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

Despite its dominance, hydrogen has been largely ignored in studies of the abundance patterns of the chemical elements in gradual solar energetic-particle (SEP) events; those neglected abundances show a surprising new pattern of behavior. Abundance enhancements of elements with 2<= Z<= 56, relative to coronal abundances, show power-law dependence, versus their average mass-to-charge ratio A/Q, that varies from event to event and with time during events; the ion charge states Q depend upon the source plasma temperature T. For most gradual SEP events, shock waves have accelerated ambient coronal material with T<2 MK to produce a decreasing power-laws in A/Q; here the proton abundances agree rather well with the power-law fits extrapolated from elements with Z>= 6 at A/Q>2 down to hydrogen at A/Q = 1. Thus the abundances of the elements with Z>= 6 fairly accurately predict the observed abundance of H, at a similar velocity, in most SEPs. However, for those gradual SEP events where ion enhancements follow positive powers of A/Q, especially those with T>2 MK where shock waves have reaccelerated residual suprathermal ions from previous impulsive SEP events, pro-ton abundances commonly exceed the extrapolated expectation, usually by a factor of order 10. This is a new and unexpected pattern of behavior that is unique to the abun-dances of protons. This proton behavior is a signature that can help distinguish the presence or absence of shock acceleration when Fe-rich impulsive material is observed.


