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A&A
Volume 686, June 2024
Solar Orbiter First Results (Nominal Mission Phase)
Article Number A132
Number of page(s) 10
Section The Sun and the Heliosphere
DOI https://doi.org/10.1051/0004-6361/202348723
Published online 04 June 2024

© The Authors 2024

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

The acceleration of energetic charged particles by collisionless shocks is a ubiquitous phenomenon in numerous astrophysical environments, such as supernova remnant shocks (Bykov et al. 2019), the heliospheric termination shock (Zank et al. 1996; Zilbersher & Gedalin 1997), interplanetary shocks (Bryant et al. 1962; Kennel et al. 1984; Rodríguez-Pacheco et al. 1998; Trotta et al. 2023a), or planetary bow shocks (Hoppe & Russell 1982; Burgess et al. 2012; Liu et al. 2020a, 2022). Theoretical studies have proposed several fundamental acceleration mechanisms (see, e.g., Kallenrode 2013, for an introduction): first-order Fermi acceleration (FFA), shock-drift acceleration (SDA), shock-surfing acceleration (SSA), and adiabatic reflection off the shock. In FFA, charged particles can be energized through multiple reflections and scattering between converging upstream and downstream waves (Fermi 1954), which is thought to be effective for parallel or quasi-parallel shocks. On the other hand, SDA (previously called gradient drift acceleration) predicts that charged particles can gain energy through the gradient drift along the motional electric field at the shock surface (Hudson 1965; Decker 1988), which is important for perpendicular or quasi-perpendicular shocks. A numerical simulation based on single-encounter SDA showed that the accelerated particles could have a steeper spectrum than the seed particles (Decker 1983). FFA and SDA can both be incorporated into the theory of diffusive shock acceleration (DSA, Krymskii 1977; Axford et al. 1977; Blandford & Ostriker 1978; Bell 1978). DSA predicts that the accelerated particles have a power-law spectrum of the form f(v)∼v−3r/(r − 1) (Drury 1983; Vainio 1999; Malkov & Drury 2001), where v is the particle velocity, and r is the gas compression ratio. Furthermore, SSA predicts that ions can gain energy by surfing the electrostatic potential gradient at the shock front (Sagdeev 1966; Shapiro & Üçer 2003), but this surfing would require the shock to be almost exactly perpendicular. In addition, Sonnerup (1969) proposed that the adiabatic reflection off the shock can also energize charged particles, with an energy gain dependent upon the deHoffman-Teller velocity of the shock (De Hoffmann & Teller 1950).

In this work, we focus on the shock acceleration of energetic particles. The energetic particles generally denote ions at energies from several dozen keV to a few MeV (Lario et al. 2019, 2022). In situ measurements from multiple generations of spacecraft have revealed several features of the acceleration of these particles at interplanetary shocks: (1) Tsurutani & Lin (1985) performed a statistical survey of 55 shocks observed by the International Sun-Earth Explorer-3 (ISEE-3). The authors suggested that the time-intensity profiles of the accelerated energetic ions typically show a spike at/near the shock or a step-like post-shock increase (see also Kallenrode 1996; Lario et al. 2003; Dresing et al. 2016). (2) Van Nes et al. (1984) reported that in ∼75% of the shock events observed by the ISEE-3 spacecraft, the power-law spectral index of ∼35–250 keV protons was consistent with the DSA prediction. However, Ho et al. (2003, 2008) observed this consistency for fewer (∼50%) of the shock events observed by the Advanced Composition Explorer (ACE). (3) Using measurements from the Pioneer 11 spacecraft, Pesses et al. (1979, 1984) reported a field-aligned anisotropy of ∼0.6–3.6 MeV protons in the upstream away from the shock and field-perpendicular pitch-angle distributions (PADs) downstream of the shock. Moreover, using more recent measurements from the Wind spacecraft, Yang et al. (2018, 2019) reported a long-lasting, anti-sunward beam of ∼1 MeV protons both upstream and downstream of the shock.

Previous studies rarely investigated the dynamic behavior of energetic ions in the close vicinity of the shock, primarily due to the limited time (≳10 s) and energy (≳30%) resolution of in situ measurements. In our study, we take advantage of the simultaneous high time- and energy-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). We present the dynamic behavior of energetic protons, including a velocity dispersion event and an inverse velocity dispersion event, that were visible adjacent to an interplanetary shock. We also investigate the spectrum and PAD of energetic protons close to the shock. We finally discuss possible explanations and implications of these observations.

