Spectral Properties and Abundances of Suprathermal Heavy Ions in Compression Regions near 1 au

Figure 3 compares the results of the two fitting methods using 11 heavy ion species in 41 SIRs. The figure shows that both the average spectral index and e-folding energy are larger when the parameters are fit independently (Method II). The mean for γ_II = 2.40 ± 0.11, with a standard deviation (σ) of 0.67, compared with Method I γ_I, which has a mean value of γ_I = 2.21 ± 0.20, with a σ of 0.93, as seen in Figure 3(a). Similarly, the e-folding energy, shown in Figure 3(b), is sensitive to the fitting method used; the average difference in e-folding energies found using Method I and Method II is 0.60 MeV nucleon⁻¹.

Zoom In Zoom Out Reset image size

Figure 6 examines the event-to-event variations in the spectral index and e-folding energies. Figures 6(a) and (b) show the spectral indices (red dots) for all heavy ion species considered in this study, and the mean value for γ is indicated by the solid black line (averaged over all species within each event). The dashed line denotes the species and event-averaged mean (from Figure 5(b)), and the dotted lines are the ±1σ and ±2σ. Figure 6(a) shows 15 events with species-averaged means outside 1σ, and one event with a mean outside 2σ. Events 1–10 have only four spectral indices because the heavy ion species from Wind/STEP are grouped into He, CNO, NeS, and Fe. Figures 6(a) and (b) show that the event-averaged spectral indices are 2.29 ± 0.11 (Method I) and 2.44 ± 0.10 (Method II). Figures 6(d) and (e) show histograms of the spectral indices for all events and all species, the distribution is Gaussian, with a secondary peak near ∼1.6. We note that the mean values for all calculated spectral indices in Figures 6(d) and (e) are and −2.21 ± 0.20 (Method I) and −2.40 ± 0.11 (Method II), with a σ 0.76 and 0.67, respectively. Figure 6(c) shows the e-folding energy for all species for which the value was within ∼3.0 MeV nucleon⁻¹. The majority of the events are observed to have more than one species with a rollover energy within the energy range used here. This allows us to further explore potential relationships between ion species and e-folding energy.

Zoom In Zoom Out Reset image size

Figure 7 compares the spectral indices (γ_II) in 29 events at 0.02–0.09 MeV nucleon⁻¹ and 0.09–0.3 MeV nucleon⁻¹ for Fe and O (CNO). Figure 7 compares 29 events because the spectral indices at 0.09–0.3 MeV nucleon⁻¹ rely on the availability of ACE data (31 events), and an additional 2 events were excluded because of contributions from upstream events at ∼0.02–0.09 MeV nucleon⁻¹. Figures 7(a) and (b) give the correlation coefficients (r) and the probabilities (p) that these values of r can be exceeded by an uncorrelated pair of parameters. With a correlation coefficient of r = 0.66 and p = 0.0001, the spectral indices for O at the lowest energies are well correlated with those obtained in the higher energy range. The spectral indices for Fe at 0.02–0.09 MeV nucleon⁻¹ and 0.09–3.0 MeV nucleon⁻¹ have a correlation coefficient of r = 0.35 with p = 0.07, which is not as statistically significant. In summary, the O and Fe spectral indices at 0.02–0.09 MeV nucleon⁻¹ and 0.09–0.3 MeV nucleon⁻¹ are reasonably similar to each other and exhibit no systematic steepening or flattening at higher energies.

Zoom In Zoom Out Reset image size

Figure 8 shows the species-averaged spectral index in each event, plotted versus the magnetic compression ratio, H; where H = 1/β, with β being the inverse of the compression ratio described in Fisk & Lee (1980). We note here that the β discussed in Fisk & Lee (1980) is given by:

$$\begin{eqnarray*}&&\beta =\displaystyle \frac{{\left(V^{\prime} +{{\rm{\Omega }}}^{2}{r}_{{\rm{s}}}^{2}\right)}^{1/2}}{{\left(V+{{\rm{\Omega }}}^{2}{r}_{{\rm{s}}}^{2}\right)}^{1/2}}\displaystyle \frac{B}{B^{\prime} }.\end{eqnarray*}$$

Here, V and B are the solar wind speed and magnetic field strength, respectively, and V' and B' refer to conditions downstream. The angular velocity of the Sun is given by Ω, and r_s is the shock location. We do not account for the ratio of the downstream to upstream solar wind speed and distance to the shock, implying the values for H shown in Figure 8 are analogous to the β of Fisk & Lee (1980) within the first order. Figure 8 shows no clear trend between γ_II and H, and γ_II does not follow the expected theoretical trend described by Fisk & Lee (1980). Furthermore, Fisk & Lee (1980) derive β from a distribution function, f, in phase space whereas this study was done using differential intensity, j, but this relationship is well known and given by j = 2Ef /m², where E and m are the ion's energy and mass.

