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A&A
Volume 673, May 2023
Solar Orbiter First Results (Nominal Mission Phase)
Article Number A73
Number of page(s) 9
Section The Sun and the Heliosphere
DOI https://doi.org/10.1051/0004-6361/202245681
Published online 10 May 2023

© The Authors 2023

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

Interplanetary collisionless shocks are known to be a strong source of energetic charged particles up to hundreds of MeV (e.g., Bryant et al. 1962; Asbridge et al. 1968; Dresing et al. 2016; Yang et al. 2018, 2019). Theoretical studies have proposed two main acceleration mechanisms (e.g., Kallenrode 2013; Desai & Giacalone 2016): first-order Fermi acceleration (FFA), and shock-drift acceleration (SDA), which are thought to be more efficient under quasi-parallel and quasi-perpendicular shock geometries, respectively. In FFA, charged particles can gain energy through multiple reflections and/or scatterings between converging upstream and downstream waves (Jokipii 1966; Fisk 1971). In a one-dimensional steady-state equilibrium, FFA predicts that the accelerated particles have a power-law velocity distribution function (VDF) of the form f(v)∼v−3r/(r − 1) (Drury 1983; Ho et al. 2003), where v is the particle velocity, and r is the shock compression ratio. In SDA, charged particles can in contrast be energized via the gradient drift along the induced electric field at the shock surface (Hudson 1965; Decker 1988). Decker (1981) performed a numerical simulation based on single-encounter SDA and showed that the fluxes of accelerated particles peak before the shock, with a field-aligned anisotropy, and they sharply decrease after the shock passage, with an anisotropy perpendicular to the magnetic field. In addition, diffusive shock acceleration theory is built on solving the particle transport equation (e.g., the Parker transport equation; Parker 1965). FFA and SDA can be included as different terms in the transport equation, and thus are incorporated under the theory of diffusive shock acceleration (see Sect. 7 in Desai & Giacalone 2016; Qin et al. 2018).

The suprathermal proton population is characterized by a power-law spectrum at energies above the thermal quasi-Gaussian component (usually above a few keV) to ∼50 keV (Lario et al. 2019). This population plays an important role in bridging the thermal regime and the more energetic (≳50 keV) regime. Previous attempts to study suprathermal protons at interplanetary shocks were very limited because the instrumental efficiency in measuring these particles was low. Frank (1970) was the first to report that the ∼5 − 50 keV protons show a bump-like energy spectrum with a peak around ∼15 keV at an interplanetary shock (see Fig. 2 in Frank 1970), using the measurements by the Low-energy Proton and Electron Differential Energy Analyzer (LEPEDEA) on board Explorer 34. Later, Gosling et al. (1984) presented 17 interplanetary shock events encountered by the International Sun-Earth Explorers (ISEEs), but quantitatively analyzed only three of them due to the limited measurement efficiency at suprathermal energies. They reported that upstream and downstream protons both show a single power-law VDF, f(v)∼v−γ, at ∼400 − 2000 km s−1, with γ ranging from ∼4 − 6 (see also Gosling et al. 1981). Recently, using measurements from the Plasma and Suprathermal Ion Composition instrument (PLASTIC) on board the Solar Terrestrial Relations Observatory Ahead spacecraft (STEREO A), Yu et al. (2018) reported that suprathermal proton spectra show a clear turnover at velocities below 2500 km s−1 far upstream of the reverse shocks associated with stream interaction regions (SIRs). After a careful reconstruction of the proton pitch-angle distributions (PADs) in the solar wind frame (SWF), Yang et al. (2020) found that ∼10 − 40 keV protons show anisotropies perpendicular to the magnetic field downstream of the shock and a clear escaping beam in the upstream region. In addition, combining the measurements from the Advanced Composition Explorer (ACE) and Wind spacecraft, Lario et al. (2019, 2022) found that suprathermal protons show a field-aligned escaping beam upstream of the shock and a power-law VDF with a γ ∼ 4 in the downstream region.

