# Ion-rich Acceleration during an Eruptive Flux Rope Event in a Multiple Null-point Configuration

Melissa Pesce-Rollins<fnref n="1" />, Alexander MacKinnon<fnref n="2" />, Karl-Ludwig Klein<fnref n="3" />,<fnref n="4" />, Alexander J. B. Russell<fnref n="5" />, Hugh Hudson<fnref n="2" />, Alexander Warmuth<fnref n="6" />, Thomas Wiegelmann<fnref n="7" />, Sophie Masson<fnref n="4" />,<fnref n="8" />, Clare Parnell<fnref n="5" />, Nariaki V. Nitta<fnref n="9" />, and Nicola Omodei<fnref n="10" />

Received 2025 May 22; revised 2025 June 30; accepted 2025 July 1; published 2025 August 12

## Abstract

We report on the γ-ray emission above 100 MeV from the GOES M3.3 flare SOL2012-06-03. The hard X-ray (HXR) and microwave emissions have typical time profiles with a fast rise to a well-defined peak followed by a slower decay. The >100 MeV emission during the prompt phase displayed a double-peaked temporal structure with the first peak following the HXR and microwaves, and the second one, about 3 times stronger, occurring $17 \pm 2$ s later. The time profiles seem to indicate two separate acceleration mechanisms at work, where the second γ-ray peak reveals a potentially pure or at least largely dominant ion acceleration. The Atmospheric Imaging Assembly imaging shows a bright elliptical ribbon and a transient brightening in the northwestern (NW) region. Nonlinear force-free extrapolations at the time of the impulsive peaks show closed field lines connecting the NW region to the southeastern part of the ribbon, and the magnetic topology revealed clusters of nulls. These observations suggest a spine-and-fan geometry, and based on these observations, we interpret the second γ-ray peak as being due to the predominant acceleration of ions in a region with multiple null points. The >100 MeV emission from this flare also exhibits a delayed phase with an exponential decay of roughly 350 s. We find that the delayed emission is consistent with ions being trapped in a closed flux tube with gradual escape via their loss cone to the chromosphere.

*Unified Astronomy Thesaurus concepts: Solar flares (1496); Gamma-rays (637); Solar coronal waves (1995)*

*Materials only available in the online version of record: animation*

## 1. Introduction

The signatures of particle acceleration during solar flares are observable over a wide range of energies, with both electrons and ions reaching relativistic energies in some cases. The main electron acceleration in a flare is at tens of keV energies that absorb a significant fraction of the total flare energy (e.g., R. P. Lin & H. S. Hudson 1976; A. G. Emslie et al. 2005). When accelerated ions reach an energy threshold of ~280 MeV, they can produce neutral pions via p-p reactions, and these decay directly into two γ-rays. This yields a broad continuum peaking at about 70 MeV, which may extend up to GeV energies (see R. J. Murphy et al. 1987 for a review of γ-ray production in solar flares). Detections of γ-ray emission from solar flares are not as abundant as those in other wavelengths, but there are indications that flare-accelerated ions may carry comparable energy to that of electrons (e.g., R. Ramaty & N. Mandzhavidze 2000; A. G. Emslie et al. 2012; M. J. Aschwanden et al. 2017). However, due to the limited number of γ-ray flare detections,

one of the unresolved questions regarding ion acceleration during solar flares is whether it shares a close physical relationship with electron acceleration.

W. T. Vestrand (1988) and R. J. Murphy et al. (1993) found correlations between >0.3 MeV electron bremsstrahlung continuum emission with 4–8 MeV nuclear excess emission and also with the 2.223 MeV neutron-capture line, while I. M. Chertok (1990) reported a similar correlation between the γ-ray fluence in the 4–7 MeV range and the microwave fluence at 15 GHz, produced by the gyrosynchrotron emission of electrons at hundreds of keV. More recently, A. Y. Shih et al. (2009) reported a correlation over a range of >3 orders of magnitude between the neutron-capture line fluence versus the >0.3 MeV bremsstrahlung fluence of solar flares observed with RHESSI (R. P. Lin et al. 2002) and the γ-Ray Spectrometer on the Solar Maximum Mission. M. Ackermann et al. (2012) studied the impulsive flare SOL2010-06-12 and found that >30 MeV γ-ray emission lags the bremsstrahlung by $6 \pm 3$ s. All of these findings provide support for a common acceleration mechanism driving the two populations of particles during the prompt phase of the γ-ray flare emission. However, there have also been observations where there was evidence for a closely connected acceleration between the 4 and 7 MeV range of

<figure><img src="image_1.png" /></figure>

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<footnote n="1">¹Istituto Nazionale di Fisica Nucleare, Sezione di Pisa I-56127 Pisa, Italy</footnote>

<footnote n="2">²School of Physics and Astronomy, University of Glasgow, UK</footnote>

<footnote n="3">³Observatoire de Paris, LIRA, Univ. PSL, CNRS, Sorbonne Univ., Univ. Paris Cité, 5 place Jules Janssen, F-92190 Meudon, France</footnote>

<footnote n="4">⁴Observatoire Radioastronomique de Nançay, Observatoire de Paris, CNRS, PSL, Université d'Orléans, Nançay, France</footnote>

<footnote n="5">⁵School of Mathematics and Statistics, University of St Andrews, Mathematical Institute, North Haugh, St Andrews, KY16 9SS, UK</footnote>

<footnote n="6">⁶Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany</footnote>

<footnote n="7">⁷Max Planck-Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany</footnote>

<footnote n="8">⁸Sorbonne Université, Ecole polytechnique, Institut Polytechnique de Paris, Université Paris Saclay, Observatoire de Paris, Université PSL, CNRS, Laboratoire de Physique des Plasmas (LPP), Paris, France</footnote>

<footnote n="9">⁹Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304, USA</footnote>

<footnote n="10">¹⁰W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA</footnote>
photon energies and hard X-ray (HXR) emission, but at the same time, episodes with different time profiles were shown to exist in the same events, as well as γ-ray peak delays by several seconds (D. J. Forrest & E. L. Chupp 1983).

