Temperature in Solar Sources of ³He-rich Solar Energetic Particles and Relation to Ion Abundances

³He-rich solar energetic particles (SEPs) are characterized by enormous enhancements of rare species like ³He or ultra-heavy ions (mass $>$ 70 AMU) by factors up to 10⁴ above the coronal or solar wind abundances (see, e.g., Kocharov & Kocharov, 1984; Mason, 2007; Reames, 2013, 2017, 2018, for a review). In a typical ³He-rich SEP event, ⁴He, ¹²C, ¹⁴N, ¹⁶O are unenhanced, while heavier species like ²⁰Ne, ²⁴Mg, ²⁸Si, show enhancement that increases with the ion mass (Reames et al., 1994; Mason et al., 2004). The abundance of the light ³He isotope is in contrast with such enhancement pattern. Whereas, with He, the abundance of the lighter isotope is enhanced, with heavy ions, the heavier isotopes are enhanced (Mason et al., 1994; Wiedenbeck et al., 2010).

Solar sources of ³He-rich SEPs have been associated with extreme ultraviolet (EUV) coronal jets (see Bučík, 2020, and references therein), indicating acceleration in magnetic reconnection region involving field lines open to interplanetary (IP) space (Reames, 2002; Wang et al., 2006). The events show a high association ($\sim$99%) with type-III radio bursts (e.g., Reames & Stone, 1986; Nitta et al., 2006), the emission generated by low-energy electrons ($<$30 keV; Krucker et al., 1999) escaping into IP space. Furthermore, ³He-rich SEP events have been accompanied by minor X-ray flares (mostly B- and C- class; e.g., Nitta et al., 2006, 2015; Mason et al., 2009; Bučík et al., 2016).

Early measurements of high ionic charge states (Luhn et al., 1987) indicated $>$10 MK source temperature of ³He-rich SEPs. However, an increase of charge states with kinetic energy (e.g., DiFabio et al., 2008) has suggested that the mechanism responsible for high charge states is an additional ionization in a dense environment after/during acceleration (e.g., Reames et al., 1994; Klecker et al., 2007). Reames et al. (1994) examined 228 ³He-rich events in August 1978 – April 1991 with ³He/⁴He $>$0.1 at the energy range of 1.2–1.6 MeV nucleon^-1. Their abundance enhancement pattern has suggested that C, N, O are fully ionized as ⁴He, but Ne, Mg, Si are only partially stripped of their orbital electrons. The data on equilibrium ionization states in astrophysical plasma shows that this can happen in a temperature range of $\sim$3–5 MK (Reames et al., 1994). In a more recent survey, Reames et al. (2014a, b, 2015) examined 111 Fe-rich impulsive events in April 1995 – April 2013 at the energy range 2–10 MeV nucleon^-1, and reported the most probable temperature range of $\sim$2.5–3.2 MK. Note that several events have been reported with enhanced abundances of C and N, suggesting temperatures $\sim$0.5–1.5 MK (Mason et al., 2002, 2016). These temperatures may indicate that ions are accelerated very early (Mason et al., 2016) and (or) on open field lines where heating is minimal (Reames et al., 2015). The required low temperatures may also be due to a cool material observed in the form of a mini-filament in some ³He-rich SEP sources (Mason et al., 2016; Innes et al., 2016; Bučík et al., 2018a).

At low energies, below $\sim$0.2 MeV nucleon^-1, both equilibrium and non-equilibrium charge states depend only on temperature (e.g., Kocharov et al., 2000; Kovaltsov et al., 2001) and not on charge stripping effects causing the energy dependence of heavy-ion charge states observed in ³He-rich events at higher energies, $\sim$0.2–1 MeV nucleon^-1 (Klecker et al., 2007; DiFabio et al., 2008). Therefore, the source temperature in ³He-rich SEP events can be determined from measurements of charge states at low energies. DiFabio et al. (2008) have obtained temperatures in the range of 1.3 to 3 MK using low-energy (0.062–0.110 MeV nucleon^-1) Fe charge states measurements in 14 ³He-rich SEP events in May 1998 – September 2000.