The studies in the last century are strongly restricted by the limited measurement efficiency and low counting statistics of suprathermal ions. The missions in recent years provided better-quality data with higher counting statistics. However, these data still have to be averaged in time and energy to ensure sufficient counting statistics. For example, the highest-quality data come from STEREO/PLASTIC, which measures protons from 0.3 to 80 keV with a time resolution of ∼1 min and an energy resolution of ∼10% (Galvin et al. 2008). To reconstruct reliable PADs, however, Yang et al. (2020) had to reduce the time and energy resolution to ≳10 min and ≳40%, respectively. With reconstructed PADs at this resolution, they were unable to study the temporal and spectral evolutions of suprathermal protons in the vicinity of shocks. Moreover, at the low energies treated in this paper, the transformation to the solar wind frame is critical to correctly reconstruct the PADs of suprathermal ions. However, previous attempts failed to carry out this transformation. For example, Lario et al. (2019, 2022) performed the transformation by assuming that particles propagate in the solar wind direction and overcorrected for the Compton-Getting effect. Therefore, we take advantage of the unprecedented high-resolution measurements by the Energetic Particle Detector (EPD; Rodríguez-Pacheco et al. 2020; Wimmer-Schweingruber et al. 2021) on board the Solar Orbiter spacecraft (Müller et al. 2020), which is the most recent and most modern instrument for this task, and reconstruct the PADs in the solar wind frame. We also study the behavior of suprathermal ions near an interplanetary shock on a much shorter timescale and at a much better energy resolution than previously possible. These studies will help us to better understand how ions are accelerated at shocks.

2. Data sources

Solar Orbiter was launched in February 2020 to a heliocentric orbit with an eventual perihelion as close as 0.28 au. The EPD on board Solar Orbiter is a key instrument suite that provides measurements of suprathermal and energetic particles to address the scientific questions pertaining to particle acceleration. As one sensor of EPD, the SupraThermal Electron Proton sensor (STEP) measures ions and electrons at energies between 6 keV (4 keV for electrons) and 60 keV in a field of view (FOV) of ∼30° ×60° around the direction of the nominal magnetic connection to the Sun (Wimmer-Schweingruber et al. 2021). The STEP sensor employs two coaligned sensor heads, which are called magnet channel and integral channel. The magnet channel contains a permanent magnet to deflect electrons out of the nominal FOV and measures only ions, while the integral channel measures both ions and electrons. Each channel contains a multipixel solid-state detector segmented in a 3 × 5 array (see Fig. 6 of Rodríguez-Pacheco et al. 2020), and each elemental pixel measures particles in a small FOV of ∼10° ×12° through the small pinhole at the entrance of the sensor head. This pixel array enables resolving the angular distribution inside the FOV of STEP. Moreover, the background is also determined by a pixel that is outside the FOV spanned by the pin hole and sensor collimator, and it therefore only measures the highly energetic particles penetrating the instrument housing.

In this paper, we use the ion measurements from the STEP magnet channel, whose data products were updated to the latest version at the end of October 2021. In this version, each of the 16 pixels provides ion measurements from 6 to 60 keV in 32 logarithmically spaced energy channels with a cadence of one second. To our knowledge, data with this high time and angular resolution have not been available before. We also use the solar wind proton density, velocity, and temperature measured in a resolution of 4 s by the Solar Wind Analyser (SWA; Owen et al. 2020) and the magnetic field data measured at 8 Hz by the fluxgate vector magnetometer (MAG; Horbury 2020). All the above data are publicly available at the Solar Orbiter Archive1.

3. Transformation to the solar wind frame

The interplanetary magnetic field (IMF) is convected away from the Sun with the solar wind. In the SWF (or more precisely, the de Hoffman Teller frame), the magnetic field is then at rest, and the induced electric field vanishes. The SWF is thus commonly used to reconstruct the three-dimensional distribution or PAD of suprathermal ions (e.g., Gosling et al. 1981; Yang et al. 2020). We used V = V p + V A B ̂ $ \boldsymbol{V}=\boldsymbol{V}_{\mathrm{p}}+V_{\mathrm{A}}\ \boldsymbol{\hat{B}} $ as an estimate of the velocity of the de Hoffman-Teller frame as the intrinsic solar wind frame of reference (Němeček et al. 2020), where V is the velocity of the frame of reference, Vp is the proton bulk velocity, VA is the Alfvén velocity, and B ̂ $ \boldsymbol{\hat{B}} $ is the direction vector of the IMF.

Figure 1 shows the ion measurements by the STEP magnet channel near an interplanetary shock that arrived at Solar Orbiter on 2021 November 3 as an example. The top panel labeled zero shows the counting rate of penetrating particles measured by the background pixel, which is ∼2% compared to the counting rates of other pixels. Because protons are the dominant ion component near interplanetary shocks (Lario et al. 2019; Yang et al. 2020), we can assume that the measured ions are all protons, and we converted the counting rate into differential flux with the response functions of the instrument. Furthermore, the orbit of Solar Orbiter is far removed from the helium focusing cone (Fahr et al. 1978; Möbius et al. 1985; Gloeckler et al. 2004), and therefore, the contribution of pickup He+ is thought to have insignificant influence on the results presented in this study. We note that the STEP dead time reaches ∼15% of the measurement cycle during the highest counting rate near the shock, and it may affect the obtained differential flux by a similar percentage, but not the angular anisotropy. We also note that the STEP energy calibration of certain pixels appears to shift over time due to aging effects of the solid-state detectors. We verified that this is not an issue for the period analyzed in this study.

thumbnail Fig. 1.