2. Data and method

Solar Orbiter was launched on 2020 February 10 into a heliocentric orbit with an eventual perihelion of 0.28 au. The EPD suite on board Solar Orbiter measures electrons and ions at energies from a few keV to several hundred MeV to address scientific questions pertaining to particle acceleration. In this paper, we use the ion measurements from one of the EPD sensors, the Electron-Proton Telescope (EPT). EPT consists of two pairs of telescopes: One pair is mounted pointing sunward and anti-sunward along the orbit-averaged nominal Parker spiral, and the other pair is mounted pointing northward and southward (for more details, see Rodríguez-Pacheco et al. 2020). Each telescope has a circular field of view (FOV) of ∼30° and provides measurements of ions from ∼50 to ∼6000 keV in 64 logarithmically spaced energy bins (∼8% in terms of energy resolution) with a cadence of one second (Wimmer-Schweingruber et al. 2021). To our knowledge, no data with this simultaneous high time- and energy-resolution were available in this energy range before. Moreover, we use the magnetic field data measured by the fluxgate vector magnetometer (MAG; Horbury et al. 2020), the solar wind proton velocity measured by the Solar Wind Analyser (SWA; Owen et al. 2020), and the solar wind electron density measured by the Radio and Plasma Waves (RPW; Maksimovic et al. 2020) instrument.

In order to account for the Compton-Getting effect (Compton & Getting 1935; Gleeson & Axford 1968), we reconstructed the PAD of energetic ions in the solar wind frame (SWF), as is common practice (e.g., Gosling et al. 1981; Yang et al. 2020). The reason is that the solar wind plasma and interplanetary magnetic field (IMF) become stationary in the SWF, and thus the motional electric field vanishes in the SWF. We assumed that the ions measured by EPT near the interplanetary shock are predominantly protons, as is common practice in the literature (e.g., Gosling et al. 1981; Tsurutani & Lin 1985; Gloeckler et al. 2005; Lario et al. 2019). Then, we reconstructed the proton PAD in the SWF using the same method as Yang et al. (2020, 2023). The reconstructed PAD covers most of the 0–180° pitch angles (PA) by the four observational directions of the EPT, depending on the magnetic field configuration. Moreover, the uncertainty on the reconstructed PAD was estimated from the statistical errors of EPT measurements via error propagation.

3. Observations

Solar Orbiter encountered an interplanetary shock with a significant acceleration of energetic protons at ∼14:04:26 on 2021 November 3 at a heliocentric distance of 0.84 au. Yang et al. (2023) fitted this shock with the nonlinear least-squares fitting technique (Viñas & Scudder 1986; Szabo 1994; Koval & Szabo 2008) and obtained a shock normal almost aligned with the Sun-spacecraft line, an angle between the shock normal and the upstream magnetic field, θBn, of 66° ±12°, a shock speed, Vsh, of 664 ± 14 km s−1 in the spacecraft frame, a magnetosonic Mach number of 2.8 ± 0.3, and a proton density compression ratio of 1.6 ± 0.2. However, Dimmock et al. (2023) fitted this shock with the mixed-mode coplanarity method (Paschmann & Daly 1998) and obtained a θBn of 37°. As pointed out by Dimmock et al. (2023), the fitted shock geometry can change by up to ∼30° when different methods are used. A more detailed discussion of the shock parameters can be found in Appendix A. In this paper, we took both fitted θBn into account to interpret our observations. Furthermore, we determined the solar wind electron density measured by RPW and obtained an electron density compression ratio of 1.9 ± 0.2.

Figure 1 shows an overview plot in the one-hour interval surrounding the shock, Fig. 2 shows a zoom of the overview plot to the 5-min vicinity of the shock, and Fig. 3 shows a further zoom of the plot to the 90-s vicinity of the shock. Given the anti-sunward motion of the shock, the sunward telescope captured the particles moving away from the shock in its upstream region and the particles moving toward it in its downstream region. Conversely, the anti-sunward telescope captured the particles traveling in the opposite direction. Due to the direction of IMF near the shock (Fig. 1i), the measurements from four telescopes shown in the sequence of Fig. 1a–d correspond to particles traveling at a PA from 180° to 0°, until Solar Orbiter encountered a current sheet at ∼14:15. We note that the observations after the current sheet was crossed will be investigated in a separate paper.

thumbnail Fig. 1.

