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Open Access
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A&A
Volume 700, August 2025
Article Number L7
Number of page(s) 5
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202555296
Published online 05 August 2025

© The Authors 2025

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

Energetic particles with energies ranging from tens to thousands of kilo-electronvolts near Earth at 1 au primarily originate from three sources: solar energetic particles accelerated on/near the Sun (e.g., Wang et al. 2012; Wimmer-Schweingruber et al. 2023), particles accelerated at interplanetary (IP) shocks driven by coronal mass ejections or corotating interaction regions (e.g., Rodríguez-Pacheco et al. 1998; Yang et al. 2018; Li et al. 2025), and particles accelerated at Earth’s bow shock (e.g., Desai et al. 2008; Liu et al. 2022). Particles from these sources typically exhibit continuous, smoothly declining energy spectra (e.g., Wang et al. 2021; Yang et al. 2019). However, several studies have reported unusual narrow peaks in the energy spectra of energetic ions observed near Earth’s bow shock and IP shocks. Using measurements from the DOK-2 instrument on board the Interball-1 spacecraft, Lutsenko & Kudela (1999) first reported observations of one, two, or three narrow peaks (ΔE/Emax ∼ 0.15 − 0.30) in the ion energy spectra observed near Earth’s bow shock. Similar narrow spectral peaks (ΔE/Emax ∼ 0.2 − 0.7) were observed by the Solar Electron and Proton Telescope (SEPT) on board the STEREO mission not only near Earth’s bow shock but also near IP shocks (Klassen et al. 2009, 2011). Such ion events with narrow spectral peaks have been termed “almost monoenergetic ions” (AMIs). Previous studies (Lutsenko & Kudela 1999; Klassen et al. 2009) showed that the ratios of peak energies in the 2- and 3-peak spectra are 1:2 and 1:2:(5−6), respectively, which could correspond to the charge numbers of H+, He2+ and CNO(5 − 6)+. Moreover, the peak energies varied for different events from 30 to 600 keV but were almost unchanged during each event.

Previous studies have proposed mainly two mechanisms capable of explaining energy spectra with narrow spectral peaks. Lutsenko & Kudela (1999) proposed that AMIs could be accelerated by bursts of strong potential electric fields arising from disruptions of the bow shock’s current sheet filaments (Lutsenko 2001). In this scenario, the disruption of current sheet filaments creates a region where the electric field is perpendicular to the magnetic field and whose width along the electric field is smaller than the ion gyroradius. Ions can traverse the region along the electric field, thereby becoming accelerated and gaining energies proportional to their charges. Lutsenko & Gavrilova (2011) refined this hypothesis into a more detailed model and predicted that the energy of accelerated ions would smoothly decrease with time until reaching a constant level. Another possible mechanism for generating such narrow spectral peaks is surfatron acceleration (Sagdeev 1966). When a wave propagates through a region with a background magnetic field, it can trap some particles that have velocities around the wave phase velocity, and rapidly accelerate them along the wave front (Simnett et al. 2005). The particles become detrapped when their velocities reach a maximum value on the order of the sum of the E × B drift velocity and the wave phase velocity (Ohsawa 1985).

The earlier studies over the past two decades were constrained by the limited time, energy, and angular resolution of the available measurements, which hindered detailed investigations of AMIs’ dynamic behavior. However, recent high-resolution data from the Energetic Particle Detector (EPD; Rodríguez-Pacheco et al. 2020) on board the Solar Orbiter spacecraft (Müller et al. 2020) have enabled comprehensive studies of proton dynamics near IP shocks (Trotta et al. 2023a; Yang et al. 2024, 2025). In this Letter, we use data from two EPD sensors, the SupraThermal Electron Proton (STEP) sensor and the Electron-Proton Telescope (EPT), to investigate the dynamic behavior of AMIs upstream of Earth’s bow shock. We examine the temporal profiles, pitch-angle distributions (PADs) in the solar wind frame, and energy spectra of the observed AMIs, and discuss their potential acceleration mechanisms.