Measurements by the STEP magnet channel around the interplanetary shock on 2021 November 3. Panels 1–15 show the counts of ions vs. time in 32 energy channels and one-second resolution measured by the 3 × 5 pixel array in the nominal FOV, while panel 0 shows the counts of penetrating particles measured by the background pixel. The energies are measured in the spacecraft frame. The red triangle marks the shock arrival at ∼14:04:26.

As shown in Fig. 1, more counts are observed in the upper right panels than in the lower left panels, indicating an anisotropic angular distribution. In the following, we reconstruct the two-dimensional PAD of suprathermal protons in the SWF, that is, we convert the proton differential flux as a function of energy and pixel in the spacecraft frame into the differential flux as a function of velocity and pitch angle (PA) in the SWF. For each combination of the 32 energy channels and 15 pixels, we calculated the corresponding proton velocity vectors in the SWF and then determined the corresponding PA coverage in the SWF with the magnetic field vector averaged in the STEP accumulation interval, that is, one second. After this, we created a fine grid with 100 velocity bins logarithmically spaced from 500 km s−1 to 3600 km s−1 and 180 PA bins with a bin width of 1°. To obtain the differential flux for a certain velocity bin and PA bin, we selected all the combinations of energy channel and pixel that overlap with the velocity bin and PA bin, and then averaged the differential flux over them. This fine grid might reduce the edge effects in the mapping and improve the accuracy of the reconstructed PAD, but to avoid oversampling, we reduced the reconstructed PAD to 32 velocity bins and 36 PA bins (5° each) that share a similar resolution with the original measurements by the instrument (Rodríguez-Pacheco et al. 2020). The reconstructed PAD in the SWF is only partially covered by the PA because the STEP FOV is fixed and the PA coverage depends on the magnetic field configuration and the SWF. Moreover, we estimated the uncertainty of the reconstructed PAD from the statistical errors of the original measurements via error propagation.

4. 2021 November 3 shock

After the update of the STEP data products at the end of 2021 October, Solar Orbiter encountered the first interplanetary shock with a strong acceleration of suprathermal protons at ∼14:04:26 on 2021 November 3. Figure 1 shows strong enhancements in the counting rate of suprathermal protons after the shock arrival. Escaping protons with a velocity dispersion on a timescale of ∼15 min are observed before the shock, which was also reported by Lario et al. (2019). However, with the unprecedented high-resolution data of STEP, we are able to study the evolution of the suprathermal protons at the shock on a much shorter timescale.

Using the nonlinear least-squares fitting techniques (Viñas & Scudder 1986; Szabo 1994; Koval & Szabo 2008), we find a physical fit of this shock as a quasi-perpendicular shock, with the shock normal lying almost along the Sun-spacecraft line and an angle between the shock normal and the upstream IMF, θBn, of 66° ±12°. It has a shock velocity, Vsh, of 664 ± 14 km s−1 in the spacecraft frame, a magnetosonic Mach number of 2.8 ± 0.3, a magnetic compression ratio of 2.6 ± 0.4, and a density compression ratio of 1.6 ± 0.2.

Figure 2 shows a summary plot of the hour surrounding the 2021 November 3 shock event, and Fig. 3 shows the summary plot zoomed in to the 3-min vicinity of the shock. As shown in Figs. 2a,b, the STEP FOV covers ∼0° −60° PA in the regions upstream and near downstream of the shock (≲10 min after the shock), but it covers ∼120° −180° in the region far downstream (∼10 − 20 min after the shock) due to a reversal in the IMF direction (see Figs. 2d–f). In the direction parallel to the IMF, the proton fluxes at ≳1000 km s−1 start to rise ∼15 min before the shock (Fig. 2c), and the fluxes at ∼1200 − 3600 km s−1 peak between ∼12 and ∼24 s before the shock in the upstream region with a velocity dispersion feature, that is, the fluxes of faster protons peak earlier than the slower protons (Fig. 3c). Then the fluxes decrease to the fluxes at the shock front by ∼30%–60% of the peak values (Fig. 3c). Although the flux peak upstream of the shock was reported for protons at ∼0.1 − 5 MeV in the literature (e.g., Decker 1981; Lario et al. 2022), a flux peak upstream of the shock at suprathermal energies like this is observed for the first time.

thumbnail Fig. 2.

