Next Article in Journal
Distance to M87 as the Mode of the Modulus Distribution
Previous Article in Journal
Deciphering the Electron Spectral Hardening in AMS-02
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Review

Solar Particle Acceleration

by
Donald V. Reames
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
Astronomy 2025, 4(1), 5; https://doi.org/10.3390/astronomy4010005
Submission received: 10 January 2025 / Revised: 7 February 2025 / Accepted: 14 March 2025 / Published: 18 March 2025

Abstract

:
High-energy particles may be accelerated widely in stellar coronae; probably by the same processes we find in the Sun. Here, we have learned of two physical mechanisms that dominate the acceleration of solar energetic particles (SEPs). The highest energies and intensities are produced in “gradual” events where shock waves are driven from the Sun by fast and wide coronal mass ejections (CMEs). Smaller, but more numerous “impulsive” events with unusual particle compositions are produced during magnetic reconnection in solar jets and flares. Jets provide open magnetic field lines where SEPs can escape. Closed magnetic loops contain this energy to produce bright, hot flares; perhaps even contributing to heating the low corona in profuse nanoflares. Streaming protons amplify Alfvén waves upstream of the shocks. These waves scatter and trap SEPs and, in large events, modify the element abundances and flatten the low-energy spectra upstream. Shocks also re-accelerate the residual ions from earlier impulsive events, when available, that characteristically dominate the energetic heavy-ion abundances. The large CME-driven shock waves develop an extremely wide longitudinal span, filling much of the inner heliosphere with energetic particles.

1. Introduction

High-energy particles are likely accelerated in the coronae of most stars, but we can only study them directly near the Sun. Energetic particle radiation constitutes a recurring hazard to modern astronauts and missions in space and may have influenced the evolution of life here and on exoplanets around other stars.
Particle acceleration can only occur where the density is low enough that particles do not immediately dissipate their energy in Coulomb collisions. We have found that the most powerful physical processes for the acceleration of solar energetic particles (SEPs) involve shock waves driven out from the Sun by fast and wide coronal mass ejections (CMEs) [1,2], but regions of magnetic reconnection and turbulence in solar jets also produce electron-rich bursts of SEPs with unusual and distinctive element abundances, although at lower average energies and intensities.
Energetic particles can be accelerated in and above the corona where the plasma densities fall rapidly below about 109 atoms cm−3; they rapidly lose energy in Coulomb scattering and stop at the higher densities of the low corona and the chromosphere. The magnetic energy of reconnection can spawn energetic particles in the corona or generate heat below. In solar flares, accelerated particles trapped on closed magnetic loops soon scatter into the loss cone and plunge into the denser plasma below to produce heat, X-rays, gamma-rays, and thermal EUV emission. Particles accelerated on open field lines in solar jets, called impulsive SEPs, escape along field lines where the streaming electrons generate type III radio emissions. A signature of these impulsive SEPs is their unusual abundances, including 10,000-fold enhancements of 3He/4He and a systematic enhancement of increasingly heavy elements, continuing as high as Pb [3,4,5,6,7,8,9,10,11,12,13,14]. In contrast, fast (>500 km s−1) CMEs drive shock waves that accelerate particles in gradual SEP events [1], including widespread, intense, energetic, and long-lasting SEP events [15,16,17,18,19,20].

2. Magnetic Reconnection

Since the Sun is composed of ionized plasma, differences in forces on ions and electrons, especially in differential rotation, cause currents that generate magnetic fields. Magnetic fields begin deep in the Sun but are deformed at the tachocline, the boundary between the inner radiative zone, which rotates uniformly, and the convective zone, which rotates faster at the equator than at the poles. As the plasma swirls, magnetically active regions or sunspots are visible at the radiatively cooled photosphere [21]. When the fields become twisted and tangled, oppositely directed fields are brought together to cancel and reconnect, releasing energy. The magnetic energy that vanishes during reconnection drives all of the activity on the Sun that we see as flares, CMEs, SEPs, X-rays, gamma-rays, and radio emissions. Energy trapped in closed field configurations is emitted eventually as photons radiated from flares or can help to drive out CMEs.
Patterns of field reconnection can be complicated, but Figure 1 shows two examples of the topology that results when reconnection occurs either between open and closed lines, which allows SEPs to escape, or among completely closed lines, where they cannot. In Figure 1a, the emerging loops have opposite polarities from the overlying field lines, with the energy in islands of reconnection driving SEP acceleration in the collapsing current sheet [22,23,24], thus producing a solar jet. In Figure 1a, newly opened field lines on the right are matched by newly closed fields on the left, which capture some SEPs. These will eventually plunge into the denser corona to produce a hot solar flare. Thus, jets may always have an accompanying flare, but the SEPs we see do not come from this flaring region. This is why SEP properties were historically found to correlate poorly with associated X-ray intensities, for example [25,26].
Figure 1b shows a topology where shear in the footpoints of an arcade of loops produces reconnection where all the field lines remain closed. All accelerated particles are trapped and eventually plunge into the footpoints of the loops to produce a flare with no SEPs in space. However, the liberated flux rope shown in the figure may rise as part of a CME, which can be fast enough to form a shock wave and produce a gradual SEP event. Note that the right-most cartoon in Figure 1 is often viewed end-on, and the flux rope is shown as a completely open region (e.g., the Kopp and Pneuman model [27]). Other cartoons show it as a closed circle, disconnected from the Sun. In the likely topology, all particles accelerated in this reconnecting region plunge into the Sun to produce flaring.
Figure 1. Examples of the topology of magnetic reconnection are shown. (a) In a solar jet, the initially open field lines of one polarity (black) reconnect with newly emerging loops (blue) in the red hashed region where accelerated SEPs can escape easily; however, some of the SEPs are captured in a newly closed region on the left, where they produce a hot flare. (b) A sheared arcade of field lines can reconnect in the red hatched regions to produce a semi-detached flux rope that can rise to form a CME. Here, all SEPs are trapped on closed field lines and eventually plunge into the denser corona to produce a flare. SEPs are accelerated in collisionless plasma; flaring is produced in collisional plasma [28].
Figure 1. Examples of the topology of magnetic reconnection are shown. (a) In a solar jet, the initially open field lines of one polarity (black) reconnect with newly emerging loops (blue) in the red hashed region where accelerated SEPs can escape easily; however, some of the SEPs are captured in a newly closed region on the left, where they produce a hot flare. (b) A sheared arcade of field lines can reconnect in the red hatched regions to produce a semi-detached flux rope that can rise to form a CME. Here, all SEPs are trapped on closed field lines and eventually plunge into the denser corona to produce a flare. SEPs are accelerated in collisionless plasma; flaring is produced in collisional plasma [28].
Astronomy 04 00005 g001
Figure 1 does not cover all of the possibilities. If the reconnection region is too deep in the corona, there are no SEPs, and the magnetic energy is dissipated as heat. Modifications of the topology in Figure 1a may also produce a CME and that CME may drive a shock wave that can re-accelerate the SEPs from the reconnection region. We will consider this possibility below. Of course, jets can be more complicated than the one shown [29,30,31].