Overview plot in the one-hour vicinity of the shock on 2021 November 3. (a)–(d) Differential flux vs. time of ∼50 − 6000 keV protons measured by the EPT telescopes pointing in the anti-sunward (a), southward (b), northward (c), and sunward (d) directions. The 64 energy bins arranged in the spacecraft frame are grouped into 13 logarithmically spaced bins. Their central energies are labeled in the right corner. (e)–(g) PAD spectrogram of protons in energy ranges of 52–84 keV (e), 195–297 keV (f), and 1697–2588 keV (g) in the SWF. The PAD is normalized by the flux averaged over all PAs for each time bin. Isotropic distributions show values around one (green) in all PA directions, and the beamed distributions exhibit higher values (red) in the beaming direction and lower values (blue) in the other directions. (h) Magnitude |B| of the IMF. (i) Elevation angle θB (black) and azimuthal angle ϕB (blue) of the IMF. (j) Solar wind proton bulk speed |Vsw|. The IMF and solar wind speed are measured in the spacecraft frame. The solid brown line marks the shock arrival. The dashed lines bound several time intervals with labels at the top, which are analyzed in Fig. 5.

thumbnail Fig. 2.

Overview plot in the 5-min vicinity of the shock on 2021 November 3. Panels (a)–(c), (e), and (g)–(h) show the same as Fig. 1, but on a shorter timescale. Panels (d) and (f) show the spectrogram of dynamic energy spectra measured by the northward (d) and sunward (f) telescopes in the spacecraft frame. The color scale represents the intensities of the differential flux multiplied by the energy squared. The dashed black line in panel (d) indicates the velocity dispersion feature, and the dashed black line in panel (f) indicates the inverse-velocity dispersion feature. (i): PA coverage of the four EPT telescopes. (j): X-component of the IMF Bx (black) and X-component of the solar wind velocity Vx (blue) in the spacecraft frame. (k): Angle between the IMF and the shock normal, local θBn, and the angle between the IMF and the radial direction, θBr. These two angles are equal to each other because the shock normal almost aligns with the radial direction. The apparent magnetic kinks or switchbacks are plotted in red, and the horizontal dotted line indicates the average angle in the ambient solar wind plasma. The vertical solid brown line marks the shock arrival. The vertical dashed lines bound an upstream and a downstream interval with labels at the top, which are analyzed in Fig. 5.

3.1. Observations by the sunward telescope

As shown in Fig. 1d, the measurements by the sunward telescope reveal that at energies of ∼50–300 keV, the proton fluxes increase ∼15 min before the shock and then decrease after the shock passage, which is similar to the temporal flux profile of ∼20–60 keV suprathermal protons near the shock (Yang et al. 2023). At higher energies of ∼300–6000 keV, the proton fluxes appear to be generally constant upstream of the shock and increase slightly after the shock passage. This temporal flux profile suggests that the ∼300–6000 keV protons constitute a different population from the ∼50–300 keV protons. However, the zoomed-in plot in panels (e) and (f) of Fig. 2 present more dynamic features on a shorter timescale. Specifically, the ∼50–200 keV proton fluxes peak between ∼10 and ∼20 s before the shock with an inverse-velocity dispersion feature, that is, the fluxes of the slower protons peak earlier than the faster protons (indicated by the dashed black line in panel (f)). This feature is more clearly visible in the still more deeply zoomed-in plot in panels (e) and (f) of Fig. 3. Panels (j) and (k) of Fig. 3 show that the inverse-velocity dispersion feature is accompanied by a magnetic kink or switchback near 14:04:00 (plotted in red), which is characterized by a reversal in Bx, an increase in Vx, and an angle deflection ΔθBr of > 25° (Bale et al. 2019; de Wit et al. 2020; Shi et al. 2022; Hou et al.2023). As a result of the Bx reversal, the local θBn reaches or surpasses 90° (Fig. 3k). Furthermore, panels (e) and (f) of Fig. 3 show that protons at different energies behave differently at the shock crossing: ∼50–300 keV proton fluxes show a local peak right at the shock, consistent with previously reported shock-spike events (e.g., Tsurutani & Lin 1985) and the shock-spike flux profile predicted by SDA (Decker 1983), ∼300–1000 keV proton fluxes remain nearly constant at the shock crossing, and ∼1000–6000 keV proton fluxes show a local minimum at the shock.

thumbnail Fig. 3.

Overview plot in the 90-s vicinity of the shock on 2021 November 3 in the same format as Fig. 2.