Summary plot of the 2021 November 3 shock event. (a) PAD spectrogram of the ∼1485 km s−1 protons in the SWF. (b) Same PAD spectrogram as in panel a, but normalized by the flux averaged over all PAs for each time bin. (c) Differential flux vs. time of ∼500 − 3600 km s−1 protons traveling at 30° −60° PA (between the horizontal dashed lines in panel a). The shaded region at 14:15–14:25 shows the differential flux of protons traveling at 120° −150° PA. To improve the counting statistics, the 32 velocity bins are grouped into 12 logarithmically spaced bins, and their center velocities are shown on the right of the panel. Panels d–f: magnitude |B|, elevation angle θB, and azimuthal angle ϕB of the IMF. Panels g and h: solar wind proton bulk speed |Vsw| and the three components Vx, Vy, and Vz measured in the spacecraft frame. The vertical dashed red line marks the shock arrival. The other vertical dashed lines bound several selected intervals with the labels at the top, which are analyzed in Fig. 4.

thumbnail Fig. 3.

Summary plot in the 3-min vicinity of the 2021 November 3 shock. Panels a–f: same as Fig. 2, but on a smaller timescale. Panel g: spectrogram of the trace power spectral density of the magnetic field fluctuations, obtained from the wavelet analysis (Torrence & Compo 1998). Panel h: spectrogram of the reduced magnetic helicity, σm, on the YZ plane of the spacecraft frame (He et al. 2011). If a wave vector points along +X (toward the Sun), positive σm (red) indicates right-hand polarization, and negative σm (blue) indicates left-hand polarization, and vice versa. The vertical dashed red line marks the shock front. The ∼26-s upstream interval bounded by the dashed blue line and the shock front is labeled U1. The ∼15-s downstream interval bounded by the shock front and the dashed purple line is labeled D1.

The suprathermal protons upstream of the shock appear to show no strong anisotropy in PAD on a timescale of ∼15 min (Fig. 2b). However, in the ∼30 s adjacent to the region upstream of the shock (Fig. 3b), the suprathermal proton PAD shows anisotropies close to the smallest PA in the PA range covered by STEP (indicated by the blue arrows). As the upstream IMF is pointing away from the Sun (also away from the shock), these parallel anisotropic protons in the region close to the upstream region are likely to be the escaping protons from the shock. In this study, we focus on this feature because we assume that closely before the shock, transport effects are less important. Figure 3h shows the reduced magnetic helicity σ m ( t , τ ) = 2 Im ( B ∼ y ( t , τ ) · B ∼ z ∗ ( t , τ ) ) / ( | B ∼ x ( t , τ ) | 2 + | B ∼ y ( t , τ ) | 2 + | B ∼ z ( t , τ ) | 2 ) $ \sigma_{\mathrm{m}}(t, \tau)=2\mathrm{Im}(\tilde{B}_{\mathit{y}}(t, \tau) \cdot \tilde{B}^*_z(t, \tau)) / (|\tilde{B}_x(t, \tau)|^2+|\tilde{B}_{\mathit{y}}(t, \tau)|^2+|\tilde{B}_z(t, \tau)|^2) $2 calculated as a function of time t and period τ (He et al. 2011), where B ∼ x $ \tilde{B}_x $, B ∼ y $ \tilde{B}_{\mathit{y}} $, and B ∼ z $ \tilde{B}_z $ represent the Morlet-wavelet transform (Torrence & Compo 1998) of the time series of the magnetic field components in the spacecraft coordinate system. In the ∼10 s before the shock, clear wave activities in a period of ∼0.8 − 5 s last for ∼5 s (indicated by the red arrow in Fig. 3h). If these waves are traveling away from the shock along the IMF, then they could be whistler waves, which are excited by the escaping suprathermal protons (He et al. 2022). Here we focus on the waves closely before the shock because we assume that these waves are likely to be excited by processes related to the shock. We note that the reduced magnetic helicity σm exactly (partially) reflects the helicity of waves if the waves are traveling along (oblique to) the X axis, and therefore, they may underrepresent the wave activities.

