Hydrogen and the Abundances of Elements in Impulsive Solar Energetic-Particle Events

Hydrogen has been almost completely ignored in studies of the abundance patterns of the chemical elements in solar energetic particles (SEPs). We seek to find impulsive events where H fits these abundance patterns and document the events that do not, suggesting possible reasons for the disparity. For 24% of the smaller impulsive SEP events, the relative abundance of H fits within one standard deviation of the power-law fit of the abundances of elements 6≤Z≤56\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$6 \leq Z \leq 56$\end{document}, relative to coronal abundances. In impulsive events with high intensities, H can be 10 to 100 times its expected value. In a few of these larger events, increased scattering at high wavenumber may preferentially detain H, perhaps with self-amplified waves; in some events pre-event proton background may contribute. In most large impulsive SEP events, however, associated shock waves must play a much greater role than previously thought; fast (>500kms−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${>}\,500~\mbox{km}\,\mbox{s}^{-1}$\end{document}) coronal mass ejections contribute to 62% of impulsive events. Shocks may sample protons from the ambient coronal plasma or residual background as well as reaccelerating heavier impulsive SEP ions injected from the region of magnetic reconnection in solar jets. Excess H may be a signature of shock acceleration.


Introduction
During decades of studies of the abundances of elements in solar energetic-particle (SEP) events, hydrogen has been ignored -the elephant in the room. Early measurements (e.g. Webber, 1975;Meyer, 1985) found that the average element abundances from He or C through Fe, in what we now call "gradual" SEP events, differ from solar photospheric abundances as a simple function of their first ionization potential (FIP). In addition, event-toevent variations were found to be power-law functions of the mass-to-charge ratio [A/Q] for elements with atomic numbers 6 ≤ Z ≤ 30 in these events (Breneman and Stone, 1985). origins of the two coronal samples (Reames, 2018a(Reames, , 2018b. The reference coronal SEP abundances are listed in the Appendix. We use the term "enhancement" for the ratio of the observed to the average coronalreference abundances. These abundance enhancements have been found to vary as a powerlaw function of A/Q (Breneman and Stone, 1985;Reames, 2016aReames, , 2016bReames, , 2018b from event to event and as a function of time during events, largely because of particle transport from the source. Power-law dependence of ion scattering upon magnetic rigidity during acceleration or transport (Parker, 1963;Ng, Reames, and Tylka, 1999Reames, 2016a) results in a power-law dependence upon A/Q when ion abundances are compared at the same particle velocity. If Fe scatters less than O in transit, Fe/O will increase early in an event and be depleted later on; this dependence on time and space, along the field B, becomes longitude dependence because of solar rotation. In the case of small impulsive events, the strong A/Q-dependence probably comes directly from acceleration in islands of magnetic reconnection in the source (e.g. Drake et al., 2009).
In early studies of element abundances in impulsive SEP events, Reames, Meyer, and von Rosenvinge (1994) saw groupings of abundances, with He, C, N, and O being unenhanced relative to the reference coronal abundances, the elements Ne, Mg, and Si were all enhanced by a factor of ≈ 2.5, and Fe was enhanced by a factor of ≈ 7. In their interpretation, C, N, and O were almost fully ionized, like He, with A/Q ≈ 2, while Ne, Mg, and Si were in a stable state containing two orbital electrons. This pattern occurs at an electron temperature of T = 3 -5 MK. At a lower T , O would begin to pick up electrons and at a higher T , Ne would become fully ionized like He. More recently, Reames, Cliver, and Kahler (2014a) compiled and studied a list on 111 impulsive SEP events occurring over nearly 20 years, identifying their solar source events, and Reames, Cliver, and Kahler (2014b) developed a best-fit scheme to determine the source temperature and the power-law fit of abundance enhancements versus A/Q for each event. Each T implies a Q-value and an A/Q for each element and the fit of enhancement versus A/Q yields a χ 2 -value for that T . For each impulsive SEP event we choose the fit, and the associated T , with the minimum χ 2 . Temperatures for nearly all of the events were found to fall in the 2.5 -3.2 MK range Kahler, 2014b, 2015), so the differences in T between impulsive events is not very significant. For gradual events, however, the range of T is 0.8 to 3.2 MK and is helpful in distinguishing events with large components of impulsive suprathermal ions. The recent article by Reames (2019) shows a detailed example of the application of this technique to three impulsive SEP events and discusses the presence of He in the abundance scheme of impulsive SEP events. The source values of He/O for gradual SEP events are found to vary rather widely from 30 to 120 (Reames, 2017c(Reames, , 2018b; perhaps these variations result from delay and difficulty in ionizing and transporting He to the corona, because of its uniquely high FIP (Laming, 2009). Impulsive SEP events mirror these variations, but they also show a unique sample of "He-poor" events of unknown origin with the observed value of He/O as low as ≈ 2.
What about H? To what extent can we organize the abundance of H within the scheme of the other elements? We begin with the 111 impulsive events in the list of Reames, Cliver, and Kahler (2014a). However, only 70 of these events have proton intensities above background in the 2 -3 MeV region where we have measurements. We use observations made by the Low-Energy Matrix Telescope (LEMT) onboard the Wind spacecraft, near Earth (von Rosenvinge et al., 1995;; see also Chapter 7 of Reames, 2017a). LEMT primarily measures elements He through Pb in the region of 2 -20 MeV amu −1 . The elemental resolution of LEMT up through Fe is shown in detail by Reames (2014). LEMT resolves element groups above Fe as shown by Reames ( , 2017a. Unlike other elements, the protons on LEMT are limited to a single sam-  Reames, Cliver, and Kahler (2014a); the solar source locations are also listed. The right panels show enhancements, labeled by Z, versus A/Q for each event, with best-fit power law for elements with Z ≥ 6 (blue line) extrapolated down to A/Q = 1. pled interval bounded by the front-detector (dome) threshold (von Rosenvinge et al., 1995;.
Throughout this text, whenever we refer to the element He or its abundance, we mean 4 He, unless 3 He is explicitly stated.