2. Data and method

The EPD suite on board Solar Orbiter measures particles spanning energies from a few kilo-electronvolts to several hundred mega-electronvolts (Rodríguez-Pacheco et al. 2020). EPT is one of the EPD sensors and comprises two pairs of telescopes: one pair is oriented sunward and anti-sunward along the nominal Parker spiral, while the other pair is oriented northward and southward. Each telescope has a circular field of view (FOV) of ∼30° and measures ions from ∼50 to ∼6000 keV. STEP is another EPD sensor and consists of a 3 × 5 multi-pixel detector array with an overall FOV of ∼30° ×60° around the nominal Parker spiral. Each pixel has an individual FOV of ∼10° ×12° and measures ions from ∼6 keV to ∼60 keV. This design enables the angular distribution to be resolved within STEP’s overall FOV. Notably, STEP’s central 9 pixels share nearly the same FOV as EPT’s sunward telescope. In addition, we use magnetic field data from the magnetometer (MAG; Horbury et al. 2020) and solar wind proton velocity data from the solar wind analyser (SWA; Owen et al. 2020).

In order to correct for the Compton-Getting effect (Compton & Getting 1935), we reconstructed the PADs in the solar wind proton bulk velocity frame, using the same method as Yang et al. (2020, 2023). In the reconstructed PADs, EPT’s four telescopes cover most of the 0−180° pitch angles (PAs), while STEP’s multi-pixel array provides a finer angular resolution in the PA range covered by EPT’s sunward telescope.

3. Observations

At ∼15:05 on 27 November, 2021, Solar Orbiter crossed the eastern flank of Earth’s bow shock and entered the upstream solar wind. Later, at ∼23:00, it encountered a moderate-strength IP shock with an Alfvén Mach number of 3.3 (Trotta et al. 2023b).

Fig. 1a presents the dynamic energy spectrum of energetic ions downstream of the IP shock. Multiple distinct ion populations are observed in this region: (1) ions accelerated by the IP shock propagating downstream in the ∼10-minute interval following the shock (e.g., Yang et al. 2023, 2024), (2) helium pick-up ions intermittently appearing at energies below ∼10 keV (approximately twice the solar wind speed) with high intensities, which will be comprehensively analyzed in a separate study, (3) burst-like upstream ion events spanning energies from ∼20 to ∼500 keV (e.g., Desai et al. 2008), and (4) AMIs exhibiting an intensity peak in a narrow energy band. In this study, we focus on the dynamic behavior of the AMIs that display clear single- or double-peak signatures (highlighted by the yellow rectangles).

thumbnail Fig. 1.

Overview plot of AMIs observed downstream of the IP shock on 27 November, 2021. (a) Spectrogram of dynamic energy spectra measured by EPT’s sunward telescope and STEP’s central 9 pixels. The yellow rectangles highlight the AMIs analyzed in this study. (b)–(c) PADs in the solar wind frame reconstructed from STEP (b) and EPT (c) measurements. The measured ions are assumed to be predominately protons. The color scale indicates the differential flux normalized by the flux averaged over all available PAs for each time bin. Beamed distributions exhibit higher values (red) in the beaming direction and lower values (blue) in other directions. (d) Magnitude |B| of the IMF. (e) Elevation angle, θB (black), and azimuthal angle, ϕB (blue), of the IMF in GSE coordinates. (f) Solar wind proton bulk speed, Vp (black), and proton number density, Np (blue). Vertical dashed lines bound several time intervals, labeled at the top as “S” for single-peak AMIs, “D” for double-peak AMIs, and “IP Shock” for the ∼5-minute interval immediately after the shock.

From ∼23:10 to ∼23:45 (highlighted by the left yellow rectangle), AMIs exhibiting single-peak signatures are evident as significant flux enhancements in the ∼15−40 keV range with peak intensities at ∼20−30 keV (see also the zoomed-in view in the appendix). The peak energy of these AMIs varies irregularly over time; for example, it remains nearly constant within intervals labeled S1 to S4 but decreases or increases abruptly at the boundaries of these intervals. The changes in peak energy typically occur on a timescale of ∼1−2 minutes, and they do not appear to consistently coincide with abrupt changes in the interplanetary magnetic field (IMF) direction (Fig. 1e) or the solar wind parameters (Fig. 1f).

