Nonlinear spatiotemporal signatures of whistler-mode wave activity around Mercury during six flybys of BepiColombo mission

Domain: physics
Published: 2025-12-01
Editorial outcome: minor_revision

Abstract
Cyclotron resonance between electromagnetic waves and plasma may be a universal acceleration phenomenon of charged particles in magnetized planets. Coherent fine structures of whistler-mode waves serve as a signature of nonlinear resonance. However, the fine wave structures at Mercury have remained unknown due to limited spacecraft observations. Here we show that plasma wave observations by the third BepiColombo mission Mercury flyby (2023) have identified discrete whistler-mode emission waves similar to those observed in Earth’s magnetosphere. The frequency sweep rates of Mercury’s wave chirping tones correspond to those at Earth, based on the scaling law for planetary magnetospheric size. Furthermore, although the spatial coverage on the dayside and dusk sectors is insufficient, the spatial characteristics of Mercury’s whistler-mode waves during all the Mercury flybys (2021 to 2025) reveal an asymmetric dawn-to-night sector, which suggests nonlinear growth characterized by the distorted magnetospheric shape. These spatiotemporal features strongly indicate that electron precipitation events occur primarily in the active wave (dawn-side) region through nonlinear resonant mechanisms similar to those in Earth’s magnetosphere. This study highlights the potential significance of nonlinear resonant processes in shaping Mercury’s unique plasma environment within its small magnetosphere.

Introduction
Whistler-mode emission waves are commonly observed at planets in our Solar System1,2. Whistler-mode waves show coherent fine structures, such as rising and falling tones in the frequency domain with time variation3–6. These discrete, coherent elements are an important signature of the nonlinear growth of the whistler-mode waves7, and can effectively accelerate and scatter energetic electrons in planetary magnetospheres8–10. On Earth, the discrete whistler-mode chorus elements act to locally accelerate dangerous MeV electrons and contribute to the formation of dynamic radiation belts11–13. Although whistler-mode waves have been identified at Mercury14 and Ganymede15, which both have smaller magnetospheres than Earth, their fine structures remain unknown. Whistler-mode chorus waves have been observed within minimagnetospheres on Mars2 and the Moon16, which are generated by localized magnetic anomalies. Identifying these fine structures in such small planetary magnetospheres is important to understanding electron acceleration physics and pitch angle scattering of energetic electrons, as well as for estimating whether resonant interactions occur within finite spatial regions in latitudes and longitudes. Particularly in confined magnetic latitudes in Mercury’s inner magnetosphere, whether resonant interactions occur has so far remained a prediction based on simulations and theoretical analyses17. The observational detection of coherent wave structures as direct evidence of resonant interactions thus provides confirmation of wave-induced plasma dynamics at Mercury, similar to those observed at Earth. Given the previously insufficient discussion of wave–particle interaction effects at Mercury, the detection of resonant interactions is essential for the quantitative understanding of the Mercury environmental system. Moreover, electron acceleration mechanisms in small bodies can be applied to laboratory plasma experiments18,19 and contributing to developing fusion plasmas20 for sustainable energy production, particularly within the limited spatial scale of industrial facilities.

The BepiColombo project, a collaboration between Japan and Europe, is the third mission aimed at comprehensively investigating Mercury’s environment21. The first mission, Mariner 10, identified the basic structure of Mercury’s magnetosphere22,23. The second mission, MESSENGER24, quantified the spatiotemporal structures of Mercury’s dynamic magnetosphere, including the fact that the magnetic moment is shifted 0.2 RM northward from the planetary center25, where RM is the planetary radius. The previous Mercury missions have revealed active magnetospheric dynamics, primarily associated with magnetic reconnection (flux rope and dipolarization events)26,27. However, neither of these missions was equipped with instruments necessary to observe plasma waves associated with electron cyclotron motions, leaving the role of wave–particle interactions in electron dynamics unresolved in the context of rapid electron acceleration and wave-induced pitch angle scattering effects in Mercury’s small magnetosphere. The Plasma Wave Investigation (PWI)28 onboard BepiColombo’s Mio spacecraft provides a valuable opportunity to observe plasma waves in Mercury’s magnetosphere and to investigate particle acceleration mechanisms in small planetary bodies29. The PWI is designed to comprehensively observe DC electric fields and electromagnetic waves over a wide frequency range (electric field from DC to 10 MHz, magnetic field from 0.3 Hz to 640 kHz)28, contributing to the direct observation of plasma waves for wave–particle interactions, which play a key role in kinetic electron dynamics. Before entering Mercury’s orbit in 2026, the Mio spacecraft had six opportunities for Mercury flybys (2021–2025).

Here, we present the spatiotemporal characteristics of Mercury’s whistler-mode waves, observed by the search coil magnetometers30 during these six flybys. These observations were made when the electric field sensors and MAST booms were not deployed, during the cruise phase. This digest of the flyby observations is crucial for efficiently detecting critical areas and wave spectral signatures, enabling the acquisition of scientific data across a region of interest with limited telemetry after the Mercury Orbit Insertion (MOI) in 2026. In particular, we show that the wave spectral details and localized spatial features on the dawn side lead to the nonlinear growth of whistler-mode waves. This provides important insights into electron dynamics in other small planetary bodies with small magnetospheres, such as that of Ganymede, where electron trapping is possible31.

Results
Spatial distribution of whistler-mode wave activity
The Mio spacecraft completed the six Mercury flybys, during which the PWI operated successfully. The PWI (see “Methods”, subsection “Mercury flyby observations”) detected clear whistler-mode wave activity during the first to fourth flybys as shown in Figs. 1 and 2. Figure 1a,b show the orbit geometry of the Mercury flybys. The first to third flybys followed similar trajectories, passing from the night to the dawn sectors. The fourth flyby trajectory passed from the north to the south near the dawn side. The fifth flyby trajectory was outside of Mercury’s magnetosphere, beyond the range shown in Fig. 1, so the PWI did not detect clear whistler-mode wave activity. Finally, the sixth flyby trajectory passed from south to north in the midnight region, also without clear whistler-mode wave activity. The sixth Mercury flyby highlighted the difficulty of wave growth in the midnight side region of Mercury’s magnetosphere. These varied flyby trajectories were useful in characterizing the spatial distribution of whistler-mode waves before the MOI in 2026.

Figure 1c,d show the spatial distribution of whistler-mode wave activity during five of the six Mercury flybys, excluding the fifth flyby, which passed outside the magnetosphere and did not exhibit clear wave activity. The magnetic latitudes ranged from +34° to −51°. The spatial distribution in the southern hemisphere was more widespread compared to that in the northern hemisphere. Furthermore, the wave activity was clearly localized in the dawn sector. Similarly to the wave activity, energetic electrons at Mercury exhibited an asymmetric dawn-to-dusk distribution32,33. This spatial localization on the dawn side may be related to energetic particle injections and dipolarization events at Mercury, which are most frequent in the dawn sector26,27. To theoretically account for this asymmetric wave distribution, we added a boundary criterion for nonlinear wave growth7 in Fig. 1d (see “Methods”, subsection “Spatial critical region for nonlinear wave growth”).

The observed whistler-mode waves are thought to be generated through a two-stage growth process7. In the initial linear growth stage, incoherent whistler-mode waves are produced via the superposition of multi-frequency components. These weakly amplified waves resemble thermal noise and act as seed waves for subsequent coherent emission waves. The electron temperature anisotropy, caused by drift-shell splitting, Shabansky orbits34, and a larger (~30°) loss cone35, can generate the seed waves for whistler-mode activity according to linear theory. Once the amplitude of the incoherent (seed) waves exceeds a threshold amplitude required for nonlinear growth7, they undergo nonlinear evolution into coherent whistler-mode emission waves with sufficiently large amplitudes during the nonlinear growth stage. In this calculation of the spatial critical region for nonlinear wave growth, we used a weak temperature anisotropy of 1 across all sectors of magnetic local time (MLT) and an empirical KT17 magnetic field model36. The nonlinear criterion region shows a clear asymmetric distribution in MLT17, even under the assumption of uniform spatial distribution of temperature anisotropy. This is because nonlinear growth is influenced not only by temperature anisotropy but also by magnetic field inhomogeneity14,17. Mercury’s small magnetosphere, strongly distorted by the solar wind’s dynamic pressure, means that the criterion for nonlinear growth can be predominantly characterized by the magnetic field inhomogeneity at the source region. The observed regions of the whistler-mode waves align well with the nonlinear criterion region, and this spatial distribution strongly supports the idea that the observed waves undergo nonlinear growth characterized by magnetic field inhomogeneity at the source region, rather than being the result of wave propagation from other generation regions. In the inner magnetosphere, the magnetic field lines are more dipole-like, exhibiting weaker magnetic field inhomogeneity compared to the highly stretched field lines in the outer magnetosphere. The weak magnetic field inhomogeneity results in a lower threshold for nonlinear growth, facilitating the transition from linear to nonlinear growth of whistler-mode waves in these regions. Consequently, the spatial distribution of the nonlinear criterion region can appear to reflect the overall dipole-like shape of Mercury’s magnetosphere, as shown in Fig. 1d.

Figure 2 shows the wave spectra of the magnetic field from the first to fourth flyby observations (2021–2024). The typical spectrum intensity ranged from 2 to 3 pT/Hz1/2, except during the third flyby (2023) observation14. The typical wave amplitude was in the tens of pT, comparable to that of chorus emission waves in Earth’s outer magnetosphere. However, the spectrum intensity of the third flyby was approximately 10 pT/Hz1/2, which is about five times larger than the others, and the maximum wave amplitude reached approximately 150 pT. This strong spectrum intensity during the third flyby may be the result of the trajectory passing near the magnetic equator (less than the magnetic latitudes of 10°). Between 2021 and 2025, the Sun advanced toward solar maximum. Mercury, the closest planet to the Sun and possessing a weak intrinsic magnetic field, experiences significant fluctuations in the solar wind. While the solar wind speed near Mercury is comparable to that near Earth, both the solar wind density and magnetic field strength show a significant negative correlation with Mercury’s heliocentric distance37. Previous studies have indicated that such variations in solar wind parameters, driven by changes in heliocentric distance, affect the precipitation of solar wind protons into the cusp region38, as well as ultra-low frequency wave activity in the foreshock region39. The heliocentric distances during the first to fifth flybys were 0.38 AU, 0.38 AU, 0.33 AU, 0.32 AU, and 0.32 AU, respectively, while that of the sixth flyby was 0.45 AU. Although the sixth flyby operated during a year of heightened solar activity, the sixth flyby featured the largest heliocentric distance among all six flybys. The sixth flyby may reflect the influence of the negative correlation between heliocentric distance and plasma wave activity. A detailed investigation into the correlation between Mercury’s heliocentric distance and whistler-mode wave activity is expected following the MOI.