3.2. Observations by the northward telescope

The northward telescope measured a similar proton flux profile (Fig. 1c) as the sunward telescope (Fig. 1d) because the two telescopes cover similar PAs near the shock, with a difference smaller than 30°. However, in the northward telescope, the ∼1000–4000 keV protons exhibit a rapid-rise, rapid-decay temporal flux profile with a clear velocity dispersion ∼2 min before the shock (Fig. 1c), similar to the well-established impulsive solar energetic particle (SEP) events (e.g., Wang et al. 2006, 2023a,b; Wimmer-Schweingruber et al. 2023). This velocity dispersion event is clearly evident as a yellow trace along the dashed black line in Fig. 2d. We note that this velocity dispersion event is accompanied by a magnetic kink or switchback near 14:02:45 (plotted in red in Fig. 2j and k), and no such clear velocity dispersion feature is observed with the sunward telescope. We examine this velocity dispersion event in depth in Sect. 3.5. On the other hand, the northward telescope does not observe the inverse-velocity dispersion event of ∼50–200 keV protons, as the sunward telescope does, even though they cover the same PAs during the event (Fig. 2i).

3.3. Observations by the anti-sunward and southward telescopes

The anti-sunward and southward telescopes observed an abrupt increase in the ∼50–200 keV proton fluxes at ∼14:08 downstream of the shock (marked by the left dashed magenta line in Fig. 1a–b), coinciding with an abrupt change in the magnitude of the IMF (Fig. 1h). This may suggest that Solar Orbiter crossed into another magnetic flux tube, and the more intense proton flux may originate from a different part of the shock in which the proton acceleration is stronger.

3.4. Proton pitch-angle distributions

The PADs of ∼50–300 keV protons (Fig. 1e–f) exhibit a clear anti-sunward beam that escapes from the shock in the ≳30 min upstream of the shock and are distributed nearly isotropically in the ∼3 min downstream of the shock, consistent with previous observations (e.g., Pesses et al. 1979, 1984; Lario et al. 2022). Downstream of the shock at ∼14:08–14:12, the PAD of ∼50–200 keV protons shows a sunward beam moving away from the shock (Fig. 1e and a), which could be the protons that escape from the shock to the downstream region. At higher energies of ∼300–6000 keV, the proton PADs exhibit a long-lasting, anti-sunward beam that travels across the shock from downstream to upstream (Fig. 1g), similar to the observation reported by Yang et al. (2018, 2019). This proton beam could originate from a source on the Sun.

Panels (g) and (h) of Fig. 3 show the proton PADs zoomed-in to the close vicinity of the shock. At the shock arrival, the ∼50–300 keV proton PADs show a field-aligned beam in the direction parallel to the IMF, which differs from the field-perpendicular anisotropy predicted by SDA (Decker 1983, 1988). However, in an interval of ∼20 s shortly after the shock (indicated by D1), the ∼50–100 keV proton PADs show an anisotropy near 90° (Fig. 3g), which is consistent with the observation of ∼20–60 keV suprathermal protons (Yang et al. 2020, 2023) and the SDA prediction.

3.5. Velocity dispersion analysis

Panels (a) to (g) of Fig. 4 show the temporal flux profile of ∼1800–3000 keV protons measured by the northward telescope during the velocity dispersion event. The small but significant peaks in the proton fluxes show a clear velocity dispersion feature. The event lasted for ≲30 s, corresponding to a spatial scale of ∼14 000 km for the observed Vsw of ∼450 km s−1, similar to the gyroradius of 1000 keV protons. The short duration may indicate that the protons were impulsively accelerated in a region comparable to the proton gyroradius on the shock surface.

thumbnail Fig. 4.

Velocity dispersion analysis of the velocity dispersion event. (a)–(g): proton fluxes measured by the northward telescope during the velocity dispersion event. The horizontal bar indicates the estimated most likely range of the peak time. (h): velocity dispersion analysis of the peak time t vs. the inverse of the velocity 1/V. The dashed line represents the linear regression to t= t 0 + L 0 * /V $ t=t_0+L_0^*/V $, where t0 is the peak injection time at the shock front, and the proton path length L 0 = L 0 * cosPA $ L_0=L_0^*\cos{\mathrm{PA}} $, where the PA is ∼60° during this event.