Zoom In Zoom Out Reset image size

Figure 8 groups the 41 SIR events further to investigate whether events with or without shocks at 1 au have different behavior. Filled symbols show SIR events with shocks at Wind. There is no indication that SIR events with shocks display any trend between H and γ_II. There are seven events with a species-averaged spectral index (considering their errors) of ∼1.5 ± 0.1, or about 17% of the events in this study, as can be seen in Figure 6(e).

To investigate the species dependence of E_o within SIRs we plot the abundance ratio verses energy, along with the abundance ratios calculated from the spectral fit parameters using Method II. (see Mason et al. 2008). Figure 9 shows eight events, four of which (Events 14, 15, 31, and 34) have statistically significant values for the e-folding energy for the majority of the species. The other four events (Events 16, 22, 24, and 35) have two or fewer species with energy spectra that have finite e-folding energies. Overall, the abundance ratios show very little variation with energy and these trends are consistent with the behavior of the ratios of the spectral fits, shown as lines. In general, the abundance ratios remain fairly constant with energy, with some events exhibiting more variation than others. For example, in Event 31 the e-folding values for five species change by more than a factor of 2, and for two species the abundances ratios increase by a factor of ∼4. Fe is observed to rollover most frequently. On average, the abundance ratios remain constant with energy within a factor of ∼1.3.

Zoom In Zoom Out Reset image size

Table 2 gives the mean heavy ion abundances obtained by dividing the total fluence measured for each species by the O fluence in the 0.32–0.45 MeV nucleon⁻¹ energy range during the corresponding sampling time interval and then averaged over 31 of the 41 SIR events. We refer to this energy range as the ∼0.38 MeV nucleon⁻¹. Table 1 also lists the Fe/O ratio for individual events. We report only 31 events because ACE was launched in 1997 August and did not observe the 10 events seen at Wind. We choose to use ACE/ULEIS rather than Wind/STEP because the higher mass resolution for ULEIS yields abundances of 11 species.

Figure 10(a) shows the ∼0.38 MeV nucleon⁻¹ event-averaged abundances in 31 SIRs normalized to those in the slow and fast solar wind, plotted versus the ion's mass-to-charge ratio (M/Q) (amu e⁻¹). The charge states are from the slow solar wind as reported by von Steiger et al. (2000). These are C^5.38+, N^5.47+, O^6.05+, Ne^7.97+, Mg^9.5+, Si^8.57+, S^8.75+, Ca^9.02+, and Fe^9.84+. Figure 10 shows that the ST heavy ion abundances in these SIRs are similar to corresponding solar wind values. However, overall the SIR ST abundances are not well organized with respect to solar wind values when plotted versus M/Q. For instance, C, N, O, Ne, and Mg have similar M/Q values but N and Ne show enhancements relative to both the fast and slow solar wind. Similarly, S shows a relative depletion compared to the solar wind. Figures 10(b) and (d) show the ST heavy ion abundances in events that occurred during solar minimum and solar maximum conditions, respectively. Solar maximum years are defined to have a monthly average sunspot number of ≥75; only six events occurred during solar maximum. Figure 10(b) shows that the average ST abundance ratios for SIRs during solar minimum are similar to the solar wind values shown in Figure 10(a). The abundances in SIR events that occurred during solar maximum have slightly elevated values compared with the fast and slow solar wind, but still exhibit no clear trend with M/Q. Figure 10(c), compares the event-averaged abundances in 31 SIRs, normalized to the average slow and fast solar wind abundances (von Steiger et al. 2000; Wurz et al. 2003), versus the element's first ionization potential (FIP). In summary, the ST abundances in SIRs are not well organized with respect to solar wind values when plotted versus FIP or the ion's M/Q ratio.

