Heavy-ion Acceleration in ³He-rich Solar Energetic Particle Events: New Insights from Solar Orbiter

The energetic particle observations reported here are from the Suprathermal Ion Spectrograph (SIS), which is part of the Solar Orbiter Energetic Particle Detector suite (Rodríguez-Pacheco et al. 2020; Wimmer-Schweingruber et al. 2021). SIS is a time-of-flight mass spectrometer that measures ion composition from H through UH nuclei over the energy range ∼0.1–10 MeV nucleon⁻¹. SIS has two identical telescopes, one facing sunward (Telescope A) and the other antisunward (Telescope B). In this paper the sunward telescope was used in order to reduce propagation effects. We also consulted data from the Solar Orbiter Radio and Plasma Wave investigation (Maksimovic et al. 2020), X-ray data from the Solar Orbiter Spectrometer/Telescope for Imaging X-rays (Krucker et al. 2020), EUV data from the Solar Orbiter Extreme Ultraviolet Imager (Rochus et al. 2020), and the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA; Lemen et al. 2012). Solar Orbiter's magnetic connection to the Sun was estimated using the IP magnetic field and solar wind data when available, and a Potential Field Source Surface model of the coronal field (Rouillard et al. 2020).

Table 1 shows properties of the two events discussed here. In both cases Solar Orbiter was magnetically connected to the Sun on the earthward hemisphere, with separation angles from Earth to the west of the Earth–Sun line as shown. The active region (AR) associations are uncertain since the remote sensing data showed no clear signatures, but rather low levels of activity with some small jets located a few degrees from the ARs. Radio data showed some type III activity but no clean events as might be expected for two particle events that were very clearly observed. Particle detectors on ACE and STEREO had magnetic connection somewhat close to the events, but saw nothing for Event 1 (2022 November 9), and only a weak event at ACE for Event 2 (2023 April 8), roughly a factor of 10 below the Solar Orbiter instrument intensities as might be expected given the factor of ∼3 larger radial distance of ACE. Lacking other signatures, ion injection times shown in the table were obtained from a "time shift analysis" in which ion data were shifted earlier according to particle speed using trial magnetic field lengths until ions over the whole energy range all lined up reasonably to a single injection time (e.g., Kollhoff et al. 2021). The deduced field line lengths were 0.57 and 0.38 au for Events 1 and 2, respectively, while the nominal Archimedes spiral distances are 0.61 and 0.29 au for 400 km s⁻¹ solar wind. The injection time uncertainties are estimated by assuming a 10% variation in field length.

Table 1. Solar Particle Event and Solar Properties

Event Number	1	2
Event start day	2022 Nov 9	2023 Apr 8
Interval (day of year)	313.25–313.90 a	98.75–99.25
Ion injection time (UT)	6:28 ± 0:15 b	20:58 ± 0:08 b
3He fluence c (particles/(cm2 sr MeV nuc−1))	7,200 ± 600	89,400 ± 2100
Fe fluence c (particles/(cm2 sr MeV nuc−1))	19,200 ± 950	1,720 ± 340 d
3He/4He c	1.35 ± 0.27	5.5 ± 0.3
Fe/O c	2.66 ± 0.25	2.0 ± 0.7 d
Si/O c	0.40 ± 0.06	2.69 ± 0.64 d
Si/S c	1.32 ± 0.24	1.30 ± 0.30 d
(mass > 100 amu)/Fe × 103 (100–900 keV nucleon−1)	3.2 ± 0.7	<2.7 e
Solar Orbiter radial distance (au)	0.59	0.29
Solar Orbiter separation angle with Earth	237	483
Nearby active regions	13140, 13141	13270
Active region location on day of event	N26E03, N14E13	S24W73
Magnetically connected Solar Orbiter?	Y if slow SW	Y
Electron event injection	6:00 f	...
Jets	weak or none	weak or none
Type III burst	Y (<1 MHz)	Y (weak)

Notes.

^a Time intervals adjusted for velocity dispersion as described by Mason et al. (2000). ^b Injection time uncertainty based on ∼10% field line meandering uncertainty and 350 keV nucleon⁻¹ ion flight time. ^c Energy interval: 320–452 keV nucleon⁻¹. ^d Ratio not available at higher energy; result is value from 226 to 320 keV nucleon⁻¹. ^e 1 count upper limit. ^f Dispersionless onset.