Later, from ∼00:10 to ∼00:23 (highlighted by the right yellow rectangle), the AMIs exhibit a clear double-peak feature comprising a low-energy peak at ∼20−40 keV and a high-energy peak at ∼80−160 keV. Both peaks show evident temporal variations on a timescale of ∼1−2 minutes: during interval D1, their energies clearly increase with time; from D2 to D4, their energies significantly decrease; and after D4, their energies increase again. Notably, the two peaks vary synchronously and maintain a nearly constant energy ratio of ∼4. In addition, these peaks do not appear to correlate with the IMF or solar wind parameters; for example, during interval D1, the peak energies clearly increase despite nearly constant IMF and solar wind conditions.

Figs. 1b–c present the PADs in the solar wind frame, reconstructed from STEP and EPT measurements under the assumption that protons are the predominant ion species. STEP’s PAD (Fig. 1b) reveals that the AMIs exhibiting a single peak at ∼20−30 keV show strong anisotropy at PAs close to 180°. Such pronounced anisotropy observed downstream of an IP shock where strong magnetic turbulence tends to isotropize ions (Trotta et al. 2025) suggests that these AMIs are intense beams traveling antiparallel to the IMF. Similarly, the AMIs exhibiting double peaks also show strong anisotropy in the antiparallel direction (Figs. 1b–c), indicating their antiparallel propagation along the IMF. We note that the EPT’s PAD reconstructed by assuming helium as the predominant species shows similar strong anisotropy in the antiparallel direction (not shown).

Fig. 2 displays the Solar Orbiter positions in geocentric solar ecliptic (GSE) coordinates, along with the IMF direction at each position. Before encountering the IP shock, the IMF at the spacecraft does not appear to connect to Earth’s bow shock. However, after the IP shock, it points toward the bow shock. Under such configurations, AMIs’ antiparallel motion may indicate their origin at the quasi-perpendicular part of the bow shock (estimated shock angle of ∼50−70°; see Fig. A.1d), consistent with previous studies (Lutsenko 2001; Lutsenko & Gavrilova 2011).

thumbnail Fig. 2.

Solar Orbiter positions projected on the X–Y plane in GSE coordinates, sampled at 10-minute intervals. The arrows, color-coded by time, indicate the IMF direction. The red curve represents the bow shock, calculated using the Slavin and Holzer model (Slavin & Holzer 1981) with a solar wind speed of 380 km/s. The dashed arrows indicate the estimated source regions on the bow shock for the single- and double-peak AMIs, based on a linear extrapolation of the IMF.

Fig. 3 presents the combined energy spectra from STEP and EPT for several time intervals defined in Fig. 1. The STEP spectra transition smoothly into the EPT spectra, exhibiting good agreement in the overlapping energy range. In Fig. 3a, the S3 spectrum shows a prominent bump in the ∼15−25 keV range, with a peak at ∼20 keV and a full width at half maximum (FWHM) of ∼5 keV, while the S4 spectrum shows a bump in the ∼20−35 keV range, with a peak at ∼30 keV and an FWHM of ∼8 keV (see Table 1). The FWHM-to-peak ratios of these two bumps are ∼0.25, consistent with previous observations (Lutsenko & Kudela 1999; Klassen et al. 2009). In contrast, the energy spectrum of the ions accelerated by the IP shock (dashed line in Fig. 3a) is smooth and shows no distinct bump, similar to earlier observations (e.g., Lario et al. 2019; Yang et al. 2025). This contrast suggests that the AMIs exhibiting single-peak features originate from a different source rather than from the IP shock. We note that the energy spectrum transformed into the solar wind frame is very similar to that in the spacecraft frame, with a slight shift in the peak energy. We also note that the STEP spectra exhibit similar shapes across different PAs in STEP’s FOV (not shown).

Table 1.

Parameters of the spectral peaks.

thumbnail Fig. 3.

Energy spectra for several time intervals defined in Fig. 1, shown in two panels (a) and (b) for clarity. Open circles and squares represent STEP and EPT measurements, respectively. The spectrum for the ∼5-minute interval immediately downstream of the IP shock is displayed as the dashed line in panel (a). The spectra in panel (b) are vertically shifted for clarity. The horizontal black bars at the top indicate the energy ranges covered by STEP and EPT. Other horizontal bars mark the spectral peaks in corresponding colors. The scale bar at the bottom of panel (b) indicates an energy ratio of 4 as a reference.