Coherent whistler-mode wave structures
Figure 3 shows the magnified spectral characteristics of the whistler-mode waves during the third flyby in 2023. Similar to Earth’s chorus emission waves, a wave damping effect was observed at half the gyrofrequency40, along with clear fine structures such as rising and falling tones3–6,41. The wave spectrum was distributed across both lower and upper bands relative to half the gyrofrequency. These fine structures are likely related to discrete chorus elements, as seen in other planetary magnetospheres1,2,10. The wave damping effect at half the gyrofrequency was not frequently observed during the six flybys, somewhat resembling the characteristics of the Moon’s chorus waves42. This may be due to the limited wave attenuation along Mercury’s short magnetic field lines, which reduces the efficiency of damping at half the gyrofrequency. The frequency sweep rates of the rising-tone elements ranged from 0.06 to 0.18 kHz/s around the magnetic equator in Mercury’s equatorial distance r of 1.2–1.3 planetary radii. Due to uncertainties in the electron observation (such as the full pitch angle distribution), directly comparing the observed sweep rate with nonlinear theory is not sufficient. Instead, we analyze these properties based on a scaling law, which indicates that the observed sweep rate does not come from spacecraft noise. As illustrated in Fig. 4a, Mercury’s magnetosphere, in contrast to Earth’s, is largely occupied by the planetary region. However, in certain regions, the scaling law between the two magnetospheres is considered to be applicable. In Earth’s magnetosphere (5 < r < 9, where the Earth’s equatorial radial distance r is approximately (7.6 ± 0.4) r, see “Methods”, subsection “Scaling factor for planetary magnetospheres”), the frequency sweep rates can be empirically expressed by ref. 43

∂f / ∂t = 17719 r−5.08 (1)

This relationship is not only supported by observational data, but can also be derived theoretically43. Since this formula is based on chorus waves near the Earth’s inner magnetosphere (specifically in the r range of 5–9), additional chorus observations in the Earth’s outer magnetosphere44–47 are helpful for the validation. It is further compared with chorus wave data observed by the GEOTAIL spacecraft44 in the Earth’s outer magnetosphere (primarily in the r range of 8–11). In Fig. 4b, the fine structures on Mercury were verified by comparing with chorus observations in the Earth’s outer magnetosphere (within the magnetic latitudes of 20° during 1992–2007) by the GEOTAIL mission. Based on the scaling law of Mercury’s magnetosphere and the comparison with chorus observations in the Earth’s outer magnetosphere44,45, the sweep rate falls within a comparable range of Earth’s chorus elements, as shown in Fig. 4b. The wave intensity reaching 150 pT is also considered a reasonable value. The validation of the frequency sweep rate based on the scaling law strongly suggests that the observed rising-tone elements are equivalent to Earth’s chorus elements and result in nonlinear growth. The observed fine structures also support early simulation results14, indicating the possibility of the nonlinear wave growth given specific electromagnetic parameters in Mercury’s magnetosphere.

We theoretically estimated the spatial source size in the latitudinal direction (see “Methods”, subsection “Latitudinal critical distance for nonlinear wave frequency variation”) to estimate whether the nonlinear wave frequency variation can occur along the notably short magnetic field lines, compared to Earth. The critical distance7 in the latitudinal direction at r = 1.2 was found to be 0.035 RM (approximately 6 c/Ωe0) at a wave frequency of 0.3 Ωe0. The critical distance of 0.035 RM corresponds to a magnetic latitude of approximately 1.3°. Within the observed latitude range of 10°, sufficient frequency variation can be achieved via nonlinear wave growth. Despite the shorter magnetic field lines at Mercury compared to Earth, nonlinear frequency variation of waves can still occur. This is because the critical distance is determined by the magnetic field inhomogeneity. Mercury’s magnetic field lines are more distorted than those at Earth, and the magnetic field inhomogeneity can be up to four orders of magnitude greater than typical terrestrial values. Similar to the relationship between Earth and Mercury, the magnetic field inhomogeneity in Mars’ magnetic anomaly regions can reach values approximately 10,000 times greater than those at Mercury2. Therefore, Mars’ chorus elements are also expected to be generated along similarly confined magnetic field lines2, which is consistent with our findings for Mercury. Consequently, the critical distance becomes significantly shorter, allowing frequency variation due to nonlinear growth to occur even within Mercury’s small magnetosphere. Together with comparisons based on the scaling law established from GEOTAIL observations, our results support the universality of the nonlinear wave–particle interaction mechanism7 responsible for chorus generation within a limited latitudinal source region.

Simulations of nonlinear pitch angle scattering
The spatial agreement between whistler-mode waves observed by the Mio spacecraft (Fig. 1) and electron-induced X-ray fluorescence33 and high-energy electron precipitation events32 detected by the MESSENGER mission suggests that the coherent whistler-mode waves can effectively scatter high-energy electrons via nonlinear pitch-angle scattering. During BepiColombo’s first Mercury flyby, variations in energetic electrons48 were observed simultaneously with whistler-mode waves14. These electrons likely triggered X-ray fluorescence events through precipitation onto Mercury’s surface. The wave-induced pitch angle scattering may lead to direct precipitation onto Mercury’s surface. Based on the previous test particle simulation studies35, the trapping region for energetic electrons in Mercury’s magnetosphere is expected to extend up to approximately r = 1.6. Furthermore, as shown in Fig. 1, whistler-mode wave activity is dominantly observed within this region. These findings suggest that the wave-induced pitch angle scattering is likely to occur within the closed magnetic field line domain (less than about r = 1.6). The wave and electron observations challenge the conventional view that electron precipitation is mainly driven by processes occurring far from the planet (r ≳ 3), such as magnetic reconnection and flux ropes49. To evaluate this near-planet source of electron precipitation, we conducted test particle simulations using coherent whistler-mode wave parameters derived from the six flyby observations (see “Methods”, subsection “Test particle simulation of nonlinear wave–particle interactions”). Both parallel and oblique (30° wave-normal angle) wave propagations were considered, as the latter allows not only cyclotron resonance but also Landau resonance to contribute to pitch angle scattering50. Assuming a dipole magnetic field at r = 1.2, referred from Fig. 1, we account for Mercury’s much shorter field line lengths (approximately 1/30th of Earth’s, with r around 10). As illustrated in Fig. 4a, this short field line length raises the question of whether significant pitch-angle scattering can still occur at Mercury.

Figure 5 shows the resulting loss rates of energetic electrons. The oblique propagation (Fig. 5b, d) produces a distinct loss peak near 1 keV due to Landau resonance, which is absent in the parallel propagation case (Fig. 5a, c). The results show that even an interaction with a single coherent whistler-mode wavepacket can cause substantial electron loss near the loss cone, up to approximately 8% via cyclotron resonance at energies of several keV, and about 3% via Landau resonance at 1 keV. Given multiple interactions50 with multiple wave packets, as shown in Fig. 3, nonlinear pitch-angle scattering could play a significant role in rapid electron precipitation within Mercury’s small magnetosphere, similar to processes observed at Earth. Our simulations used a constant-frequency coherent wave model without frequency sweep for simplicity. In reality, variations in wave frequency affect a broad energy range due to the differing resonant energies associated with each wave frequency51. We also did not include the northward dipole offset25 in our model, although this asymmetry likely affects the whistler-mode wave growth and can lead to north–south differences in electron precipitation51. Conventionally, X-ray fluorescence33 and high-energy electron bursts32 at Mercury have been attributed to direct solar wind precipitation, particularly near cusp regions and open–closed field line boundaries52. While previous models emphasized distant drivers such as reconnection or flux ropes, our results suggest that nonlinear pitch-angle scattering by coherent whistler-mode waves in Mercury’s inner magnetosphere provides a viable and efficient local mechanism for driving electron precipitation. The observations from the first Mercury flyby, including simultaneous wave and electron measurements, strongly support this idea.

Methods
Mercury flyby observations
The PWI was developed through international collaboration between Japan and Europe28, with the search coil magnetometers onboard the Mio spacecraft jointly developed by Japan and France30. The PWI successfully captured whistler-mode waves at Mercury during four of the six flybys conducted on 1 October 2021, 23 June 2022, 19 June 2023, 4 September 2024, 1 December 2024, and 8 January 2025. For all the datasets, the wave amplitude was calculated using the squared sum of the search coil output components along the beta and gamma axes30. The time resolution of the wave spectrum was 1 s during the first and third flybys, and 4 s during the second, fourth, fifth, and sixth flybys. The spatial coverage of BepiColombo’s six Mercury flybys included the dusk, night, and dawn sectors, as shown in Fig. 1. Due to limited data telemetry prior to the MOI, only spectral data without waveforms were collected. The polarization and wave normal vectors will be investigated after the MOI. The gyrofrequency was calculated using an empirical magnetic field model36. The frequency sweep rates were visually analyzed only for clearly distinguishable fine structures. Due to the limited frequency resolution, the frequency sweep rates of the rising-tone elements were analyzed based on the scaling law (Fig. 4). The frequency sweep rate of Mercury was distributed at lower values compared to those observed by GEOTAIL. This may be due to the lower temporal resolution (1 s spectrum) of the PWI data, as opposed to the waveform data with 12 Hz frequency resolution observed by GEOTAIL. The frequency sweep rate is proportional to the nonlinear growth theory7,45, but the PWI observed only two components (beta and gamma) from the search coil magnetometers with the same temporal and frequency resolutions. The quantitative relationship between wave intensity and sweep rate will be studied in future work after the MOI. In Figs. 2 and 3, the frequency resolution is not a constant in order to reduce data telemetry28.

Spatial critical region for nonlinear wave growth
Nonlinear growth7 can be characterized by the optimum amplitude Ωop and threshold amplitude Ωth. To classify the wave growth into linear and nonlinear categories, the region criterion is defined by the wave amplitude ratio Ωop / Ωth > 1, where Ωop means the maximum ideal amplitude of a nonlinear whistler-mode wave, and Ωth is the threshold for the transition from linear to nonlinear growth7. The criterion is evaluated at the frequency corresponding to the maximum linear growth rate7,17. The magnetic fields used an empirical model36 and the background electron density used a diffusive equilibrium model, taking into account the magnetic field-aligned force for plasmas, the planet’s gravity, and centrifugal force17. We assumed a uniform spatial distribution of temperature anisotropy (with a value of 1) for energetic electrons across all MLT sectors, in order to impose the same free energy source for instabilities. The temperature anisotropy was simply set to 1, based on GEOTAIL observations45. Although temperature anisotropy is important for determining the absolute wave amplitude, but the dominant parameter controlling the spatial scale of nonlinear growth at Mercury is the magnetic field inhomogeneity, resulting from the strongly distorted field lines17.

Scaling factor for planetary magnetospheres
We calculated the scaling value based on the magnetic field inhomogeneity a of the planetary magnetosphere, as the magnetic field inhomogeneity can be a dominant parameter for characterizing nonlinear wave growth in distorted Mercury’s magnetosphere17. The threshold value for nonlinear wave growth7 can be characterized by the square of the normalized magnetic field inhomogeneity ae2. The normalized magnetic field inhomogeneity is defined as ae = ac2 / Ωe02, where c is the speed of light, and Ωe0 is the equatorial gyrofrequency. The magnetic field inhomogeneity a can be expressed as Ωe(h) = Ωe0(1 + ah2), where Ωe is the gyrofrequency and h is the small distance from the equator along a magnetic field line. We calculated the magnetic field inhomogeneity using the KT17 model36 for Mercury and the Tsyganenko 89 model58 for Earth. This approach has the advantage of determining the scaling factor by taking into account not only the magnetic field strength characterized by Ωe but also the influence of the magnetic field inhomogeneity. The scaling factor A is determined by minimizing the mean square error (MSE), given by MSE = 1 / (NM) Σi=1N Σj=1M (ae2(xi, yj, 0) - A ae2(xi, yj, 0))2, where the subscript on ae2 indicates each planet, and xi, yj, 0 and xi, yj, 0 are the coordinates in solar magnetic (SM) coordinates for Mercury and Earth, respectively. The scaling factor A was defined as 7.6 ± 0.4, even when assuming an extreme range for the disturbance index from 1 to 9 for Mercury and the Kp index from 0 to >6 for Earth. The value of the scale factor was similar to that reported in a previous study (8 ± 0.5), which was based on the magnetopause standoff distance23. However, the variation in the present scale factor is small, making it a more robust parameter for characterizing chorus wave properties compared to the scaling factor determined solely by the planetary magnetopause standoff distance.

Latitudinal critical distance for nonlinear wave frequency variation
In the nonlinear wave growth theory7, the critical distance can be expressed as s = 5c / (ω Ωw0), where ω is the wave frequency, Ωw0 is the wave amplitude at the initial generation region, and s and s2 are dimensionless parameters representing the inhomogeneity factor in the nonlinear theory, respectively. Because Mercury’s magnetic field inhomogeneity is 10,000 times greater than that of Earth’s typical magnetosphere, the critical distance at Mercury becomes shorter even under similar plasma conditions. We assumed pitch angle α = 60° and ω = 0.3 Ωe0 with Ωw0 = 0.05% Ωe0 ≃ 56 pT at the initial generation region (r = 1.2) within the critical distance. The initial wave amplitude Ωw0 can grow further during propagation beyond the critical distance if the resonance condition is satisfied. Based on a typical electron density of 10–100 cm−3 in Mercury’s inner magnetosphere59, a ratio of ωpe / Ωe = 10 is assumed along the magnetic field line, where ωpe is the electron plasma frequency.