The spatially integrated time evolution of accelerated electrons and ions during the course of the 2003 October 28 X17 flare showed that the emission from accelerated electrons dominated the initial phase while the γ-ray line emission from accelerated ions became prominent during the following several hundred seconds (J. Kiener et al. 2006). S. Masson et al. (2009) showed that pion-decay γ-rays were emitted together with relativistic electrons in the impulsive phase in the 2005 January 20 event, but that the impulsive phase itself consisted of different particle releases with varying ratios of the γ-ray to HXR or microwave intensities. E. L. Chupp et al. (1993) reported that, as the 1989 September 9 flare developed, the proton acceleration became slightly more efficient than the acceleration of electrons. Differences between ion and electron acceleration also seemed to be supported by the finding (G. J. Hurford et al. 2003, 2006) that the locations of electron HXR bremsstrahlung and ion 2.2 MeV γ-ray line emission may differ (see also the review in N. Vilmer et al. 2011). But recent work (A. F. Battaglia & S. Krucker 2025) suggests that this result may have been over interpreted.

The question whether the differences in detailed timing analyses are due to species-dependent propagation and emission, as advocated, e.g., by D. J. Forrest & E. L. Chupp (1983) and E. Hulot et al. (1992), or whether they do reveal truly different acceleration scenarios is still open.

The γ-ray observations of the M3.3 flare of SOL2012-06-03 provide an excellent case study to further investigate the question of whether electron and ion acceleration share a close physical relationship. The time profile of the >100 MeV emission detected by the Fermi-Large Area Telescope (LAT; W. B. Atwood et al. 2009) during the impulsive phase displays two distinct peaks occurring within the first minute of the flare (see also G. H. Share et al 2018; M. Ajello et al. 2020). The first γ-ray peak coincides with the 100–300 keV peak whereas the second one does not appear to have any corresponding counterpart in X-rays or radio, suggestive of a potentially pure ion acceleration mechanism. Following the impulsive phase, the γ-ray time profile exponentially decays for roughly 8 minutes until the Sun leaves the Fermi-LAT field of view. In this paper, we report on the multiwavelength observations of this flare with the goal to identify the sources of the γ-ray emission during the prompt and delayed phases.

## 2. Gamma-Ray Observations

### 2.1. Fermi-LAT

The LAT is a pair-conversion telescope sensitive to γ-rays in the energy range from 30 MeV to >300 GeV. It is the main instrument of the Fermi γ-ray space telescope that surveys the entire sky, observing the Sun when it passes through the field of view (roughly 15%–20% of the time). To analyze the flare SOL2012-06-03, we performed an unbinned likelihood analysis of the Fermi-LAT data within the Multi-Mission Maximum Likelihood (3ML)<fnref n="11" /> framework using fermitools<fnref n="12" /> version 2.0.8. We selected Pass 8 Transient class events from a 10°

circular region centered on the Sun and within 100° from the local zenith (to reduce contamination from the Earth limb). We first analyze the flare integrating over the full duration selecting all the events above 60 MeV to better constrain the shape of the spectrum at low energies and test three models to the Fermi-LAT data. The first two, a simple power law (PL) and a PL with an exponential cutoff (PLEXP),<fnref n="13" /> are phenomenological functions that may describe bremsstrahlung emission from relativistic electrons. The third model uses templates based on a detailed study of the γ-rays produced from the decay of pions originating from accelerated protons with an isotropic pitch angle distribution in a thick-target model (R. J. Murphy et al. 1987, 2009). In all the three analyses, the background is modeled by a fixed contribution coming from the galactic γ-ray emission (described by the standard template available in the fermitools), and by an isotropic emission describing the unresolved particle background (also described by the standard available template). This latter background component is left free to vary as it encompasses the background variation due to orbital modulation. We rely on the likelihood ratio test and the associated test statistic (TS; J. R. Mattox et al. 1996) to estimate the significance of the detection. The TS of the PL fit (TS<sub>PL</sub>) indicates the significance of the source detection under the assumption of a PL spectral shape, and the ΔTS = TS<sub>ALT</sub> - TS<sub>PL</sub> quantifies how much an alternative model improves the fit. Note that the significance in σ can be roughly approximated as $\sqrt{\text{TS}}$.

The impulsive phase of the flare, shown by the red symbols in the bottom panel of Figure 1, displays two peaks, and given the importance of the timing of these peaks, we decided to use the finest time binning possible by requiring that each bin contains at least 12 photons and that the start of the detection (when we have a TS > 5) coincides with the arrival of the first photon, with a probability greater than 0.9 of being associated with the Sun. This choice clearly results in limited statistics in each temporal bin, and consequently, the ΔTS between the PL and PLEXP model is marginal (of the order of 2σ in each bin). The time integrated data, on the other hand, are best fit with the curved model with a significance of 6σ.

In order to evaluate the statistical significance of the double peak structure in LAT data, we fit the time profile during the impulsive phase of the LAT data with a single Gaussian and with a double Gaussian. These two simple models are meant to represent the case with a single peak and one with a double peak. The $\chi^2$ and the corresponding p-values are reported in Table 1.