Fig. 3b shows that the D2, D3, and D4 spectra each exhibit two prominent peaks: a low-energy peak at ∼15−30 keV, similar to the single peaks in Fig. 3a, and a high-energy peak at ∼60−120 keV (see Table 1). In all three spectra, the energy ratio between the high-energy and low-energy peaks is nearly constant at ∼4, which contrasts with the previously reported ratio of 2 (Lutsenko & Kudela 1999; Klassen et al. 2009). Moreover, the FWHM-to-peak ratios for both peaks are ∼0.3, similar to those of the single peaks in Fig. 3a. In addition, the differential flux at the high-energy peak is ∼50 times lower than that at the low-energy peak.

4. Summary and discussion

We investigated the AMIs observed near Earth’s bow shock using high-resolution measurements from EPD/STEP and EPT on board Solar Orbiter. These AMIs propagate antiparallel to the IMF that points toward Earth’s bow shock. They exhibit either a single spectral peak at ∼20−30 keV or a double-peak feature comprising a low-energy peak at ∼15−30 keV and a high-energy peak at ∼60−120 keV. All peaks are relatively narrow, with FWHM-to-peak ratios of ∼0.25−0.3, and their peak energies show dynamic behavior on a timescale of ∼1−2 minutes. Notably, the low-energy and high-energy peaks in the double-peak AMIs vary synchronously and maintain a nearly constant energy ratio of ∼4. Furthermore, these AMIs do not appear to correlate with local IMF or solar wind conditions.

The single-peak AMIs share a similar peak energy and FWHM-to-peak ratio with the low-energy peak of the double-peak AMIs, indicating that they are likely the same population. In the double-peak AMIs, the high-energy peak varies synchronously with the low-energy peak, maintaining a nearly constant energy ratio of ∼4 and exhibiting a similar FWHM-to-peak ratio. Moreover, the differential flux at the high-energy peak is much lower than that at the low-energy peak, which aligns with previous observations of multiple ion species (e.g., Mason et al. 2023). These observations suggest that the low-energy and high-energy peaks could correspond to protons and alpha particles, respectively, both accelerated by the same mechanism in the source region. The interpretation of ion species is consistent with previous studies (Lutsenko & Kudela 1999; Klassen et al. 2009).

The antiparallel propagation of AMIs along the IMF pointing toward Earth’s bow shock suggests that they likely originate from the bow shock, as was previously proposed by Lutsenko (2001), Lutsenko & Gavrilova (2011). These authors also introduced a model in which AMIs are accelerated by bursts of strong potential electric fields arising from disruptions of current sheet filaments at the bow shock, thereby gaining energies proportional to their charge numbers. However, our observations reveal that protons and alpha particles in the double-peak AMIs exhibit an energy ratio of ∼4, which corresponds to their mass ratio rather than their charge ratio. Furthermore, we find that the peak energies of AMIs evolve dynamically and irregularly on a timescale of ∼1−2 minutes, which is inconsistent with the model prediction that the peak energy would smoothly decrease with time until reaching a constant level (Lutsenko & Gavrilova 2011). Therefore, we suggest that acceleration by bursts of strong potential electric fields cannot fully account for the observed properties of AMIs in our study. In addition, we note that the adiabatic reflection off the bow shock (Sonnerup 1969) can also be ruled out, as the reflected ions are typically detected at energies of below ∼10 keV (e.g., Johlander et al. 2016).