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Figure 1 shows SIS observations for 2022 November 9. The top panel shows intensities of H, ³He, ⁴He, O, and Fe from the sunward-facing telescope. Both H and ⁴He were elevated due to prior activity, and their intensities rose only a factor of ∼2. ³He, Fe, and O rose over 2 orders of magnitude over background, with Fe exceeding the ⁴He intensity by a factor of ∼2, a very unusual occurrence. The middle panel shows mass tracks with clear ³He signature along with heavy ions. The bottom panel spectrogram shows 1/ion speed versus time, with clear velocity dispersion. The more intense portion of the 1/ion speed spectrogram extrapolates to the 06:28 UT injection time in Table 1, but it can be seen that there appears to be a smaller injection preceding this with approximate injection time of 05:31 UT. For masses above 50 amu, the ratio of events from the sunward to antisunward telescopes was >20:1.

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The high Fe abundance in the 2022 November 9 event was accompanied by a large number of UH ions shown in Figure 2 (top panel), where filled red circles show the SIS mass histogram above 100 keV nucleon⁻¹. Above 100 amu where there are only single counts, the SIS data have been smoothed with a 20-bin running average. Although individual mass peaks are not resolved, the broad peaks in the SIS data for 78–100 and 125–150 amu are similar to features seen in solar system abundances (Anders & Grevesse 1989). The thin blue line in the panel is the mass histogram from the ACE survey (Mason et al. 2004), normalized to the Fe peak. The SIS and ACE histograms are similar but relative to Fe the SIS abundances are ∼5 times higher than ACE. Although the ACE counting statistics are ∼10 times higher than for SIS, they were summed over 295.7 days when Fe/O was elevated and UH enhancement could be expected (for details see Mason et al. 2004), whereas the SIS data were summed over roughly 12 hr. The bottom panel of Figure 2 repeats the 1/ion speed arrival distribution from Figure 1, overplotted with filled red circles for each ion of mass >80 amu. The similarity of the arrival times is consistent with the UH nuclei being accelerated, released, and propagated simultaneously with the 10–70 amu heavy ions that make up the spectrogram, and therefore were likely accelerated in the same event. Such a correspondence between UH nuclei and heavy ions has not been seen before since prior observations at 1 au registered only single or very small numbers of counts for each accumulation period.

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SIS observations for the event starting 2023 April 8 are shown in Figure 3. Solar Orbiter was close to perihelion and the prior background was extremely low. The intensity increases associated with the event were roughly 2 orders of magnitude. The striking similarity of the time–intensity profiles indicates that the species were all from a common event. Nevertheless, this is a very small event: the peak Fe intensity is roughly a factor of 100 lower than the 2022 November 9 event. The middle panel mass tracks show relatively high counts in the Si–S region. The middle panel energy threshold is 0.2 MeV nucleon⁻¹, lower than usual since setting the threshold higher leaves the panel largely empty of nuclei heavier than He. The bottom panel shows the 1/ion speed arrival distribution showing clear velocity dispersion. There is a hint of a somewhat earlier very weak injection as well. There are brief "dropouts" around 03:05 UT and 04:18 UT on April 9 where magnetic connection to the source is temporarily lost (e.g., Ho et al. 2022). Above 100 keV nucleon⁻¹ and 50 amu, the ratio of the events from the sunward to antisunward telescopes was 10:1.

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Abundance enhancements in the Si–S region in the 2023 April 8 event are more easily seen in Figure 4, which shows mass histograms for both events for ion energies above 150 keV nucleon⁻¹. In order to facilitate the comparison, the y-axis scale has been adjusted so that the O peak is visually about the same height in both panels. While we emphasize the Si–S region in this paper, note also the different relative abundances for C and N in the two panels. The events with enhanced Si–S appear to be a distinct subset of all ³He-rich events. The first reported event enhanced in Si–S as shown in the figure was on 1977 October 12–13 (see Figure 9 in Mason et al. 1980), which was overlooked when a report of three such events found in 1997–2002 was published (Mason et al. 2002). More recently, a survey found 16 such events over the period 1999–2015, establishing their rare but continued appearance (Mason et al. 2016). Some ³He-rich events observed on Solar Orbiter have also been rich in Si–S (e.g., Event 5 in Bučík et al. 2023). Their small size is probably the reason they have not been reported from instruments with higher energy thresholds.

