphere, and red emissions from the southern hemisphere. Panels (f–g) give the linear and total polarization of selected L-O mode emissions, respectively. The red lines represent when the spacecraft crosses the equatorial plane. Panels (h–n) showcase the second case in the same format as Panels (a–g).</figcaption></figure>

shows a preference of L-O mode emissions below ~400 kHz, with an average of 136 kHz and a dominant peak at ~50 kHz. Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al. (2008) found through the long-term superposition of SKR spectrograms that the identified L-O emissions span a frequency range from ~20 to 400 kHz. This implies that the observation of the L-O SKR is swamped by the strong R-X mode emissions above ~400 kHz.

The spectral flux density distribution is given in Panel (b). A considerable portion of L-O mode SKR emissions have spectral flux densities ranging from $10^{-24}$ to $10^{-18}$ W/(m$^2$ Hz), with some weaker cases close to the background noise level and the identification threshold. These values are consistent with the previous studies, which indicated that L-O mode emissions are 2 – 4 orders of magnitude weaker than the R-X mode emissions (Cecconi et al., 2009; Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008).

Figure 2c gives the distribution of circular polarization. The gap between $V = -0.2$ and $V = 0.2$ indicates the elimination of weakly polarized pixels during selection.

The L-O mode SKR exhibits significant hemispheric disparity (Nakamura et al., 2019). Emissions from the southern hemisphere ($V < 0$) exceed those from the northern hemisphere ($V > 0$) by a factor of 1.45 (20.79 vs.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Statistics of left-hand (L-O) mode Saturn kilometric radiation. Panel (a) displays the frequency distribution of the detected L-O mode emissions, with the blue line indicating the average frequency and the red and yellow lines marking two peak frequencies ($f_1 = 50$ kHz, $f_2 = 180$ kHz). Panel (b) depicts the spectral flux density distribution. Panels (c–e) present histograms of circular polarization, linear polarization, and total polarization. Panels (f–h) give the Cassini observation time distribution in latitude, local time and radial distance. The orange and blue lines in Panels (i–k) show the observed proportion of the identified L-O mode emissions in different frequency bands as a function of spacecraft latitude, local time, and radial distance. The green dashed line represents the average of the observed values, while the gray dotted lines indicate the mean plus and minus one standard deviation.</figcaption></figure>

14.81 days), despite the longer Cassini observation time in the northern hemisphere. Notably, a significant fraction of events with low-medium circular polarization is noted.

Figures 2d and 2e depict histograms of linear and total polarization, respectively. These histograms indicate that most L-O mode emissions exhibit low linear polarization and high total polarization, consistent with previous findings (Cecconi et al., 2006). Some emissions show the total polarization <1, suggesting a certain depolarization process possibly due to the propagation effects. Observations with linear polarization ≈1 are attributed to a few polarized events. While the L-O mode SKR in Figure 1 suggests a fully circularly polarized wave, certain observations display strong elliptical polarization, as discussed in Section 5.

Occurrence distributions of the L-O mode emissions as a function of the spacecraft positions are given in Figures 2i and 2k. The number of the L-O mode emission samples is categorized into frequency bands based on the distribution in Figure 2a to check for any significant frequency dependence on the spatial occurrence. Figures 2f and 2h give the distribution of Cassini observation time. As the L-O mode observation is affected by the modulation of the Cassini orbit, it is necessary to normalize the L-O mode observation time. Since L-O mode emissions can appear at different frequencies simultaneously, we compute the average occurrence rate by integrating over the entire frequency band. The occurrence rates of L-O mode observations are calculated by using the following formula:

$$ \text{Occurrence rates} = \frac{\text{identified L-O mode SKR points (minutes)}}{\text{observation time (minutes)}} $$
Results reveal that L-O mode emissions are more observed in the low latitude region (Latitude <25°) with one peak at the equator for $f_{L-O} > 100$ kHz; for example, blue line in Figure 2i and three peaks around the equator for $f_{L-O} < 100$ kHz (orange line). This result suggests that L-O mode SKR below 100 kHz may not be able to propagate across the equator, whereas the higher frequency emissions above 100 kHz can indicate a propagation effect that will be discussed in Section 4. The 70°N peak was attributed to a singular event, with the occurrence rate reaching 1% due to insufficient observational coverage.

As shown in Figure 2j, high-frequency SKR (>100 kHz) exhibits a strong dayside (11.3 days observation) preference with 1.95 times occurrence rate higher than nightside (5.8 days observation) detections. In contrast, low-frequency SKR (<100 kHz) is predominantly observed on the nightside, with detection counts 1.46 times higher than those on the dayside (13 vs. 8.9 days). The L-O mode SKR (total observations) exhibits local time preferences, particularly on the dayside (10:00–15:00 LT) and nightside (20:00–05:00 LT). It is rarely observed near dusk and dawn at both low and high frequencies, with only 0.2% occurring at 05:00–06:00 LT and 17:00–18:00 LT. Majorities of the L-O mode emissions are observed within 25 Rs, peaking at 4–10 Rs, and with a decreasing trend of observations as the spacecraft radial distance increases from Saturn. To further explore the occurrence features and decouple the relations between frequency and the spacecraft positions, a more detailed analysis is carried out in Section 4.