Test particle simulation of nonlinear wave–particle interactions
The resonance condition7 between a coherent whistler-mode wave and an electron is given by ω − k k V R = n Ω / γ, where k k is the parallel component of the wave number, V R is the resonance velocity, and γ is the Lorentz factor. The case n = 0 corresponds to Landau resonance, while n = 1 corresponds to the first-order cyclotron resonance. The change in the local pitch angles is given by dα / dt = u 1 / 2 u k d u ? / d t − u ? d u k / d t / u 2, where α is the local pitch angle, u is the momentum magnitude, u k and u ? are the components of the momentum parallel and perpendicular to the background magnetic field line, respectively. In the simulation, the pitch angle changes are computed using the fourth-order Runge-Kutta method within a simple dipole magnetic field60, assuming a whistler-mode wave packet with constant frequency and constant wave amplitude along a magnetic field line. If the pitch angle is smaller than the loss cone angle, it is counted as a loss toward the planetary surface. Based on the wave observations, a constant wave amplitude of 0.001 B0 is assumed at a frequency of 0.3 Ωe0 with ωpe / Ωe = 10, where B0 is the equatorial magnetic field strength. The wave model is distributed from the magnetic equator up to a latitude of ±20° in one hemisphere to estimate the loss rate from a single interaction. We injected 720 particles for each equatorial pitch angle, with a resolution of 0.5° in the relative angle between the wave and the electron.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This review covers the submitted manuscript entitled ‘Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys’ by Ozaki et al. I have reviewed the submission carefully and have a number of questions for clarification as well as just a couple of points on grammar and spelling that should be fixed. The work does support the conclusion and claims presented. There are no major flaws in the analysis or presentation - except for the moderate questions that need to be addressed below. There is not quite enough detail included to reproduce the results (see comments #4, #5, and #10) but it can be easily rectified. However, I am not certain that the results as presented here are noteworthy to the extent that it meeds the standards for a Nature publication. I explain this more thoroughly in my first comment, #1. In summary, while the results are robust, they show minimal increase in new understanding of the Mercury system and instead backup previous results published in this very journal two years earlier.\nMain Comments:\n#1: This is a comment on the significance of the overall results. I have reviewed the previous publication on similar results (Ozaki et al. 2023, https://doi.org/10.1038/s41550-023-02055-0). The additions in this paper are minimal, I believe. It is interesting to have additional measurements from the Mercury system and of course we have such few observations that it’s very important to publish these additional observations. However, it is not a significant contribution in changing our understanding of the system, thus it is more appropriate as a report in a planetary or magnetospheric journal, rather than a multi-discipline journal like Nature that is used for disseminating findings of the highest impact.\nThe MAST booms are still not deployed and thus the fidelity of the wave observations is the same in these additional flybys. These additional flybys do contribute to having more local time statistics but they do not change the result of the 2023 paper that the chorus is well-confined to the dawn side of Mercury’s magnetosphere. In Lines 81-83, it is stated that “we show that the wave spectral details and localized spatial features on the dawn side lead to the nonlinear growth of whistler-mode waves.” This would be a nice result, but you already showed that in the 2023 paper, with simulation results. This is referred to later when it is stated in Lines 152-154 that “The observed fine structures also support early simulation results [9] indicating the possibility of the nonlinear wave growth given specific electromagnetic parameters in Mercury’s magnetosphere.” The “early simulation results” are the ones from the 2023 Nature publication. Thus, while it’s very nice to have additional Mercury chorus wave observations, it does not change any of our current understanding or expand it significantly in any way. This is my overall major critique of the submission, although I have further comments that I think are worth addressing in the following points.\n#2 (Figure 1 caption): specify the empirical magnetic field model used (I assume it’s Ref 39, as it is cited later on, but it needs to be referred to here in the first mention)\n#3 (Figure 2d): The hook feature is not verifiable. The noise level is too high relative to the signal to resolve. These kinds of features might be resolvable after the boom deployment.\n#4 (Lines 142-144): What does this mean that you compare Mercury observations with GEOTAIL? Are the dots in Figure 2e the chorus frequency sweep rates as determined from GEOTAIL? If so, this should be made more clear in the text and in the Figure caption.\n#5 (Figure 2e): Please better explain in the paper text how you determine this boundary of the shaded region shown on the figure panel. In the Methods section, you say that the boundary is determined due to “the uncertainty in the scaling law”, but please provide more details.\n#6 (Line 179-180): What does this mean? “The electron temperature anisotropy … can generate seed waves for whistler-mode activity according to linear theory” What are the seed waves you refer to?\n#7 (Line 182-183): In the 2023 paper, you used an assumed anisotropy of 1.2, but here you use 1. Can you explain the motivation for choosing this value?\n#8 (Lines 203-206): This sentence is not accurate: “Through comparison with the Earth’s chorus observations by the GEOTAIL mission, we found discrete chorus emission waves in Mercury’s magnetosphere, equivalent to those observed in Earth’s magnetosphere, including rising, falling, and hook structures in the frequency domain.” You did not present the fine structure from GEOTAIL and compare with the BepiColombo observations. You used GEOTAIL observations to schematically show a scaling law that aligns the frequency sweep rate at Earth with that at Mercury. This whole sentence/section should be rewritten to reflect what you have really done.\n#9 (Line 215-216): What does this mean? “The dynamic effects on electron drift currents” Is this effects of the waves on electron drifts? What effects?\n#10 (Line 270-271): Why is the Zenodo repository not already set up? It is meaningless to say it will eventually be offered on Zenodo if there is no way to locate it without a link to it. It would be useful to have the data up on the repository now and an actual link given, as was done with PWI data.\nSpelling/Grammar points:\nLine 131: Not an accurate phrase: “is more effectively associated”. Please try to rephrase to be more precise on your meaning.\nLine 179: Need to correct to “Shabansky”", "reviewer_2": "The manuscript presents noteworthy results on chorus wave, possibly whistler wave-type, observations from BepiColombo's Mercury flybys, which offer valuable insights into planetary magnetospheres. These findings may contribute to comparative studies of wave-particle interactions across different planetary environments.\nHowever, while the work provides some interesting results, several aspects, especially the reviewer has some concerns on the planetary scaling, need further clarification to ensure that conclusions are well-supported by the data. The reviewer's other comments or suggestions include to further explain the prior references, improve methodology, provide more detail on the descriptions of the data etc.\nThe reviewer thinks that strengthening these areas will ensure that the study meets expected standards of nature communications and maximizing its impact.\nComments:\n#1, Abstract, Line 29: The statement regarding plasma wave observations from BepiColombo Mercury flybys (2021–2025) should be more precise, since only PWI measurements from the third flyby are presented in detail.\n#2, Abstract, Line 33: The phrase \"asymmetric dawn-to-night sector\" may not be necessary, because BepiColombo did not sample the duskside inner magnetosphere as close as those sampling on the dawnside magnetosphere. Consider refining this wording.\n#3, Introduction, Line 50: Consider mentioning the observation of chorus waves at Mars (Teng et al. 2023, Nature Communications) for broader context.\n#4, Introduction, Lines 50–52: The connection between particle drift and fine structures of whistler-mode waves is unclear. If the implication is that cyclotron resonance dominates due to the absence of drift resonance, this should be stated explicitly.\n#5, Introduction, Lines 57–64: The discussion of previous missions is lengthy, and their scientific results are not addressed. Since the key point is that these spacecraft lacked plasma wave instruments, consider making this section more concise and clear.\n#6, Introduction, Line 72: Providing an exact frequency range would improve clarity.\n#7, Figures 1a–b: Labels should be added to panels to distinguish the trajectories from different flybys.\n#8, Figures 1c–f: If these spectra are presented without removing noises, a brief explanation of potential noise sources would be helpful.\n#9, Results, Lines 91–94: The observations from the 5th and 6th flybys are not directly relevant to whistler-mode wave studies. Consider refining this section for clarity.\n#10, Results, Figure 1 Caption, Line 110: Cite Korth et al., 2017 to properly acknowledge previous research.\n#11, Results, Lines 114–115: Converting \"6 to 10 dB pT/sqrt(Hz)\" to “pT/sqrt(Hz)” for consistency.\n#12, Results, Lines 119–121: The observed variations may be associated with the solar maximum and Mercury's orbital phase. As shown in Sun et al. (2022; https://doi.org/10.1007/s11430-021-9828-0), the solar wind parameters are much stronger near the Sun. May consider incorporating these possibilities into the discussion.\n#13, Results, Line 137: The term \"compelling\" may not be appropriate for authors to declare themselves. Please rephrase this.\n#14, Results, Lines 138–139: Provide further details on how the scaling law \"r0E ~ (8±0.5) r0M\" was derived. This probably the largest concern that the reviewer has for this study. This is an important concern since the scaling study is the most important result of this study. The reviewer also would like to note that planetary magnetosphere scaling may not always apply due to differences in dipole intensity between Mercury and Earth.\n#15, Results, Line 140: This scaling law can also be derived theoretically, see Tao et al., 2012 (AGU Publications). The authors might include this reference's result.\n#16, Results, Lines 144–146: Chorus waves have been observed in multiple missions, including THEMIS (Agapitov et al., 2010—Ann. Geophys.) and Cluster (jgra.50312). Consider citing these studies.\n#17, Results, Figure 2: The non-uniform sampling frequency of spectra panels (a)–(d) should be explained. In addition, if the gray-shaded regions represent observational results from this study, this should be clearly stated.\n#18, Results, Line 171: Flyby measurements are spatially biased since the coverage of the duskside inner magnetosphere was highly limited. This should be acknowledged.\n#19, Results, Line 172: The term \"hot\" electrons may not be appropriate here, as references 36 and 37 do not indicate temperature. Consider using \"high-energy\" or \"energetic electrons\" (>10s keV) instead.\n#20, Results, Line 179: The mention of Shebansky orbit could be more clear, and also should consider adding a citation (see Zhao et al., 2022, Nature Communications), which reports Shebansky orbits of ring current ions at Mercury.\n#21, Results, Lines 182–183: Define \"a weak temperature anisotropy of 1\" more explicitly. A brief introduction of density and temperature distribution in the Methods section would enhance clarity.\n#22, Results, Lines 190–193: The manuscript suggests that the nonlinear criterion region is influenced by magnetospheric shape. However, observations from these flybys do not directly reflect the special shape, and detected chorus waves could mainly originate from the inner magnetosphere. This could be revised for better alignment with observations.\n#23, Results, Figure 3: Adding time range annotations for the bolded trajectories would improve clarity and readability.", "reviewer_3": "Whistler-mode wave activity is the natural electromagnetic emission in the planetary magnetospheres. The authors had presented the direct probing of chorus waves in the localized dawn sector during the first and second Mercury flybys by the BepiColombo/Mio spacecraft (Ozaki et al., 2023). In this manuscript, they further analyzed the coherent fine structures of whistler-mode waves from all six Mercury flybys. The main results are (1) The discrete whistler-mode emission waves are identified, and (2) The activity tendency of waves occurs in the dawn side of the magnetosphere. However, the former result is similar to those observed in the Earth’s magnetosphere. What readers might be interested in is the differences between Mercury and Earth and what inluences Mercury’s unique plasma environment. The second result has been concluded in Ozaki et al., (2023). As such, I do not think the current form of the manuscript provides sufficient new information about the physics of Mercury’s magnetosphere to ensure its publication in Nature Communications.", "reviewer_4": "The authors report observational findings from the BepiColombo mission’s Mio spacecraft during its Mercury flybys between 2021 and 2025. Their analysis focuses on whistler-mode wave activity within Mercury’s magnetosphere, revealing fine spectral structures—such as rising and falling tones—that align with nonlinear wave growth processes observed in Earth’s magnetospheric chorus emissions. The study suggests that Mercury’s compact magnetosphere can sustain nonlinear wave-particle interactions capable of generating energetic electron belts.\nThis study can potentially mark a significant advance with broad implications for understanding electron acceleration in compact magnetospheric environments.\nThe methodology is technically sound and well documented. The authors correctly recognize limitations and justify choices (e.g., visual identification of tones due to data limitations). However, while applying Earth-based scaling laws to Mercury is conceptually sound, it has not yet been empirically confirmed. Therefore, the frequency sweep comparisons are indicative but not definitive.\nAlso, without simultaneous electron measurements, claims about electron acceleration and resonance are based on inference and cannot be directly validated.