The ionic charge states were inferred with help of measured isotopic ratio enhancements such as ²²Ne/²⁰Ne (Cohen et al., 1999a, b; Wiedenbeck et al., 2010). Wiedenbeck et al. (2010) have reported a corresponding source temperature of $\sim$4 MK for a single ³He-rich SEP event and Cohen et al. (1999a) have reported the same temperature for nine large SEP events that were heavy-ion rich but show small ³He abundance (³He/⁴He $<$0.01 in most events).

Reames (1988) reported an increase of 2–3 MeV nucleon^-1 heavy ion (C, Mg, Si, S, Fe) enhancements (relative to ⁴He) with soft X-ray temperature in the range 10–16 MK. The origin of the reported dependencies remains unclear since many of these species are fully stripped at these temperatures (Reames, 1988). Reames (1990) has suggested that plasma waves escaping from heated closed regions accelerate nearby ³He-rich SEPs, possibly causing an increase of heavy-ion enhancements. The 1.3–1.6 MeV nucleon^{-1 3}He/⁴He ratio showed no correlation with soft X-ray temperature (Reames et al., 1988). The temperature was determined from ISEE soft X-ray measurements at the time of hard X-ray maximum or at the time of type-III radio burst (at 2 MHz that corresponds to $\sim$6 R_☉) when hard X-rays were not observed or hard X-ray time profile was complex (Reames, 1988; Reames et al., 1988). The authors have pointed out that the correlation between elemental ratios and temperature does not strongly depend on the choice of this time. They have reported the average hard X-ray to 2 MHz radio peak delay of $\sim$1 min.

It is believed that anomalous abundances of ³He-rich SEPs are the signature of a unique acceleration mechanism associated with magnetic reconnection in solar flare sites (e.g., Miller, 1998). The models of ³He-rich SEPs usually involve temperature in ion acceleration (e.g., Roth & Temerin, 1997; Liu et al., 2006; Mason & Klecker, 2018; Kartavykh et al., 2020). Temerin & Roth (1992) and Roth & Temerin (1997) have reported a model of ³He and heavy-ion acceleration by obliquely propagating electromagnetic ion cyclotron waves. Roth & Temerin (1997) have found that among discrete values of 2, 4, 6, and 10 MK, the abundance ratios are close to observed values at temperature 4 MK. In the model of ³He and ⁴He acceleration by parallel-propagating plasma waves, Liu et al. (2006) have found a temperature range of 0.8–3.0 MK (median and mean 1.4 MK and 1.6 MK, respectively) by fitting the observed spectra of ³He and ⁴He for six events. The mechanism of heavy-ion enhancement in ³He-rich events based on charge-to-mass ($Q/M$) dependence of Coulomb energy losses below the Bragg peak ($\sim$1 MeV nucleon^-1) requires temperatures 0.1–0.6 MK (Mason & Klecker, 2018). In an approach that combines $Q/M$ dependent Coulomb losses with $Q/M$ dependent stochastic acceleration, the enrichment of heavy and ultra-heavy ions that is similar to the measured one can be obtained with temperatures of $\sim$1 MK (Kartavykh et al., 2008, 2020).

The temperature in solar sources of ³He-rich SEPs (that can be only determined indirectly) and the effect on ion abundances is largely unexplored. In this paper, we study 24 ³He-rich SEP events in the period 2010–2015. To determine the temperature in ³He-rich source flares, we use EUV imaging observations that can monitor lower temperatures when ions are not fully stripped. Furthermore, to examine a linkage between the ion abundances and temperature in ³He-rich sources, we use low-energy ($\lesssim$0.2 MeV nucleon^-1) measurements, where ion charge states are dominated by thermal collisions.

The elemental abundances of the ³He-rich SEP events in this survey are measured with the time-of-flight mass spectrometer Ultra Low Energy Isotope Spectrometer (ULEIS; Mason et al., 1998) on the Advanced Composition Explorer (ACE; Stone et al., 1998). Depending on ion species, ULEIS roughly covers the energy range 0.1–10 MeV nucleon^-1. For example, the Fe measurements can extend down to 0.04 MeV nucleon^-1. The solar sources of ³He-rich SEPs are investigated using high-resolution observations from the Atmospheric Imaging Assembly (AIA; Lemen et al., 2012) on the Solar Dynamics Observatory (SDO; Pesnell et al., 2012). The AIA provides full-disk images of the Sun with 1.5$\arcsec$ spatial and 12 s temporal resolution at seven EUV, two UV, and one visible-light band. The AIA data were processed with the standard AIA SolarSoft procedure aia_prep.pro available via SolarSoft library and normalized by the exposure time.