Introduction
Hydrogen is, by far, the most abundant element in typical astrophysical settings, including the Sun, where the pattern of element abundances is believed to have changed little during the 4.6 billion years since its formation. As elements evaporate from the solar photosphere up into the corona, those that are ionized, i.e. with first ionization potential (FIP) < 10 eV, are preferentially enhanced by a factor of about 4 relative to the elements with FIP > 10 eV that are initially neutral atoms. Once in the 1-MK corona, all elements are highly ionized, and at altitudes where the plasma becomes collisionless, ion acceleration by electromagnetic fields can be sustained. The effects of those fields on acceleration and transport depends upon the magnetic rigidity of the ions, which, when compared at a constant velocity, varies as the ion mass-to-charge ratio A/Q. Thus it is not surprising that the effects of acceleration and transport on the abundances of solar energetic particles (SEPs) are found to vary as power laws in A/Q. The surprise is that scientists have advanced this picture of abundance variations of the elements for decades without including the abundance of hydrogen. Do protons ever fit this abundance pattern?
Early measurement of abundances, averaged over the large SEP events we now call "gradual" events, began to show clear evidence of the FIP effect (e.g. Webber, 1975;Meyer, 1985;Reames, 1995Reames, , 2014 especially for the elements from He or C through Fe. Once typical element ionization states Q first became available (Luhn et al. 1984), eventto-event variations in some events were found to be power-law functions of A/Q for elements with atomic numbers 6 ≤ Z ≤ 30 by Breneman and Stone (1985), but H was also omitted from more-recent similar studies by Reames (2016aReames ( , 2016bReames ( , 2018b. Even the inclusion of He is rather complicated (Reames 2017c). Power-law behavior of abundances in "impulsive" SEP events was proposed by Reames, Meyer, and von Rosenvinge (1994) using abundances of elements with 2 ≤ Z ≤ 26 and the extension to high Z shows an especially strong behavior as the third power of A/Q for 2 ≤ Z ≤ 82 (Reames, 2000(Reames, , 2017aMason et al., 2004;Reames and Ng, 2004;Reames, Cliver, and Kahler, 2014a).
The terms "impulsive" and "gradual" have come to refer to the dominant physical process of particle acceleration in these SEP events as evidence for two mechanisms has evolved (Reames, 1988(Reames, , 1999(Reames, , 2013(Reames, , 2015(Reames, , 2017aGosling, 1993). The evidence of Hydrogen Abundance in Gradual SEP Events D. V. Reames 3 unique physics in the small "impulsive" SEP events was first shown by huge 1000-fold enhancements of 3 He/ 4 He (Serlemitsos and Balasubrahmanyan, 1975;Mason, 2007;Reames, 2017a). While 3 He/ 4 He ≈ 5 × 10 -4 is found in the solar wind, even the early measurements found SEP events with 3 He/ 4 He ≈ 1.5 ± 0.1. A few events even have 3 He/H > 1 (Reames, von Rosenvinge, and Lin, 1985). The events were associated with streaming non-relativistic electrons and type III radio bursts (Reames, von Rosenvinge, and Lin, 1985;Reames and Stone, 1986). In the most complete theory, the streaming electrons produce electromagnetic ion-cyclotron (EMIC) waves in resonance with the gyrofrequency of 3 He to produce the unique enhancements (Temerin and Roth, 1992;Roth and Temerin, 1997). Further complicating the behavior, power-law enhancements of elements, also 1000-fold, between He and the heavy elements up to Pb (Reames, 2000(Reames, , 2017aMason et al., 2004;Reames and Ng, 2004;Reames, Cliver, and Kahler, 2014a) were found and were better explained by particle-in-cell simulations of magnetic reconnection (Drake et al., 2009) which produce the power-law dependence on A/Q from rigidity dependence during acceleration. Impulsive SEP events are associated with narrow coronal mass ejections (CMEs) related to solar jets (Kahler, Reames, and Sheeley, 2001;Bučík et al., 2018) driven by magnetic reconnection involving open field lines.
In "gradual" or long-duration SEP events, particles are accelerated at shock waves driven out from the Sun by fast, wide CMEs (Kahler et al. 1984). These shock waves accelerate SEPs (Lee, 1983(Lee, , 2005Zank, Rice, and Wu, 2000;Cliver, Kahler, and Reames, 2004;Ng and Reames, 2008;Gopalswamy et al. 2012;Lee, Mewaldt, and Giacalone, 2012;Desai and Giacalone, 2016;Reames, 2017a), requiring shock speeds above 500 -700 km s -1 (Reames, Kahler, and Ng, 1997), and accelerating ions over an extremely broad region of the heliosphere (Reames, Barbier, and Ng, 1996;Rouillard et al., 2012;Cohen, Mason, Mewaldt, 2017;Reames, 2017b). Generally, the shock waves sample the 1 -2 MK coronal plasma (Reames, 2016a(Reames, , 2016b(Reames, , 2018b. Power-law dependence in gradual events can come from rigidity-dependent scattering of ions during transport (Parker, 1963;Ng, Reames, and Tylka, 1999Reames, 2016aReames, , 2016b which results in dependence upon A/Q when ion abundances are compared at the same particle velocity. If Fe scatters less than O in transit, for example, Fe/O will Hydrogen Abundance in Gradual SEP Events D. V. Reames 4 increase early in an event and be depleted later on; this dependence on time and space traveling along the field B also become longitude dependence because of solar rotation. However, SEP abundances become complicated because shock waves can also reaccelerate residual ions from a seed population that includes pre-accelerated ions from the ubiquitous small impulsive SEP events, complicating the SEP abundance story. Mason, Mazur, and Dwyer (2002) noted the presence of modest enhancements of 3 He in large SEP events that would otherwise be called gradual and the complexity of the seed population was soon realized Tylka et al., 2005;Tylka and Lee, 2006;Bučík et al., 2014Bučík et al., , 2015Bučík et al., , 2018Chen et al., 2015;Reames 2016aReames , 2016b. Thus gradual SEP events sometimes exhibit the abundance enhancement patterns of impulsive SEP events which we can recognize from power-law enhancements increasing with A/Q and source plasma temperatures of ≈3 MK (Reames, Cliver, and Kahler, 2014a, 2014bReames, 2019aReames, , 2019b which actually dominate 24% of gradual events (Reames 2016a(Reames , 2016b. The 3 He/ 4 He ratio is also enhanced in these events (Reames, Cliver, and Kahler, 2014b) but its extreme variation with energy and from event to event (Mason 2007) makes Fe/O a more stable and reliable indicator of impulsive material. Hence we prefer Fe/O rather than 3 He/ 4 He to identify impulsive SEP events and reaccelerated impulsive ions (Reames, Cliver, and Kahler, 2014a). Recently, the abundance patterns of H (Reames, 2019b) and 4 He (Reames 2019a) have been found for impulsive SEP events.
Protons have been studied for many aspects of gradual SEP events (e.g. Reames, 2017a), including acceleration (Lee, 1983(Lee, , 2005Zank, Rice, and Wu, 2000;Ng and Reames, 2008), transport (Parker, 1963;Ng, Reames, and Tylka, 1999, time variations Reames, 2009), and energy spectra (Reames and Ng, 2010), but not for FIP or power-law abundance patterns. If we seek guidance from the case of the solar wind, we find variations are seen in H/He with solarwind speed and phase in the solar cycle (Kasper et al., 2007). However, while the solar wind is coronal in origin and does display a FIP effect (e.g. Schmelz et al. 2012), it is clear that SEPs have a different source than the solar wind (Mewaldt et al., 2002;Reames, 2018a) that may be related to differing open-and closed-field origins (Laming, 2009(Laming, , 2015 of the two coronal samples (Reames, 2018a(Reames, , 2018b. For our purposes, the SEP reference coronal abundances (derived from averaged gradual SEP Hydrogen Abundance in Gradual SEP Events D. V. Reames 5 events) and the solar photospheric abundances are provided in Appendix A. We define an element "enhancement" to be its observed abundance, normalized to O, divided by its corresponding reference abundance, similarly normalized.
To what extent can we organize the abundance of H within the scheme of the other elements in gradual SEP events? We consider the gradual events studied and listed by Reames (2016a) using observations made by the Low-Energy Matrix Telescope (LEMT) on the Wind spacecraft, near Earth (von Rosenvinge et al., 1995;; see also Chapt. 7 of Reames, 2017a). LEMT primarily measures elements He through Pb in the region of 2 -20 MeV amu -1 . The element resolution of LEMT up through Fe is shown in detail by Reames (2014). LEMT resolves element groups above Fe as shown by Reames (2000Reames ( , 2017a. Unlike other elements, the protons in LEMT are limited to a small interval sampled near ≈2.5 MeV 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.