\nIn addition, the magnetic field and electron density models are based on empirical data and may not fully capture Mercury’s dynamic environment, which can reduce the accuracy of nonlinear wave growth threshold calculations", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Authors’ Responses to Reviewers’ comments on Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys\nWe sincerely appreciate the supportive comments from all five reviewers regarding our scientific findings on nonlinear wave–particle interactions occurring at Mercury, despite the inherent limitations of wave data obtained from flyby observations, such as temporal resolution etc. We are also grateful for the recognition of our appropriate technical approach. In response to the suggestions from Reviewers #1 and #3, we have added further explanation and expanded the revised manuscript to describe the role of the first observational evidence of coherent wave structures associated with nonlinear wave–particle interactions in the Mercury system. In particular, based on BepiColombo observations and simulation results, we emphasize the proposal of a new source region of electron precipitation near Mercury (L < 1.6) characterized by wave-induced pitch angle scattering (please see a new 2.3 section), which supplements the conventional concept of a distant (L ≈ 3) source region based on flux ropes. As Reviewers #2 and #4 also supported, these findings predict that wave–particle interactions extend their influence from Mercury’s magnetosphere to its exosphere, contributing broadly to the understanding of the Mercury system, including from the perspective of comparative planetology. Moreover, while scale laws are generally considered a standard technical approach in comparative planetology, we have revised the manuscript to clarify ambiguities pointed out by Reviewers #1, #2, and #4. Specifically, beyond the conventional empirical scaling based on the magnetopause standing distance, we have used a more robust scale law that uses magnetic field inhomogeneity as a primary parameter governing chorus wave generation. These revisions strengthen the scientific significance of the first plasma wave observations at Mercury by BepiColombo, demonstrating common physics in magnetized planets through nonlinear wave–particle interactions. Considering the previous studies in Mercury’s plasma environments, where discussions on the effects of wave–particle interactions have been insufficient due to its small magnetosphere, we are very pleased that these revisions have strengthened the significance of the first plasma wave observations at Mercury by BepiColombo. Through nonlinear wave–particle interactions that demonstrate common physical processes in magnetized planets, our results are expected to maximize the scientific outcomes of the upcoming MOI operation and provide a valuable foundation for advancing comparative studies between the Mercury environment and other planetary systems.\nOur point-by-point responses to the comments are listed below in blue, and the reviewers’ original comments are italicized in black. Revisions in the manuscript are highlighted in yellow.\nAuthors’ responses to Reviewer #1\nThis review covers the submitted manuscript entitled ‘Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys’ by Ozaki et al. I have reviewed the submission carefully and have a number of questions for clarification as well as just a couple of points on grammar and spelling that should be fixed. The work does support the conclusion and claims presented. There are no major flaws in the analysis or presentation - except for the moderate questions that need to be addressed below. There is not quite enough detail included to reproduce the results (see comments #4, #5, and #10) but it can be easily rectified. However, I am not certain that the results as presented here are noteworthy to the extent that it meeds the standards for a Nature publication. I explain this more thoroughly in my first comment, #1. In summary, while the results are robust, they show minimal increase in new understanding of the Mercury system and instead backup previous results published in this very journal two years earlier.\nThank you very much for your valuable comments and careful review. We would like to emphasize that the main contribution of this study is not simply an extension of observational data from Ozaki et al. (2023), but rather the presentation of new and important scientific insights regarding nonlinear wave-particle interactions in Mercury’s magnetosphere. Specifically, this study:\n Provides the first observational evidence that coherent nonlinear whistler-mode waves occur in Mercury’s small magnetosphere. While linear wave growth due to temperature anisotropy is well established, the nonlinear evolution forming coherent wave packets involves fundamentally different physics.\n Demonstrates, through numerical simulations informed by observed parameters, the occurrence of electron precipitation events caused by nonlinear pitch-angle scattering within Mercury’s inner magnetosphere, revealing a previously unreported surface impact mechanism.\n Identifies a new near-planet source region for high-energy electrons precipitating onto Mercury’s surface, complementing and expanding upon known flux rope-related precipitation mechanisms located further from the planet.\nThese novel findings offer new perspectives on Mercury’s plasma environment and exosphere composition via nonlinear whistler-mode waves, beyond the conventional flux rope paradigm. We believe these contributions significantly advance understanding of Mercury’s magnetospheric dynamics.\nWe have revised the manuscript accordingly to clarify these points (please see the Introduction, Lines 238 to 259, Section 2.3, and Discussion).\nMain Comments:\n#1: This is a comment on the significance of the overall results. I have reviewed the previous publication on similar results (Ozaki et al. 2023, https://doi.org/10.1038/s41550-023-02055-0). The additions in this paper are minimal, I believe. It is interesting to have additional measurements from the Mercury system and of course we have such few observations that it’s very important to publish these additional observations. However, it is not a significant contribution in changing our understanding of the system, thus it is more appropriate as a report in a planetary or magnetospheric journal, rather than a multi-discipline journal like Nature that is used for disseminating findings of the highest impact.\nThank you again for your valuable comments. As addressed in our response to the general comments above, we believe this study provides significant and novel contributions to the understanding of nonlinear wave-particle interactions in Mercury’s magnetosphere, and thus will be of great interest and benefit to the diverse readership. In particular, based on simultaneous wave and electron observations from the first Mercury flyby, along with our simulation results, we propose a new source region for electron precipitation near the planet (please see the new Section 2.3).\nThe MAST booms are still not deployed and thus the fidelity of the wave observations is the same in these additional flybys. These additional flybys do contribute to having more local time statistics but they do not change the result of the 2023 paper that the chorus is well-confined to the dawn side of Mercury’s magnetosphere. In Lines 81-83, it is stated that “we show that the wave spectral details and localized spatial features on the dawn side lead to the nonlinear growth of whistler-mode waves.” This would be a nice result, but you already showed that in the 2023 paper, with simulation results. This is referred to later when it is stated in Lines 152-154 that “The observed fine structures also support early simulation results [9] indicating the possibility of the nonlinear wave growth given specific electromagnetic parameters in Mercury’s magnetosphere.” The “early simulation results” are the ones from the 2023 Nature publication. Thus, while it’s very nice to have additional Mercury chorus wave observations, it does not change any of our current understanding or expand it significantly in any way. This is my overall major critique of the submission, although I have further comments that I think are worth addressing in the following points.\nWe appreciate the reviewer’s observation regarding the MAST boom deployment status and acknowledge that wave measurement fidelity remains consistent with previous flybys. Our study does not contradict the earlier finding that chorus waves are confined to Mercury’s dawn sector (Ozaki et al., 2023). Rather, it expands on this foundation by:\n Increasing local time coverage with additional flybys, thereby providing more robust statistical constraints on the spatial distribution and variability of nonlinear whistler-mode wave activity.\n Presenting newly observed fine wave structures that directly support previously proposed nonlinear growth mechanisms.\n Offering comparative planetology insights by characterizing nonlinear wave-particle interactions unique to Mercury’s small magnetosphere, such as latitudinal source size differences.\n Enhancing the overall understanding of energy transport and magnetospheric dynamics at Mercury, essential for guiding future orbital missions.\nTo address potential ambiguity, we have clarified these contributions in the revised manuscript, particularly in the Introduction, Lines 238 to 259, Section 2.3, and Discussion.\n#2 (Figure 1 caption): specify the empirical magnetic field model used (I assume it’s Ref 39, as it is cited later on, but it needs to be referred to here in the first mention)\nWe have added the relevant reference to the caption of Figure 1 (Line 172).\n#3 (Figure 2d): The hook feature is not verifiable. The noise level is too high relative to the signal to resolve. These kinds of features might be resolvable after the boom deployment.\nWe have removed the previous Figure 2d, which showed the hook wave structure, in the revised manuscript.\n#4 (Lines 142-144): What does this mean that you compare Mercury observations with GEOTAIL? Are the dots in Figure 2e the chorus frequency sweep rates as determined from GEOTAIL? If so, this should be made more clear in the text and in the Figure caption.\nWe apologize for the insufficient explanation. The color dots represent the GEOTAIL observations. We have clarified this point in the figure caption accordingly in Lines 265 to 271 and added a new Figure 2.\n#5 (Figure 2e): Please better explain in the paper text how you determine this boundary of the shaded region shown on the figure panel. In the Methods section, you say that the boundary is determined due to “the uncertainty in the scaling law”, but please provide more details.\nIn the previous study, the scaling factor was determined based on the assumption that the planetary magnetic pressure balances the solar wind dynamic pressure at the magnetopause standoff point. Under the simplifying assumption that dipole tilt effects can be neglected, the dipolar magnetic pressure at the planetary dayside magnetopause is approximately proportional to {M2⁄(R )6}, where M is the planetary magnetic moment (M = -195 nT R3 for Mercury and M = 31000 nT R3 for Earth, where R and R are Mercury’s and Earth’s radii, respectively) and R is the Chapman-Ferraro stagnation distance (R = 1.6R for Mercury and R = 10R ). In the case of a simple closed magnetosphere, R ≈ R , where R is the actual distance of the sub-solar magnetopause (R = 1.5R for Mercury and R = 8 to 12R ). The typical scaling coefficient between Mercury’s (R = 1.45R ) and Earth’s (R = 11.1R ) magnetospheres can then be estimated as (195R3⁄31000R3) 2 (11.1⁄1.45)6(R ⁄R )6 ≈ 8,\nbased on the assumption that the planetary magnetic pressure balances the solar wind dynamic pressure at the magnetopause standoff point.\nAdditionally, we calculated the scaling value based on the magnetic field inhomogeneity a of the planetary magnetosphere, since this parameter can play a dominant role in characterizing nonlinear wave growth, particularly in Mercury’s magnetosphere. The threshold for nonlinear wave growth can be characterized by the normalized magnetic field inhomogeneity ã2, where ã = ac2⁄Ω2 and Ω (h) = Ω (1+ah2). Here, Ω is the equatorial gyrofrequency, Ω is the gyrofrequency, h is the small distance from the equator along a magnetic field line. We calculated the magnetic field inhomogeneity using the KT17 model for Mercury and the Tsyganenko 89 model for Earth. This approach offers the advantage of accounting not only for magnetic field strength (Ω ) but also for magnetic field inhomogeneity. Moreover, the variation of the scaling factor due to magnetic field perturbations is relatively small, making this a more robust scaling metric for chorus wave characteristics than one based solely on magnetopause standoff distance. Please see Lines 428 to 452 in the Methods section.\n#6 (Line 179-180): What does this mean? “The electron temperature anisotropy … can generate seed waves for whistler-mode activity according to linear theory” What are the seed waves you refer to?\nWe are referring to incoherent linear waves that precede the nonlinear growth of coherent chorus waves. To clarify this point, we have revised the manuscript accordingly and added sentences to explicitly describe this linear stage in Lines 127 to 137.\n#7 (Line 182-183): In the 2023 paper, you used an assumed anisotropy of 1.2, but here you use 1. Can you explain the motivation for choosing this value?\nThe temperature anisotropy was simply set to 1(= T ⁄T -1), in accordance with chorus observations of the Earth's outer magnetosphere by GEOTAIL. Previous studies have shown that the most influential parameter for chorus wave generation is magnetic field inhomogeneity. Therefore, varying the anisotropy from 1.2 to 1 does not lead to any fundamental change in characterizing the spatial distribution. The description has been added in Lines 419 to 426.\n#8 (Lines 203-206): This sentence is not accurate: “Through comparison with the Earth’s chorus observations by the GEOTAIL mission, we found discrete chorus emission waves in Mercury’s magnetosphere, equivalent to those observed in Earth’s magnetosphere, including rising, falling, and hook structures in the frequency domain.” You did not present the fine structure from GEOTAIL and compare with the BepiColombo observations. You used GEOTAIL observations to schematically show a scaling law that aligns the frequency sweep rate at Earth with that at Mercury. This whole sentence/section should be rewritten to reflect what you have really done.\nWe have revised the sentence to clarify that the scaling law was established based on GEOTAIL observations of the Earth's outer magnetosphere in Lines 256 to 259.\n#9 (Line 215-216): What does this mean? “The dynamic effects on electron drift currents” Is this effects of the waves on electron drifts? What effects?\nThe original description referred to fluctuations in precipitating electron flux resulting from wave-driven pitch-angle scattering. For clarity and conciseness, we have revised it to “wave-induced electron precipitation events” in Lines 350 to 353.