Based on the results in Table 1, we confirm that there are two distinct peaks during the impulsive phase, the first occurring at 17:53:20 UT ±2.5 s and a second one at 17:53:36 UT ±1 s. To further test the validity of the first smaller peak in the LAT data, we fit the main peak in the Fermi-Gamma-Ray Burst Monitor (GBM) data between 100 and 300 keV with a single Gaussian to obtain the value of the mean, 2012 June 3 17:53:21 ±0.5 s, which is consistent within the errors with the mean of the first peak in the LAT data suggesting a common origin.

The first peak in the LAT data reaches a flux value above 100 MeV of $(43 \pm 14) \times 10^{-5} \text{ ph cm}^{-2} \text{ s}^{-1}$ whereas the second peak reaches $(104 \pm 31) \times 10^{-5} \text{ ph cm}^{-2} \text{ s}^{-1}$.

<footnote n="11">¹¹ https://threeml.readthedocs.io/en/stable/index.html</footnote>

<footnote n="12">¹² https://github.com/fermi-lat/Fermitools-conda/wiki</footnote>

<footnote n="13">¹³ The definition of the models used can be found here: https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html.</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Multiwavelength light curves of SOL2012-06-03. Top panel: meter-wave radio combined Bleien–Birr spectrogram. Bottom panel: Fermi-LAT >100 MeV flux points (red markers, left-hand axis) and on the right-hand axis are the 100–300 keV GBM time profiles (blue), RHESSI 25–50 keV time profile (gray), radio RSTN at 8.8 GHz in yellow and POEMAS 45 GHz in green (all in arbitrary units). The times in which the γ-ray flux peaks are 17:53:19 ±1.5 s and 17:53:36 ±1 s UT (red dashed lines in the upper panel). Fermi-LAT observed significant emission from this flare until 18:02 UT (when the Sun left the field of view). The impulsive and delayed Fermi-LAT emission, lasting until 18:02 UT, is shown in the insert of the figure. The blue shaded box in the insert indicates the time range of the extended emission of the flare not shown in the bottom panel of the figure.</figcaption></figure>

proceeds to drop by more than a factor of 10 within 10 s from
this second peak. Following this drastic drop, the flux level
remains at a >5σ significance but exponentially decays with
an estimated decay timescale, τ value of 350 s until the Sun
leaves the field of view of the LAT at 18:02 UT. The Fermi-
LAT time profile is shown in the bottom panel of Figure 1
together with the normalized Fermi-GBM (C. Meegan et al.
2009) 100–300 keV light curve, RHESSI (R. P. Lin et al.

2002) 25–50 keV light curve, and microwave time profiles
observed by whole-Sun radio telescopes at 8.8 GHz (RSTN;
O. Giersch & J. Kennewell 2022) and 45 GHz (POEMAS;
A. Valio et al. 2013).

We also performed a time-resolved spectral analysis centered
on the individual peaks as well as on the impulsive and the
delayed phases of the >100 MeV time profile. We define the
impulsive phase to take place in the time range 17:53:10–17:54:01
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Spectrum observed in the GBM B0 (high-energy) detector during the interval 17:53:10–17:53:46 UT, as a function of photon energy. Also shown is the best-fit spectrum combining a broken power-law continuum spectrum and a narrow deexcitation line template, with the parameter values given in the text.</figcaption></figure>

<table><caption>**Table 1**

χ² over the Degrees of Freedom and *p*-values from the Fit to the Time Profile of the LAT Data with a Single and Double Gaussian Model</caption><thead><tr><td>Model</td><td>χ²/d.o.f.</td><td>p-value</td></tr></thead><tbody><tr><td>Single Gaussian</td><td>37/9</td><td>3 × 10<sup>-5</sup></td></tr><tr><td>Double Gaussian</td><td>18/7</td><td>1 × 10<sup>-2</sup></td></tr></tbody></table>

**Note.** degrees of freedom.

and the delayed phase from 17:54:01 to 18:02:11 UT. We found that there is insufficient statistics to be able to distinguish a spectral variation between the two peaks in the impulsive phase. In the impulsive and delayed intervals, we find that the ΔTS<sub>PLEXP</sub> is greater than 4σ indicating that this curved model best describes the data. We also repeated the fit with the pion-decay model and found that the preferred proton spectral indices<sup>14</sup> are 5.5 ± 0.4 and 4.4 ± 0.5, respectively. With the best proton index and the normalization of the spectral fit, we can get an estimate of the total number of >500 MeV protons needed to produce the observed γ-ray emission over the observed time range, which is (3.73 ± 0.17) × 10<sup>28</sup> and (2.08 ± 0.23) × 10<sup>27</sup> for the impulsive and delayed phases.

The flux values, spectral index, and significance of the fit with a PL model in the time resolved analysis are reported in Table 2. Very little spectral variation is observed throughout the 9 min of Fermi-LAT detection of this flare, and no correlation is seen between the spectral index and the flux values.

## 2.2. Fermi-GBM

The GBM instrument comprises NaI detectors for HXRs and low-energy γ-rays, plus two bismuth germanate (BGO) detectors; these together cover the range 0.3–30 MeV (C. Meegan et al. 2009), i.e., the range in which nuclear line signatures of energetic ions are found. GBM BGO data thus have the potential to give information on flare ion

properties complementary to LAT, from the ion energy range ~1–100 MeV (R. J. Murphy et al. 2007).