3. Impulsive Events

Impulsive events were first associated with the streaming electrons that produce type III radio bursts, being distinct from the shock-accelerated electrons producing type II bursts [32,33]. Later, some small SEP events were found to have 10,000-fold enhancements of 3He/4He > 1 [34], and these electron- and 3He-rich events were subsequently found to be the same [35,36]. It became clear that 3He enhancements were a resonance phenomenon produced by waves near the 3He gyrofrequency = p/A, where ωp is the proton gyrofrequency, and the charge-to-mass ratio Q/A = 2/3 for 3He. The wave spectrum could be damped at the gyrofrequencies of the dominant ions, H at Q/A = 1 and 4He at Q/A = 2/4, but the low abundance of plasma 3He (3He/4He ≈ 5 × 10−4) was unable to damp the resonant waves at that gyrofrequency. Many wave-modes were suggested for the selective preheating of 3He [37,38,39,40,41,42,43,44]; however, Temerin and Roth [45] suggested a more complete model with electromagnetic ion cyclotron waves being generated by the streaming electrons that could be resonantly absorbed by mirroring 3He ions to accelerate them. As acceleration increases, available 3He can become completely depleted [46], which contributes to the spectral differences between 3He and 4He [47,48,49].
Subsequent observations also showed heavy-ion enhancements up to Fe [10,50] that seemed to increase as A/Q [8]. Later observations extended this pattern across the periodic table of elements, seen up to about Pb [4,9,11,12]. This behavior was unlike the sharp resonance for 3He and was first associated with cascading waves [51,52,53] and later associated with a shock-like acceleration, as ions were scattered back and forth from the ends of the collapsing islands of magnetic reconnection [22].

4. Shock Acceleration

The dominant mechanism for producing high-energy particles is acceleration by shock waves [54] driven out from the Sun by fast, wide CMEs with speeds of ~800–3000 km s−1. When the magnetic field is quasi-parallel to the shock normal, particles can be scattered back and forth across the shock by resonant scattering against upstream and downstream waves [15,16,55,56,57]. As the particles stream away from the shock at each higher energy, they increase the scattering by amplifying the resonant waves [58,59] of wave number k with
k ≈ B/μP
where P is the magnetic rigidity, i.e., the momentum per unit charge of the particle; and μ is its pitch angle with respect to the magnetic field of vector B. On each transit of the shock, the particles gain an increment in velocity related to the plasma-wave velocity difference across the shock. The growth of self-amplified waves is an essential aspect of shock acceleration. For quasi-perpendicular regions of the shock, where the magnetic field lies nearly in the shock plane, particles are also accelerated in the Vshock × B electric field [60]. Some early authors [15] assumed μ ≈ 1, so each rigidity had its own unique resonant wave number, which was a convenient simplification.
For even greater simplicity, many authors assume that particle scattering does not vary at all with time. More generally, Bell [56,57] assumed that equilibrium was maintained between particles and resonant waves and this assumption was applied to SEP shocks by Lee [15,16]. Later, Ng and Reames [57] allowed for the ful time evolution of both particles and waves, allowing estimates of the timescale of shock acceleration.
Element abundances accelerated by shock waves tend to reflect the abundances in the corona at 2–3 solar radii [61,62,63], where the ions are first sampled. The coronal abundances differ from the abundances in the photosphere as a function of the first ionization potential (FIP) because of ion-neutral fractionation as the particles cross the chromosphere to the corona [64,65], where they all become ionized. Averaged SEP abundances can be a good measure of coronal abundances [66,67], although their FIP pattern differs from that seen in the solar wind [68,69,70,71]. SEPs are not just accelerated solar wind.
For impulsive SEP events, we were able to neglect the scattering of the ions during transport; since impulsive events have low intensities, the particles tend to propagate scatter-free [72], and they are focused by the diverging magnetic field. However, wave scattering is a basis of shock acceleration, since the particles streaming away grow waves which are resonant with higher and higher energy ions during acceleration, and these waves extend farther and farther from the shock as their intensities increase [16,57]. The wave intensity and thus the particle scattering is a strong function of space and time. For different ion species of a given velocity, the rigidity dependence of scattering tends to trap low-rigidity (low-A/Q) ions near the shock while the higher rigidity (higher A/Q) ions leak away. This power-law dependence upon A/Q was first directly observed by Breneman and Stone [73]. Thus, early in an event, Fe/O, for example, will first be observed to be enhanced, although later, when the shock approaches, Fe/O will always be depressed from its coronal value. With proper averaging, we should be able to recover the source coronal abundance. In small gradual events, the depletion of Fe/O from Fe loss by preferential leakage will be most noticeable throughout. In large gradual events, the preferential trapping of O near the shock can cause elevated Fe/O to persist for a day or so at moderate energies until the shock actually passes over the observer [7].
During the early acceleration, as the intensities of protons of a given rigidity rise at a shock, they first stream away, causing more and more resonant waves to grow. Wave scattering reduces this streaming until an equilibrium limit is reached where increasing intensities at the shock grow just enough additional waves to stop the streaming out to observers away from the shock. This has been called the “streaming limit” that causes an intensity plateau [74,75,76], or the “flat spectra”, which was rediscovered recently [77]. Figure 2a shows superposed time profiles for several large SEP events where the early proton intensities near 1 AU are bounded at just over 200 protons cm−2 sr−1 s−1 MeV−1; although, in some events, intensities rise to much higher values later, near the shock [74]. If source intensities increase, the protons streaming outward simply grow more resonant waves, so as to restrict the streaming, and therefore trapping ions near the source. Figure 2b shows the flattening of plateau H and O spectra, typical of all species, for five SEP events [76]. Figure 2c shows the importance of high intensities at ~10 MeV for flattening the intensities at energies below this [78,79,80]. Ng [81] discussed the way that the limiting proton intensities vary with radii and with plasma and shock parameters.
The streaming limit is a common feature in all large gradual SEP events with sufficiently high intensities. For stronger shocks, the flattening extends to higher energies. It is a transport-generated limit involving the equilibrium between streaming protons and resonant waves. When there is no streaming, e.g., at the shock, there is no intensity limit. Also, when intensities rise extremely rapidly, they can briefly exceed the limit, until enough waves grow to re-establish it. This situation occurred in the 20 Jan 2005 event, as shown in [80], and is well described by theories that follow the time evolution of both particles and waves [79].
The streaming limit decouples particle intensities near the shock from those farther upstream, creating an intensity-peak structure near the shock, historically called the energetic storm particle (ESP) event. Following Bell [55,56] and Lee [15,16], Vainio et al. [82] produced a model of this ESP structure in the foreshock region. As the ESP event moves away from the Sun, the average field intensity decreases and waves of a given k tend to resonate with particles of lower rigidity, allowing the highest energy particles to leak away first. However, in very large events, continued acceleration can slow this leakage.