Zoom In Zoom Out Reset image size

It is well understood that CIR-associated shocks can accelerate particles to MeV energies (Barnes & Simpson 1976; Fisk & Lee 1980) and that diffusive shock acceleration is generally thought to be responsible (Lee & Fisk 1982; Scholer 1999). At lower energies, however (i.e., <500 keV nucleon⁻¹), adiabatic deceleration makes it much more difficult for ions that are accelerated between ∼3 and 5 au to propagate back long distances upstream against the outflowing solar wind into the inner heliosphere (Fisk & Lee 1980). This is expected to create a spectral turnover below ∼500 keV nucleon⁻¹ near 1 au. However, such deficits in the low-energy ion intensities have not been observed by Mason et al. (1997), Ebert et al. (2012b), or this study of SIRs.

Figure 8 shows the relationship between the spectral index and the compression ratio, H. The majority of events fall above the curve predicted by the Fisk & Lee (1980) model, implying that the observed spectra are steeper than those predicted by the model. There seems to be no preference for higher or lower spectral index values with increasing compression ratio. Spectral indices in SIRs do not follow the theoretical relationship, γ = (H+2)/2(H–1), proposed by Fisk & Lee (1980). Desai et al. (1999) examined the forward and reverse shocks of CIRs as measured by Ulysses and, similar to this study, also found that the spectral indices were steeper and departed substantially from the theoretical relationship predicted by the Fisk & Lee (1980) model.

Giacalone et al. (2002) proposed that gradual compressions near 1 au could accelerate particles up to ∼10 MeV without a shock and produce energy spectra similar to recent observations. We compared the species-averaged spectral index (given in Table 2) to the radial thickness of the SIRs in this study, calculated by Broiles et al. (2012), and found a correlation coefficient of r = 0.16 and p = 0.35. If we consider the events with (N = 12) or without (N = 29) shocks the results are still statistically insignificant, with r = 0.24, p = 0.46, and r = 0.15, p = 0.43, respectively. Similarly, Bučík et al. (2009) compared the peak He intensities in simple and compound CIRs, both with and without shocks to the compression region width. Bučík et al. (2009) found a statistically significant result between peak ion intensities and compression region widths for simple CIRs with reverse shocks, but found that the correlations for CIRs without shocks was statistically insignificant, similar to the results discussed here.

More recently, Fisk & Gloeckler (2006) proposed a "pump mechanism" for accelerating low-energy particles through stochastic acceleration in compressional turbulence in the solar wind. The pump mechanism predicts that once the system reaches an isentropic dynamic equilibrium, the ST ion differential energy spectrum should exhibit a universal spectrum with index of 1.5, and a rollover at some undetermined higher energy. We investigate whether this mechanism can be applied to the SIRs studied here. We first note that the spectral indices in the 41 SIRs were generally steeper than 1.5. Figure 6(a) indicates that the spectral indices varied significantly on an event-to-event basis. Only one event had a species-averaged index significantly less than 1.5, and 17% of the events have values ∼1.5 as indicated by the clustering of spectral indices near 1.5 in the histogram in Figure 6(e). Mason et al. (2008) found very similar results, with insignificant clustering near, and only one or two cases below, a spectral index of 1.5. The predictions of the pump mechanism are relevant if the system has come to equilibrium or reached steady-state. Thus, the presence of steeper spectral indices could indicate that either the system has not yet reached equilibrium or that the energy range considered in this study is higher than the purported universal power-law portion of the spectrum. We rule out the latter using Figure 7 because a comparison between the spectral indices at 0.02–0.09 MeV nucleon⁻¹ and 0.09–0.3 MeV nucleon⁻¹ does not show a systematic steepening at higher energies, and our results actually show rollovers in many of these events above ∼0.5 MeV nucleon⁻¹. We note that Fisk & Gloeckler (2006) reported universal power-law spectra between ∼1.5–10 V_sw and our study overlaps with their energy range corresponding to ∼4.4–19 V_sw. Thus, regardless of whether the pump mechanism has reached equilibrium or not, if it is responsible for accelerating the ST heavy ions in the SIRs studied here, then the universal power-law spectral index of 1.5 must occur in a very narrow energy range that corresponds to ∼1.5–4.4 V_sw.