We analyzed the data from the GBM B0 detector using the OSPEX software (K. Tolbert & R. Schwartz 2020), initially considering the impulsive period described in Section 2.1. We estimated the background by extrapolating from two preflare intervals since the LAT data indicate ion acceleration continuing throughout the extended period up to spacecraft night at 18:02 UT. Although there are some photons above the background at >1 MeV, these are few in number. Spectral fits are poorly constrained but provide interesting upper limits.

Figure 2 shows the GBM B0 spectrum for the interval 17:53:10–17:53:46 UT, together with the best fit to the data for a spectrum comprising three components: broken PL continuum, narrow line at 2.223 MeV, and a narrow deexcitation line template. The neutron-capture line is unobservably narrow, so we used the OSPEX default line width of 0.1 keV, much less than the instrumental resolution. From those available via OSPEX, the narrow line template assumed a heliocentric angle of 43°; photospheric target abundances and coronal abundances for the fast ions; alpha-to-proton ratio α/p = 0.1; and a PL proton energy distribution, ~E<sup>-δ</sup> with δ = 5.4. Although the broken PL allows the spectral index γ to vary with photon energy, an almost constant value γ = 2.6 is found throughout the fitted energy range, 0.3–7 MeV. The fitting also assigns a negligible amplitude to the 2.223 MeV line and an amplitude of 0.02 ± 0.03 to the deexcitation line template. An equally acceptable fit (χ<sup>2</sup> ≃ 1 in both cases) is found if we carry out the fit using only PL continuum. We conclude that there is scant evidence for any nuclear ion signatures at all during the impulsive time interval.

We can treat the estimated amplitude of the line template as an upper limit on nuclear line flux, and thus on proton numbers. Taken at face value, it implies a total of 2.1 × 10<sup>29</sup> protons above 30 MeV. If we assume that the E<sup>-5.4</sup> distribution extends unbroken to hundreds of MeV, this implies 8.7 × 10<sup>23</sup> protons above 500 MeV, giving an upper limit orders of magnitude less than the number deduced from LAT (Section 2.1). We conclude that the ion distribution interacting with the dense atmosphere must be much flatter or

<footnote n="14">14 The best proton spectral index is obtained by fitting the data with the pion-decay template models calculated for a range of proton spectral indices.</footnote>
possibly even increasing with energy, below the >200 MeV range where pion production occurs.

We also considered a period immediately following, 17:53:46–17:53:56 UT. The neutron thermalization time, several tens of seconds (e.g., R. J. Murphy et al. 2003), leads us to expect 2.223 MeV line appearing at such a later time. The same fitting procedure again yielded an indefinite value for the nuclear line template, but a slightly better defined flux in the 2.223 MeV line: $0.43 \pm 0.27 \text{ cm}^{-2}$. With the OSPEX-supplied photon yield for the same assumed ion distribution as above, this fluence implies $(1.7 \pm 1.0) \times 10^{30}$ protons above 30 MeV or $(6.9 \pm 4.3) \times 10^{24}$ protons above 500 MeV—still requiring a flattening of the distribution below the hundreds of MeV range.

After this initial period, with its low-significance 2.223 MeV line detection, there is very little signal above the background in the BGO detectors. For the whole of the period 17:53:46–18:02:00 UT, the same sort of three-component spectrum gives a poor fit to the few counts above the background ($\chi^2 = 11$). The amplitude of the 2.223 MeV line is essentially undetermined ($0.006 \pm 0.006 \text{ s}^{-1} \text{cm}^{-2}$) while the amplitude of the line template, assuming $\delta = 4.4$ as found above from the LAT data, implies $(1.9 \pm 0.6) \times 10^{31}$ protons above 30 MeV. Extrapolating the distribution found from LAT to lower energies implies $(3.0 \pm 0.3) \times 10^{31}$ protons above 30 MeV, so a single PL distribution from ~MeV to GeV energies is consistent with both GBM and LAT data during the period following the second $\gamma$-ray peak.

### 3. X-Ray and Radio Observations

The Fermi-GBM 100–300 keV time profile is shown in Figure 1 together with the Fermi-LAT >100 MeV fluxes and the microwave time profiles at 8.8 and 45 GHz between 17:53 and 17:55 UT and up to 18:02 UT in the insert of the figure. This is the time range over which the flare was significantly detected by the LAT. Two distinct peaks are observed in the HXRs, a bright initial peak occurring at 17:53:19 UT and a second minor peak occurring at 17:53:48 UT. The latter is also observed at 8.8 GHz, but not at 45 GHz. The RHESSI light curves at all energies $\ge 25$ keV show the same time profiles. The theory of synchrotron emission, where electrons are assumed to have energy well in excess of their rest energy, predicts that an electron with Lorentz factor $\gamma$ emits up to a frequency of $3/2\gamma^2\nu_{ce}$ (e.g., Equation (3.28) of A. G. Pacholczyk 1970), where $\nu_{ce}$ is the electron cyclotron frequency. For a magnetic field, weaker than 0.4 T emission at 45 GHz implies $\gamma > 3$ and therefore a kinetic energy above 1 MeV. This is a lower limit, since the magnetic field and the efficiency of the emission are overestimated. The burst decays to a plateau, which is probably due to thermal bremsstrahlung. The comparison of the light curves shows how the HXRs correlate well with the microwave fluxes, as expected from the gyrosynchrotron interpretation of the microwaves. But what is also evident from this figure is how the second $\gamma$-ray peak does not appear to have any evident counterpart in microwaves or X-rays, except for a small bump superimposed on the general decay of the main HXR and 8.8 GHz emission.