We employed the well-established velocity dispersion analysis (VDA; Wang et al. 2006, 2016, 2021, 2023a), which is widely used to analyze SEP events (e.g., Vainio et al. 2013; Laitinen & Dalla 2019; Xu et al. 2020; Kollhoff et al. 2021), to analyze the proton peak times in our event. The peak time is expected to be linearly related with the inverse of the velocity, t= t 0 + L 0 * /V $ t=t_0+L_0^*/V $. In this equation, t0 is the peak release time on the shock surface, and L 0 * = L 0 / cosPA $ L_0^*=L_0/\cos{\mathrm{PA}} $, where L0 is the path length traveled by the protons. Considering the errors in both variables in the linear regression and a PA of ∼60° during the event, we obtain t0 = 14 : 01 : 12 ± 40 s and L0 = 7.6 ± 5.4 × 105 km (Fig. 4h).

These parameters can be tested independently through the shock motion and the magnetic field configuration, and this validates the above scenario. We assumed a straight upstream magnetic field line and then determined the distance along the magnetic field between the shock front and Solar Orbiter at t0, D0 = Vsh(tsh − t0)/cos θBn, where tsh is the shock arrival time. For θBn = 66°, D0 is 3.1 ± 1.5 × 105 km and agrees with L0; for θBn = 37°, D0 is 1.6 ± 0.7 × 105 km, which is on the same order of magnitude as L0. These agreements could support the above scenario of impulsive acceleration in a confined source region on the shock front. We note that a curved upstream magnetic field line would yield a larger D0 that aligns better with L0.

3.6. Proton spectra

Based on the temporal flux profile and PAD of protons, we selected several time intervals labeled U3, U2, and D2 in Fig. 1 and U1 and D1 in Fig. 2. Panels (a) and (b) of Fig. 5 present the omnidirectional averaged spectra for these time intervals. The upstream and downstream spectra both exhibit two proton populations with a transition at ∼7000 km s−1 (∼300 keV). At velocities below the transition, the upstream proton fluxes increase and the spectrum steepens as Solar Orbiter approaches the shock, while they remain relatively constant at velocities above the transition (Fig. 5a). This is consistent with the distinct temporal flux profiles at energies below and above ∼300 keV shown in Fig. 1. Considering the uncertainties in phase-space density and velocity (Liu et al. 2020b), the proton spectrum below the transition velocity fits a power law, with a power-law index of 7.0 ± 0.1 in U1 and a lower index of 6.0 ± 0.3 in D1. These spectral indices are consistent with the spectral indices of the ∼20–60 keV suprathermal protons near the shock (Yang et al. 2023). Moreover, the downstream spectral index is consistent with the DSA prediction of 6.3 ± 1.3 derived from the electron density compression ratio and are also close to the DSA prediction of 7.8 ± 1.5 derived from the proton density compression ratio. Panel (c) of Fig. 5 shows that the proton spectrum in the inverse-velocity dispersion event appears to have a similar shape but higher intensities than the average spectrum in the 12-s interval centered at the shock. Moreover, the spectrum of the peak fluxes in the velocity dispersion event appears to be steeper than the spectrum at the shock. This is similar to the previous observation that proton spectra soften after they are accelerated by the shock (Ho et al. 2003, 2008), and it is also consistent with the SDA simulation (Decker 1983).

thumbnail Fig. 5.

Omnidirectional averaged phase-space density vs. proton velocity in the SWF for different time intervals. Three upstream intervals (a) and two downstream intervals (b) are labeled in Figs. 1 and 2. In panel (c), “Shock” indicates the average spectrum in the 12-s interval centered at the shock front, “Inverse event (sun)” indicates the average spectrum in the inverse-velocity dispersion event (same interval as U1) measured by the sunward telescope, and “Event (north)” indicates the spectrum of the peak fluxes in the velocity dispersion event measured by the northward telescope. The dashed lines indicate the slope of the power-law fit to the spectra in corresponding colors. The uncertainties are plotted as vertical or horizontal bars (but smaller than the symbols).

4. Summary and discussion

We investigated the in situ acceleration of energetic protons at the shock on 2021 November 3 with unprecedented high-resolution measurements by EPD/EPT on board Solar Orbiter. We find that the ∼1000–4000 keV protons exhibit a rapid-rise, rapid-decay temporal flux profile with a clear velocity dispersion ∼2 min before the shock, similar to impulsive SEP events. The proton path length based on VDA of this event is consistent with the length derived from the shock motion and IMF configuration. Moreover, we find that ∼50–200 keV proton fluxes peak between ∼10 and ∼20 s before the shock with an inverse-velocity dispersion. The velocity dispersion event and the inverse velocity dispersion event are both accompanied by magnetic kinks or switchbacks. In addition, two distinct proton populations appear near the shock. The first population at energies below ∼300 keV is characterized by a power-law spectrum with an index of ∼6–7 and a flux profile that increases before and decreases after the shock. This proton population could be an extension of the ∼20–60 keV suprathermal protons and is efficiently accelerated by the shock. The other population at energies above ∼300 keV shows a long-lasting, anti-sunward-beamed PAD across the shock and a flux profile that remains relatively constant before and increases slightly after the shock, suggesting a nonshock origin.