Small Impulsive SEP Events
We begin with some of the smallest of our impulsive SEP events. The particles in these small events are generally regarded to travel scatter-free (i.e. scattering mean free path [λ] > 1 AU) based upon careful studies of these events by Mason et al. (1989). Under these circumstances the observed element abundances should directly sample the source. Figure 1 shows principal ion intensities and abundance ratios as a function of time and the ion enhancements versus A/Q for two small impulsive SEP events. The least-squares fits only include the enhancements of elements with Z ≥ 6; H and He are not included in the fits, but this fitted line is extrapolated to A/Q = 1 and the error of extrapolation is plotted. The fit to H and He is coincidental.
Intensities, enhancements, and power-law fits are shown for two more small events from Solar Cycle 24 in Figure 2. Event 105, shown in the left panels of Figure 2, is a slowly evolving event while Event 107, in the right panels, has a fast rise and rapid decay. Again, the power-law fit to H and He is coincidental. What all four events (in Figures 1 and 2) share is low proton intensities of < 0.1 (cm 2 sr s MeV) −1 at ≈ 2 MeV.  Reames, Cliver, and Kahler (2014a); the solar source locations are also listed. The upper panels show enhancements, labeled by Z, versus A/Q for each event, with best-fit power law for elements with Z ≥ 6 (blue line) extrapolated down to A/Q = 1.

He-Poor Events
He-poor impulsive SEP events were originally noted by Reames, Cliver, and Kahler (2014a) and have been discussed as a function of energy in the context of power-law fits by Reames (2019). In our current context, the events are small, quite apart from their unusual suppression of He. Figure 3 shows a pair of He-poor events where the power-law fits in the right panels are extrapolated below He to A/Q = 1. While H exceeds the extrapolated value in

Large Impulsive SEP Events
There are two classic large impulsive SEP events that have been discussed in the literature: Event 37 on 1 May 2000 (e.g. Reames, Ng, and Berdichevsky, 2001) and Event 49 on 14 April 2001 (e.g. Tylka et al., 2002). These events are shown in Figure 4.
For the events in Figure 4, the proton enhancement exceeds the expected value by an order of magnitude. For Event 37, pre-event proton background certainly seems an unlikely issue, since the proton intensity increases from 0.049 ± 0.007 (cm 2 sr s MeV) −1 before the event to 3.9 ± 0.07 (cm 2 sr s MeV) −1 at the peak. However, higher proton intensities can amplify Alfvén waves which begin to scatter the particles Tylka, 1999, 2003). Particles of rigidity P and pitch angle μ resonate with waves of wave number k = B/μP in a magnetic-field strength B. Streaming protons of 2 MeV amplify their own resonant waves, but waves that resonate with He of 2 MeV amu −1 are produced by 8 MeV protons, which are much less numerous. Angular distributions of various ions during impulsive Event 37 are shown in Figure 5.
Particle-arrival directions in LEMT are binned relative to the direction of B so that outward-flowing ions such as He and even Fe peaks at 0 • early in this event and continue out-  For Event 54 in Figure 6, protons stream out from the Sun just as well as the other ions. When the field polarity reverses at about 1700 UT on 20 February 2000, the ion anisotropies are reduced but their outward flow continues. The proton intensity peak is also spread in time somewhat in this event, but the protons flow away as easily as the ions.