#### 3.1. X-Ray Imaging

We reconstructed the nonthermal X-ray sources by applying the expectation-maximization algorithm MEM_GE

<figure><img src="image_4.png" /><figcaption>**Figure 3.** RHESSI sources at 12–25 keV (red, at contour levels of 10%, 20%, 30%, 40%, 60%, and 80%) and 50–100 keV (blue, contours at 30%, 40%, 60%, and 80%) overplotted on AIA 94 Å during the main HXR peak (top two panels) and during the second $\gamma$-ray peak (bottom two panels). Time intervals are reported on the top of each panel.</figcaption></figure>

(P. Massa et al. 2020) to the RHESSI data. Whereas to reconstruct the images in the 12–25 keV range, we used the CLEAN algorithm, which gives better results for extended sources as compared to MEM_GE. In Figure 3, we show the 12 s time integrated 12–25 keV (red contours) and 50–100 keV (blue contours) RHESSI sources overplotted on Atmospheric Imaging Assembly (AIA; J. R. Lemen et al. 2012) 94 Å images covering the time interval of the main HXR peak and during the second $\gamma$-ray peak. A pair of nonthermal footpoints is clearly visible during the two peaks. During the first peak (top two panels in Figure 3), the footpoint locations show little evolution. However, in the following time intervals (bottom two panels), the northern footpoint becomes stronger and clearly moves to the NW, indicating that reconnection and acceleration are now active in a magnetic field structure, which has a different connectivity than earlier in the event. The thermal emission is concentrated in the southern part of the flare (where also EUV emission is brightest, as will be discussed in Section 4, and the nonthermal footpoints are located). There do not appear to be any other sources with emission above the 10% level within the AIA region shown in the figure. Note that Fourier-type imagers like RHESSI are limited in their dynamic range to typically less than an order of magnitude.

#### 3.2. Radio

The light curves at HXR and microwave frequencies and the dynamic spectrum in the decimeter to meter wave range are compared in Figure 1 with the evolution of the $\gamma$-ray flare. They trace the history of electron acceleration in an extended volume around the flaring active region. The similar time profiles at HXRs and microwaves (8.8 and 45 GHz) trace nonthermal electrons with energies between a few tens of keV and at least 1 MeV in the low corona. The light curve at 8.8 GHz evolves smoothly, but it shows discontinuities (near
17:53:00 and 17:53:10 UT, for instance) where the rise accelerates, indicating a succession of acceleration episodes.

The dynamic spectrum (top panel) shows an enhanced background continuum (gray shading; type IV burst), on top of which spectral fine structure is distinguished: a series of type J bursts between about 450 and 130 MHz and a dense series of bursts with a smaller bandwidth between 200 and 500 MHz. The type IV continuum starts near 17:52:30, which is also the time when Fermi-GBM sees the first enhancements of the HXR emission. In light curves of the radio emission in the 900–600 MHz range (not shown), the continuum is seen to have a similar time profile as in the microwave range (e.g., 8.8 GHz), but it lasts longer, and the maximum (about 17:54 UT) is increasingly delayed with decreasing frequency. In the dynamic spectrum, the continuum is seen down to at least 20 MHz, with a delayed onset at frequencies below 80 MHz. The broad bandwidth of this continuum emission reveals nonthermal electrons in an extended height range, reaching from the bottom of the corona to, say, half a solar radius above.

On top of the continuum, the type J bursts are emitted by electron beams propagating upwards into extended magnetic loops, ceasing emission near the loop tops. The type J bursts start near 17:52:20 UT, 10–20 s before the HXR and microwave bursts. They continue through the rise of the HXR and microwave profile. The last J-burst starts near 17:53:30 UT.

Some of the bursts in the 200–500 MHz range are type III bursts. They are hence also emitted by upward-propagating electron beams. For harmonic radio emission, the thermal electron density at the start of the type J bursts (450 MHz) is $6 \times 10^8 \text{ cm}^{-3}$, the electron density corresponding to the turnover frequency $0.5 \times 10^8 \text{ cm}^{-3}$. The start frequency of the type J group hence suggests an acceleration region of rather low density, higher in the corona than the regions usually considered as the typical acceleration regions of the HXR emitting electrons (see, e.g., reviews in M. J. Aschwanden 2002; K.-L. Klein 2021), but similar to a simple impulsive flare as reported by N. Vilmer et al. (2002). We note that the series of type J bursts ceases abruptly during the decay of the main HXR and microwave peak, when the HXR source configuration changes (Section 3.1 and Figure 3). This commonality corroborates the conclusion that the magnetic connectivity changes at this time, just before the rise to the second γ-ray peak. Since the type J bursts are emitted in much larger structures than the X-rays, the change of connectivity must be related with the evolution of the coronal magnetic field on large spatial scales. Such an evolution is also illustrated by the EUV images in Figure 3, which show the evolution and eventual disappearance of the erupting flux rope (see Section 4.3) on the northwestern side of the main EUV brightening and the soft X-ray source.

The common occurrence of the HXRs, type IV-continuum, and type J bursts argues in favor of coordinated episodes of electron acceleration at different coronal altitudes and the release of nonthermal electrons into a wide range of magnetic structures. While a burst near 17:53:12 UT that drifts from about 500 MHz toward higher frequencies indicates downward-precipitated electrons, the HXR emission and the type IV continuum are well underway at that time. Previous bursts seen in the 500–900 MHz range actually show rapid drifts toward lower frequencies and hence cannot be attributed to downward-propagating electrons. However, these bursts occur at times (e.g., 17:52:57 and 17:53:08 UT) when the microwave

continuum emission accelerates its rise. They are therefore rather related to energy release episodes in the low corona, below the region where the electrons emitting the type J bursts are accelerated.