Previous work by Mason et al. (2008) examined the abundance ratios of heavy ion species versus energy and found they were constant within a factor of ∼2. In our study, the average abundance ratios remain constant with energy within a factor of ∼1.3, although some species can exhibit a much larger change, such as those in Event 31 shown in Figure 9. The energy spectra in many of the events in this study were observed to rollover between 0.7 and 2.3 MeV nucleon⁻¹ which is consistent with observations of spectral rollovers near ∼1 MeV nucleon⁻¹ (e.g., Mason et al. 1997).

The model discussed by Fisk & Gloeckler (2008) also predicts that the high-energy cutoff, ε₀, should be linearly dependent on the ion's M/Q ratio, but they note that if diffusion due to field line random walk is important then the M/Q dependence could be weakened. In contrast, our study shows that the e-folding energy in SIRs did not exhibit a M/Q dependence as the ST heavy ion abundance ratios remain fairly constant with increasing energy, consistent with the results of Mason et al. (2008).

In stark contrast to SEP events (e.g., Mewaldt et al. 2005), the heavy ion spectra in SIRs did not show evidence of species-dependence in the rollover energy. Filwett et al. (2017) studied these same 41 events and found source locations with ∼1 au upstream of the SIRs. Li & Lee (2015) and Zhao et al. (2016, 2017) discussed how interplanetary transport mechanisms may be responsible for the M/Q dependence observed in heavy ion spectra in SEP events. If scatter-dominated interplanetary transport is responsible for the M/Q dependence of rollovers in SEP events, then there should also be a M/Q dependence in the spectral rollover energies in the SIRs studied here. This is because like SEPs, SIR ST ions should also encounter interplanetary turbulence as they propagate from ∼2 to 1 au; the only difference is that SEPs travel from <0.1 to 1 au. However, our results indicate that interplanetary turbulence does not affect the heavy ion spectral features observed in SIRs at 1 au. This indicates that either the interplanetary turbulence and transport associated conditions that affect SEP spectra are remarkably different inside of 1 au or that the SEP spectral breaks occur due to acceleration processes at near-Sun CME shocks, as alternatively proposed by Desai et al. (2016), Schwadron et al. (2015), and Li et al. (2009).

Our survey of the ∼0.02–3.0 MeV nucleon⁻¹ heavy ion spectral properties in SIRs shows that spectral indices vary from event-to-event with no systematic M/Q dependence in the spectral rollover energy. Additionally, the SIR ST abundances at ∼0.38 MeV nucleon⁻¹ are similar to but not well organized when compared to the fast and slow solar wind abundance ratios when plotted versus the ion's M/Q or FIP. We note that using the average abundances has limitations; for instance, Table 1 shows that the Fe/O ratio varies significantly from event to event. Similarly, Filwett et al. (2017) showed that the Fe/CNO ratio varied from event-to-event and with solar activity cycle, with higher Fe/CNO SEP-like ratios during solar maximum and lower Fe/CNO solar-wind-like during solar minimum. This led to the conclusion that, similar to the quiet-time ST heavy ion population, SIRs also draw their source material from a suprathermal pool of material originating in prior solar and interplanetary activity (e.g., Dayeh et al. 2017).

Finally, if the SIR ST ions originate primarily from the bulk solar wind, then this should also be reflected in the heavy ion abundance ratios when compared to solar wind values. However, Figure 10 shows that although the abundances are very similar, the SIR abundances are not well-organized with respect to the fast and slow solar wind values when plotted verses either M/Q or FIP. Specifically, ions with similar M/Q ratios show no obvious trends in their depletion or enhancement with respect to solar wind values. Separating the SIRs into those observed during solar minimum or solar maximum also does not organize the ST abundances with respect to the fast or slow solar wind abundances as a function of M/Q. Similarly, there is no correlation between the SIR abundance ratios when compared to the solar wind values as a function of FIP. Filwett et al. (2017) also found no correlations between the Fe/CNO ratio with the upstream solar wind Fe/O ratio. This indicates that if SIR ST ions originate from the solar wind, then some portion of the heated solar wind must undergo processing via as yet poorly understood mechanisms prior to being injected into the SIRs for acceleration up to the ST energies studied here.