After the shock passage, the suprathermal proton fluxes in the parallel direction appear to be relatively constant on a time scale of ∼10 min. However, in the ∼15 s adjacent to the shock, the proton fluxes at ∼1200–3600 km s−1 decrease rapidly by ∼30% to 60% of the fluxes at the shock. This temporal flux profile suggests that the thin downstream layer (∼8000 km, or ∼10 gyroradii of 1500 km s−1 proton) adjacent to the shock is more relevant to the shock acceleration than the region farther downstream. Figure 3g shows the trace power spectral density (PSD) of the IMF, which is calculated as ( | B ∼ x | 2 + | B ∼ y | 2 + | B ∼ z | 2 ) · 2 · δ t $ (|\tilde{B}_x|^2+|\tilde{B}_{\mathit{y}}|^2+|\tilde{B}_z|^2) \cdot 2 \cdot \delta t $, where δt is the time cadence of the magnetic field data. We find that the trace PSD in this thin layer appears to have the highest intensity around the shock, especially in the period range of ∼1 − 10 s (Fig. 3g). In addition, the proton PADs in the near downstream region show significantly higher intensities at > 60° PA than the other PAs in the FOV (Figs. 2b and 3b), consistent with the previous observations reported by Yang et al. (2020).

When Solar Orbiter crossed a current sheet and entered a special region from ∼14:15 to ∼14:25, STEP measured protons traveling at ∼120° −180° PA. These protons appear to have much lower fluxes at ≲2000 km s−1 and more dynamic temporal flux profiles than the protons traveling at ∼0° −60° PA in the near downstream region (Figs. 2a,c), which may suggest that this special region is isolated from the shock front and the near downstream region. Moreover, the proton PADs in this special region vary as the IMF switches between magnetic flux tubes on a timescale of ∼2 min (Fig. 2b).

According to the changes in the IMF, proton flux, and proton PAD, we selected the time intervals labeled Pre-event, U4, U3, U2, D2, S1, S2, and S3 in Fig. 2 and U1 and D1 in Fig. 3 (U1 and D1 are very short in Fig. 2). The start and end time of these time intervals are shown in Table 1. Figure 4 presents the VDFs (panels a–c) and PADs (panels d–f) averaged over the above time intervals, and panels g–j in Fig. 4 present the VDFs in different PA directions and their ratios for the time intervals U1 and D2. Panels a–c in Fig. 4 show that the suprathermal population dominates at ≳1000 km s−1 near the shock. In the U1 region, the suprathermal VDF averaged over 30° −60° PA fits to a double power law, with a spectral index γ of 3.4 ± 0.2 at velocities below ∼1800 ± 100 km s−1 and a γ of 5.8 ± 0.3 at velocities higher than this (Fig. 4a). The VDF appears to have a similar spectral shape in all observed PA directions (Fig. 4g), but the intensity decreases with PA (Fig. 4i). The average PAD in U1 shows higher flux toward smaller PAs close to 0° in the covered PA range (Fig. 4d), consistent with the above observation. We note that the above power-law indices were fit with the uncertainties in both phase-space density and velocity (Liu et al. 2020b), and they are significantly smaller than the FFA prediction of 7.8 for this shock case.

thumbnail Fig. 4.

VDFs and PADs averaged over the time intervals defined in Table 1. Panels a–c: phase space density at 30° ≤PA ≤ 60° upstream of the shock (a), at 30° ≤PA ≤ 60° downstream of the shock (b) and at 120° ≤PA ≤ 150° in a special downstream region (c) vs. proton velocity in the SWF. The dashed lines indicate the spectral shapes of the single or double power law fit to the spectra in the same colors. Vb indicates the break of the double power law. Panels d–f: phase space density at ∼1485 km s−1 vs. PA in the SWF. The dashed lines in panel d mark the maximum values of the corresponding solid lines, while the purple dashed line in panel e indicates the purple solid line multiplied by 1.7 in order to be compared with the solid red line. Panels g and h: phase space density in three different PA directions vs. velocity in the SWF for time intervals U1 and D1. Panels i and j: ratio of the phase space density between different PA directions vs. velocity in the SWF for time intervals U1 and D1. The colors indicate different time intervals in panels a–f, but different PA directions in panels g–j. The uncertainties are plotted as vertical or horizontal bars. The background caused by the penetrating particles has been removed.

Table 1.

Selected time intervals on 2021 November 3.

In the U2 region, the suprathermal VDF fits to a double power law with a γ of 3.4 ± 0.2 below a break at ∼1800 ± 100 km s−1 and a γ of 4.7 ± 0.2 at velocities higher than this, similar to the double power law observed in U1, but with a flatter spectral shape at velocities above the break. Further upstream in U3 and U4, the proton VDFs show clear turnovers at ∼1000 − 1500 km s−1 and ∼1500 − 2000 km s−1, respectively, compared to the Pre-event spectrum. Clear turnovers like this were first reported by Yu et al. (2017, 2018) in the upstream regions of the reverse shocks associated with SIRs. Furthermore, the proton PAD evolves from a parallel anisotropy toward isotropy away from the shock to the region far upstream (Fig. 4d).