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Figure 5 shows event-averaged differential energy spectra for the two events. The left panel shows the 2022 November 9 event, which has a curved Fe spectrum of the type commonly seen in ³He-rich events, but with the very unusual situation where the Fe spectrum exceeds ⁴He. The H and ⁴He spectra were corrected by subtracting out the average ambient background before and after the event; this lowered the H intensity by a factor of ∼3.5, and the ⁴He intensity by a factor of ∼2.5. The He and heavier ion spectra do not extend beyond ∼1 MeV nucleon⁻¹, with a slope of ⁴He at the higher energies of −4.6. The right panel of Figure 5 shows the 2023 April 8 event, where the Fe and O spectra typically lie well below ⁴He, but also where the ³He spectrum exceeds the proton spectrum above 300 keV nucleon⁻¹. The higher-energy ⁴He spectral slope is −5.0. Because of the extremely low ambient intensities at the time of this event (Figure 3), these spectra are likely the best observations of energetic particles solely from a ³He-rich SEP event, and show that the mechanism accelerates H and ⁴He although apparently with low efficiency. The ULEIS instrument on ACE saw a few isolated counts from the 2023 April 8 event.

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Filled red circles in Figure 6 show the 160–226 keV nucleon⁻¹ abundances for the two events, with protons from higher energy (due to threshold). The left panel for 2022 November 9 compares closely with the ³He-rich event survey shown by the blue dashed blue line (Mason et al. 2004), except for H and ⁴He, which are >10 times lower. The Ca/O and Fe/O abundances are about a factor of 2 higher than the survey, but this is not unusual since elements further from the normalizing element tend to show larger dispersion. For example, the small blue dots at mass 56 show the individual event's Fe/O ratios in each survey, showing large variation. We conclude that for C–Fe the 2022 November 9 is a typical ³He-rich event. The right panel of Figure 6 shows the abundance pattern in the 2023 April 8 event, where the observed abundances O and above (filled red circles) are reasonably close to the survey average of 16 high Si–S events (Mason et al. 2016). The high C and N abundances lie above the survey average, but such a pattern has been seen at least once previously (e.g., Figure 2 in Mason et al. 2016). The small blue dots in the right panel at mass 56 show the individual events Fe/O ratios from the survey. Orange lines in the figure are from the model calculation discussed below.

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To preferentially heat heavy ions, Roth & Temerin (1997) assumed a wave power spectrum that covers the gyrofrequencies "between but not too close" to the H and ⁴He frequencies, where presumably the wave amplitude is damped due to the high H and ⁴He abundances. Figure 10 in their paper shows heavy ions of coronal elements available for acceleration in the range [0.28, 0.44] in units of H gyrofrequency, where the gyrofrequency of ⁴He⁺² is 0.5. In particular, the figure showed increases in Si and S whose Q/M ratio falls in range of acceleration frequencies as temperatures increase above a few MK, which motivates the calculation here.

Figure 7 shows a plot of Q/M ratios for major ions in ³He-rich flares, along with several representative UH ions. The figure shows the unique location of ³He, and a yellow band at the ⁴He gyrofrequency. The lines labeled 100 K–10 MK show average Q/M for the species at each temperature. As expected, the cyclotron frequencies for C–Fe move toward the yellow band (i.e., fully stripped) with increasing temperatures, eventually placing them in the region of the waves damped by the abundant ⁴He. So with increasing temperatures, the Q/M ratio of heated species moves to the yellow band where heating is depleted compared with heavier species whose Q/M ratios fall below the frequency damped by ⁴He. This can lead to an increase in the Fe/O ratio, but the reason is not due to the enhancement of Fe but rather the depletion of O. This is qualitatively consistent with the observed increase in Fe/O seen with increasing Fe ionization states (e.g., Klecker et al. 2007).

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Figure 8 shows Q/M values for those neutron-rich nuclei of Ne, Mg, and Si, which have abundances of at least a few percent of the main isotope. These neutron-rich nuclei have Q/M values that lie outside Q/M = 0.5, and thereby avoid depletion, as do Fe and the UH nuclei. Figure 9 explores this further with a plot of the fraction of major elements in the range C–Fe that have a Q/M ratio <0.49 as a function of temperature. The broad range of temperatures over which an element's fraction decreases is due to the distribution of multiple ionization states at each temperature: only fully ionized Q/M = 0.5 elements contribute to the decrease. At higher temperatures in the plot, the flattening of the C, Ne, Mg, and Si curves is due to their neutron-rich isotopes (assuming solar system abundances; Lodders 2003, Table 6). The plot assumes a limit of 0.49 for the damped wave region instead of the limit 0.44 in Roth & Temerin (1997) because the observed enhancements of neutron-rich ²⁵Mg and ²⁶Mg would not occur with the 0.44 limit since they would fall into the damped wave range. Qualitatively, Figure 9 shows that as temperatures increase above a few MK, O is depleted causing observed high Ne/O through Fe/O ratios. Above ∼10 MK, increasing fractions of Ne and Mg have Q/M ratios entering the damped wave region, which will result in high Si/O and S/O ratios.