\n#10 (Line 270-271): Why is the Zenodo repository not already set up? It is meaningless to say it will eventually be offered on Zenodo if there is no way to locate it without a link to it. It would be useful to have the data up on the repository now and an actual link given, as was done with PWI data.\nInstead of using the Zenodo repository, we provided the GEOTAIL analysis data as the source data. Including the source data as Supplementary Material immediate access for readers, eliminating the need to consult external platforms. We think that the data remains closely integrated with the manuscript.\nLine 131: Not an accurate phrase: “is more effectively associated”. Please try to rephrase to be more precise on your meaning.\nThe wave damping effect at half the gyrofrequency is caused by the propagation effects from the source to the observation location. We have revised the sentence to be more precise in Lines 209 to 211.\nLine 179: Need to correct to “Shabansky”\nWe apologize for the typographical error. It has been corrected in the revised manuscript (Line 133).\nAgain, we appreciate all of your valuable comments. We hope that our revisions address your concerns. Thank you very much for taking time to give a valuable opportunity to enhance our scientific findings.\nAuthors’ responses to Reviewer #2\nThe manuscript presents noteworthy results on chorus wave, possibly whistler wave-type, observations from BepiColombo's Mercury flybys, which offer valuable insights into planetary magnetospheres. These findings may contribute to comparative studies of wave-particle interactions across different planetary environments.\nHowever, while the work provides some interesting results, several aspects, especially the reviewer has some concerns on the planetary scaling, need further clarification to ensure that conclusions are well-supported by the data. The reviewer's other comments or suggestions include to further explain the prior references, improve methodology, provide more detail on the descriptions of the data etc.\nThe reviewer thinks that strengthening these areas will ensure that the study meets expected standards of nature communications and maximizing its impact.\nWe sincerely appreciate your constructive and insightful comments, which have significantly contributed to improving our manuscript. In particular, based on simultaneous wave and electron observations from the first Mercury flyby, along with our simulation results, we propose a new source region for electron precipitation near the planet (see the new Section 2.3 in the revised manuscript). We hope that our new findings on electron precipitation at Mercury provide a significant and novel contribution to the understanding of nonlinear wave–particle interactions in Mercury’s magnetosphere, and that they will be of broad interest and benefit to the journal’s diverse readership by highlighting the role of coherent wave structures.\nComments:\n#1, Abstract, Line 29: The statement regarding plasma wave observations from BepiColombo Mercury flybys (2021–2025) should be more precise, since only PWI measurements from the third flyby are presented in detail.\nWe have revised the abstract to clarify that the temporal structure is analyzed focusing on the third flyby, while the spatial structure is investigated using data from all flybys in Lines 28 to 34.\n#2, Abstract, Line 33: The phrase \"asymmetric dawn-to-night sector\" may not be necessary, because BepiColombo did not sample the duskside inner magnetosphere as close as those sampling on the dawnside magnetosphere. Consider refining this wording.\nWe have clarified in both the abstract and the main text that the observational coverage on the dusk side is limited in Lines 32 to 33 and Line 346, while also emphasizing that the flyby observations provide a strong foundation for the understanding that whistler-mode wave activity is concentrated on the dawn side of Mercury’s magnetosphere.\n#3, Introduction, Line 50: Consider mentioning the observation of chorus waves at Mars (Teng et al. 2023, Nature Communications) for broader context.\nAdditional references on chorus wave activity at Mars and the Moon have been included in Lines 54 to 56 to provide broader context. We have also added the discussion on the critical distance of Mars’ chorus in Lines 238 to 253.\n#4, Introduction, Lines 50–52: The connection between particle drift and fine structures of whistler-mode waves is unclear. If the implication is that cyclotron resonance dominates due to the absence of drift resonance, this should be stated explicitly.\nTo avoid potential confusion for readers caused by listing various resonance conditions, we have simplified the explanation to focus on the possibility of resonance with whistler-mode waves in a finite spatial domain in Lines 57 to 59.\n#5, Introduction, Lines 57–64: The discussion of previous missions is lengthy, and their scientific results are not addressed. Since the key point is that these spacecraft lacked plasma wave instruments, consider making this section more concise and clear.\nIn the previous manuscript (Lines 64 to 65), we clearly stated that previous Mercury missions did not carry plasma wave instruments; however, in the revised manuscript, this point has been made more concise in Lines 77 to 83.\n#6, Introduction, Line 72: Providing an exact frequency range would improve clarity.\nWe have added specific frequency information of the PWI used in the plasma wave measurements in Lines 87 to 88.\n#7, Figures 1a–b: Labels should be added to panels to distinguish the trajectories from different flybys.\nTo improve visibility, we have added labels to identify each flyby in the new Figure 1.\n#8, Figures 1c–f: If these spectra are presented without removing noises, a brief explanation of potential noise sources would be helpful.\nBecause Figure 1 displays raw wave data without noise interference filtering, we have included additional explanations regarding known noise sources in Lines 172 to 174.\n#9, Results, Lines 91–94: The observations from the 5th and 6th flybys are not directly relevant to whistler-mode wave studies. Consider refining this section for clarity.\nThe fact that no whistler-mode wave events were observed during the 5th and 6th flybys helps to indicate that the detected wave events originate from Mercury’s inner magnetosphere. In particular, the 6th flyby provides important results suggesting that wave generation near the midnight sector is difficult and that plasma wave activity is influenced by the heliocentric distance. Therefore, we have added explanations in the main text to emphasize the significance of the absence of wave events during these flybys in Lines 109 to 116 and Lines 185 to 200.\n#10, Results, Figure 1 Caption, Line 110: Cite Korth et al., 2017 to properly acknowledge previous research.\nWe have added the relevant reference to the caption of Figure 1 (Line 172).\n#11, Results, Lines 114–115: Converting \"6 to 10 dB pT/sqrt(Hz)\" to “pT/sqrt(Hz)” for consistency.\nWe have corrected the values from dB to linear scale in Line 177 and Line 182.\n#12, Results, Lines 119–121: The observed variations may be associated with the solar maximum and Mercury's orbital phase. As shown in Sun et al. (2022; https://doi.org/10.1007/s11430-021-9828-0), the solar wind parameters are much stronger near the Sun. May consider incorporating these possibilities into the discussion.\nThank you very much for your important comments. The six flybys occurred at different heliocentric distances, and notably, despite the 6th flyby passing close to Mercury, no clear plasma wave activity was observed. This observation, consistent with previous studies, suggests an influence of plasma waves by heliocentric distance. We have incorporated relevant sentences regarding this point into the main text (Lines 185 to 200).\n#13, Results, Line 137: The term \"compelling\" may not be appropriate for authors to declare themselves. Please rephrase this.\nWe have used “indicates” instead of “compelling” in Line 216.\n#14, Results, Lines 138–139: Provide further details on how the scaling law \"r0E ~ (8±0.5) r0M\" was derived. This probably the largest concern that the reviewer has for this study. This is an important concern since the scaling study is the most important result of this study. The reviewer also would like to note that planetary magnetosphere scaling may not always apply due to differences in dipole intensity between Mercury and Earth.\nWe have added descriptions of the scaling law in the Methods section (Lines 428 to 452). Our analysis takes into account differences in planetary dipole intensity. We calculated the scaling value based on the magnetic field inhomogeneity a of the planetary magnetosphere, since this parameter can play a dominant role in characterizing nonlinear wave growth, particularly in Mercury’s magnetosphere. The threshold for nonlinear wave growth can be characterized by the normalized magnetic field inhomogeneity ã2, where ã = ac2⁄Ω2 and Ω (h) = Ω (1+ah2). Here, Ω is the equatorial gyrofrequency, Ω is the gyrofrequency, h is the small distance from the equator along a magnetic field line. We calculated the magnetic field inhomogeneity using the KT17 model for Mercury and the Tsyganenko 89 model for Earth. This approach offers the advantage of accounting not only for magnetic field strength (Ω ) but also for magnetic field inhomogeneity. Moreover, the variation of the scaling factor due to magnetic activity perturbations is relatively small, making this a more robust scaling metric for chorus wave characteristics than one based solely on magnetopause standoff distance.\n#15, Results, Line 140: This scaling law can also be derived theoretically, see Tao et al., 2012 (AGU Publications). The authors might include this reference's result.\nWe have added a relevant description referring to the theoretical derivation of the scaling law by Tao et al. (2012) in Line 221.\n#16, Results, Lines 144–146: Chorus waves have been observed in multiple missions, including THEMIS (Agapitov et al., 2010—Ann. Geophys.) and Cluster (jgra.50312). Consider citing these studies.\nWe have removed the original sentence in the revised manuscript and have added references related to chorus wave observations in the Earth’s outer magnetosphere in Line 224.\n#17, Results, Figure 2: The non-uniform sampling frequency of spectra panels (a)–(d) should be explained. In addition, if the gray-shaded regions represent observational results from this study, this should be clearly stated.\nWe have added an explanation in the Methods section (Lines 408 to 409) that the frequency resolution in these panels is not plotted linearly, in order to reduce data telemetry. Although it was already stated in the previous manuscript (Lines 162 and 163) that the gray boxes represent the results for Mercury, we have now explicitly clarified this again in the revised manuscript (new Figure 2, Lines 265 to 268, and Line 400).\n#18, Results, Line 171: Flyby measurements are spatially biased since the coverage of the duskside inner magnetosphere was highly limited. This should be acknowledged.\nDespite the spatial limitations of the flyby observations, as noted in the main text (Line 346), the full flyby dataset provides strong evidence that whistler-mode wave activity is predominantly concentrated on the dawn side.\n#19, Results, Line 172: The term \"hot\" electrons may not be appropriate, as references 36 and 37 do not indicate temperature. Consider using \"high-energy\" or \"energetic electrons\" (>10s keV) instead.\nWe have revised the term to “energetic electrons” in Line 123.\n#20, Results, Line 179: The mention of Shebansky orbit could be more clear, and also should consider adding a citation (see Zhao et al., 2022, Nature Communications), which reports Shebansky orbits of ring current ions at Mercury.\nWe have added relevant literature in Line 133.\n#21, Results, Lines 182–183: Define \"a weak temperature anisotropy of 1\" more explicitly. A brief introduction of density and temperature distribution in the Methods section would enhance clarity.\nWe have added a description in the Methods section to improve clarity for the readers in Lines 419 to 426.\n#22, Results, Lines 190–193: The manuscript suggests that the nonlinear criterion region is influenced by magnetospheric shape. However, observations from these flybys do not directly reflect the special shape, and detected chorus waves could mainly originate from the inner magnetosphere. This could be revised for better alignment with observations.\nWe appreciate the reviewer’s insightful comment. We would like to clarify that the manuscript referred not to the global magnetospheric shape, but to the magnetic field inhomogeneity along magnetic field lines in the chorus source region. At higher L-shells, the distortion of field lines increases the magnetic field inhomogeneity a, which raises the threshold for nonlinear growth. This makes it difficult for linear growth waves to transition into nonlinear growth in those regions. As a result, the spatial distribution of the nonlinear criterion can appear to be associated with the overall magnetospheric shape when viewed in the XY plane. To clarify this point, we have revised the relevant sentences in the manuscript (Lines 148 to 157). We also acknowledge the reviewer’s point that wave propagation effects were not considered in our analysis. In agreement with the reviewer’s suggestion, we now explicitly state that the observed chorus waves are likely to originate from the inner magnetosphere of Mercury.\n#23, Results, Figure 3: Adding time range annotations for the bolded trajectories would improve clarity and readability.\nWe have revised Figure 1 by incorporating the previous Figure 3, in order to improve the visibility of the relationship between the wave observation regions and the flyby trajectories.\nAgain, we appreciate all of your valuable comments. We hope that our revisions address your concerns. Thank you very much for taking time to help improve our manuscript.\nAuthors’ responses to Reviewer #3\nWhistler-mode wave activity is the natural electromagnetic emission in the planetary magnetospheres. The authors had presented the direct probing of chorus waves in the localized dawn sector during the first and second Mercury flybys by the BepiColombo/Mio spacecraft (Ozaki et al., 2023). In this manuscript, they further analyzed the coherent fine structures of whistler-mode waves from all six Mercury flybys. The main results are (1) The discrete whistler-mode emission waves are identified, and (2) The activity tendency of waves occurs in the dawn side of the magnetosphere. However, the former result is similar to those observed in the Earth’s magnetosphere. What readers might be interested in is the differences between Mercury and Earth and what inluences Mercury’s unique plasma environment. The second result has been concluded in Ozaki et al., (2023). As such, I do not think the current form of the manuscript provides sufficient new information about the physics of Mercury’s magnetosphere to ensure its publication in Nature Communications.