Power-laws in A/Q
The theory of diffusive transport provides support for our expectation that element enhancements in gradual events will vary approximately as power laws in A/Q. It is common to expect that the scattering mean free path λ X of species X depends upon as a power law on the particle magnetic rigidity P as P α and upon distance from the Sun R as R β so that the expression for the solution to the diffusion equation (Equation C3 in Tylka 2003 based upon Parker 1963) can be used to write the enhancement of element X relative to oxygen as a function of time t as cles of speed v . Since we compare different ions at the same velocity, their rigidities can be replaced by their corresponding values of A/Q. The factor r S is included to represent Hydrogen Abundance in Gradual SEP Events D. V. Reames 6 any A/Q-dependent power-law enhancement at the source. For shock acceleration of impulsive suprathermal ions, it describes the power-law enhancement of the seed particles expected from acceleration in impulsive SEP events (e.g. Drake et al., 2009). For shock acceleration of the ambient coronal material, S = 0.
To simplify Equation (1), we can achieve a power-law approximation if we expand log x = (1-1/x) + (1-1/x) 2 /2 +…. (for x > ½ ). Using only the first term to replace 1- as an expression for the power-law dependence of enhancements on A/Q for species X.
More generally, we can write Equation (2) in the form X/O= r p , where the exponent p is linear in the variable 1/t, so that the average parameters are directly measurable from the time behavior of SEP-abundance observations (Reames, 2016b). Fits to the time behavior of typical gradual SEP events show that late in events where impulsive material is not present p ≈ -1 to -2 (Reames, 2016b) while the average power-law for impulsive events suggests S ≈ 3 Kahler, 2014a, Mason, et al. 2004). The ions in small impulsive events generally propagate scatter free (Mason et al., 1989), but in the more intense gradual events any shock-accelerated impulsive suprathermal ions are scattered, so that the power for the heavy-element enhancements is reduced (Reames, 2016b).
Thus we can expect that the enhancements will vary as a power law in A/Q, but the pattern of the average value of Q for each element depends upon the source plasma temperature T of the ions. approaching Ar and Ca. We will see that the χ 2 values of fits can be quite sensitive to these variations.
Given a temperature and the associated values of A/Q, we can determine, by leastsquares fitting, the best fit line and the associated value of χ 2 /m, where m is the number of degrees of freedom. Repeating this fitting for every T of interest, we can plot χ 2 /m versus T (e.g. Figure 2d) to choose the most likely temperature and fit line (Reames 2016a(Reames , 2016b(Reames , 2018b. In the present paper, we include only the elements Z ≥ 6 in the fits, and compare that best fit line with He and extrapolated to H. In the fits an error of 15% is assumed for random abundance variations in addition to the statistical errors.