Distributions and Properties of Impulsive SEP Events
We have already indicated that size, i.e. proton or He intensity, is a factor in the relative enhancement of H in these events and that proton scattering may sometimes be a consideration. To study the effects of scattering, Figure 7a shows the distribution of the 70 events with measurable protons with the abscissa as the ratio of the observed H enhancement divided by the expected value extrapolated from the fit of the ions with Z ≥ 6 and the ordinate as frontto-back azimuth of the proton flow during the first six hours of the event. The symbol size and color of each event depends upon peak proton intensity. An observed/expected ratio = 1 means that the H enhancement lies on the fit line of the other elements; this value is shown as a solid line in Figure 7. Figure 7b shows how the observed/expected H ratio varies with event size, i.e. with peak proton intensity, and Figure 7c shows the overall histogram of the distribution.
In Figure 7, 17 events (24%) of the impulsive SEP events have proton intensities within one standard deviation of the value predicted from the least-squares fit of the elements with Z ≥ 6 and 44 events (63%) are within two standard deviations. However, it is clear that the small events fit rather well while the larger, more intense events, beginning with peak proton intensities > 0.1 (cm 2 sr s MeV) −1 , contribute to a broad maximum centered about ten times above the expected H intensity.
Recent studies of H enhancements in gradual SEP events (Reames, 2019b) show clearly that those gradual SEP events with positive powers of A/Q, like impulsive SEP events, tend to have H abundances a factor of ten or more above expectation, while most gradual SEP events, with negative powers of A/Q, tend to have H enhancements nearer expectation. For Figure 7 Panel a: the front/back directional anisotropy of protons during the first six hours is shown versus the observed enhancement of H relative to that expected from the power-law fit for elements Z ≥ 6 for 70 impulsive SEP events; the symbol size and color show the peak proton intensity of each event. Panel b: the peak proton intensity versus the observed/expected H ratio for each event, and panel c shows a histogram of the distribution of observed/expected H enhancement ratio. An observed/expected H enhancement = 1 is shown as a solid line in panels a and b.
gradual SEP events, these two distributions can also be distinguished based upon source plasma temperature. Our impulsive SEP events here all have similar positive powers of A/Q and source temperatures, so they are less easy to distinguish.
For the larger events, shock acceleration could be a consideration, so we replot the lower panels of Figure 7 using CME speed from the table in Reames, Cliver, and Kahler (2014a) as the symbol for each event in Figure 8.
Unfortunately we now have only 40 events with CME measurements in our sample, although most of the unassociated events are small. Reames, Kahler, and Ng (1997) found that essentially all CMEs with speeds above 750 km s −1 accelerated SEPs and most of those with 500 ≤ V CME ≤ 750 km s −1 did. Here, 18 of the 39 events (45%) have V CME ≥ 750 km s −1 and 25 (62%) have V CME ≥ 500 km s −1 . However, of the 15 (37%) events have V CME < 500 km s −1 , only two of them (Events 52 and 55) are more than two standard deviations above the proton enhancement predicted from the least-squares fit from the elements with Z ≥ 6; both of these events have high or even rising pre-event proton background. Generally the large events with fast CMEs have the ten-fold excess of protons.

Discussion
For small impulsive SEP events, H fits on the increasing power-law trend line of the abundance enhancements of the other elements. H fits even when He does not, as in the He-poor events. He is bypassed. This suggests that the He suppression in He-poor events exists in Figure 8 Panel a: the front/back directional anisotropy of protons during the first six hours is shown versus the enhancement of H relative to that expected from the power-law fit for elements Z ≥ 6 for 39 impulsive SEP events with CMEs. Panel b: the peak proton intensity versus the observed/expected H for each event. In both panels the symbol size and color depend upon the associated CME speed. An observed/expected H enhancement = 1 is shown as a solid line in both panels.