In the velocity dispersion event, the rapid-rise, rapid-decay flux profile lasts for ≲30 s, corresponding to a spatial scale on the order of the ∼1000 keV proton gyroradius. The short duration may suggest that protons are impulsively accelerated in a region comparable to the proton gyroradius on the shock surface. This scenario gains support from the agreement between the proton path length given by VDA and the IMF length derived from the shock motion and IMF configuration. Moreover, the acceleration of protons up to ∼4000 keV in ≲30 s suggests that the shock acceleration can be impulsive and remarkably efficient, in direct contrast to the previous expectation that a few hours are required to accelerate protons to ∼200 keV at strong interplanetary shocks (Giacalone 2012). The protons in this event also show a lower energy limit of ∼1000 keV. Since the event is observed closely before the shock, this lower energy cutoff likely reflects the acceleration process in the source region rather than a transport effect. One possibility is that this acceleration is only efficient for protons with a sufficiently large gyroradius.

Based on the magnetic kink or switchback that accompanies the velocity dispersion event (Fig. 2j), we propose that the interaction between a magnetic kink or switchback and the shock may give rise to the impulsive and efficient acceleration of the protons that form the velocity dispersion event. This hypothesis is particularly compelling when we consider the S-shape of the magnetic kink or switchback (Tenerani et al. 2020; Zank et al. 2020), which may effectively confine particles close to the shock front and thereby induce significant acceleration. In addition, a magnetic kink or switchback would lead to a large θBn and thereby to a more efficient acceleration, as predicted by SDA (Decker 1988; Matsukiyo et al. 2011; Gargaté & Spitkovsky 2011). Other temporal or spatial structures on the shock front, such as the waves or ripples propagating on the shock front (e.g., Johlander et al. 2016, 2018), may also contribute to the impulsive and efficient acceleration. Furthermore, we assume that the proton spectrum at the shock could represent the spectrum of the seed particles for the velocity dispersion event. In this case, the observation that the peak spectrum in the event is steeper than the spectrum at the shock (Fig. 4c) is consistent with SDA (Decker 1983; Ho et al. 2003). We note that the velocity dispersion event is not observed in the sunward telescope, probably due to the high background caused by the long-lasting proton beam in its FOV. It is worthwhile to note that this impulsive and efficient acceleration by coronal shocks may contribute to the acceleration of impulsive SEP events.

We observe an inverse-velocity dispersion event of ∼50–200 keV protons almost immediately before the shock. This event has a short duration of ≲15 s, suggesting that its source is confined to a region comparable to the ∼200 keV proton gyroradius. This inverse event is also accompanied by a magnetic kink or switchback (Fig. 2j). The interaction between a magnetic kink or switchback and the source region could be a possible acceleration mechanism for this event. Furthermore, the peak fluxes in this inverse event show a systematic delay from ∼50 to ∼200 keV, with a delay of ∼5 s between the lowest and highest energies. One possibility is that this delay is due to the time needed to accelerate protons from low to high energies in the source region. Another possibility is that these protons originate from the parts of the shock front with an increasing θBn and therefore lead to an increase in the accelerated energy, which was previously proposed by Lee et al. (2017). However, the local θBn during the inverse-velocity event does not increase monotonically (Fig. 2k).