\nWe sincerely appreciate your constructive and thoughtful comments. As you noted, whistler-mode wave activity is a well-known phenomenon in Earth’s magnetosphere, and our previous study (Ozaki et al., 2023) confirmed the dawnside localization of such waves at Mercury based on the first and second flybys. However, the present study advances beyond this prior work in several key aspects.\nFirst, we present the first detailed observational evidence of coherent fine structures of whistler-mode waves in Mercury’s magnetosphere, where direct observations have been extremely limited to date. While discrete whistler-mode emissions may resemble those at Earth, the identification of coherent, nonlinear wave structures in Mercury’s compact and strongly distorted magnetospheric environment represents a significant advancement. This is particularly important because, while linear growth of whistler-mode waves may be expected from temperature anisotropy or loss cone instabilities, the evolution into coherent nonlinear structures involves fundamentally different physics.\nSecond, our study offers new insights into the nonlinear wave–particle interaction processes unique to Mercury, supported by both observational data and test-particle simulations. In particular, we propose a new source region for electron precipitation close to the planet (L < 1.6), driven by nonlinear pitch-angle scattering—a mechanism fundamentally different from the previously assumed distant-source scenarios such as magnetic flux ropes. This finding offers a novel perspective on the energetic electron dynamics in Mercury’s inner magnetosphere.\nTherefore, we believe our manuscript does not merely add more observational cases, but rather provides novel physical insights into how Mercury’s unique magnetic field configuration influences nonlinear wave dynamics, contributing meaningfully to the field of comparative magnetospheric physics.\nIn response to your comments, we have revised the manuscript to more clearly emphasize these points and to highlight the unique scientific contributions of our study. In particular, please refer to the Introduction, Lines 238 to 259, Section 2.3, and the Discussion for these clarifications.\nWe are pleased that our findings provide observational evidence supporting the occurrence of nonlinear wave–particle interactions in a small magnetosphere, thereby making a broad contribution to the research field, including comparative planetology. Again, thank you very much for helping us see our work from a broader perspective. Your comments have enriched our understanding and presentation of the findings.\nAuthors’ responses to Reviewer #4\nThe authors report observational findings from the BepiColombo mission’s Mio spacecraft during its Mercury flybys between 2021 and 2025. Their analysis focuses on whistler-mode wave activity within Mercury’s magnetosphere, revealing fine spectral structures—such as rising and falling tones—that align with nonlinear wave growth processes observed in Earth’s magnetospheric chorus emissions. The study suggests that Mercury’s compact magnetosphere can sustain nonlinear wave-particle interactions capable of generating energetic electron belts.\nThis study can potentially mark a significant advance with broad implications for understanding electron acceleration in compact magnetospheric environments.\nThe methodology is technically sound and well documented. The authors correctly recognize limitations and justify choices (e.g., visual identification of tones due to data limitations). However, while applying Earth-based scaling laws to Mercury is conceptually sound, it has not yet been empirically confirmed. Therefore, the frequency sweep comparisons are indicative but not definitive.\nWe sincerely appreciate your thorough and constructive evaluation of our manuscript. As you pointed out, while we analyze nonlinear wave growth processes in Mercury’s magnetosphere using scaling laws developed for Earth, our approach differs from conventional methods that rely on scaling laws tied to the magnetopause standoff distance. Instead, we apply a scaling law focused on magnetic field inhomogeneity, which is directly relevant to nonlinear growth. This approach provides robustness against external fluctuations, as Mercury’s whistler-mode waves are largely controlled by intrinsic field inhomogeneity rather than solar wind pressure. This is supported by previous studies and justifies the minimal variation in the scaling we observe. Moreover, numerical simulations of Mercury’s plasma environment have predicted the generation of chorus elements with frequency variation. In light of these theoretical and modeling results, we believe our observation provides strong empirical evidence for the existence of such frequency-varying chorus emissions at Mercury. We have clarified these points in the revised manuscript, particularly in the new Section 2.2 and the Methods (Lines 428 to 452) section.\nAlso, without simultaneous electron measurements, claims about electron acceleration and resonance are based on inference and cannot be directly validated.\nRegarding the point about electron acceleration and resonance not being directly validated:\nDuring the first Mercury flyby, whistler-mode waves were observed simultaneously with enhancements in energetic electrons, which are likely responsible for electron precipitation events. Additionally, we conducted simulations demonstrating that these electrons can undergo pitch-angle scattering and precipitate to the planetary surface. This supports the plausibility of wave-induced precipitation at Mercury. We address this more clearly in the new Section 2.3.\nIn addition, the magnetic field and electron density models are based on empirical data and may not fully capture Mercury’s dynamic environment, which can reduce the accuracy of nonlinear wave growth threshold calculations\nAs for the concern about the accuracy of the magnetic field and electron density models:\nWhile we acknowledge the limitations of using empirical models, we emphasize that magnetic field inhomogeneity, rather than electron density, is the dominant factor for nonlinear wave growth at Mercury. This is consistent with previous theoretical work. Even if in-situ magnetic field measurements were available, identifying magnetic field inhomogeneity at the wave source region would still require multi-point observations, which are currently not possible. Thus, although not a direct measurement, we believe the KT17 model remains the most reliable available proxy for evaluating magnetic field inhomogeneity in Mercury’s magnetosphere. While we recognize the limitations inherent in the current analysis, we firmly believe this study provides the first observational evidence of nonlinear whistler-mode waves at Mercury, and highlights their physical significance. It demonstrates that the spatial and energetic conditions required for pitch-angle scattering and electron acceleration indeed exist in Mercury’s compact magnetosphere. This contributes new understanding in a context where wave–particle interactions have often been considered negligible due to Mercury’s small-scale environment. We have revised the manuscript to emphasize these key points, particularly in the new Discussion section.\nWe would be grateful for your expert insight into the remarkable physical background behind the generation of chorus waves within Mercury’s uniquely small magnetospheric environment. Again, we sincerely appreciate your insightful comments and suggestions. We hope our revisions have adequately addressed your concerns and contributed to improving the clarity and impact of our work.\nAuthors’ responses to Reviewer #5\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nWe sincerely thank you for taking the valuable time to review our work and strengthen our results. By utilizing data from all flybys, we are honored to provide a robust foundation confirming the concentrated wave activity on Mercury’s dawn side. Furthermore, the identification of coherent wave structures enables us to present a new source of electron precipitation in Mercury’s inner magnetosphere caused by local pitch-angle scattering. We are pleased that our findings provide observational evidence supporting the occurrence of nonlinear wave–particle interactions in a small magnetosphere, thereby making a broad contribution to the research field, including comparative planetology."}, {"round": 2, "reviewer_comments": {"reviewer_1": "This review covers the resubmitted and revised manuscript entitled ‘Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys’ by Ozaki et al.\nOverall comments:\nThe authors have done quite a bit of work to address the previous 4 reviewers’ comments. I applaud the extra effort, as I believe it has made the paper a much better product. However, I still do not agree that it rises to the level of signficance necessary for a Nature publication. This is not to say that the analysis presented and the modeling performed is not valid or useful for the community, but that it does not represent results that “advance understanding in a way that will move the field forward” (quoted from the Nature reviewer guidelines).\nI am going to explain my position in detail, so that it is clear to both the authors and the editors. Below are supporting points that back up my assessment that this paper stands as an interesting extension to the results already published in Ozaki et al. 2023 (https://doi.org/10.1038/s41550-023-02055-0) - and that it is not able to stand up as a wholly separate and new insight which warrants the broad readership of a Nature-level journal.\n(1) The results are an extension of the previously published results from flyby #1 (Ozaki et al. 2023) including modeling of coherent chorus elements. In that paper, modeling work was performed showing nonlinear wave growth and particle scattering using parameters from that first flyby. Here, the coherent structure is confirmed (with the following few flyby observations) but it does not change the assertion of that first paper. Thus, this new work is a step further in providing evidence that backs up the theory in the first paper yet does not provide a new, significant result. As stated in the manuscript, “The observations from the first Mercury flyby, including simultaneous wave and electron measurements, strongly support this idea.” The results written here were already supported by flyby #1. Now we simply have additional flybys that also support the same idea.\n(2) Much of the work presented in this paper could have been performed using only the flyby #1 data. The test particle simulations, Section 2.3 (an entirely new section, consisting only of content that was not included in the first draft of this manuscript), could have been done using data from the first flyby alone. The Methods section describes the parameters used in the simulation, which could have been derived from flyby #1 (the additional flybys were not strictly necessary except to prove that these emissions were indeed coherent - although that was already the guess in Ozaki et al. 2023). Not only could this have been done with flyby #1 data, that data was actually superior for this idea, since it included observations of energetic particles, which is not included in these subsequent flybys. As stated in the manuscript, “During BepiColombo’s first Mercury flyby, variations in energetic electrons were observed simultaneously with whistler-mode waves”. Again, the hypothesis and testing presented here could have been done without the subsequent flybys at all.\n(3) The most interesting part of this work is the part that cannot be shown prior to Mars Orbit Insertion and the deployment of the MAST booms - it is only hinted at slightly in this paper. The association of these coherent whistlers with variation in energetic electrons as well as their correlation with heliocentric distance cannot be assessed until the orbit insertion and higher fidelity data. It seems that the best plan is to submit those results at that time, which will no doubt be revolutionary and fully meet the criteria for Nature to impact the field in a significant way. The manuscript itself seems to recognize this, by stating in one place, “A detailed investigation into the correlation between Mercury’s heliocentric distance and whistler-mode wave activity is expected following MOI.” And in another place stating, “These varied flyby trajectories were useful for characterizing the spatial distribution of whistler-mode waves before MOI in 2026.” — I take this to indicate that the spatial distribution of waves is the main product here from the flybys and that the real impactful results will be forthcoming following the orbit insertion. I believe that all that could be done with the data has really been accomplished by presenting the flyby #1 results in Ozaki et al. 2023. This manuscript represents an incremental step in trying to understand those first results, as well as a bit more evidence of the expected distribution and coherent structure. The “new ideas” presented here (namely, that the waves are coherent, nonlinear scattering can take place and the source region is near the planet) have all been hypothesized and modeled or shown directly in Ozaki et al. 2023.\nTaking all 3 of the above points together, I will reiterate my statement from the first review that this “is not a significant contribution in changing our understanding of the system, thus it is more appropriate as a report in a planetary or magnetospheric journal, rather than a multi-discipline journal like Nature that is used for disseminating findings of the highest impact.”\nRegarding the new material added, it is valid and sound methodologically, the referencing is still appropriate and the topic is still of great interest - but simply not for the Nature audience. The figures, however, are not appropriate simply because they are of such poor quality I could not easily read them. Figures 1 and 2 are repackaged versions of Figures 1-3 in the first version of this article, but Figure 3 is now new and I could guess but not quite read the labels on a few of the y-axes. I got the summary from the text, so I understand what the figures convey, but it is disappointing to receive the poor quality as part of a revised manuscript.", "reviewer_2": "Second review of “Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys” by Ozaki et al.\nThe manuscript presents valuable observations of chorus waves from BepiColombo’s Mercury flybys. The study investigates the nonlinear growth rate, possible electron scattering/precipitation, and scaling relations between the magnetospheres of Mercury and Earth.\nThe authors have addressed most of the reviewer’s earlier comments. While certain assumptions are difficult to justify due to the lack of in situ measurements, this work still represents a pioneering contribution to the study of nonlinear chorus waves, electron scattering and comparative wave analysis.