The suprathermal protons in D1 appear to have a double power-law VDF with a γ of 4.3 ± 0.7 below a break at ∼1600 ± 200 km s−1 and a γ of 5.8 ± 0.2 at velocities higher than this (Fig. 4b). The shape of the VDF in D2 appears to be similar to that in D1, but with a lower intensity. Furthermore, these downstream VDFs appear to have a similar spectral shape in all observed PA directions (Fig. 4h), but with significantly higher intensities at > 60° PA (Fig. 4j). The PADs in D1 and D2 also show a tendency of anisotropies toward 90° PA (Fig. 4e), consistent with the above observation. Although we cannot rule out that there is an unobserved beam in the anti-parallel direction due to the limited PA coverage, our observations are consistent with the anisotropic PAD in the direction perpendicular to the IMF downstream of the shock, which was previously clearly observed by Yang et al. (2020).

In the S1, S2, and S3 regions, the suprathermal VDFs fit to a single power law with a γ of 4.0 ± 0.1 in S1 and S2 (Fig. 4c), while the spectrum in S3 bends up at > 2000 km s−1. These spectral shapes clearly indicate that the suprathermal protons in these regions belong to a different population than those observed close to the shock or in the near downstream region. This again supports the idea that the special region after the current sheet is not magnetically connected to the shock front or the near downstream region. Moreover, in the covered PA range, the averaged PAD shows an anisotropy close to 180° PA in S1 and S3 and an anisotropy close to 90° PA in S2 (see Fig. 4f), consistent with the PAD shown in panel b of Fig. 2.

Figure 5 shows the suprathermal proton PADs zoomed in to the 45-s vicinity of the shock for different velocity bins. Proton PADs on this timescale are enabled by the STEP measurements. The maximum differential flux in each velocity bin is detected as a red region in each panel. The maximum flux of fast protons is observed earlier than the flux of slow protons. After the maximum flux region, the proton fluxes at all velocities decrease towards the shock front (also see Fig. 3c). Although the averaged proton PAD in U1 shows an anisotropy near 0° PA (Fig. 4d), the proton PADs in one-second resolution (Fig. 5) show dynamic behaviors on a timescale of ∼10 s. These dynamic behaviors are not fully understood yet. We note that the proton PADs at ∼1200 − 1900 km s−1 appear to show a V-shape feature from ∼14:04:08 to 14:04:16 (Fig. 5a–c), which coincides with the rotation of the IMF (Fig. 3e–f). This V-shape feature may be due to the wave-particle interactions or the varying PA coverage of STEP and requires further analysis in the future.

thumbnail Fig. 5.

PAD spectrograms of ∼1200 − 3600 km s−1 protons in the 45-s vicinity of the 2021 November 3 shock. The color bar of each panel indicates the flux intensity for each velocity bin. The vertical dashed red line marks the shock front. The ∼26-s upstream interval bounded by the blue dashed blue line and the shock front is labeled U1.

5. Summary and discussion

We examined the in situ acceleration of suprathermal protons near the 2021 November 3 shock with the unprecedented high-resolution measurements by EPD/STEP on board Solar Orbiter. After reconstructing the two-dimensional proton PADs in the SWF, we find that the suprathermal proton fluxes peak between ∼12 and ∼24 s before the shock in the upstream region. The suprathermal proton fluxes decrease rapidly in a thin layer (∼8000 km) adjacent to the shock in the downstream region and become constant farther downstream. Furthermore, the VDFs of suprathermal protons in the region close to upstream (downstream) fit a double power law, with a γ of ∼3.4 ± 0.2 (∼4.3 ± 0.7) at velocities below a break at ∼1800 ± 100 km s−1 (∼1600 ± 200 km s−1) and a γ of ∼5.8 ± 0.3 (∼5.8 ± 0.2) at velocities higher than this. These indices are all significantly smaller than the prediction by FFA. In addition, the proton PADs in the covered PA range show anisotropies in the direction parallel to the IMF (also away from the shock) in the region close to the upstream region and become nearly isotropic further upstream, while downstream of the shock, they show a tendency of anisotropies towards 90° PA.