4.1. Spatial Distributions

The spatial distributions of SEPs driven by shock acceleration can be quite extensive. The earliest particles are released at ~2 solar radii [61,62] and particles from these earliest spectra are effectively the dominant seed population for all additional acceleration. As the shock moves outward, wave turbulence tends to trap particles with the shock, but B decreases on average, so the existing waves tend to resonate with ions of lower rigidity (Equation (1)), allowing the highest rigidity ions to leak away first.
The earliest particles that escape the shock when it is near the Sun usually contain the energies of the greatest radiation hazard. Figure 2b shows the early proton spectra up to 700 MeV, and some are flat until ~50 MeV. A recent measurement near the Sun at 0.35 AU [23] also observed the flat spectra, but only below ~1 MeV. Figure 3 shows measurements by spacecraft conveniently located to show the radial evolution of the central region in a gradual SEP event. Helios 1 is well connected to the center of the shock when it is near the Sun, Helios 2 and IMP 8 when it is near 1 AU, and Voyager 2 when it is near 2 AU, as shown in Figure 3b. Proton intensities at 6–11 MeV are compared in Figure 3a and more complete energy coverage is shown in Figure 3c–e. Protons of 100–200 MeV peak early and are still visible at 1 AU, but have dissipated by 2 AU. In contrast, 20–40 MeV protons still peak at the shock near 2 AU in this event.
While the Helios–IMP8–Voyager period provided several revealing coincidences, including a case of successive strikes of field lines by both flanks of a wide shock in September 1978 [18,83], the STEREO period showed the wide distribution of SEPs and of the shock waves that produce them. The example in Figure 4 shows the intensities of the 20 MeV protons at the widely spaced spacecraft distribution shown in Figure 4b. The shock itself is seen at all three spacecraft at similar times, suggesting a nearly spherical shape.

4.2. Element Abundances and Seed Particles

The abundances of elements which are accelerated by shock waves to a given velocity or energy per nucleon tend to reflect the abundances of the seed particles initially injected into the shock. In most gradual SEP events, this is the ambient abundance of the solar corona near the active region where the shock begins, but shocks will accelerate any (and all) seed particles that are available. The question is: which will dominate?
Mason, Mazur, and Dwyer [84] first noticed that shocks could re-accelerate 3He and other impulsive ions provided by earlier impulsive SEP events. It was recognized [85,86,87,88] that quasi-perpendicular shocks might selectively prefer the pre-accelerated seed population of ions that had sufficient speed to overtake the shock from behind, i.e., residual suprathermal particles from impulsive events. It turns out that residual ions from many persistent impulsive flares can accumulate above active regions, providing a seed population in addition to the ambient corona plasma, thus complicating the abundance pattern of elements in SEP events. Reames [89] identified four processes leading to different SEP abundance patterns:
  • SEP1: “Pure” impulsive SEPs with enhanced heavy elements from reconnections in solar jets, but no fast shocks.
  • SEP2: Impulsive SEP1 ions re-accelerated as seed particles of a fast CME-driven shock from the same jet [90,91,92], dominating high Z.
  • SEP3: Enhanced abundances accelerated by a fast CME-driven shock traversing an active region with residual seed ions from many small impulsive events that will dominate high Z.
  • SEP4: Particles accelerated by a fast, wide, CME-driven shock with only ambient coronal abundances available as the dominant seed particles.
Since shock waves will accelerate any ions available, SEP2 and SEP3 events tend to reflect both types of seed particles; the heavy-ion-rich impulsive seeds dominate the high-Z SEPs, and the ambient abundances are left to dominate protons. These patterns are compared in Figure 5. The fits to the abundance enhancements vs. A/Q involve varying plasma temperatures to determine ion A/Q values from their well-determined temperature dependences [93,94]. Best-fit temperatures are shown in Figure 5b and the fit lines in Figure 5c for each of three time-intervals to the right. The events in the left panel in Figure 5c show rising enhancements vs. A/Q for shockless SEP1 impulsive SEP events, while the event in the right panel shows SEP4 falling enhancements vs. A/Q, where higher A/Q elements from the ambient coronal seeds have preferentially leaked away, and the middle panel shows an SEP2 or SEP3 event with the components of both rising and falling seed populations.
In the impulsive SEP1 events, protons either lie on the fit line, or perhaps, in theory, the increase is allowed to begin above He [22], so H and 4He would both be equally unenhanced. For SEP4 events, protons again lie on the fit line, since all ions belong to a single seed-particle population. For SEP2 and SEP3 events, proton enhancements signal the presence of two seed populations. Sequences of SEP3 events, dominated by impulsive seed ions, can come from a single active region [97]. These help to distinguish SEP3 events from smaller, isolated SEP2 events.
Very intense SEP4 events do have a rising initial A/Q dependence when only the higher Z ions can penetrate out to the observer. For these SEP4 events, the A/Q-dependence suddenly declines as the shock passes; for SEP3 events, the enhancements persist across the shock, since they are a fundamental property of the impulsive seeds, not of transport. Element abundances and their time dependences are powerful tools in the study of SEP acceleration and transport.
Using the assumption of power-law abundance enhancements to derive source plasma temperatures may seem uncertain, but Bučík et al. [98] have now directly confirmed similar temperatures of ~2.5 MK in the source jets that produce impulsive SEP events. Also, nearly all of the SEP abundance studies have used Maxwellian electron distributions to determine A/Q vs. temperature. However, using kappa distributions for the thermal electrons, Lee et al. [99] have shown that the Maxwellian distributions used to derive A/Q vs. temperature [93,94] did not produce large errors. They also suggested that since the SEP and source temperatures are similar, the SEPs must leave the acceleration region on a time scale shorter than their ionization time. After acceleration, these ions evidently pass through enough matter to strip them to an equilibrium ionization state that varies with velocity [100] and leaves QFe ≈ 20 near 1 MeV amu−1. This stripping suggests [100] that impulsive SEP events occur at about 1.5 solar radii. These ions from SEP1 events must retain their higher “stripped” charge states if they are re-accelerated by shock waves to produce SEP2 or SEP3 events, even though the shock acceleration may occur at much lower densities at 2–3 solar radii. Thus, the events with impulsive seeds have an enhanced Fe/O and charge states appropriate to their stripping energy after the SEP1 phase, but their abundance-derived temperatures and Q values are appropriate to their earlier state before and during the SEP1 phase. In contrast, the SEP4 events have ambient coronal charge states (at ~1 MK) with coronal source abundances modified only by transport.

4.3. Energetic Storm Particle (ESP) Events

The ESP structure of particles being trapped by self-amplified waves near strong shocks, forms early when the shock is near the Sun [16,82], but decreasing field with time allows the highest energies leak away as the shock travels out to 1 AU. Nevertheless, it is important to recognize that ESP events may still contain significant intensities of >100 MeV protons at 1 AU, as seen in the examples shown in Figure 6. An ESP spike at the shock can even be observed in >700 MeV protons in the 2001 November 6 ESP event (see Figure 5.1 in [2]).
Kouloumvakos et al. [101] have used the ESP model of Vainio et al. [82] as a source function at the shock to model the multi-spacecraft spatial distribution and onset timing of SEPs. They found that cross-field diffusion was completely unnecessary for their model. Finally, a shock model may have completely replaced the old shockless “flare plus perpendicular-diffusion” models that once prevailed [2]