Low-T Events and Decreasing Powers of A/Q
Guided by the power-law fits of gradual events for Z ≥ 2 by Reames (2016a), we first examine events with T < 2 MK which seem to represent shock acceleration of the ambient solar coronal plasma.   October 2003 from W38 and E08 with CME speeds of 1537 and 2459 km s -1 , respectively. Extrapolation of the least-squares fits for Z ≥ 6 to A/Q = 1 fit H rather well, even when the slope reverses for the last interval in Figure 4e. These events have been studied Hydrogen Abundance in Gradual SEP Events D. V. Reames 11 previously for their protons  and their heavier ions  separately.   The proton enhancement in this event is an order of magnitude higher than expected from the extrapolation of the fit for the ions with Z ≥ 6. This behavior was seen recently for the impulsive events where there is additional reacceleration of ions by shock waves (Reames 2019b) and we will find this behavior common for many gradual SEP events with positive powers of A/Q and with T > 2 MK since they are dominated by reacceler-  Figure 4) the event in Figure 6 shows a 2.5 MK seed population of impulsive SEP ions with an order-of-magnitude ex-Hydrogen Abundance in Gradual SEP Events D. V. Reames 15 cess of protons. This event is not influenced by the properties of its immediate predecessor in Figure 4.    The event in Figure 8 shows a consistent temperature of 1.5 MK indicating a lack of hotter material with impulsive suprathermal ions, yet the proton enhancement is sig-Hydrogen Abundance in Gradual SEP Events D. V. Reames 18 nificantly above expectation early, when the enhancements are rising with A/Q, but are well within expectations when the enhancements are falling with A/Q.

Other Variations
Does the large proton excess depend upon the presence of impulsive material or on the slope of the power law? Figure 8e suggests that only the slope matters, but Figure   7e shows predicted proton abundances for both positive slope and T = 2.5 MK.

Proton Excess and Distributions in A/Q and T
We have seen several examples of events that show typical behavior of proton enhancement in gradual SEP events and a few events that show atypical behavior. What remains is to examine the probability distributions for a wide range of cases. Since the behavior can vary with time during an event we must look at the distributions of the basic 8-hr averages, nearly 400 intervals within the SEP events originally studied by Reames (2016a).
The upper panel of Figure 9 shows the distribution of proton enhancements during the 8-hr intervals as a function of the slope, or power of A/Q, of the fit. Clearly, the peak of the distribution lies at a negative slope near -1, where most intervals have a proton enhancement within a factor of about 3 of having the value correctly predicted by the ions with Z ≥ 6 or modest excesses. Grouping the intervals by temperature, in the lower panels of Figure 9, shows that intervals with T ≥ 2.5, on the right, identify with the positive slope involving reaccelerated impulsive ions with typical power-of-10 proton excesses.
Lower temperatures of ambient coronal plasma in the lower left panel have a much better chance of predicting the proton intensity using only the Z ≥ 6 ions, but there are some event intervals with positive slope that usually occur early in these events.
Hydrogen Abundance in Gradual SEP Events D. V. Reames 19 Figure 9. In all panels, the enhancement of H relative to that expected from the power-law fit of elements Z ≥ 6 is shown versus the "slope" or power of A/Q from the fit of elements Z ≥ 6. The