Figure 9
Element enhancements, labeled by Z, versus A/Q for Event 54 (see Figure 6), together with possible sources for shock acceleration from pre-accelerated impulsive ions (blue) and ambient corona or pre-event plasma (red). Helium is assumed to receive comparable contributions from both sources in this event.
the source plasma and is unrelated to the physics of acceleration. Perhaps He is poorly conducted into the corona because of its high FIP (Laming, 2009); however, Ne and Ar seem quite plentiful.
While disproportionate scattering may detain H in some large SEP events and selfamplification of waves may contribute, scattering also depends upon pre-existing conditions, and this is not likely to be a significant contributor to the excess enhancement of H. An analysis of scattering is not particularly helpful in explaining H abundances. However, the early analysis of scatter-free transport in impulsive SEP events (Mason et al., 1989) was made using He, not H.
The most probable contributor to excess enhancement of H in large impulsive SEP events is acceleration by the CME-driven shock wave of the direct ambient coronal plasma or pre-existing background SEPs as well as pre-accelerated impulsive ions from magnetic reconnection in the jet. Figure 9 suggests a way that these components might contribute to Event 54 (shown previously in Figure 6). The power law describing the impulsive component (blue) comes from the fit of the enhancements observed elements with Z ≥ 6. Protons from this component contribute almost nothing. The power law describing the ambient component (red) includes H and assumes that both components contribute similar amounts of He. The ambient abundances of Z ≥ 6 ions (only uncertain C and O are shown) fall on this line at higher values of A/Q since they probably have lower T , perhaps ≈ 1 MK, instead of 2.5 MK for the impulsive ions. The shock wave in Event 54 has a speed of 954 km s −1 (Reames, Cliver, and Kahler, 2014a). The decreasing slope of the red line in Figure 9 has probably also caused a decrease in the slope of the impulsive component relative to its initial value at the jet source (Reames, 2016b(Reames, , 2018b. We have assumed that the red line in Figure 9 passes near He and that the ambient component contributes to it, as may be the case in several events with elevated He. If not, the descent of the red line is undefined, and it may be much steeper. However, the line cannot pass above He. He is an unfortunate fulcrum for balancing the two possible components of the seed population, since its abundance can be quite variable (Reames, 2019). There may also be events where the ambient corona dominates the C and O observations as well, but such events would have reduced values of Fe/O and would not be included with "impulsive" events. In any case, shocks treat the two components of the seed population independently; both are present in the output, at some level, if they are present in the input.
We should note that a possible component of the seed population for shock acceleration includes residual ions from previous SEP events. The presence of a high proton background prior to an event may contribute a source which can replace "ambient corona" in Figure 9, or simply add a third component, increasing the complexity of the observations. However, the observed proton excess does not scale with the proton background. Pre-event proton background is higher for small SEP events, yet it is the large impulsive events, with minimal background, that have the ten-fold excesses of protons.
If this analysis is correct, the presence of an excessive proton enhancement, whatever the proton source, may, in fact, be evidence of the presence of shock acceleration in events that are otherwise dominated by characteristics of impulsive SEP events. Shock acceleration requires streaming protons to generate the waves that scatter resonant ions back and forth across the shock (Lee, 1983(Lee, , 2005Ng and Reames, 2008). Shocks cannot accelerate impulsive suprathermal ions without an adequate source of protons, which always dominate the absolute intensities and the wave amplification.
Clearly, the possibility of multiple components to the seed population also applies to shock acceleration in gradual SEP events. Thus it is not surprising that there are events where a single power law does not fit at any source temperature. The combination of multiple components and variations with time complicates some gradual events but also explains the origin of their complexity.
In summary: i) In small impulsive SEP events, H fits the power-law dependence of the heavier ions.
ii) The small He-poor events are no exception. In these events, only the He abundance is unique and it must be a property of the source, not the acceleration. iii) Larger impulsive SEP events show excess H abundance, probably accelerated by a CME-driven shock wave from ambient coronal material or other residual ions along with the "impulsive" pre-accelerated ions with Z ≥ 2 from magnetic reconnection in the associated solar jet. Shocks sample all components of the seed population independently, but protons are required to produce waves. iv) Multiple components in the seed population could lead to regions of A/Q with different power-law enhancement behavior. A single power law may not always fit.

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