## 4. Spatial Distributions

Occurrence maps of L-O mode SKR are derived in the meridian and equatorial planes, as shown in Figure 3. They are categorized in different wave frequency ranges to check possible asymmetries of the occurrence, as previously reported (Lamy, Zarka, Cecconi, Prangé, Kurth, & Gurnett, et al., 2008). The spatial pixels in Figure 3 are defined with resolution of 0.5 Rs × 0.5 Rs. Figures 3a–3d show the occurrence rates of the L-O mode SKR in equatorial view at four frequency bands (<30 kHz, 30–100 kHz, 100–300 kHz, >300 kHz), separately.

Within the 4–6 Saturn radii range, L-O mode emissions exhibited the highest cumulative duration (171.63 hr), accounting for 20% of the total observation time. The fact that high-frequency L-O mode emissions are predominantly observed in regions close to Saturn is consistent with the beaming pattern of SKR (Lamy et al., 2011). Unlike the R-X mode SKR, which is rarely observed inside 4 Rs. The L-O mode events are mostly detected at smaller radial distance. This apparent discrepancy with Wu et al. (2024) may reflect the broader beaming angle of L-O mode emissions, potentially reducing the equatorial shadow zone and enabling detections inside 4 Rs.

In the meridional plane, low-frequency L-O emissions (Figures 3e and 3f) don't occur around the equator within 8 Rs. The “forbidden” zone coincides with the Enceladus plasma torus, formed by the cryovolcanic activity of Saturn's moon Enceladus (centered at ~4 Rs; Persoon et al., 2020). However, as the wave frequency increases (>100 Hz), L-O mode SKR emissions become observable in this region. This distribution feature confirms the influence of the Enceladus plasma torus on the propagation of the L-O mode SKR. It is reminiscent of the occurrence map of Saturn NB emissions, which are also L-O mode emissions and cannot propagate into the plasma torus (Wu et al., 2021, Wu, Ye, Fischer, Taubenschuss, 2022). A recent ray-tracing analysis of the R-X mode SKR also indicated that these low-frequency emissions cannot penetrate the dense plasma torus (Wu et al., 2024), consistent with the results presented here.

The spacecraft dwell time (Figures 3k and 3l) and the total occurrence rates of L-O mode SKR emissions (Figures 3i and 3j) are presented. The occurrence rates are calculated from frequency bands ranging from 3 to 1,100 kHz. Most L-O mode observations occur within ~10 Rs and 20° of both north and south latitudes, consistent with Figure 2. The L-O mode SKR is largely absent above 30° latitude, unlike R-X mode SKR, as weak L-O mode emissions may be obscured by stronger R-X mode SKR at higher latitudes. A two-peak occurrence pattern in the meridional view (Figure 3j) suggests L-O mode emissions are primarily observable at the plasma torus's north and south edges. Additionally, L-O mode SKR is scarce around dusk (~18 hr), as shown in Figures 3a–3d and 3i, reflecting typical SKR behavior, also noted in Nakamura et al. (2019). The low occurrence rate at dawn-side local times is not as clearly visible as on the dusk side due to adjacent bins with higher occurrence rates. We refer to the LT occurrence rates shown in Figure 2j to highlight this feature.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Global spatial distributions of left-hand (L-O) mode Saturn kilometric radiation (SKR) at four different frequency bands (frequency >30, 30–100, 100–300, >300 kHz) in equatorial and meridional view. Equatorial planes map data perpendicular to the rotation axis, while meridional planes use a plane parallel to the axis. Panels (a–d) depict the equatorial distribution, while (e–h) display the meridional distribution, with the color-code representing the occurrence rate. The white pixels represent there is no orbital coverage, and the gray pixel represent there is no L-O mode SKR observation. Panels (i, j) show the occurrence rate of L-O mode SKR, with all frequencies merged. Panels (k, l) present the dwell time of the Cassini spacecraft in the equatorial and meridional planes, respectively.</figcaption></figure>

5. Polarization Patterns

The polarization features of the L-O mode SKR emissions are displayed in Figure 4. We provide the proportions of emissions with circular polarization ≥0.6, linear polarization ≥0.6 and total polarization ≥0.6 with respect to the total emissions points in the corresponding spatial bins. The proportion in each bin is calculated through:

$$ \text{Percentage} = \frac{\text{identified L-O mode SKR points with polarization parameter} > 0.6}{\text{identified L-O mode SKR points}} $$

As shown in Figures 4a and 4b and within a radial distance range inside ~5 Rs, the L-O mode SKR emissions are highly polarized with more than 90% emissions with the total polarization exceeding 0.6. Figures 4e and 4f show that the spatial patterns of highly circular polarization are similar between hemispheres, although the southern hemisphere has more L-O mode observational data. The broader beaming angles of L-O mode emissions may facilitate cross-hemispheric propagation beyond the torus-induced shadow zone.