The HXR and 8.8 GHz time profiles have a secondary bump near 17:54 UT. It has no counterpart at decimeter to meter wavelengths and is therefore likely to be due to electrons that remain in the low corona. This event marks also the break of the decay of the γ-ray light curve, which transits into a slow gradual decay. Higher up, the radio emission evolves now independently of the acceleration processes in the low corona. A new cluster of bursts occurs between 17:54 and 17:55 UT in the range 200–650 MHz, and a type II burst occurs between 18:00 and 18:16 UT below 150 MHz (not shown). The HXR, microwave, and γ-ray emissions show no new enhancement until 18:02 UT, when the Sun leaves the field of view of Fermi-LAT 30 minutes.

# 4. Extreme Ultraviolet Imaging and Time Evolution

## 4.1. Overview

The apparent lack of an X-ray or radio counterpart to the second γ-ray peak observed during the impulsive phase of this flare suggests an ion-rich particle acceleration. To constrain the sources of the high-energy γ-ray emissions and the locations and mechanisms of the particle acceleration, we examined the time evolution of the SOL2012-06-03 flare in all the AIA on board Solar Dynamics Observatory (SDO; W. D. Pesnell et al. 2012) channels.

An overview movie showing all the channels with the maximum 10 s cadence of the instrument is provided as an online material; a snapshot of the event is shown in Figure 4.

The light curve at the top of the movie shows the evolution of the whole-Sun X-ray flux in the wavelength ranges 1–8 Å and 0.5–4 Å observed by the GOES satellites. From this movie, it is possible to see a flare ribbon with an approximately elliptical shape. The eastern part of the ribbon is very bright, while the northwestern part has a more complex structure with multiple localized regions of moderate brightness. This is a region of pronounced changes. During the early slow rise of the soft X-rays, this is best seen at 131 Å. During the following steeper rise, the brightening continues and becomes visible in a broader region surrounding the compact initial one, and in a wider range of coronal emission lines. During the final rise to the soft X-ray peak, the EUV images show brighter emission with a complex spatial structure:

1. The flare ribbon evolves into its elliptical shape, mainly clockwise from SE to NW.

2. As it does, a diffuse broad arc-shaped feature ranging from westward to northward of the flaring active region propagates away from it. Depending on the wavelength, it is seen from 17:53:30 to 17:55:00 UT. We identify this feature as an EUV wave.

3. On the northwestern side of the active region, two localized brightenings (henceforth referred to as hot spots) appear near 17:53:30 UT and remain visible at stable positions for about a minute (until 17:54:36 UT at 171 Å). Both hot spots are faintly visible in the EUV image of Figure 5; the northern one is within the yellow rectangle and will be discussed in more detail below.

4. The two hot spots fade from view when a bright structure connecting them is seen to move northwestward (e.g.,
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Snapshot of the event in all of the SDO channels. Top panel shows the GOES soft X-ray time profile. An animation of this figure is available. It shows the evolution from 17:50:10 to 18:09:50. Its real-time duration is 7 s. A copy is also available at https://www.lmsal.com/nitta/outgoing/fermi_events/20120603/aia_9ch_0304_time_20120603_17.mp4.</figcaption></figure>

(An animation of this figure is available in the online article.)

17:54:45 UT at 131 Å) and to develop into the geometry of an extended loop, with footpoints that remain rooted in the flaring active region. The feature does not evolve from the hot spots, but appears to come from the bright main flaring region (blue rectangle) and to travel through the region of the hot spots. It is seen in coronal wavelengths and also clearly at 304 Å. We identify this feature as an erupting magnetic flux rope.

5. Major structural changes are seen in the northern part of the flaring region around 17:52:23 UT, with the short appearance of a bright loop. They could be at the origin of the outward (northwestward in projection on the disk) expansion of the presumed flux rope.

## 4.2. EUV Intensity around the Flare Ribbon

We analyzed the time evolution of the intensity in selected regions of the flare at 94 Å (Figure 5). At this wavelength, AIA has a significant response to plasma temperatures above $10^{6.5}$ K (P. Boerner et al. 2012), and therefore, these time histories reveal the evolution of the heating in these areas. We also analyzed images with the 335 Å filter, which has a peak of sensitivity near $10^{6.5}$ K, too, albeit less pronounced and with a higher sensitivity to plasma below $10^6$ K than does the 94 Å filter.

The movie shows that the northern branch of the ribbon forms gradually between about 17:53 and 17:54 UT, proceeding clockwise from its southeastern extremity. The light curves in the three rectangular regions overplotted on the AIA image are displayed in the right panel of Figure 5 with the same colors as the rectangles. These three regions are (1; blue rectangle) the

most prominent brightening within the flare ribbon, (2; yellow) the northwestern hot spot, and (3; red) a region on the southeastern part of the flare ribbon, to which the magnetic field lines from the northwestern hot spot connect, as reported in Section 5. The light curves are the average intensities in the rectangular fields, normalized by their values at the first instant of the plot. The emission of the extended bright region within the elliptical ribbon (blue rectangle and curve) rises gradually until a peak near 17:56 UT. The two other light curves start late, and rise simultaneously in two phases, with an acceleration near 17:53 UT, to maxima near 17:54 UT, i.e., before the peak of the main EUV emission. The maximum in the northwestern hot spot (yellow) is slightly delayed, and the decay phases differ. The light curve of the southeastern part of the ribbon starts a secondary rise at 17:54:50 UT with a peak near the peak time of the main brightening within the ribbon. This statement has to be taken with some reserve since the saturation of the images during the phase of brightest emission may cause a spillover of the signal from the bright region (blue) into the field of the red southeastern rectangle.