5. Discussion

Recently, Mason et al. [102] suggested that the enhancement of Fe/O could come from the suppression of O, which resonates with waves damped by 4He at A/Q = 2; however, this fails to explain the strong continuing enhancement of heavier elements well above Fe, fairly well approximated as a power-law in A/Q and observed at all energies [9,11,12]. This power-law increase does not exclude the possibility that additional resonant wave absorption can produce selective peaks in Si and S in some small events [103], presumably near A/Q ~3.0 as the second harmonic of 3He at A/Q = 1.5. Turbulent reconnection in jets may well produce both power-law reconnection [22] and resonant [104] processes, especially in the small SEP events with steep spectra that have only been seen below ~1 MeV amu−1. Jets that produce larger impulsive SEP events with O and Fe spectra measurable out to 10 MeV amu−1 or more are likely to include CMEs that can drive shock waves to 500 km s−1 or more, re-accelerate the SEPs, and perhaps even smooth the A/Q dependence by including extensive or multiple reconnection regions that average differing characteristics. In the list of Fe-rich events at 3–10 MeV amu−1 presented by Reames et al. [9], about 40% of the events have CMEs with measured speeds above 500 km s−1; these are surely SEP2 events, and many of them are probably SEP3 events that average the extensive sources of seeds. Generally, they are fit with power-laws in A/Q determined at temperatures of 2.5–3.2 MK [6,95]. Despite the dominance of power-law dependence, resonant wave absorption processes may still contribute the occasional additional enhancements of some elements.
For gradual SEP events, we have come a long way since Gosling’s “Solar flare myth” [105,106] pointed out the dominance of CMEs and shock waves, rather than flares, in interplanetary phenomena, including SEPs. The STEREO mission has shown how shock waves, and the SEPs they accelerate, can envelope the Sun (e.g., Figure 5) [83], while gamma-ray-line measurements suggest that the particles that are accelerated and magnetically trapped in flares are 3He-rich [107,108] and Fe-rich [109], like those of the impulsive SEPs we now know to come from jets [14]. Thus, impulsive SEPs are logically connected to flares, but do not actually come from flares; they come out from jets. For gradual events, we must consider the hierarchy of seed particles, when available, and their re-acceleration by shocks.
In most large gradual events, heavy ion abundances seem to be dominated by either impulsive (SEP3) or ambient coronal (SEP4) seed ions across the whole longitudinal span of the shock [96,110]. However, one might expect to find SEP events where the shock has sampled different ions at different longitudes. Recently, Xu et al. [111] have found just such an event, where spacecraft separated by a ~60° longitude clearly saw Fe-rich material at one spacecraft and Fe-poor material at the other, over the full energy range of 0.1–10 MeV amu−1.
Resonant wave–particle interactions are an essential factor in SEP acceleration. They selectively enhance 3He in impulsive SEP events [39,45], enable the dominant acceleration as they scatter ions back and forth across a shock [15,16,57], and, as intensities increase, they produce rigidity-dependent scattering that can flatten spectra and enhance or suppress element abundances [75,76,79,112,113]. These abundances and spectra tell us about the underlying physical processes.
Parker [114] proposed the release of magnetic energy in the current sheets of many small nanoflares as a mechanism for heating the entire solar corona. If this is the case, it is easy to imagine the acceleration of energetic particles in magnetic loops that carry that energy downward and deposit it in the footpoints of the loops. Electrons emit much of their energy as X-ray bremsstrahlung, but stopping ions largely heat the plasma. Thus, SEP acceleration may actually be a significant agent in the heating of solar and stellar coronae.
For stars other than the Sun, there is information on flares but not on CMEs or SEPs. Kahler’s [115] paper on “big flare syndrome” provided the first caution that a correlation between SEPs and flare-related parameters, for example, does not mean that flares cause SEPs, but rather suggests that the increasingly large dissipation of magnetic energy can result in many increasing phenomena. Nevertheless, big flare syndrome does suggest that flare stars may have more intense SEPs, so the underlying correlation is explored further by Kahler and Ling [116]. Other studies like Hu et al. [117] applied CME models to superflares, while Fu et al. [118] studied the dependence of SEP properties on stellar rotation speeds.
Recently, Mohan et al. [119,120] have detected 550–850 MHz radio emission similar to solar type IV radio emission from the young active M dwarf star AD Leo. Solar type IV radio bursts are produced by energetic electrons in post-flare loops and the moving flux ropes associated with fast (>900 km s-1), wide (>60°) CMEs [121], the same type of CMEs known to produce large, gradual SEP events [1,20]. The ability to detect and measure fast, wide CMEs could greatly increase our knowledge about large SEP events in other stellar systems.