Alternatively, surfatron acceleration remains a candidate mechanism for generating the observed AMIs. This process predicts that internal structures and irregularities of shock waves can trap particles for extended periods at the shock transition (e.g., Trotta et al. 2022), thereby effectively increasing the associated energy gain (Zank et al. 1996; Simnett et al. 2005). Our observation of an energy ratio of ∼4 between protons and alpha particles in the double-peak AMIs suggests that these two ion species are accelerated to similar velocities. This is consistent with the surfatron acceleration model, wherein particles become detrapped when they are accelerated to a maximum velocity on the order of the sum of the E × B drift velocity and the wave phase velocity (Ohsawa 1985), a velocity threshold that is independent of ion species. However, the detailed acceleration processes remain unclear. For example, it is not yet known under which conditions only protons, or both protons and alpha particles, are accelerated, or what drives the dynamic evolution of their peak energies. Given that the observed AMIs show no correlation with local IMF or solar wind conditions, we speculate that small-scale variations in the source region, such as shock ripples (Johlander et al. 2016) or irregularities (Trotta et al. 2023a), may modulate the wave phase velocity, thereby leading to dynamic variations in the peak energies of accelerated AMIs. Future high-resolution measurements of AMIs within their source region may shed light on the detailed acceleration processes.

Acknowledgments

Solar Orbiter is a mission of international cooperation between ESA and NASA, operated by ESA. EPD is supported by DLR under grant 50OT2002 and the MINCIN Project PID2023-150952OB-I00 funded by MICIU/AEI/10.13039/501100011033 and by FEDER, UE. L.Y. is partially supported by DFG under grant HE 9270/1-1. This research at Peking University is supported in part by NSFC under contracts 42225404, 42127803, and 42150105. Solar Orbiter post-launch work at JHU/APL is supported by NASA contract NNN06AA01C, and at the Southwest Research Institute by NASA contract 80GFSC25CA035.

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Appendix A: Zoomed-in view around the AMI periods

thumbnail Fig. A.1.

Zoomed-in plot around the AMI periods, presented in a similar format to Fig. 1. In panel (d), the blue curve shows the angle between the IMF and the bow shock normal at their linearly extrapolated intersection point, denoted as θBnBS.

All Tables

Table 1.

Parameters of the spectral peaks.

In the text

All Figures

thumbnail Fig. 1.

Overview plot of AMIs observed downstream of the IP shock on 27 November, 2021. (a) Spectrogram of dynamic energy spectra measured by EPT’s sunward telescope and STEP’s central 9 pixels. The yellow rectangles highlight the AMIs analyzed in this study. (b)–(c) PADs in the solar wind frame reconstructed from STEP (b) and EPT (c) measurements. The measured ions are assumed to be predominately protons. The color scale indicates the differential flux normalized by the flux averaged over all available PAs for each time bin. Beamed distributions exhibit higher values (red) in the beaming direction and lower values (blue) in other directions. (d) Magnitude |B| of the IMF. (e) Elevation angle, θB (black), and azimuthal angle, ϕB (blue), of the IMF in GSE coordinates. (f) Solar wind proton bulk speed, Vp (black), and proton number density, Np (blue). Vertical dashed lines bound several time intervals, labeled at the top as “S” for single-peak AMIs, “D” for double-peak AMIs, and “IP Shock” for the ∼5-minute interval immediately after the shock.
In the text
thumbnail Fig. 2.

Solar Orbiter positions projected on the X–Y plane in GSE coordinates, sampled at 10-minute intervals. The arrows, color-coded by time, indicate the IMF direction. The red curve represents the bow shock, calculated using the Slavin and Holzer model (Slavin & Holzer 1981) with a solar wind speed of 380 km/s. The dashed arrows indicate the estimated source regions on the bow shock for the single- and double-peak AMIs, based on a linear extrapolation of the IMF.
In the text
thumbnail Fig. 3.

Energy spectra for several time intervals defined in Fig. 1, shown in two panels (a) and (b) for clarity. Open circles and squares represent STEP and EPT measurements, respectively. The spectrum for the ∼5-minute interval immediately downstream of the IP shock is displayed as the dashed line in panel (a). The spectra in panel (b) are vertically shifted for clarity. The horizontal black bars at the top indicate the energy ranges covered by STEP and EPT. Other horizontal bars mark the spectral peaks in corresponding colors. The scale bar at the bottom of panel (b) indicates an energy ratio of 4 as a reference.
In the text
thumbnail Fig. A.1.

Zoomed-in plot around the AMI periods, presented in a similar format to Fig. 1. In panel (d), the blue curve shows the angle between the IMF and the bow shock normal at their linearly extrapolated intersection point, denoted as θBnBS.
In the text

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