The two γ-ray peaks, at the times marked by vertical dashed lines, occur during the accelerated rise phase of the emissions from within the northwestern and southeastern rectangles. We examined the rise phase in other rectangular fields along the flare ribbon. The direct neighbors of the southeastern (red) rectangle outlined in Figure 5 display a similar time evolution. More remote fields on the northern part are delayed, while fields on the southern part share the smooth rise displayed by the main brightening. The comparison suggests that the regions in the northwestern (yellow) and the southeastern (red) rectangle comprise footpoints of the magnetic fields to which energy is transferred from a common release region in the corona. This finding meets the expectation from the field-line extrapolation described in Section 5. The projected distance between the centers of the two rectangles is about 76,000 km.

To better visualize the timing between the second γ-ray peak and the EUV brightening in the NW region, we describe the AIA 94 Å and 335 Å intensity profiles using a piecewise polynomial function (spline<fnref n="15" />) and compute its derivative. The results are shown in Figure 6 together with the Fermi-GBM and LAT time profiles. From this figure, it is possible to see how the time derivative of the AIA 335 Å intensity profile peaks at the same time as the second γ-ray peak, and that of the 94 Å peaks 7 s later. The difference in peak times between the two AIA wavelengths can be attributed to the different ion populations and temperatures that each channel is most sensitive to. The occurrence of the γ-ray peak at the time of the fastest rise of the extreme ultraviolet (EUV) emission is reminiscent of the Neupert effect between thermal X-rays and nonthermal microwaves and X-rays, and a similar coupling was observed also for the behind-the-limb γ-ray flares, as reported in M. Pesce-Rollins et al. (2022). The timing suggests that the two γ-ray peaks are associated with energy releases in different parts of the flaring active region and potentially due to different particle populations.

## 4.3. Erupting Flux Rope

An EUV bright loop is visible in all the AIA coronal EUV filters starting from 17:53:05 and remains visible until

<footnote n="15">¹⁵ The degree of smoothing of the spline is equal to 4.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Snapshot of the SOL2012-06-03 flare at 94 Å (left panel; the lower left and upper right corners of the image are, respectively, at coordinates [−718", 153"] and [−394", 460"] with respect to the center of the solar disk) and time histories of the average intensity (right panels) in three selected fields delimited by the colored rectangles (the colors of the curves are those of the rectangles). The time histories are normalized to the values at the first instant in the plot. The two vertical dashed lines show the times of the two Fermi-LAT γ-ray peaks.</figcaption></figure>

17:53:38 UT. According to the dynamics of this event in EUV, this EUV loop is most likely located along a section of the erupting flux rope. Thanks to the fact that the flux rope is visible in multiple filters, we were able to track the eruption at high cadence and find that it evolves toward the NW direction of the flare ribbon. To illustrate the progress of the eruption, we manually identified points along the flux rope in each AIA frame, and interpolated between them using an Akima spline, to overlay the loop at multiple times on one of the AIA images and a line of sight (LOS) of the Helioseismic and Magnetic Imager (HMI; P. H. Scherrer et al. 2012) magnetogram of the region, shown in Figure 7. We note that the interpolated loops are useful to visualize the evolution of the erupting structure, but do not allow to reproduce the flux rope topology. Loop fits are omitted for 94 Å, 211 Å, and 335 Å because the relatively long exposure times for these images produced a motion blur, and other filters offered sharper images at nearby times. For a comparison of timings, the NW hot spot is first detected in AIA images at 17:53:31 UT, and the Fermi-LAT >100 MeV light curve peaks at 17:53:36 UT, i.e., during the later part of the flux rope eruption. The relative timings, locations, and directionality strongly support a causal connection in which the flux rope eruption drives the processes that produce the second γ-ray peak.

## 4.4. EUV Wave

Figure 8 shows that the flare excited a bright wave front in the AIA 304 Å filter channel. It is strongly directed and travels in an NW direction, away from the NW end of the flare. The plane-of-sky speed is ≈2000 km s⁻¹, implying a high Mach number (see, A. Warmuth 2015). The AIA 304 Å channel is sensitive to emission from the chromosphere and transition region, with a characteristic temperature of 10⁴.⁷ K (J. R. Lemen et al. 2012); therefore, we interpret Figure 8 as showing a wave front at chromospheric altitudes, similar to classic Hα observations of Moreton waves. The wave front is first detected at 17:53:56 UT, in the second 304 Å image obtained after the second γ-ray peak. Although we do not see the bright front in the immediately preceding 304 Å image, this may simply be because it is obscured by diffraction patterns coupled with the brightness of

the flare. Extrapolating backwards in time by 20 s, the propagation is consistent with having originated from the NW hot spot at the time of the second γ-ray peak.

Propagating disturbances are also evident in the AIA 171 Å and 193 Å channels, with these being most clearly seen in running difference movies. The emission in these channels includes a counterpart to the chromospheric disturbance that travels to the NW. Additionally, coronal intensity perturbations travel large distances toward the E and NE at speeds of ≈800 km s⁻¹. The expanding front appears to cause dynamic brightenings at low altitudes near the E limb and N pole (171 Å 17:55–18:05). We also remark that an intensity perturbation in the 193 Å channel leaves the instrument’s eastern field of view during 18:02–18:04, propagating away from the Sun.