Funding

This research received no external funding.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Kahler, S.W.; Sheeley, N.R., Jr.; Howard, R.A.; Koomen, M.J.; Michels, D.J.; McGuire, R.E.; von Rosenvinge, T.T.; Reames, D.V. Associations between coronal mass ejections and solar energetic proton events. J. Geophys. Res. 1984, 89, 9683. [Google Scholar] [CrossRef]
  2. Reames, D.V. Solar Energetic Particles, 2nd ed.; Springer Nature: Cham, Switzerland, 2021. [Google Scholar] [CrossRef]
  3. Reames, D.V. Bimodal abundances in the energetic particles of solar and interplanetary origin. Astrophys. J. Lett. 1988, 330, L71. [Google Scholar] [CrossRef]
  4. Reames, D.V. Abundances of trans-iron elements in solar energetic particle events. Astrophys. J. Lett. 2000, 540, L111. [Google Scholar] [CrossRef]
  5. Reames, D.V. The two sources of solar energetic particles. Space Sci. Rev. 2013, 175, 53. [Google Scholar] [CrossRef]
  6. Reames, D.V. Abundances, ionization states, temperatures, and FIP in solar energetic particles. Space Sci. Rev. 2018, 214, 61. [Google Scholar] [CrossRef]
  7. Reames, D.V. Element abundances and the physics of solar energetic particles. Front. Astron. Space Sci. 2024, 11, 1368043. [Google Scholar] [CrossRef]
  8. Reames, D.V.; Meyer, J.P.; von Rosenvinge, T.T. Energetic-particle abundances in impulsive solar flare events. Astrophys. J. Suppl. 1994, 90, 649. [Google Scholar] [CrossRef]
  9. Reames, D.V.; Cliver, E.W.; Kahler, S.W. Abundance enhancements in impulsive solar energetic-particle events with associated coronal mass ejections. Solar Phys. 2014, 289, 3817. [Google Scholar] [CrossRef]
  10. Mason, G.M.; Reames, D.V.; Klecker, B.; Hovestadt, D.; von Rosenvinge, T.T. The heavy-ion compositional signature in He-3-rich solar particle events. Astrophys. J. 1986, 303, 849. [Google Scholar] [CrossRef]
  11. Mason, G.M.; Mazur, J.E.; Dwyer, J.R.; Jokippi, J.R.; Gold, R.E.; Krimigis, S.M. Abundances of heavy and ultraheavy ions in 3He-rich solar flares. Astrophys. J. 2004, 606, 555. [Google Scholar] [CrossRef]
  12. Reames, D.V.; Ng, C.K. Heavy-element abundances in solar energetic particle events. Astrophys. J. 2004, 610, 510. [Google Scholar] [CrossRef]
  13. Mason, G.M. 3He-rich solar energetic particle events. Space Sci. Rev. 2007, 130, 231. [Google Scholar] [CrossRef]
  14. Bučík, R. 3He-rich solar energetic particles: Solar sources. Space Sci. Rev. 2020, 216, 24. [Google Scholar] [CrossRef]
  15. Lee, M.A. Coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks. J. Geophys. Res. 1983, 88, 6109. [Google Scholar] [CrossRef]
  16. Lee, M.A. Coupled hydromagnetic wave excitation and ion acceleration at an evolving coronal/interplanetary shock. Astrophys. J. Suppl. 2005, 158, 38. [Google Scholar] [CrossRef]
  17. Reames, D.V. Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 1999, 90, 413. [Google Scholar] [CrossRef]
  18. Reames, D.V. How do shock waves define the space-time structure of gradual solar energetic-particle events? Space Sci. Rev. 2023, 219, 14. [Google Scholar] [CrossRef]
  19. Zank, G.P.; Rice, W.K.M.; Wu, C.C. Particle acceleration and coronal mass ejection driven shocks: A theoretical model. J. Geophys. Res. 2000, 105, 25079. [Google Scholar] [CrossRef]
  20. Desai, M.I.; Giacalone, J. Large gradual solar energetic particle events. Living Rev. Sol. Phys. 2016, 13, 3. [Google Scholar] [CrossRef]
  21. Parker, E.N. The formation of sunspots from the solar toroidal field. Astrophys. J. 1955, 121, 491. [Google Scholar] [CrossRef]
  22. Drake, J.F.; Cassak, P.A.; Shay, M.A.; Swisdak, M.; Quataert, E. A magnetic reconnection mechanism for ion acceleration and abundance enhancements in impulsive flares. Astrophys. J. Lett. 2009, 700, L16. [Google Scholar] [CrossRef]
  23. Kramoliš, D.; Bárta, M.; Varady, M.; Bučík, R. Preferential acceleration of heavy ions in a spontaneously fragmenting flare current sheet. Astrophys. J. 2022, 927, 177. [Google Scholar] [CrossRef]
  24. Fitzmaurice, A.; Drake, J.F.; Swisdak, M. Wave generation by flare-accelerated ions and implications for 3He acceleration. Astrophys. J. 2024, 964, 97. [Google Scholar] [CrossRef]
  25. Reames, D.V.; Dennis, B.R.; Stone, R.G.; Lin, R.P. X-ray and radio properties of solar 3He-rich events. Astrophys. J. 1988, 327, 998. [Google Scholar] [CrossRef]
  26. Reames, D.V. Temperature dependence of the abundances of elements in solar 3He-rich events. Astrophys. J. Lett. 1988, 325, L53. [Google Scholar] [CrossRef]
  27. Kopp, R.A.; Pneuman, G.W. Magnetic reconnection in the corona and the loop prominence phenomena. Sol. Phys. 1976, 50, 85. [Google Scholar] [CrossRef]
  28. Reames, D.V. Magnetic topology of impulsive and gradual solar energetic particle events. Astrophys. J. Lett. 2002, 571, L63. [Google Scholar] [CrossRef]
  29. Archontis, V.; Hood, A.W. A numerical model of standard to blowout jets. Astrophys. J. Lett. 2013, 769, L21, Erratum in: Astrophys. J. Lett. 2013, 770, L41.. [Google Scholar] [CrossRef]
  30. Lee, E.J.; Archontis, V.; Hood, A.W. Plasma jets and eruptions in solar coronal holes: A three-dimensional flux emergence experiment. Astrophys. J. Lett. 2015, 798, L10. [Google Scholar] [CrossRef]
  31. Pariat, E.; Dalmasse, K.; DeVore, C.R.; Antiochos, S.K.; Karpen, J.T. Model for straight helical solar jets. I. Parametric studies of the magnetic field geometry. Astron. Astrophys. 2015, 573, A130. [Google Scholar] [CrossRef]
  32. Wild, J.P.; Smerd, S.F.; Weiss, A.A. Solar Bursts. Annu. Rev. Astron. Astrophys. 1963, 1, 291. [Google Scholar] [CrossRef]
  33. Lin, R.P. The emission and propagation of 40 keV solar flare electrons. I: The relationship of 40 keV electron to energetic proton and relativistic electron emission by the sun. Sol. Phys. 1970, 12, 266. [Google Scholar] [CrossRef]
  34. Serlemitsos, A.T.; Balasubrahmanyan, V.K. Solar particle events with anomalously large relative abundance of 3He. Astrophys. J. 1975, 198, 195. [Google Scholar] [CrossRef]
  35. Reames, D.V.; von Rosenvinge, T.T.; Lin, R.P. Solar 3He-rich events and nonrelativistic electron events—A new association. Astrophys. J. 1985, 292, 716. [Google Scholar] [CrossRef]
  36. Reames, D.V.; Stone, R.G. The identification of solar 3He-rich events and the study of particle acceleration at the sun. Astrophys. J. 1986, 308, 902. [Google Scholar] [CrossRef]
  37. Ibragimov, I.A.; Kocharov, G.E. Possible mechanism for enrichment of solar cosmic rays by helium—Three and heavy nuclei. In Proceedings of the 15th International Cosmic Ray Conference, Plovdiv, Bulgaria, 13–26 August 1977; Volume 11, p. 340. [Google Scholar]
  38. Kocharov, G.E.; Kocharov, L.G. Present state of experimental and theoretical investigations of solar events enriched by helium-3. In Proceedings of the 10th Symposium on Cosmic Rays, Aligarh, India, 12–16 December 1967; p. 37. [Google Scholar]