\nThe reviewer has only a few additional comments and suggestions for improvement before recommending the manuscript for acceptance.\nLine 38: The statement “the energetic electron belts can be formed” is too strong. Current evidence does not support such a definitive conclusion.\nLines 111 to 113: Please remove this sentence. Whistler-mode waves in the solar wind are already observed from recent Parker Solar Probe observations.\nLines 282 to 283: Clarify how the closed magnetic field line region (rM < 1.6) was determined.\nLine 303: Change “panels a and b” to “panels a and c.”? This is typo?\nFigure 2d. The meaning of this panel is unclear. Unless better explained, it should be removed.\nFigure 3. The loss peak due to Landau resonance should be highlighted by arrows in the panels b and d.", "reviewer_3": "Thank you for your detailed and careful responses to my earlier comments. I appreciate the clarifications you have added. These revisions make the distinct contributions of this work clearer compared with your earlier publication, and now better highlights Mercury’s unique environment and its implications for wave–particle interactions.\nAlthough the additional explanations enhanced the novelty of the manuscript, only more specialized researchers would be able to recognize it. Considering that the innovative points of broad interest have already been published in Nature (Ozaki et al., 2023), I believe this paper is better suited for publication in a specialized journal. Together, these two papers will strengthen your series of work and help it receive wider attention and citation.", "reviewer_4": "I appreciate the authors’ detailed and thoughtful replies to my comments and concerns. The clarifications provided regarding the use of magnetic field inhomogeneity–based scaling, as opposed to magnetopause standoff distance–based laws, are convincing. I agree that this choice is more directly relevant to nonlinear wave growth processes and that its relative insensitivity to external solar wind fluctuations strengthens the robustness of the interpretation. The addition of Section 2.2 and the expanded Methods section (Lines 428–452) make the rationale for this approach much clearer.\nRegarding electron acceleration and resonance, I find the additional discussion of coincident whistler-mode waves and energetic electron enhancements during the first flyby to be an important improvement. The supporting simulations of pitch-angle scattering and precipitation strengthen the plausibility of the proposed mechanism. While the lack of simultaneous in-situ electron pitch-angle distributions remains a limitation, I recognize that the authors have been careful to frame their conclusions in terms of plausibility and consistency with available evidence, rather than definitive proof.\nOn the issue of empirical models for magnetic field and density: the authors’ emphasis on magnetic field inhomogeneity as the dominant driver for nonlinear growth at Mercury is well reasoned and consistent with theory. The acknowledgment of model limitations, while justifying the use of KT17 as the best currently available proxy, is satisfactory. I also appreciate the authors’ careful re-framing of these results as the first observational evidence of nonlinear whistler-mode waves at Mercury, rather than as a complete characterization.\nOverall, the revisions have significantly improved the manuscript. The arguments are clearer, the limitations are appropriately acknowledged, and the physical implications are well framed. The study provides an important and timely contribution by demonstrating that nonlinear wave–particle interactions—traditionally thought to be less significant in Mercury’s compact magnetosphere—are indeed possible and observable. This has strong implications for both Mercury science and comparative planetary magnetospheric studies.\nI recommend the manuscript for publication", "reviewer_5": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Authors’ Responses to Reviewers’ comments on Nonlinear spatiotemporal signatures of whistler-mode wave activity around Mercury during six flybys of BepiColombo mission\nWe sincerely thank all five reviewers for their careful reading and constructive feedback, which has greatly helped enhance the clarity, rigor, and broader relevance of our manuscript. At this pre-Mercury Orbital Insertion (MOI) stage, we sincerely appreciate the reviewers’ recognition of the validity of our study in terms of its scientific significance, methodological approach, and the robustness of its results.\nBased on the most up-to-date flyby data, our work offers detailed insights into plasma wave phenomena associated with electron cyclotron motion in Mercury’s magnetosphere. We acknowledge that the broader significance of our findings may be interpreted in different ways depending on perspective. Nevertheless, we consider this study to offer a meaningful advancement by presenting the first observational confirmation of nonlinear wave–particle interactions in Mercury’s magnetosphere. This result resolves what had previously remained a speculative hypothesis in earlier studies, including Ozaki et al. (2023), and establishes a concrete foundation for interpreting such interactions in Mercury’s unique plasma environment. We also hope that these findings will offer useful perspectives for future comparative studies across diverse planetary magnetospheres, including those of Ganymede and Mars. In revising the manuscript, we have carefully addressed all reviewer comments and incorporated additional improvements based on the editor’s checklist, including enhanced figure clarity through separation. By presenting a timely contribution to the BepiColombo mission, we hope our results will support the scientific return of the upcoming Mercury Orbital Insertion and provide a foundation for further exploration of wave–particle interactions across planetary systems. Our point-by-point responses to the comments are listed below in blue, and the reviewers’ original comments are italicized in black. Revisions in the manuscript are highlighted in yellow.\nAuthors’ responses to Reviewer #1\nReviewer #1 (Remarks to the Author):\nThis review covers the resubmitted and revised manuscript entitled ‘Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys’ by Ozaki et al.\nOverall comments:\nThe authors have done quite a bit of work to address the previous 4 reviewers’ comments. I applaud the extra effort, as I believe it has made the paper a much better product. However, I still do not agree that it rises to the level of signficance necessary for a Nature publication. This is not to say that the analysis presented and the modeling performed is not valid or useful for the community, but that it does not represent results that “advance understanding in a way that will move the field forward” (quoted from the Nature reviewer guidelines).\nI am going to explain my position in detail, so that it is clear to both the authors and the editors. Below are supporting points that back up my assessment that this paper stands as an interesting extension to the results already published in Ozaki et al. 2023 (https://doi.org/10.1038/s41550-023-02055-0) - and that it is not able to stand up as a wholly separate and new insight which warrants the broad readership of a Nature-level journal.\nThank you very much for your detailed and thoughtful comments on our revised manuscript.\nWe sincerely appreciate your recognition of the improvements made and your acknowledgment of the methodological soundness and relevance of the topic. We understand and respect your position regarding the level of significance required for publication in a broad-scope journal. While we acknowledge that the present study builds upon our previous work (Ozaki et al., 2023), we believe that the additional flyby observations and simulation results provide important new observational evidence of coherent whistler-mode waves and nonlinear scattering processes in Mercury’s magnetosphere.\n(1) The results are an extension of the previously published results from flyby #1 (Ozaki et al. 2023) including modeling of coherent chorus elements. In that paper, modeling work was performed showing nonlinear wave growth and particle scattering using parameters from that first flyby. Here, the coherent structure is confirmed (with the following few flyby observations) but it does not change the assertion of that first paper. Thus, this new work is a step further in providing evidence that backs up the theory in the first paper yet does not provide a new, significant result. As stated in the manuscript, “The observations from the first Mercury flyby, including simultaneous wave and electron measurements, strongly support this idea.” The results written here were already supported by flyby #1. Now we simply have additional flybys that also support the same idea.\nWe sincerely appreciate the reviewer’s thoughtful assessment and recognition of the scientific value of our work as an extension of Ozaki et al. (2023). We understand the concern regarding the threshold for novelty required by a high-impact journal, and we are grateful for the opportunity to clarify the significance of our findings. While this study builds upon the theoretical framework of our previous work, it takes a meaningful step forward by providing new observational evidence of coherent chorus structures across multiple Mercury flybys. These observations not only reinforce the initial theory but also allow for a more robust evaluation of nonlinear pitch-angle scattering processes in Mercury’s magnetosphere. As illustrated in our manuscript, the behavior of pitch-angle scattering induced by large-amplitude coherent whistler-mode waves differs fundamentally from that caused by weak, incoherent waves. The repeated confirmation of coherent wave structures allows us to discuss, with greater confidence, the possibility of rapid and nonlinear pitch-angle scattering beyond the quasi-linear regime. This distinction is crucial for understanding particle dynamics in Mercury’s unique magnetospheric environment, and it has not been previously demonstrated with such clarity.\n(2) Much of the work presented in this paper could have been performed using only the flyby #1 data. The test particle simulations, Section 2.3 (an entirely new section, consisting only of content that was not included in the first draft of this manuscript), could have been done using data from the first flyby alone. The Methods section describes the parameters used in the simulation, which could have been derived from flyby #1 (the additional flybys were not strictly necessary except to prove that these emissions were indeed coherent - although that was already the guess in Ozaki et al. 2023). Not only could this have been done with flyby #1 data, that data was actually superior for this idea, since it included observations of energetic particles, which is not included in these subsequent flybys. As stated in the manuscript, “During BepiColombo’s first Mercury flyby, variations in energetic electrons were observed simultaneously with whistler-mode waves”. Again, the hypothesis and testing presented here could have been done without the subsequent flybys at all.\nWe respectfully clarify that the presence of coherent whistler-mode waves, which is critical for evaluating nonlinear pitch-angle scattering, was not definitively established in the first flyby. As we have emphasized in the revised manuscript, the behavior of pitch-angle scattering induced by large-amplitude coherent waves differs fundamentally from that caused by weak, incoherent waves. Without confirmation of coherence, it would not have been possible to robustly assess the instantaneous nonlinear scattering effects presented in Figure 5. While the first flyby allowed us to hypothesize the possibility of coherent nonlinear pitch-angle scattering, the subsequent flybys provided the necessary observational evidence to substantiate this claim. We believe this confirmation is essential because it enables us to discuss with greater confidence the occurrence of rapid and nonlinear pitch-angle scattering that extends beyond the quasi-linear regime, even within the limited data available from Mercury flybys. We hope this clarification clearly conveys the importance of the additional observations in strengthening the scientific foundation of our study.\n(3) The most interesting part of this work is the part that cannot be shown prior to Mars Orbit Insertion and the deployment of the MAST booms - it is only hinted at slightly in this paper. The association of these coherent whistlers with variation in energetic electrons as well as their correlation with heliocentric distance cannot be assessed until the orbit insertion and higher fidelity data. It seems that the best plan is to submit those results at that time, which will no doubt be revolutionary and fully meet the criteria for Nature to impact the field in a significant way. The manuscript itself seems to recognize this, by stating in one place, “A detailed investigation into the correlation between Mercury’s heliocentric distance and whistler-mode wave activity is expected following MOI.” And in another place stating, “These varied flyby trajectories were useful for characterizing the spatial distribution of whistler-mode waves before MOI in 2026.” — I take this to indicate that the spatial distribution of waves is the main product here from the flybys and that the real impactful results will be forthcoming following the orbit insertion. I believe that all that could be done with the data has really been accomplished by presenting the flyby #1 results in Ozaki et al. 2023. This manuscript represents an incremental step in trying to understand those first results, as well as a bit more evidence of the expected distribution and coherent structure. The “new ideas” presented here (namely, that the waves are coherent, nonlinear scattering can take place and the source region is near the planet) have all been hypothesized and modeled or shown directly in Ozaki et al. 2023.\nWe fully share the excitement and anticipation for the high-fidelity data that will become available post-MOI, which we expect will reveal both predicted and unforeseen phenomena in Mercury’s magnetospheric environment. At the same time, we would like to respectfully emphasize the scientific significance of the current flyby data. Despite the limitations in instrumentation prior to MOI, these flybys have provided the first-ever measurements in the kilohertz range near the electron cyclotron frequency in Mercury’s magnetosphere. These observations represent the most valuable data currently available for understanding this unique environment, and the physical insights derived from them offer compelling evidence that contributes meaningfully to the field. As the reviewer rightly notes, our study builds on the initial findings of Ozaki et al. (2023). However, we believe this work goes a step further by presenting observational confirmation of coherent whistler-mode waves and their spatial distribution across multiple flybys. This confirmation allows us to discuss, with greater confidence, the possibility of nonlinear pitch-angle scattering near the planet, which is an effect that could not be robustly evaluated using the first flyby alone. We are honored that the reviewer acknowledges these ideas, and we hope it is clear that this manuscript provides not only continuity but also a novel and important advancement beyond the initial study.