We calculated the linear polarization of data points across different latitudes. The mean linear polarization of L-O mode SKR is 0.65 ± 0.28 at latitudes above 60°, decreasing to 0.24 ± 0.19 at latitudes below 30°. According to Cecconi and Zarka (2005), the measurement error is typically ±0.1 at low and high northern latitudes but
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Percentage and spatial distribution of highly polarized emissions. Panels (a) and (b) depict the percentage distribution of highly total polarized emissions (Stokes parameter, with the apparent total polarization degree $d_{tot} = \sqrt{Q^2 + U^2 + V^2}$) denoting total polarization, $d_{tot} \ge 0.6$) in the equatorial and meridional planes, respectively. Similarly, Panels (c, d) illustrate highly linearly polarized emissions (Stokes parameters, with Q and U denoting linear polarization $d_{lin} \ge 0.6$). Panels (e, f) exhibit highly circular polarized emissions (parameter circular polarization degree $d_{cir} \ge 0.6$ and $d_{cir} \le -0.6$) in the meridional planes. The white pixels represent there is no orbital coverage, and the black pixels represent no observation of highly polarized emissions.</figcaption></figure>

increases to approximately ±0.2 in certain cases as shown in (Fischer et al., 2009). Considering measurement errors, emissions at low latitudes are highly circularly polarized, whereas those at high latitudes exhibit elliptical polarization.

The detection of highly linearly polarized emissions at high latitudes recalls previous findings of elliptical polarization in R-X mode SKR emissions at high latitudes, evolving from linear to circular polarization during
propagation (Fischer et al., 2009; Lamy et al., 2011). This can be explained by mode coupling theory, applied to both Jovian decametric emissions (Goertz, 1974; Lecacheux et al., 1991; Melrose and Dulk, 1991; Shaposhnikov et al., 1997) and SKR (Fischer et al., 2009; Lamy et al., 2011). Polarization transfer in an inhomogeneous plasma involves gradual or rapid changes of the medium, affecting mode coupling and polarization transfer (Cohen, 1960; Daigne & Ortega-Molina, 1984; Melrose, 1980). As L-O mode SKR, excited in the auroral region, travels toward denser equatorial plasma, the increasing plasma density may alter its polarization pattern. This aligns with the observation in Figure 4d, where L-O mode SKR starts with strong linear polarization and gradually becomes more circular, as also demonstrated during an SKR source crossing (Lamy et al., 2011).

However, note that the polarization characteristics obtained when Cassini was at a position close to Saturn may lead to a violation of the pre-assumption on the wave incoming direction from the center of Saturn (See Section 2). Therefore, these polarization features obtained close to Saturn may be prone to errors.

## 6. Conclusion

This study gives a statistical analysis of the L-O mode SKR emissions based on ~13 years of Cassini RPWS data. The basic characteristics, occurrence rates, and polarization states of the L-O mode SKR emissions are derived. The key findings, that confirm and extend the work of Lamy, Zarka, Cecconi, Hess, and Prangé (2008), are summarized as follows:

1. L-O mode SKR demonstrates local time preferences, particularly on the day side (10:00–15:00) and night side (20:00–05:00) with minima around dawn and dusk. The spatial occurrence rates also show dependence on wave frequency. The low frequency ($f < 100$ kHz) L-O mode SKR are mostly observed in the north and south edge of the plasma torus and high frequency ($f > 100$ kHz) emissions can penetrate the dense torus unhindered.

2. With spectral flux densities ranging from $10^{-24}$ to $10^{-18}$ W/(m$^2$ Hz) at 1 AU distance, the L-O mode SKR is weaker compared to R-X mode. The average L-O mode has a level of $10^{-21}$ W/(m$^2$ Hz), which is about two orders of magnitude below the R-X mode level.

3. Most L-O mode SKR emissions show full polarization, with more elliptical polarization at high latitudes and predominance of circular polarization at low latitudes.

Through statistical constraints on L-O mode SKR, such as its frequency-dependent suppression by the Enceladus torus and latitude-controlled polarization evolution, we provide critical observational evidence that the generation and mode coupling of SKR are fundamentally shaped by Saturn's magnetospheric plasma structure. More work is required to clarify the detailed role of L-O mode emissions in the broader context of cyclotron maser processes.

## Data Availability Statement

The Cassini RPWS data used in this work were downloaded from the LESIA/Kronos collection with n2 level data (Cecconi et al., 2017a) and n3d data (Cecconi et al., 2017b) and n3e data (Cecconi et al., 2017c; goniopolarimetric data obtained using the method Cecconi & Zarka, 2005).

## Acknowledgments

This work was supported by NSFC project 42274221. SY thank the support of the Guangdong province program (Grant 2021CX02Z468). GF and UT acknowledge support from the FWF and the Czech Science Foundation GACR, respectively, for the joint Austrian-Czech project "Open questions about Saturn's radio emissions" (10.55776/16710 and 24–11046L). LL and PZ acknowledge support from CNES and CNRS/INSU programs of Planetology (PNP) and Solar-Terrestrial interactions (PNST, also funded by CEA).

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