  39. Fisk, L.A. 3He-rich flares—A possible explanation. Astrophys. J. 1978, 224, 1048. [Google Scholar] [CrossRef]
  40. Varvoglis, H.; Papadopoulis, K. Selective nonresonant acceleration of He-3(2+) and heavy ions by H(+) cyclotron waves. Astrophys. J. Lett. 1983, 270, L95. [Google Scholar] [CrossRef]
  41. Kocharov, G.E.; Kocharov, L.G. 3He-rich solar flares. Space Sci. Rev. 1984, 38, 89. [Google Scholar] [CrossRef]
  42. Weatherall, J. Turbulent heating in solar cosmic-ray theory. Astrophys. J. 1984, 281, 468. [Google Scholar] [CrossRef]
  43. Winglee, R.M. Heating and acceleration of heavy ions during solar flares. Astrophys. J. 1989, 343, 511. [Google Scholar] [CrossRef]
  44. Riyopoulos, S. Subthreshold stochastic diffusion with application to selective acceleration of 3He in solar flares. Astrophys. J. 1991, 381, 578. [Google Scholar] [CrossRef]
  45. Temerin, M.; Roth, I. The production of 3He and heavy ion enrichment in 3He-rich flares by electromagnetic hydrogen cyclotron waves. Astrophys. J. Lett. 1992, 391, L105. [Google Scholar] [CrossRef]
  46. Ho, G.C.; Roelof, E.C.; Mason, G.M. The upper limit on 3He fluence in solar energetic particle events. Atrophys. J. Lett. 2005, 621, L141. [Google Scholar] [CrossRef]
  47. Liu, S.; Petrosian, V.; Mason, G.M. Stochastic acceleration of 3He and 4He in solar flares by parallel-propagating plasma waves. Astrophys. J. Lett. 2004, 613, L13. [Google Scholar] [CrossRef]
  48. Liu, S.; Petrosian, V.; Mason, G.M. Stochastic acceleration of 3He and 4He in solar flares by parallel-propagating plasma waves: General results. Astrophys. J. 2006, 636, 462. [Google Scholar] [CrossRef]
  49. Petrosian, V.; Jiang, Y.W.; Liu, S.; Ho, G.C.; Mason, G.M. Relative distributions of fluences of 3He and 4He in solar energetic particles. Astrophys. J. 2009, 701, 1. [Google Scholar] [CrossRef]
  50. Mogro-Campero, A.; Simpson, J.A. Enrichment of very heavy nuclei in the composition of solar accelerated particles. Astrophys. J. Lett. 1972, 171, L5. [Google Scholar] [CrossRef]
  51. Eichler, D. Particle acceleration in solar flares by cyclotron damping of cascading turbulence. Astrophys. J. 1979, 229, 413. [Google Scholar] [CrossRef]
  52. Miller, J.A.; Reames, D.V. Heavy ion acceleration by cascading Alfvén waves in impulsive solar flares. AIP Conf. Proc. 1996, 374, 450. [Google Scholar] [CrossRef]
  53. Eichler, D. Ultraheavy element enrichment in impulsive solar flares. Astrophys. J. 2014, 794, 6. [Google Scholar] [CrossRef]
  54. Jones, F.C.; Ellison, D.E. The plasma physics of shock acceleration. Space Sci. Rev. 1991, 58, 259. [Google Scholar] [CrossRef]
  55. Bell, A.R. The acceleration of cosmic rays in shock fronts—I. Mon. Not. Roy. Astron. Soc. 1978, 182, 147–156. [Google Scholar] [CrossRef]
  56. Bell, A.R. The acceleration of cosmic rays in shock fronts—II. Mon. Not. Roy. Astron. Soc. 1978, 182, 443–455. [Google Scholar] [CrossRef]
  57. Ng, C.K.; Reames, D.V. Shock acceleration of solar energetic protons: The first 10 minutes. Astrophys. J. Lett. 2008, 686, L123. [Google Scholar] [CrossRef]
  58. Stix, T.H. Waves in Plasmas; AIP: New York, NY, USA, 1992. [Google Scholar]
  59. Melrose, D.B. Plasma Astrophysics; Gordon & Breach: New York, NY, USA; CRC: Boca Raton, FL, USA, 1980. [Google Scholar]
  60. Decker, R.B. Formation of shock-spike events at quasi-perpendicular shocks. J. Geophys. Res. 1983, 88, 9959. [Google Scholar] [CrossRef]
  61. Reames, D.V. Solar release times of energetic particles in ground-level events. Astrophys. J. 2009, 693, 812. [Google Scholar] [CrossRef]
  62. Reames, D.V. Solar energetic-particle release times in historic ground-level events. Astrophys. J. 2009, 706, 844. [Google Scholar] [CrossRef]
  63. Cliver, E.W.; Kahler, S.W.; Reames, D.V. Coronal shocks and solar energetic proton events. Astrophys. J. 2004, 605, 902. [Google Scholar] [CrossRef]
  64. Meyer, J.P. The baseline composition of solar energetic particles. Astrophys. J. Suppl. 1985, 57, 151. [Google Scholar] [CrossRef]
  65. Laming, J.M. The FIP and inverse FIP effects in solar and stellar coronae. Living Rev. Sol. Phys. 2015, 12, 2. [Google Scholar] [CrossRef]
  66. Reames, D.V. Coronal Abundances determined from energetic particles. Adv. Space Res. 1995, 15, 41. [Google Scholar] [CrossRef]
  67. Reames, D.V. Element abundances in solar energetic particles and the solar corona. Sol. Phys. 2014, 289, 977. [Google Scholar] [CrossRef]
  68. Reames, D.V.; Richardson, I.G.; Barbier, L.M. On the differences in element abundances of energetic ions from corotating events and from large solar events. Astrophys. J. Lett. 1991, 382, L43. [Google Scholar] [CrossRef]
  69. Mewaldt, R.A.; Cohen, C.M.S.; Leske, R.A.; Christian, E.R.; Cummings, A.C.; Stone, E.C.; von Rosenvinge, T.T.; Wiedenbeck, M.E. Fractionation of solar energetic particles and solar wind according to first ionization potential. Adv. Space Res. 2002, 30, 79. [Google Scholar] [CrossRef]
  70. Reames, D.V. The “FIP effect” and the origins of solar energetic particles and of the solar wind. Sol. Phys. 2018, 293, 47. [Google Scholar] [CrossRef]
  71. Laming, J.M.; Vourlidas, A.; Korendyke, C.; Chua, D.; Cranmer, S.R.; Ko, Y.-K.; Kuroda, N.; Provornikova, E.; Raymond, J.C.; Raouafi, N.-E.; et al. Element abundances: A new diagnostic for the solar wind. Astrophys. J. 2019, 879, 124. [Google Scholar] [CrossRef]
  72. Mason, G.M.; Ng, C.K.; Klecker, B.; Green, G. Impulsive acceleration and scatter-free transport of about 1 MeV per nucleon ions in 3He-rich solar particle events. Astrophys. J. 1989, 339, 529. [Google Scholar] [CrossRef]
  73. Breneman, H.H.; Stone, E.C. Solar coronal and photospheric abundances from solar energetic particle measurements. Astrophys. J. Lett. 1985, 299, L57. [Google Scholar] [CrossRef]
  74. Reames, D.V. Acceleration of energetic particles by shock waves from large solar flares. Astrophys. J. Lett. 1990, 358, L63. [Google Scholar] [CrossRef]
  75. Reames, D.V.; Ng, C.K. Streaming-limited intensities of solar energetic particles. Astrophys. J. 1998, 504, 1002. [Google Scholar] [CrossRef]
  76. Reames, D.V.; Ng, C.K. Streaming-limited intensities of solar energetic particles on the intensity plateau. Astrophys. J. 2010, 723, 1286. [Google Scholar] [CrossRef]
  77. Giacalone, J.; Cohen, C.M.S.; McComas, D.J.; Chen, X.; Dayeh, M.A.; Matthaeus, W.H.; Klein, K.G.; Bale, S.D.; Christian, E.R.; Desai, M.I.; et al. Analyses of ~0.05–2 MeV ions associated with the 2022 February 16 energetic storm particle event observed by Parker Solar Probe. Astrophys. J. 2023, 958, 144. [Google Scholar] [CrossRef]
  78. Ng, C.K.; Reames, D.V.; Tylka, A.J. Solar energetic particles: Shock acceleration and transport through self-amplified waves. AIP Conf. Proc. 2012, 1436, 212. [Google Scholar] [CrossRef]