\nTaking all 3 of the above points together, I will reiterate my statement from the first review that this “is not a significant contribution in changing our understanding of the system, thus it is more appropriate as a report in a planetary or magnetospheric journal, rather than a multi-discipline journal like Nature that is used for disseminating findings of the highest impact.”\nIn light of the above feedback and our responses, we have revised the manuscript to better emphasize the unique contributions of the flyby data and the broader implications of our findings, as reflected in Lines 361 to 370.\nLines 361 to 370\nFinally, these six flyby observations, despite being obtained prior to the MOI, provide direct evidence of coherent whistler-mode waves in Mercury’s small magnetosphere and enable a confident evaluation of nonlinear pitch-angle scattering beyond the quasi-linear regime. They offer unique insights that extend the initial findings from the first and second flybys. Furthermore, to clarify the broader relevance of this study beyond Mercury-specific plasma environments, we note that the observational evidence of nonlinear wave–particle interactions in Mercury’s small magnetosphere, particularly the coherent wave structures, provides a valuable comparative framework for understanding similar processes in other planetary environments, including those with weak or crustal magnetic fields such as Ganymede or Mars.\nRegarding the new material added, it is valid and sound methodologically, the referencing is still appropriate and the topic is still of great interest - but simply not for the Nature audience. The figures, however, are not appropriate simply because they are of such poor quality I could not easily read them. Figures 1 and 2 are repackaged versions of Figures 1-3 in the first version of this article, but Figure 3 is now new and I could guess but not quite read the labels on a few of the y-axes. I got the summary from the text, so I understand what the figures convey, but it is disappointing to receive the poor quality as part of a revised manuscript.\nThank you very much for pointing this out. We have carefully reviewed the resolution and formatting of new Figure 5 and confirmed that it meets the journal’s technical specifications. We hope this resolves the readability issue.\nAgain, we are grateful for your constructive feedback throughout the review process and for helping us improve the quality and clarity of our work.\nAuthors’ responses to Reviewer #2\nReviewer #2 (Remarks to the Author):\nSecond review of “Nonlinear spatiotemporal signatures of Mercury’s whistler-mode wave activity by BepiColombo flybys” by Ozaki et al.\nThe manuscript presents valuable observations of chorus waves from BepiColombo’s Mercury flybys. The study investigates the nonlinear growth rate, possible electron scattering/precipitation, and scaling relations between the magnetospheres of Mercury and Earth.\nThe authors have addressed most of the reviewer’s earlier comments. While certain assumptions are difficult to justify due to the lack of in situ measurements, this work still represents a pioneering contribution to the study of nonlinear chorus waves, electron scattering and comparative wave analysis.\nThe reviewer has only a few additional comments and suggestions for improvement before recommending the manuscript for acceptance.\nThank you very much for your continued engagement and thoughtful comments on our manuscript. We are grateful for your recognition of the study’s contribution to the understanding of nonlinear chorus waves, electron scattering, and comparative wave analysis. We have carefully considered your remaining suggestions and have revised the manuscript accordingly.\nLine 38: The statement “the energetic electron belts can be formed” is too strong. Current evidence does not support such a definitive conclusion.\nIn response to your suggestion, we removed the sentence regarding the electron acceleration from the Abstract. While this study focuses on wave-induced pitch angle scattering, we are currently working toward a more detailed evaluation of electron acceleration using observed particle data in future analyses.\nLines 111 to 113: Please remove this sentence. Whistler-mode waves in the solar wind are already observed from recent Parker Solar Probe observations.\nThank you for pointing this out. The sentence in Lines 111 to 113 of the previous version has been removed in the revised manuscript.\nLines 282 to 283: Clarify how the closed magnetic field line region (rM < 1.6) was determined.\nWe have clarified this point in the revised manuscript. The possible boundary of r < 1.6 was determined based on the test particle simulation showing the trapping region of energetic electrons in Mercury’s magnetosphere Walsh et al. (JGR, 2013). In addition, our analysis of the wave activity shown in Figure 1 indicates that the observed whistler-mode waves are concentrated within this region, further supporting the use of r < 1.6 as a representative threshold for the closed field line domain in this study. We have added a brief explanation to clarify this rationale.\nLines 256 to 261\nBased on the previous test particle simulation studies35, the trapping region for energetic electrons in Mercury’s magnetosphere is expected to extend up to approximately r =1.6. Furthermore, as shown in Figure 1, whistler-mode wave activity is dominantly observed within this region. These findings suggest that the wave-induced pitch angle scattering is likely to occur within the closed magnetic field line domain (less than about r =1.6).\nLine 303: Change “panels a and b” to “panels a and c.”? This is typo?\nWe apologize for the typographical error. The text has been corrected to “Figure 5a, c” in the revised manuscript (Line 276).\nFigure 2d. The meaning of this panel is unclear. Unless better explained, it should be removed.\nDuring the previous review process, a reviewer noted the difficulty in interpreting Figure 2e. Although the equivalence between Mercury’s magnetosphere and Earth’s outer magnetosphere is expressed numerically, the absence of a corresponding visual representation may have contributed to this difficulty. To address the issue, we have added supplementary explanations in both the main text and the figure caption, and have introduced a new panel, Figure 2d. Figure 2d was specifically included to provide a visual representation of the equivalence between Mercury’s magnetosphere and Earth’s outer magnetosphere, thereby improving the interpretability of Figure 2e. In addition, Figure 2d highlights that, unlike Earth’s outer magnetosphere, the majority of Mercury’s magnetic field lines are occupied by the planetary region. This visual insight supports the rationale for the test particle simulations presented in the subsequent section, which are conducted within a limited field line length. Therefore, we believe that Figure 2d (new Figure 4a) contributes meaningfully to the reader’s understanding. To clarify its role, we have revised the main text accordingly (please see Lines 199 to 202, 272, and 768 to 773).\nFigure 3. The loss peak due to Landau resonance should be highlighted by arrows in the panels b and d.\nWe have added arrows in Figures 5b and 5d to highlight the loss peaks associated with Landau resonance. We hope this makes the relevant features clearer to the reader.\nAgain, we sincerely appreciate your constructive feedback throughout the review process and your recommendation for acceptance.\nAuthors’ responses to Reviewer #3\nReviewer #3 (Remarks to the Author):\nThank you for your detailed and careful responses to my earlier comments. I appreciate the clarifications you have added. These revisions make the distinct contributions of this work clearer compared with your earlier publication, and now better highlights Mercury’s unique environment and its implications for wave–particle interactions.\nAlthough the additional explanations enhanced the novelty of the manuscript, only more specialized researchers would be able to recognize it. Considering that the innovative points of broad interest have already been published in Nature (Ozaki et al., 2023), I believe this paper is better suited for publication in a specialized journal. Together, these two papers will strengthen your series of work and help it receive wider attention and citation.\nThank you very much for your thoughtful and constructive feedback on our manuscript. We sincerely appreciate your recognition of the clarifications we made and your comments regarding the distinct contributions of this work relative to our earlier publication. We understand your concern that the novelty of the present study may be more apparent to specialized readers, and we acknowledge your suggestion that a more specialized journal might be appropriate. However, we believe that this study provides the first observational evidence of coherent whistler-mode wave structures and offers a timely contribution by demonstrating that nonlinear wave–particle interactions can be observed in Mercury’s magnetosphere. At this pre-MOI stage, based on the most up-to-date flyby data, our study offers detailed insights into nonlinear wave phenomena associated with electron cyclotron motion in Mercury’s magnetosphere. We hope that these findings will be of broad interest and relevance to a wide readership, including those engaged in comparative planetary magnetospheric studies. We have added sentences in the Discussion section to emphasize how our observational evidence of nonlinear wave–particle interactions at Mercury can inform comparative studies of magnetospheric processes in other planetary environments, including those with weak or crustal magnetic fields.\nLines 361 to 370\nFinally, these six flyby observations, despite being obtained prior to the MOI, provide direct evidence of coherent whistler-mode waves in Mercury’s small magnetosphere and enable a confident evaluation of nonlinear pitch-angle scattering beyond the quasi-linear regime. They offer unique insights that extend the initial findings from the first and second flybys. Furthermore, to clarify the broader relevance of this study beyond Mercury-specific plasma environments, we note that the observational evidence of nonlinear wave–particle interactions in Mercury’s small magnetosphere, particularly the coherent wave structures, provides a valuable comparative framework for understanding similar processes in other planetary environments, including those with weak or crustal magnetic fields such as Ganymede or Mars.\nAgain, we are grateful for your insights and believe that, together with our previous work, this study will contribute meaningfully to the field and reach a wide audience.\nAuthors’ responses to Reviewer #4\nReviewer #4 (Remarks to the Author):\nI appreciate the authors’ detailed and thoughtful replies to my comments and concerns. The clarifications provided regarding the use of magnetic field inhomogeneity–based scaling, as opposed to magnetopause standoff distance–based laws, are convincing. I agree that this choice is more directly relevant to nonlinear wave growth processes and that its relative insensitivity to external solar wind fluctuations strengthens the robustness of the interpretation. The addition of Section 2.2 and the expanded Methods section (Lines 428–452) make the rationale for this approach much clearer.\nRegarding electron acceleration and resonance, I find the additional discussion of coincident whistler-mode waves and energetic electron enhancements during the first flyby to be an important improvement. The supporting simulations of pitch-angle scattering and precipitation strengthen the plausibility of the proposed mechanism. While the lack of simultaneous in-situ electron pitch-angle distributions remains a limitation, I recognize that the authors have been careful to frame their conclusions in terms of plausibility and consistency with available evidence, rather than definitive proof.\nOn the issue of empirical models for magnetic field and density: the authors’ emphasis on magnetic field inhomogeneity as the dominant driver for nonlinear growth at Mercury is well reasoned and consistent with theory. The acknowledgment of model limitations, while justifying the use of KT17 as the best currently available proxy, is satisfactory. I also appreciate the authors’ careful re-framing of these results as the first observational evidence of nonlinear whistler-mode waves at Mercury, rather than as a complete characterization.\nOverall, the revisions have significantly improved the manuscript. The arguments are clearer, the limitations are appropriately acknowledged, and the physical implications are well framed. The study provides an important and timely contribution by demonstrating that nonlinear wave–particle interactions—traditionally thought to be less significant in Mercury’s compact magnetosphere—are indeed possible and observable. This has strong implications for both Mercury science and comparative planetary magnetospheric studies.\nI recommend the manuscript for publication\nWe sincerely thank you for your thorough and thoughtful review of our manuscript. We are grateful for your positive evaluation and for recommending our work for publication. We appreciate your recognition of the clarifications we provided regarding the use of magnetic field inhomogeneity, and we are pleased that the additions to Section 2.2 and the Methods section helped clarify our rationale. Your comments on the discussion of electron acceleration and resonance, as well as the use of empirical models, were particularly insightful. We are honored by your assessment that our study makes a timely and significant contribution to the understanding of nonlinear wave–particle interactions in Mercury’s magnetosphere. Once again, thank you very much for your valuable feedback and for recommending our work for publication.\nAuthors’ responses to Reviewer #5\nReviewer #5 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nWe sincerely thank you for your valuable contribution to the peer review of our manuscript as part of the Nature Communications initiative to support Early Career Researchers. Your thoughtful input and collaboration with the primary reviewer helped us improve the clarity and rigor of our work, and we are truly grateful for your time and expertise. Again, we appreciate your engagement in the peer review process."}]

Decision letter