The anisotropy toward parallel streaming of suprathermal protons in the region close to the upstream region suggest that they are likely to be accelerated at the shock front and then escape to the upstream region, which is consistent with the prediction by SDA (Decker 1981). A similar anisotropy toward parallel streaming has previously been reported in the literature (Lario et al. 2019; Yang et al. 2020), but with a considerably lower time and energy resolution than is achieved by STEP. Here we find that the suprathermal proton fluxes peak ∼12 − 24 s before the shock in the upstream region (Fig. 3c, and Fig. 5a–g). This peak in the proton flux could not have been observed with previous measurements but would instead have been hidden within a single data point at a one-minute time resolution, for instance. One possible explanation for the above observation is that protons are accelerated at the shock with varying efficiency, maybe due to the influence of waves or turbulence close to the shock front (Decker & Vlahos 1985; Ellison et al. 1995). When we assume that the proton acceleration is spatially uniform along the shock surface and the proton fluxes measured closely before the shock would reflect the accelerated proton fluxes at the shock, then the observed time-varying flux profile closely before the shock could be a result of time-varying acceleration efficiency at the shock. Another possibility is that these observed protons may come from different parts of the shock that may have different local θBn and therefore different acceleration efficiencies as a result of shock rippling (Johlander et al. 2016, 2018; Yang et al. 2018). A temporally or spatially varying acceleration efficiency like this might also explain the previous observations that proton fluxes do not always peak at the shock (e.g., Lario et al. 2003; Cohen 2006; Ho et al. 2008). We note that the dynamic structures observed in the proton PADs in the region close to the upstream region (Fig. 5) could also be a result of the wave activity during this time period.

Taking advantage of the high time-resolution data of STEP, we observe a rapid decrease (∼50% in ∼15 s) of proton fluxes along with the strongest magnetic turbulence in a thin downstream layer adjacent to the shock. These observations suggest that this thin layer could be the most important region for acceleration, in which downstream particles are efficiently reflected and/or scattered back to the shock front and are further accelerated at the shock. This rapid decrease of proton fluxes immediately downstream of the shock is consistent with the predicted flux temporal profile by SDA (Decker 1983). Moreover, the phase-space density of suprathermal protons in the downstream region is significantly higher at > 60° PA than at the other PAs in the STEP FOV (Fig. 4e), which is consistent with the previously reported field-perpendicular PAD (Yang et al. 2020; Fraschetti & Giacalone 2020). A downstream PAD with these properties may indicate that the proton acceleration through the shock is more efficient in the direction perpendicular to the IMF than in other directions. This also agrees with SDA theory (Hudson 1965; Decker 1983, 1988) because the gradient drift would accelerate protons in the direction perpendicular to the IMF, and the protons traveling perpendicular to the IMF also have the highest gradient drift velocity. Furthermore, the shock is fit to be a quasi-perpendicular shock with a θBn of 66° ±12°. Under this quasi-perpendicular shock geometry, the induced electric field at the shock surface is relatively strong, while the proton reflection and scattering back to the shock along the magnetic field are relatively inefficient. SDA is therefore expected to work more efficiently than FFA at this shock (Desai & Giacalone 2016). We also note that the anisotropic PADs downstream of the shock are inconsistent with the formation of isotropic PADs in the downstream region under FFA (e.g., Drury 1983; Giacalone 2015).

The VDFs of suprathermal protons close to the shock fit a double power law at ∼1000 − 3600 km s−1 with a break at ∼1800 km s−1, different from the previous observations of a single power law at this velocity range (Gosling et al. 1984; Lario et al. 2019). This double power-law VDF of suprathermal protons is observed for the first time with the high-energy resolution data of STEP. The formation of the double power law is not fully understood. Liu et al. (2020a, 2022) proposed, however, that SDA may produce a double power-law VDF with a break associated with the ramp thickness of the shock. This theoretical prediction is consistent with our observation of double power-law VDFs with a similar spectral break in the upstream and downstream regions. Furthermore, all the fitted power-law indices are significantly smaller than the FFA prediction (Drury 1983). However, the power-law indices at velocities higher than the break appear to be consistent with the prediction by the empirical equation of γ = 6r/(2r − 1.5) = 5.6 from Rodríguez-Pacheco et al. (1998).

In the region far upstream of the shock, the proton PAD becomes less anisotropic and evolves toward isotropy (Fig. 4d), which is probably due to the increasing effect of pitch-angle scatterings by waves or turbulence (Li et al. 1997; Saul et al. 2007). The proton VDFs show clear turnover spectra at ∼1000 − 1500 km s−1 and ∼1500 − 2000 km s−1 in the U3 and U4 regions, respectively (Fig. 4a). Similar turnover spectra were previously reported by Yu et al. (2017, 2018). However, with the high time and energy resolution data of STEP, we also find that the spectral turnover appears at higher velocities in the region farther away from the shock, suggesting that the turnover spectrum might be formed due to a transport effect of suprathermal protons upstream of the shock. We note that a turnover spectrum with a positive slope like this might excite instabilities and contribute to wave growth in the upstream region (Treumann & Baumjohann 1997). Future studies should include proton measurements at higher energies. This would help us to better understand the in situ acceleration of protons at interplanetary shocks.