  79. Ng, C.K.; Reames, D.V.; Tylka, A.J. Modeling shock-accelerated solar energetic particles coupled to interplanetary Alfvén waves. Astrophys. J. 2003, 591, 461. [Google Scholar] [CrossRef]
  80. Reames, D.V.; Ng, C.K. The streaming limit of solar energetic-particle intensities. arXiv 2014, arXiv:1412.2279. [Google Scholar] [CrossRef]
  81. Ng, C.K. Effect of solar-wind velocity, magnetic field and density on solar energetic particle transport. ASP Conf. Ser. 2014, 484, 156. [Google Scholar]
  82. Vainio, R.; Pönni, A.; Battarbee, M.; Koskinen, H.E.J.; Afanasiev, A.; Laitinen, T. A semi-analytical foreshock model for energetic storm particle events inside 1 AU. J. Space Weather Space Clim. 2014, 4, A08. [Google Scholar] [CrossRef]
  83. Reames, D.V. Review and outlook of solar-energetic-particle measurements on multispacecraft missions. Front. Astron. Space Sci. 2023, 10, 1254266. [Google Scholar] [CrossRef]
  84. Mason, G.M.; Mazur, J.E.; Dwyer, J.R. 3He enhancements in large solar energetic particle events. Astrophys. J. Lett. 1999, 525, L133. [Google Scholar] [CrossRef]
  85. Desai, M.I.; Mason, G.M.; Dwyer, J.R.; Mazur, J.E.; Gold, R.E.; Krimigis, S.M.; Smith, C.W.; Skoug, R.M. Evidence for a suprathermal seed population of heavy ions accelerated by interplanetary shocks near 1 AU. Astrophys. J. 2003, 588, 1149. [Google Scholar] [CrossRef]
  86. Tylka, A.J.; Cohen, C.M.S.; Dietrich, W.F.; Lee, M.A.; Maclennan, C.G.; Mewaldt, R.A.; Ng, C.K.; Reames, D.V. Shock geometry, seed populations, and the origin of variable elemental composition at high energies in large gradual solar particle events. Astrophys. J. 2005, 625, 474. [Google Scholar] [CrossRef]
  87. Tylka, A.J.; Lee, M.A. Spectral and compositional characteristics of gradual and impulsive solar energetic particle events. Astrophys. J. 2006, 646, 1319. [Google Scholar] [CrossRef]
  88. Sandroos, A.; Vainio, R. Simulation results for heavy ion spectral variability in large gradual solar energetic particle events. Astrophys. J. 2007, 662, L127. [Google Scholar] [CrossRef]
  89. Reames, D.V. Four distinct pathways to the element abundances in solar energetic particles. Space Sci. Rev. 2020, 216, 20. [Google Scholar] [CrossRef]
  90. Kahler, S.W.; Reames, D.V.; Sheeley, N.R., Jr. Coronal mass ejections associated with impulsive solar energetic particle events. Astrophys. J. 2001, 562, 558. [Google Scholar] [CrossRef]
  91. Nitta, N.V.; Reames, D.V.; DeRosa, M.L.; Yashiro, S.; Gopalswamy, N. Solar sources of impulsive solar energetic particle events and their magnetic field connection to the earth. Astrophys. J. 2006, 650, 438. [Google Scholar] [CrossRef]
  92. Wang, Y.-M.; Pick, M.; Mason, G.M. Coronal holes, jets, and the origin of 3He-rich particle events. Astrophys. J. 2006, 639, 495. [Google Scholar] [CrossRef]
  93. Mazzotta, P.; Mazzitelli, G.; Colafrancesco, S.; Vittorio, N. Ionization balance for optically thin plasmas: Rate coefficients for all atoms and ions of the elements H to Ni. Astron. Astrophys. Suppl. 1988, 133, 403. [Google Scholar] [CrossRef]
  94. Post, D.E.; Jensen, R.V.; Tarter, C.B.; Grasberger, W.H.; Lokke, W.A. Steady-state radiative cooling rates for low-density, high temperature plasmas. At. Data Nucl. Data Tables 1977, 20, 397. [Google Scholar] [CrossRef]
  95. Reames, D.V.; Cliver, E.W.; Kahler, S.W. Variations in abundance enhancements in impulsive solar energetic-particle events and related CMEs and flares. Solar Phys. 2014, 289, 4675. [Google Scholar] [CrossRef]
  96. Reames, D.V. Temperature of the source plasma in gradual solar energetic particle events. Solar Phys. 2016, 291, 911–930. [Google Scholar] [CrossRef]
  97. Reames, D.V. Seeds and sequences of element abundances in solar energetic particle events. Eur. Phys. J. Plus 2024, 139, 710. [Google Scholar] [CrossRef]
  98. Bučík, R.; Mulay, S.M.; Mason, G.M.; Nitta, N.V.; Desai, M.I.; Dayeh, M.A. Temperature in solar sources of 3He-rich solar energetic particles and relation to ion abundances. Astrophys. J. 2021, 908, 243. [Google Scholar] [CrossRef]
  99. Lee, J.Y.; Kahler, S.; Raymond, J.C.; Ko, Y.K. Solar energetic particle charge states and abundances with nonthermal electrons. Astrophys. J. 2024, 963, 70. [Google Scholar] [CrossRef]
  100. DiFabio, R.; Guo, Z.; Möbius, E.; Klecker, B.; Kucharek, H.; Mason, G.M.; Popecki, M. Energy-dependent charge states and their connection with ion abundances in impulsive solar energetic particle events. Astrophys. J. 2008, 687, 623. [Google Scholar] [CrossRef]
  101. AKouloumvakos, A.; Wijsen, N.; Jebaraj, C.; Afanasiev, A.; Lario, D.; Cohen, C.M.S.; Riley, P.; Mitchell, D.G.; Ding, Z.; Vourlidas, A.; et al. Shock and SEP modeling study for the 2022 September 5 SEP event. Astrophys. J. 2025, 797, 100. [Google Scholar] [CrossRef]
  102. Mason, G.M.; Roth, I.; Nitta, N.V.; Bučík, R.; Lario, D.; Ho, G.C.; Allen, R.C.; Kouloumvakos, A.; Wimmer-Schweingruber, R.F.; Rodriguez-Pacheco, J. Heavy-ion acceleration in 3He-rich solar energetic particle events: New insights from Solar Orbiter. Astrophys. J. 2023, 957, 112. [Google Scholar] [CrossRef]
  103. Mason, G.M.; Nitta, N.V.; Wiedenbeck, M.E.; Innes, D.E. Evidence for a common acceleration mechanism for enrichments of 3He and heavy ions in impulsive EP events. Astrophys. J. 2016, 823, 138. [Google Scholar] [CrossRef]
  104. Roth, I.; Temerin, M. Enrichment of 3He and heavy ions in impulsive solar flares. Astrophys. J. 1997, 477, 940–957. [Google Scholar] [CrossRef]
  105. Gosling, J.T. The solar flare myth. J. Geophys. Res. 1993, 98, 18937. [Google Scholar] [CrossRef]
  106. Gosling, J.T. Corrections to “The solar flare myth”. J. Geophys. Res. 1994, 99, 4259. [Google Scholar] [CrossRef]
  107. Mandzhavidze, N.; Ramaty, R.; Kozlovsky, B. Determination of the abundances of subcoronal 4He and of solar flare-accelerated 3He and 4He from gamma-ray spectroscopy. Astrophys. J. 1999, 518, 918. [Google Scholar] [CrossRef]
  108. Murphy, R.J.; Kozlovsky, B.; Share, G.H. Evidence for enhanced 3He in flare-accelerated particles based on new calculations of the gamma-ray line spectrum. Astrophys. J. 2016, 833, 166. [Google Scholar] [CrossRef]
  109. Murphy, R.J.; Ramaty, R.; Kozlovsky, B.; Reames, D.V. Solar abundances from gamma-ray spectroscopy: Comparisons with energetic particle, photospheric, and coronal abundances. Astrophys. J. 1991, 371, 793. [Google Scholar] [CrossRef]
  110. Cohen CM, S.; Mason, G.M.; Mewaldt, R.A. Characteristics of solar energetic ions as a function of longitude. Astrophys. J. 2017, 843, 132. [Google Scholar] [CrossRef]
  111. Xu, Z.G.; Cohen, C.M.S.; Leske, R.A.; Muro, G.D.; Cummings, A.C.; McComas, D.J.; Schwadron, N.A.; Christian, E.R.; Wiedenbeck, M.E.; McNutt, R.L.; et al. Composition variation of the May 16 2023 Solar Energetic Particle Event observed by SolO and PSP. Astrophys. J. Lett. 2024, 976, L3. [Google Scholar] [CrossRef]