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The question arises about the strength of the damping: if it was extreme, then in principle the Fe/O ratio might reach extremely high values, but observations show it is almost always less than 2, limiting the size of the damping factor for heavy ions to less than a factor of ∼10. In order to calculate an abundance pattern due to these effects, a reference population needs to be selected. Most candidates (e.g, slow solar wind, fast solar wind, coronal, low- and high-energy SEPs) are similar and we used the large SEP abundances from Desai et al. (2006) since they apply to an energy range close to the SIS observations. The main difference between this reference abundance and some others is that Fe/O ∼0.4, instead of ∼0.1. This affects the size of the damping factor by a factor of 2–3, and is not critical in the discussion below.

The orange curves in both panels of Figure 6 show the abundance of heated ions, calculated starting with the reference population along with a damped wave region of Q/M < 0.28 or Q/M > 0.49. Minor isotope values were from Lodders (2003), and ionization states obtained from Mazzotta et al. (1998), who tabulated abundances of each individual ionization state for H–Ni over the temperature range 10⁴–10⁹ K. This leaves unspecified a factor for damped waves, which was treated as a free parameter of value ∼0.1–1.0 times the undamped wave factor. Then for each temperature an abundance pattern for the elements was calculated by summing over the isotopes. For a damping factor of 1.0 (no damping) this procedure returns the reference population abundances at all temperatures. As the damping factor is decreased, for different temperatures isotopes falling into the damped region are weighted by the damping factor. For example, if the damping factor is 0.2, then at a temperature where 70% of the O falls in the damped region (about 3.5 MK; see Figure 9), the relative abundance of O would be (0.3 + 0.7*0.2) or 0.44 of the reference. For this case the Fe/O ratio would then be ∼2.3 times enhanced over the reference.

The orange line in the left panel of Figure 6 shows calculated abundances for 3.2 MK and a damping factor of 0.4. The right panel orange line fit uses a higher temperature, 10 MK, and stronger damping factor of 0.2. For O and heavier ions the calculated abundances are with some exceptions reasonably close to the observed pattern, in particular, the enhancement of Si in the right versus left panel. The relatively high abundances of C and N in the right panel lie well above the calculation. Another puzzling discrepancy is the low S value from the model seen in both panels of Figure 6, but more pronounced for the 2023 April 8 event. Since the H Q/M ratio lies outside the range considered in the model, agreement is not expected. However, ⁴He is in the considered range, and perhaps serendipitously for the S–Si–rich case in the right panel the value is not far from the model. This is not the case in the left "typical ³He-rich" panel, whose low ⁴He value in the 2022 November 9 event would imply damping factor ∼10 times smaller than the one used. However, for ⁴He there are other considerations in the eventual energization such as differing Coulomb loss rates compared to heavy ions that might be important for ⁴He but are beyond the scope of the calculation here (see the discussion in Roth & Temerin 1997). Note that at the temperatures in Figure 6, the region of low damping with Q/M < 0.28 does not play a role for ions below Fe due to their high-ionization states (see Figure 7).

Figure 10 explores other results from the model calculation, assuming a damping factor of 0.2 as in the Si–S–rich event in Figure 6. The left panel shows the Fe/O ratio versus the average ionization state of Fe plotted along with data from the 18-event survey of Möbius et al. (2000; see their Table 1 and Figure 2). The survey included both large shock-associated SEP events and ³He-rich events. Filled and open circles denote ³He-rich and gradual SEP events, respectively, which were identified by reexamining the events in their table. The solid blue line shows the model calculation for temperatures above 3 MK, with a dashed blue line showing the reference population for lower temperatures, which are presumably shock-associated events not addressed by the model.