The energetic proton measurements near the shock present two distinct proton populations. The presence of multiple populations is consistent with previous observations at the Earth’s bow shock (Kennel et al. 1985) and interplanetary shocks (Cohen et al. 2019; Hanson et al. 2020). At energies below ∼300 keV, proton fluxes increase before the shock with an anti-shockward beamed PAD, and they decrease after the shock passage. These protons exhibit a power-law spectrum with an index of ∼6–7. These observations are similar to those of ∼20–60 keV suprathermal protons (Yang et al. 2023), suggesting that protons at energies from ∼20 through ∼300 keV are parts of the same population. Moreover, these observations suggest that ∼20–300 keV protons are continually and efficiently accelerated by the shock. However, the observations of the inverse-velocity dispersion event shortly before the shock and the escaping proton beam ∼3 min after the shock suggest that the efficiency of this acceleration may vary temporally or spatially, for instance, due to possible interaction with the magnetic kink or switchback or due to the varying θBn. The observed spectral indices of ∼60–300 keV protons are consistent with the spectral index predicted by DSA based on the electron density compression ratio. On the other hand, the observations of the escaping beam upstream of the shock, the local peak fluxes at the shock passage (Fig. 3e), and the angular anisotropy near ∼90° closely downstream of the shock (Fig. 3g) are consistent with previous observations (Yang et al. 2020, 2023; Fraschetti & Giacalone 2020) and the SDA theory (Hudson 1965; Decker 1983, 1988). We note that the observation of the field-aligned anisotropy right at the shock is inconsistent with both SDA and DSA.

At energies above ∼300 keV, the proton PAD shows a long-lasting, anti-sunward beam across the shock, similar to the previous observations of ∼1000 keV protons at interplanetary shocks (Yang et al. 2018, 2019). A long-lasting, anti-sunward proton beam like this may originate from a source on the Sun. Since this proton beam travels across the shock from downstream to upstream, the relatively constant flux profile upstream and the higher fluxes downstream than upstream both suggest that protons at energies above ∼300 keV are not effectively accelerated by the shock, except for the surprisingly efficient acceleration in the velocity dispersion event.

Our observations suggest that the shock acceleration of energetic protons is highly dynamic due to temporal and/or spatial variations at/along the shock front. Furthermore, the observation of the velocity dispersion event may suggest that shock acceleration can be impulsive and efficient, possibly due to an interaction between the shock and magnetic kinks or switchbacks. This raises the possibility that an impulsive and efficient acceleration by coronal shocks could contribute to the acceleration of impulsive SEP events. Future simulation studies of the interaction between magnetic kinks or switchbacks and the shock, for example, by combining magnetohydrodynamic turbulence and hybrid models (e.g., Trotta et al. 2023b), may help advance our knowledge of the particle acceleration at interplanetary collisionless shocks.

Acknowledgments

This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – HE 9270/1-1. EPT 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 42225404, 42127803, and 42150105. Solar Orbiter post-launch work at JHU/APL is supported by NASA contract 80MSFC19F0002.

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Appendix A: Discussion of the shock parameters

In this appendix, we first compare the fitted shock geometries given by Yang et al. (2023) and Dimmock et al. (2023). We then test the fitted shock parameters with the Rankine-Hugoniot (RH) solver1 (Russell et al. 2016). We then compare the obtained Alfvén Mach numbers with the number derived using the proxy devised by Gedalin et al. (2021).

A.1. Comparison of fitted shock geometries

Dimmock et al. (2023) used the mixed-mode coplanarity method (Paschmann & Daly 1998) and obtained a θBn of 37°. However, Yang et al. (2023) used the nonlinear least-squared fitting technique (Viñas & Scudder 1986; Szabo 1994; Koval &Szabo 2008) to fit the RH equations and obtained a θBn of 66° ±12°. The differences in shock geometry are mainly due to the different methods. Dimmock et al. (2023) pointed this out as well: The fitted shock geometry can change by up to ∼30° for different methods. Therefore, it is hard to conclude whether the shock on 2021 November 3 is a quasi-perpendicular or a quasi-parallel shock, but this shock should be a moderate oblique shock with a θBn between 37° and 66°. In this paper, we took the two fitted θBn into account to interpret our observations. Furthermore, under a moderate oblique shock geometry, SDA and DSA could both be candidate acceleration mechanisms.

A.2. Fitted shock parameters

First we tested Yang’s fitted shock parameters with the RH solver (Russell et al. 2016). The fitted θBn, Alfvén Mach number MA, the magnetic compression ratio rB, and the proton density compression ratio r are listed in Table A.1. The ratio of the thermal pressure to the magnetic pressure β is calculated to be 0.45 upstream of the shock. With a default adiabatic index γ of 5 3 $ \frac{5}{3} $, the RH solver gives an rB of 2.8 and an r of 3.0. The rB given by the RH solver is consistent with the fitted rB, but the r given by the RH solver is larger than the fitted r. Then we tested Dimmock’s fitted shock parameters (listed in Table A.1) with the RH solver. The RH solver gives an rB of 2.5 and an r of 3.6. Similarly, the rB given by the RH solver is consistent with Dimmock’s rB, but the r given by the RH solver is also larger than Dimmock’s r.