Numerous ³He-rich SEP events were measured at L1 during the SDO era in solar cycle 24 (Reames et al., 2014b; Bučík et al., 2014, 2016, 2018b; Chen et al., 2015; Nitta et al., 2015; Mason et al., 2016), however, for this study, we select only some of these events. The reason is that seven previously reported events (2010 Sep 4, Nov 4; 2012 Jan 13; 2013 Dec 24; 2014 Feb 6, Apr 24, May 29) have the source close or behind the limb with weak or no activity observed from the Earth. Another five events (2010 Oct 19; 2011 Dec 14; 2012 Nov 18, Jul 3; 2014 Jan 1) have the AIA images saturated, and not usable for further analysis. Table 1 lists the properties of the examined 24 ³He-rich SEP events and the associated solar sources. Column 1 indicates the event number, column 2 the SEP event start date, and column 3 the time intervals used for computing elemental ratios based on the ion intensities near 0.2 MeV nucleon^-1. Columns 4 and 5 provide the event integrated (averaged) ³He/⁴He and Fe/O ratios, respectively, at the energy range of 0.320–0.453 MeV nucleon^-1 where ion abundances have been often reported. Column 6 gives the type-III radio burst start time from WAVES/Wind (Bougeret et al., 1995) data with 60 s cadence. Columns 7 and 8 indicate the GOES 14–15 (Bornmann et al., 1996) X-ray flare class and start time, respectively. Column 9 gives the flare site in AIA images. Column 10 shows the NOAA active region (AR) number. The X-ray flare class, start time, and NOAA AR number were taken from the Edited Solar Events, compiled by the NOAA Space Weather Production Center (ftp://ftp.swpc.noaa.gov/pub/warehouse). Column 11 provides a decadic logarithm of the temperature in the solar source, derived from AIA channels by the differential emission measure (DEM) analysis. Specifically, the column gives the EM-weighted temperature (see Section 3.1). The last column indicates references to earlier studies of these events.

In most of the investigated events (17 out of 24), there was an EUV jet observed in the associated solar source. Another type of activity includes EUV coronal wave (events #1, #4, #11), ejection (events #13, #21) or just EUV brightening (events #5, #22). Except for events #17 and #24, the solar sources for the remaining events have been identified in the earlier papers.

The remote-sensing approach with EUV observations performed for ³He-rich SEP sources at the time of type-III radio bursts provides a temperature range of 1.4–4.5 MK with a median of 2.2 MK. This value is in good agreement with a median temperature of 2.1 MK derived from in-situ Fe ion charge states at 0.062–0.110 MeV nucleon^-1 (DiFabio et al., 2008). This agreement, on the other hand, implies that ³He-rich SEPs in this survey may be accelerated very close to the type-III radio burst onset times. Our temperature range is also consistent with the temperature of the source plasma (2.5–3.2 MK) that is accelerated in ³He-rich SEP events as deduced from the abundance measurements in 3–5 MeV nucleon^-1 (Reames et al., 2014a, 2015).

We found a significant negative correlation between the ³He/⁴He ratio and the temperature in ³He-rich sources that may be associated with the strong link between the temperature and X-ray (EUV) peak flux. It is consistent with earlier work that has shown that 1.3–1.6 MeV nucleon^{-1 3}He/⁴He (Reames et al., 1988) as well as 1–10 MeV nucleon^-1 ultra-heavy ion enhancement (Reames & Ng, 2004) anti-correlates with soft X-ray peak intensity. The authors argued that in small flares, much of the energy is absorbed by the rare ³He and ultra-heavy elements, while in large flares, there is enough energy for the acceleration of more abundant elements, decreasing the relative abundances of the rare species. Remarkably, the negative trend between ³He/⁴He and the temperature found here does not show up at higher temperatures ($>$10 MK) as reported by Reames et al. (1988). Liu et al. (2006) have reported a decrease of the ³He/⁴He ratio with increasing background plasma temperature as a result of thermal damping of waves that accelerate ⁴He. In their model (Figure 9, left in Liu et al., 2006), the ³He/⁴He ratio decrease slows down at higher temperatures and almost stops at $>$10 MK. Thus, the negative correlation at low temperatures found in this study and zero correlation at high temperatures reported by Reames et al. (1988) may well correspond with this model.