Another feature of ³He-rich events is the surprisingly large enhancement of neutron-rich isotopes such as ²²Ne/²⁰Ne, ²⁶Mg/²⁴Mg, etc. (Dwyer et al. 2001; Leske et al. 2001, 2007; Mason et al. 1994). The right panel of Figure 10 shows the calculated ²²Ne/²⁰Ne ratio versus Fe/Mg compared with observations below ∼1 MeV nucleon⁻¹ from Dwyer et al. (2001). As in the left panel, we reexamined the individual events and classified them as ³He-rich (filled circles) or gradual (open circles). The model reasonably fits the enhanced values although the uncertainties are large. The enhancement compared to the reference population is roughly a factor of 4, about the same as the Fe/O enhancement in the same calculation. The rough equality of the ²²Ne/²⁰Ne enrichment and Fe/O enrichment has been a long-standing puzzle since the difference in Q/M ratio for the Ne isotopes is only 10%, while for Fe/O the difference is roughly 30% ([18/56]/[8/16]). Dwyer et al. (2001) discussed this issue in detail. In the model presented here the similarity in enhancements for Fe/O and, e.g., ²²Ne/²⁰Ne is expected since it is the depletion of the reference element (¹⁶O, ²⁰Ne) that causes the effect and both are depleted by the effect of the damped waves.

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Another long-standing puzzle in ³He-rich events is the lack of correlation between the ³He/⁴He ratio and the Fe/O ratio (e.g., Mason et al. 1986; Reames et al. 1994). Since the heavy-ion enrichments are a fundamental property of ³He-rich events, how could the degree of ³He enrichment be uncorrelated with the Fe/O enrichment? In the mechanism explored here the solution lies in the mechanism wherein the Fe enrichment and ³He enrichment are coming from different processes. First, the Fe/O enrichment comes from O depletion due to damping of waves corresponding to fully stripped Q/M = 0.5 ions. The ³He is not heated by these damped waves but rather by those closer to its gyrofrequency. Viewed this way, there is no reason to expect such a correlation, and its absence does not present a problem.

Although UH/O ratio will be enhanced by the mechanism discussed here, it will be no larger than the Fe/O enhancement since all Fe and UH fall below the damped wave cutoff (Figure 7) and so would participate equally. However, at the temperatures considered here most or all the Q/M values for UH nuclei are much lower than those for ⁴He–Fe, so they might be in a different regime altogether. For example, Eichler (1979, 2014) describes how the large gyroradii of UH nuclei could lead to preferential acceleration (see also Miller 1998, 2002; Miller & Reames 1996). These considerations are beyond the scope of this paper. However, we note in the context of particle motion along a magnetic field gradient the large gyroradius of UH nuclei would lead to different mirroring altitudes, which could play a role in the dynamics of the acceleration (e.g., Fitzmaurice et al. 2022).

In this model, because the UH acceleration and O depletion are in essence decoupled, it is not physically meaningful to discuss a UH/O ratio in exploring UH enhancements. Rather the UH/Fe ratio appears more meaningful since the depletion of O is removed, and the challenge for particle acceleration is with respect to Fe. Figure 11 plots the UH enhancements compared to Fe from the 2022 November 9 event, and replots the UH enhancements from Mason et al. (2004), where they were originally shown compared to oxygen. The fitted slope is the same as the earlier survey; however, the enhancements required for the UH nuclei are smaller, ranging from ∼6 (mass 78 to 100) to ∼30 (mass 180 to 220). The pattern in the figure can be reasonably fitted if the acceleration factor in our model is a power law in Q/M with the slope shown, but such an addition is without physical motivation and not addressed in the model of Roth & Temerin (1997).

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The calculation presented here explores implications of the preferential heating of species forming a seed population, and does not address other aspects such as spectral form, abundance ratios and ionization states increasing with energy, etc. We speculate that some of the energy dependences could be related to acceleration times wherein the additional time to accelerate particles to higher energies may also lead to further heating of the plasma and increased ionization states. Other types of accelerating plasma waves might serve as well as those in Roth & Temerin's (1997) model. Additionally, other mechanisms such as ion stripping may sometimes play a role (Kartavykh et al. 2020, 2008; Mason & Klecker 2018), but these mechanisms do not address the ³He enrichment, nor can they reproduce the large enrichments of neutron-rich isotopes of Ne and Mg. With these limitations in mind we suggest that the observations discussed here can provide a framework for a single mechanism operating in ³He-rich events: namely, (1) stochastic acceleration over a broad range of frequencies including ³He and heavy ions through to Fe; (2) a range of damped waves near the gyrofrequencies of abundant H and ⁴He; (3) enhancement of heavy ions depending on temperature due to the depletion of fully stripped Q/M = 0.5 species, which fall into the wave range damped by ⁴He; (4) acceleration taking place in coronal loops, which provide the required magnetic field gradient and the presence of emerging magnetic flux leading to reconnection; (5) access to IP space through coronal holes or scattered open field lines; and (6) possible additional enhancement of UH nuclei compared to Fe due to wave cascading or some other mechanism involving their large gyroradii.