2

The asterisk denotes the complex conjugate, and | ⋅ | calculates the modulus of the complex number.

Acknowledgments

This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – HE 9270/1-1. STEP and EPD are supported by the German Space Agency, DLR, under grant 50OT2002 and the Spanish MINCIN Project PID2019-104863RBI00/AEI/10.13039/501100011033. This research at Peking University is supported in part by NSFC under contracts 42127803, 42225404, 42150105, 42174194 and 42204166, and by CNSA D050106, as well as by National Key R&D Program of China (2021YFA0718600). Solar Orbiter post-launch work at JHU/APL is supported by NASA contract 80MSFC19F0002.

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All Tables

Table 1.

Selected time intervals on 2021 November 3.

In the text

All Figures

thumbnail Fig. 1.

Measurements by the STEP magnet channel around the interplanetary shock on 2021 November 3. Panels 1–15 show the counts of ions vs. time in 32 energy channels and one-second resolution measured by the 3 × 5 pixel array in the nominal FOV, while panel 0 shows the counts of penetrating particles measured by the background pixel. The energies are measured in the spacecraft frame. The red triangle marks the shock arrival at ∼14:04:26.
In the text
thumbnail Fig. 2.

Summary plot of the 2021 November 3 shock event. (a) PAD spectrogram of the ∼1485 km s−1 protons in the SWF. (b) Same PAD spectrogram as in panel a, but normalized by the flux averaged over all PAs for each time bin. (c) Differential flux vs. time of ∼500 − 3600 km s−1 protons traveling at 30° −60° PA (between the horizontal dashed lines in panel a). The shaded region at 14:15–14:25 shows the differential flux of protons traveling at 120° −150° PA. To improve the counting statistics, the 32 velocity bins are grouped into 12 logarithmically spaced bins, and their center velocities are shown on the right of the panel. Panels d–f: magnitude |B|, elevation angle θB, and azimuthal angle ϕB of the IMF. Panels g and h: solar wind proton bulk speed |Vsw| and the three components Vx, Vy, and Vz measured in the spacecraft frame. The vertical dashed red line marks the shock arrival. The other vertical dashed lines bound several selected intervals with the labels at the top, which are analyzed in Fig. 4.
In the text
thumbnail Fig. 3.

Summary plot in the 3-min vicinity of the 2021 November 3 shock. Panels a–f: same as Fig. 2, but on a smaller timescale. Panel g: spectrogram of the trace power spectral density of the magnetic field fluctuations, obtained from the wavelet analysis (Torrence & Compo 1998). Panel h: spectrogram of the reduced magnetic helicity, σm, on the YZ plane of the spacecraft frame (He et al. 2011). If a wave vector points along +X (toward the Sun), positive σm (red) indicates right-hand polarization, and negative σm (blue) indicates left-hand polarization, and vice versa. The vertical dashed red line marks the shock front. The ∼26-s upstream interval bounded by the dashed blue line and the shock front is labeled U1. The ∼15-s downstream interval bounded by the shock front and the dashed purple line is labeled D1.
In the text
thumbnail Fig. 4.

VDFs and PADs averaged over the time intervals defined in Table 1. Panels a–c: phase space density at 30° ≤PA ≤ 60° upstream of the shock (a), at 30° ≤PA ≤ 60° downstream of the shock (b) and at 120° ≤PA ≤ 150° in a special downstream region (c) vs. proton velocity in the SWF. The dashed lines indicate the spectral shapes of the single or double power law fit to the spectra in the same colors. Vb indicates the break of the double power law. Panels d–f: phase space density at ∼1485 km s−1 vs. PA in the SWF. The dashed lines in panel d mark the maximum values of the corresponding solid lines, while the purple dashed line in panel e indicates the purple solid line multiplied by 1.7 in order to be compared with the solid red line. Panels g and h: phase space density in three different PA directions vs. velocity in the SWF for time intervals U1 and D1. Panels i and j: ratio of the phase space density between different PA directions vs. velocity in the SWF for time intervals U1 and D1. The colors indicate different time intervals in panels a–f, but different PA directions in panels g–j. The uncertainties are plotted as vertical or horizontal bars. The background caused by the penetrating particles has been removed.
In the text
thumbnail Fig. 5.

PAD spectrograms of ∼1200 − 3600 km s−1 protons in the 45-s vicinity of the 2021 November 3 shock. The color bar of each panel indicates the flux intensity for each velocity bin. The vertical dashed red line marks the shock front. The ∼26-s upstream interval bounded by the blue dashed blue line and the shock front is labeled U1.
In the text

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