The abundances of heavier elements, relative to oxygen, generally behave with the temperature as expected from the calculated enhancement factor using equilibrium charge states. The two elements, C and Mg, are an exception. Their relative abundances show no relation with temperature, although the computed enhancement factor suggests a positive trend. The C and Mg, together with ⁴He, are the elements with the smallest or no change in $Q/M$ in the measured temperature range (see Figure 7(left)). However, this probably does not explain the missing temperature dependence for the relative abundances of C and Mg as ⁴He shows the strongest one. We may speculate that the processes (other than charge-changing) that cause a negative correlation for the ³He/⁴He ratio might eliminate the presumed positive correlation for C/O and Mg/O. Specifically, the effect of the size of the flare on less abundant C and Mg in comparison to O would cause the C/O and Mg/O to decrease with the temperature. The same effect would cause ⁴He/O to increase with temperature.

The choice of the time and location for the temperature determination may introduce uncertainty to the relationship between the temperature and ion abundances. It is unknown at what time ions are accelerated in ³He-rich SEP events. It is believed that it is in the impulsive phase of solar flares along with non-relativistic ($\sim$10–100 keV) electrons (Reames et al., 1985; Wang et al., 2012). Timing analysis of these small events would not be helpful due to significant errors in estimations of ion solar release time that can be tens of minutes (Mason et al., 2000; Wang et al., 2016). Furthermore, energetic ions in ³He-rich SEP events do not show optical signatures as energetic electrons that could narrow down the time of the ion acceleration. Also, it is not well-known at what particular place at the flare sites ions are accelerated (jet spire or foot-points). If particles are accelerated at the cooler jet spire, it is probably a larger area, involving the hotter foot-point region, that affects the ion charge states. Some recent works have investigated the temperature of jets associated with type-III radio bursts (Chen et al., 2013; Mulay et al., 2016, 2019). Mulay et al. (2016) have examined 20 AR jets and reported the temperature of the jet spire in the range of 1.6–2.0 MK. In a study of one AR jet, Mulay et al. (2019) found a similar low temperature of 2 MK at the spire and 5–8 MK hot plasma at the foot-point region. Chen et al. (2013) have examined the temporal evolution of the temperature in one jet. The authors have reported 7 MK hot foot-points and cooler (1.3–2.5 MK) jet spire at type III-radio burst onset. The temperature distribution in this survey peaks at slightly higher temperatures (2.0–2.5 MK) compared to the temperatures in the jet spire reported by Chen et al. (2013) and Mulay et al. (2016).

We confirm steep power-law dependence of abundance enhancement factor on $Q/M$ for heavy-ion species (⁴He–Fe) as previously reported by Mason et al. (2004) and Reames et al. (2014a). The slope of the power-law dependence is in good agreement with these studies that involve ultra-heavy elements. The trend seen in the abundance enhancement factor is consistent with the most recent models on heavy ion acceleration by cyclotron resonance, showing that the efficiency of acceleration increases inversely with the $Q/M$ (Kumar et al., 2017; Fu et al., 2020). In the model of ion scattering on reconnecting magnetic islands (Drake et al., 2009), the heavy-ion production rate can be expressed as a power-law in $Q/M$.

We have examined 24 ³He-rich SEP events and for the first time (i) determined temperature in the event associated source flare using EUV imaging observations and (ii) analyzed the relationship between the suprathermal ion abundances and the EUV temperature. A similar analysis for $>$1 MeV nucleon^-1 ions was performed more than 30 years ago with temperature inferred from the soft X-ray observations of the whole solar disk. The study presented here shows

1. 1.

   a remarkably good agreement between temperature inferred from EUV images and the temperature obtained from ion charge states and abundance measurements,

2. 2.

   a negative correlation between ³He/⁴He ratio and the source temperature that is apparently caused by non-charge changing mechanisms,

3. 3.

   the behavior of the elemental ratios ⁴He/O, N/O, Ne/O, Si/O, S/O, Ca/O, Fe/O with the source temperature as expected from the calculated enhancement factor assuming ionization equilibrium.