  112. Ng, C.K.; Reames, D.V. Focused interplanetary transport of approximately 1 MeV solar energetic protons through self-generated Alfven waves. Astrophys. J. 1994, 424, 1032. [Google Scholar] [CrossRef]
  113. Ng, C.K.; Reames, D.V.; Tylka, A.J. Effect of proton-amplified waves on the evolution of solar energetic particle composition in gradual events. Geophys. Res. Lett. 1999, 26, 2145. [Google Scholar] [CrossRef]
  114. Parker, E.N. Nanoflares and the solar X-ray corona. Astrophys. J. 1988, 330, 474. [Google Scholar] [CrossRef]
  115. Kahler, S.W. The role of the big flare syndrome in correlations of solar energetic proton fluxes and associated microwave burst parameters. J. Geophys. Res. 1982, 87, 3439. [Google Scholar] [CrossRef]
  116. Kahler, S.W.; Ling, A.G. Forecasting solar energetic particle (SEP) events with flare X-ray peak ratios. J. Space Weather Space Clim. 2018, 8, A47. [Google Scholar] [CrossRef]
  117. Hu, J.; Airapetian, V.; Li, G.; Zank, G.; Jin, M. Extreme energetic particle events by superflare-asssociated CMEs from solar-like stars. Sci. Adv. 2022, 8, eabi9743. [Google Scholar] [CrossRef] [PubMed]
  118. Fu, S.; Jiang, Y.; Airapetian, V.; Hu, J.; Li, G.; Zank, G. Effect of star rotation rates on the characteristics of energetic particle events. Astrophys. J. Lett. 2019, 878, L36. [Google Scholar] [CrossRef]
  119. Mohan, A.; Mondal, S.; Wedemeyer, S.; Gopalswamy, N. Energetic particle activity in AD Leo: Detection of a solar-like type-IV burst. Astron. Astrophys. 2024, 686, A51. [Google Scholar] [CrossRef]
  120. Mohan, A.; Gopalswamy, N.; Mondal, S.; Kumari, A.; Sindhuja, G. CME-associated type-IV radio bursts: The solar paradigm and the unique case of AD Leo. In Solar and Stellar Coronal Mass Ejections, Proceedings of the IAU Symposium No. 388, Krakow, Poland, 5–10 May 2024; Gopalswamy, N., Malandraki, O., Vidotto, A., Manchester, W., Eds.; IAU: Paris, France, 2024. [Google Scholar] [CrossRef]
  121. Mohan, A.; Gopalswamy, N.; Kumari, A.; Akiyama, S.; Sindhuja, G. Interplanetary Type IV Solar Radio Bursts: A Comprehensive Catalog and Statistical Results. Astrophys. J. 2024, 971, 86. [Google Scholar] [CrossRef]
Figure 2. (a) Superposed time profiles of 3–6 MeV protons show limited plateau intensities early in large SEP events that often rise later when the shock approaches [74]. (b) H and O plateau spectra for several events show flattening at low energies [76]. (c) Theoretical fits (grey and rose curves, respectively) are compared, using the Ng et al. [79] theory, for the flattened plateau proton spectra of the large 28 October 2003 event and the un-flattened power-law spectrum in the smaller event of 2 May 1998 [78]. The ~100-fold intensity difference above ~10 MeV is emphasized by the gray arrow; the higher intensities amplify more waves that restrict outward flows, trapping ions and flattening the spectra.
Figure 2. (a) Superposed time profiles of 3–6 MeV protons show limited plateau intensities early in large SEP events that often rise later when the shock approaches [74]. (b) H and O plateau spectra for several events show flattening at low energies [76]. (c) Theoretical fits (grey and rose curves, respectively) are compared, using the Ng et al. [79] theory, for the flattened plateau proton spectra of the large 28 October 2003 event and the un-flattened power-law spectrum in the smaller event of 2 May 1998 [78]. The ~100-fold intensity difference above ~10 MeV is emphasized by the gray arrow; the higher intensities amplify more waves that restrict outward flows, trapping ions and flattening the spectra.
Astronomy 04 00005 g002
Figure 3. (a) The radial evolutions of 6–11 MeV proton intensities are captured by four spacecraft as the accelerating shock wave moves out to ~2 AU in the 1978 Jan 1 SEP event. (b) The spatial distribution of the spacecraft is shown and the four shock positions S1–S4 correlate with the times in (a). The full energy coverage vs. time from ~3–200 MeV are shown for (c) Helios 1, (d) IMP 8, and (e) Voyager 2 [18,83].
Figure 3. (a) The radial evolutions of 6–11 MeV proton intensities are captured by four spacecraft as the accelerating shock wave moves out to ~2 AU in the 1978 Jan 1 SEP event. (b) The spatial distribution of the spacecraft is shown and the four shock positions S1–S4 correlate with the times in (a). The full energy coverage vs. time from ~3–200 MeV are shown for (c) Helios 1, (d) IMP 8, and (e) Voyager 2 [18,83].
Astronomy 04 00005 g003
Figure 4. (a) Intensities of 20 MeV protons vs. time are shown for three spacecraft located as in (b). The similar shock arrival times at the spacecraft as indicated in (a) suggest a nearly spherical shock [82]. The pink field lines labeled 1 and 2 in (b) will rotate to intercept Wind when the shock reaches 1 or 2 AU, respectively, bearing some of the SEPs acquired at their initial longitudes.
Figure 4. (a) Intensities of 20 MeV protons vs. time are shown for three spacecraft located as in (b). The similar shock arrival times at the spacecraft as indicated in (a) suggest a nearly spherical shock [82]. The pink field lines labeled 1 and 2 in (b) will rotate to intercept Wind when the shock reaches 1 or 2 AU, respectively, bearing some of the SEPs acquired at their initial longitudes.
Astronomy 04 00005 g004
Figure 5. (a) The intensities of H, 4He, O, and Fe in the listed intervals of MeV amu−1 are shown for three time-intervals. (b) Temperatures derived from the best-fits of enhancement vs. A/Q shown with power-law fits which are in the same color in (c) above [89,95,96].
Figure 5. (a) The intensities of H, 4He, O, and Fe in the listed intervals of MeV amu−1 are shown for three time-intervals. (b) Temperatures derived from the best-fits of enhancement vs. A/Q shown with power-law fits which are in the same color in (c) above [89,95,96].
Astronomy 04 00005 g005
Figure 6. For large SEP events near central meridian, the intensities of high-energy protons trapped near the shock can sometimes exceed those released early, even at energies > 100 MeV, as seen in samples here.
Figure 6. For large SEP events near central meridian, the intensities of high-energy protons trapped near the shock can sometimes exceed those released early, even at energies > 100 MeV, as seen in samples here.
Astronomy 04 00005 g006
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Reames, D.V. Solar Particle Acceleration. Astronomy 2025, 4, 5. https://doi.org/10.3390/astronomy4010005

AMA Style

Reames DV. Solar Particle Acceleration. Astronomy. 2025; 4(1):5. https://doi.org/10.3390/astronomy4010005

Chicago/Turabian Style

Reames, Donald V. 2025. "Solar Particle Acceleration" Astronomy 4, no. 1: 5. https://doi.org/10.3390/astronomy4010005

APA Style

Reames, D. V. (2025). Solar Particle Acceleration. Astronomy, 4(1), 5. https://doi.org/10.3390/astronomy4010005

Article Metrics

Back to TopTop