Discussion
The abundances we study depend upon two underlying factors. First, elements suffer the "FIP effect" as they are brought into the corona to produce the reference SEP abundances tabulated in Appendix A. Second, their acceleration and transport depend, not only upon particle rigidity, but approximately as a power law on rigidity. Similar processes apply, not only to SEPs, but even to energetic ions in corotating interaction regions where shock waves accelerate ions, from the solar wind in this case, to produce enhancements that usually decline with A/Q (Reames, 2018c) like most SEP events here. All ions experience this process, but the protons in shock acceleration have a dual role; they are not only accelerated like other ions, but they must generate waves as they stream away so as to scatter subsequent ions back and forth across the shock (Bell 1978;Lee, 1983Lee, , 2005Ng and Reames, 2008;Desai and Giacalone, 2016). Are extra protons sometimes required for the latter task? If we adjust the abundance normalization from O to H, events with formerly "excess protons" are now seen as unable to accelerate the expected number of heavy ions given the available protons and the wave spectrum they have produced.
When we compare ions at the same velocity, as we do for studies of abundance enhancements, the ions interact with different parts of the proton-generated wave spectrum. For example, for 2.5 MeV protons the wave spectrum is approximately generated by streaming 2.5 MeV protons, for 2.5 MeV amu -1 He, C, or O with A/Q = 2 the spectrum is generated by streaming 10 MeV protons, for 2.5 MeV amu -1 Fe at A/Q = 4 the spectrum is generated by streaming 39 MeV protons, and for 2.5 MeV amu -1 heavy ions with A/Q = 10 the spectrum is generated by streaming 224 MeV protons. Thus the proton spectrum and the slope of the A/Q-dependence of heavy ion enhancements are related.
Probably, any downward breaks in the proton spectrum will especially tend to depress heavy ions perhaps such as may be occurring for the 50 ≤ Z ≤ 56 ions in Figures 6 and 7.
Breaks can also disrupt the power-law lower in A/Q as seen by the break at Mg in the multi-spacecraft study of the SEP event of 23 January 2012 (Reames 2017b).
Do the excess protons come from the same ion population as the heavy ions? Recently, Reames (2019b) suggested that two components contributed to the shock acceleration in "impulsive" SEP events with significant excess protons, the heavy ions may Hydrogen Abundance in Gradual SEP Events D. V. Reames 21 come from residual impulsive suprathermal ions with positive power of A/Q, while the protons come from the ambient plasma with a negative power of A/Q (see Figure 9 in Reames 2019b). However, excess protons are seen rather often and in similar amounts, making this dual-source explanation less probable, since two components might be expected to produce a larger range of relative variation. Also, two components would not explain the event in Figure 8 where a proton excess and positive power of A/Q coexists for ions with an ambient 1.5 MK source plasma temperature. Apparently, more protons are required to support shock conditions that can produce or can maintain a strong positive power of A/Q in the enhancements of heavy elements, even when injected abundances already have a positive power of A/Q initially. However, cases do exist where positive powers of A/Q extrapolate to predict the observed proton enhancement (Figures   4 and 7).
We summarize the general behavior of gradual SEP events as follows: (i) Most time intervals in most gradual SEP events (> 60 %) have source temperatures 0.7 ≤ T ≤ 1.6 MK and abundances that decrease as a power of A/Q. Proton enhancements are predicted by the power-law pattern of the other elements.
(ii) Time periods during those events (> 20%) dominated by pre-accelerated impulsive ions, with T > 2 MK and abundances that increase as a power of A/Q, usually have proton enhancements a factor of about 10 above the expected values.
In SEP events overall, three situations can exist. Proton abundances can be consistent with the expectations of a power law in A/Q in (i) "pure" small Fe-rich impulsive SEP events (Reames, 2019b) and in (ii) "pure" large gradual SEP events with decreasing powers of A/Q with few impulsive ions. However, proton abundances significantly exceed expectations primarily in (iii) "compound" SEP events where shock waves reaccelerate impulsive SEP material. This new three-way behavior of proton abundances can help identify the physical processes involved. Thus, Fe-rich SEPs with expected proton abundances were probably accelerated in a magnetic reconnection region without involvement of shocks, while Fe-rich SEPs with a 10-fold excess of protons were probably reaccelerated by a shock wave. This is a powerful new insight.
Hydrogen Abundance in Gradual SEP Events D. V. Reames

22
In contrast to H , He shows substantial source abundance variations 30 ≤ He/O ≤ 100 in both impulsive and gradual events (Reames, 2017c(Reames, , 2019a) with a few impulsive SEP events showing extreme suppression of He/O ≈ 2 (Reames, 2019a). These variations in He may result from FIP-related inefficient ionization of He during transport up into the corona (Laming, 2009). H and He do not share the same behavior; this is why we study H/O and He/O rather than He/H. In view of the comparisons of other elements (e.g. Reames 2018a), it is not surprising that variations of H and He in SEP events also seem to differ completely from variations of H and He in the solar wind.

Disclosure of Potential Conflicts of Interest
The author declares he has no conflicts of interest.
Hydrogen Abundance in Gradual SEP Events D. V. Reames

Appendix A: Reference Abundances of Elements
The average element abundances in gradual SEP events are a measure of the coronal abundances sampled by SEP events (Reference gradual SEPs in Table 1). They differ from photospheric abundances (Table 1) by a factor which depends upon FIP (e.g. Reames 2018a; 2018b). Ion "enhancements" are defined as the observed abundance of a species, relative to O, divided by the reference abundance of that species, relative to O. Table 1 Reference gradual SEP abundances, photospheric, and impulsive SEP abundances are shown for various elements. 1 Lodders, Palme, and Gail (2009), see also Asplund et al. (2009). * Caffau et al. (2011). 2 Reames (1995Reames ( , 2014Reames ( , 2017a. 3 Reames, Cliver, and Kahler (2014a)