Table A.1.

Fitted shock parameters

A.3. Estimation of the Alfvén Mach number

We estimated the Alfvén Mach number MA using the proxy devised by Gedalin et al. (2021). For an rB of 2.6, MA(proxy) is estimated to be 2.9 (see also Appendix B in Dimmock et al. 2023), consistent with Yang’s fitted MA of 3.2±0.6, but inconsistent with Dimmock’s fitted MA of 5.1.

All Tables

Table A.1.

Fitted shock parameters

In the text

All Figures

thumbnail Fig. 1.

Overview plot in the one-hour vicinity of the shock on 2021 November 3. (a)–(d) Differential flux vs. time of ∼50 − 6000 keV protons measured by the EPT telescopes pointing in the anti-sunward (a), southward (b), northward (c), and sunward (d) directions. The 64 energy bins arranged in the spacecraft frame are grouped into 13 logarithmically spaced bins. Their central energies are labeled in the right corner. (e)–(g) PAD spectrogram of protons in energy ranges of 52–84 keV (e), 195–297 keV (f), and 1697–2588 keV (g) in the SWF. The PAD is normalized by the flux averaged over all PAs for each time bin. Isotropic distributions show values around one (green) in all PA directions, and the beamed distributions exhibit higher values (red) in the beaming direction and lower values (blue) in the other directions. (h) Magnitude |B| of the IMF. (i) Elevation angle θB (black) and azimuthal angle ϕB (blue) of the IMF. (j) Solar wind proton bulk speed |Vsw|. The IMF and solar wind speed are measured in the spacecraft frame. The solid brown line marks the shock arrival. The dashed lines bound several time intervals with labels at the top, which are analyzed in Fig. 5.
In the text
thumbnail Fig. 2.

Overview plot in the 5-min vicinity of the shock on 2021 November 3. Panels (a)–(c), (e), and (g)–(h) show the same as Fig. 1, but on a shorter timescale. Panels (d) and (f) show the spectrogram of dynamic energy spectra measured by the northward (d) and sunward (f) telescopes in the spacecraft frame. The color scale represents the intensities of the differential flux multiplied by the energy squared. The dashed black line in panel (d) indicates the velocity dispersion feature, and the dashed black line in panel (f) indicates the inverse-velocity dispersion feature. (i): PA coverage of the four EPT telescopes. (j): X-component of the IMF Bx (black) and X-component of the solar wind velocity Vx (blue) in the spacecraft frame. (k): Angle between the IMF and the shock normal, local θBn, and the angle between the IMF and the radial direction, θBr. These two angles are equal to each other because the shock normal almost aligns with the radial direction. The apparent magnetic kinks or switchbacks are plotted in red, and the horizontal dotted line indicates the average angle in the ambient solar wind plasma. The vertical solid brown line marks the shock arrival. The vertical dashed lines bound an upstream and a downstream interval with labels at the top, which are analyzed in Fig. 5.
In the text
thumbnail Fig. 3.

Overview plot in the 90-s vicinity of the shock on 2021 November 3 in the same format as Fig. 2.
In the text
thumbnail Fig. 4.

Velocity dispersion analysis of the velocity dispersion event. (a)–(g): proton fluxes measured by the northward telescope during the velocity dispersion event. The horizontal bar indicates the estimated most likely range of the peak time. (h): velocity dispersion analysis of the peak time t vs. the inverse of the velocity 1/V. The dashed line represents the linear regression to t= t 0 + L 0 * /V $ t=t_0+L_0^*/V $, where t0 is the peak injection time at the shock front, and the proton path length L 0 = L 0 * cosPA $ L_0=L_0^*\cos{\mathrm{PA}} $, where the PA is ∼60° during this event.
In the text
thumbnail Fig. 5.

Omnidirectional averaged phase-space density vs. proton velocity in the SWF for different time intervals. Three upstream intervals (a) and two downstream intervals (b) are labeled in Figs. 1 and 2. In panel (c), “Shock” indicates the average spectrum in the 12-s interval centered at the shock front, “Inverse event (sun)” indicates the average spectrum in the inverse-velocity dispersion event (same interval as U1) measured by the sunward telescope, and “Event (north)” indicates the spectrum of the peak fluxes in the velocity dispersion event measured by the northward telescope. The dashed lines indicate the slope of the power-law fit to the spectra in corresponding colors. The uncertainties are plotted as vertical or horizontal bars (but smaller than the symbols).
In the text

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