# 5. Nonlinear Force-free Extrapolations

## 5.1. Extrapolation Method

We used SHARP vector magnetograms from SDO/HMI (M. G. Bobra et al. 2014) and performed nonlinear force-free extrapolations that solve

$$ (\nabla \times \mathbf{B}) \times \mathbf{B} = \mathbf{0}, \qquad (1) $$

$$ \nabla \cdot \mathbf{B} = 0, \qquad (2) $$

where B is the magnetic field vector. These equations have to be solved with the boundary condition

$$ \mathbf{B} = \mathbf{B}_{\text{obs}} \text{ on the bottom boundary.} \qquad (3) $$

A general overview of force-free solar magnetic fields and various methods to compute them can be found in the review article by T. Wiegelmann & T. Sakurai (2021). In the present paper, the input magnetograms were preprocessed to make them force-free consistent as outlined in T. Wiegelmann et al. (2006), and the force-free equations were solved using an optimization code that has been developed specifically for SDO/HMI vector magnetograms, which is described in T. Wiegelmann et al. (2012). Briefly, to solve the force-free
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Comparison of time histories during the impulsive phase of the flare. Fermi-LAT >100 MeV flux shown in red, Fermi-GBM 100–300 keV counting rates, arbitrarily normalized, shown in black, mean intensity of the northwestern region (yellow box in Figure 5) in 335 Å/ 94 Å (top panel/bottom panel), and its time derivative (dashed line). The 335 Å time derivative peaks at 17:53:36, and 94 Å peaks at 17:53:43 UT. The second γ-ray peak reaches its maximum value at 17:53:36 UT, in coincidence with the 335 Å time derivative and 7 s prior to the 94 Å suggesting that the EUV emission observed in the northwestern region is physically related to the ion acceleration. The differences in peak time between the 335 Å and 94 Å time derivatives is either due to the variation in diffraction patterns between the two channels or the difference in ions and temperatures that each channel is sensitive to.</figcaption></figure>

problem, we define a functional

$$L = \int_V w_f \frac{|(\nabla \times \mathbf{B}) \times \mathbf{B}|^2}{B^2} + w_d |\nabla \cdot \mathbf{B}|^2 d^3V \\ + \nu \int_S (\mathbf{B} - \mathbf{B}_{\text{obs}}) \cdot \mathbf{W} \cdot (\mathbf{B} - \mathbf{B}_{\text{obs}}) d^2S. \quad (4)$$

The first two terms in the volume integral are zero if the force-free Equations (1) and (2) are fulfilled. The $w_f$ and $w_d$ are weighting functions. The surface integral takes care of the boundary condition Equation (3), and the $\mathbf{W}$ in this term is a diagonal matrix whose elements are inversely proportional to the estimated measurement errors of the photospheric field vector. The parameter $\nu$ controls the injection speed of the boundary data into the computational domain, and $\nu = 0.001$ is (usually and also in this case) the optimal choice for HMI vector magnetograms. Further details of the method and code can be found in T. Wiegelmann et al. (2012). The result of the

optimization is the 3D magnetic field vector in the computational domain above the observed active region.

## 5.2. Magnetic Topology

### 5.2.1. Analysis Methods and Visualization

The 3D structure of the reconstructed magnetic field was analyzed using the Magnetic Skeleton Analysis Tools (MSAT) package, which is described in B. M. Williams (2018) and available from B. M. Williams & C. E. Parnell (2022). This analysis package identifies the 3D magnetic skeleton (i.e., the magnetic null points, their separatrix surfaces and spines, and the separators identified by the intersection of the separatrix surfaces) of the magnetic field by the following steps. First, grid cells containing magnetic null points are identified using the trilinear method (A. L. Haynes & C. E. Parnell 2007), which provides definite confirmation that a null point exists within a specific grid cell. The locations of nulls within grid
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Temporal evolution of the erupting flux rope as traced by the AIA coronal EUV filters overplotted on an AIA 94 Å image and the HMI LOS magnetogram. The color bar reports the midpoint times *tobs* of the AIA exposures used to determine the positions of the erupting loop. The AIA 94 Å image shown in the left panel has *tobs* = 17:53:50 UT. The white boxes indicate the location of the NW hot spot in the AIA 94 Å image.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** AIA 304 Å wave linked to the second γ-ray peak. Here, we have shown every second AIA 304 Å image, giving a constant 24 s cadence. The location of the wave front at each time is indicated by the superimposed straight blue line.</figcaption></figure>

cells are then iteratively refined by applying the trilinear method to subgrids inside each null-containing cell, until required tolerances have been achieved. The most difficult steps are the classification of the null points (as positive or negative, determined by eigenvalues of the magnetic field in the vicinity of each null) and identifications of the local directions of their spines and separatrix surfaces (determined by the eigenvectors). Full details are given in B. M. Williams (2018). The separatrix surfaces and spines are then traced outwards from the null points, with care taken to identify where the separatrix surfaces meet null points of the opposite polarity. The tracing of the separatrix surfaces and separators are based on the methods used in A. L. Haynes & C. E. Parnell (2010).

The MSAT package also produces 3D visualizations of the magnetic skeleton. In the following figures, magnetic nulls are shown as red and blue balls, and field lines are drawn that include the spines and a sample of field lines in the separatrix

surfaces associated to the nulls. Positive nulls, whose separatrix field lines are directed away from the null and whose spine field lines are directed into the null, are colored red, and their fan and spine field lines are colored salmon and red, respectively. Negative nulls, for which separatrix field lines are directed toward the null and spine field lines point away from the null, are colored blue, and their fan and spine field lines are colored pale blue or blue, respectively. Separators, which are special field lines that connect pairs of null points, are shown as thick yellow lines.

### 5.3. Full Magnetic Skeleton

The MSAT null finder identified 99 magnetic null points in the extrapolated magnetic field of our event. This number is not surprising given the complexity of the photospheric magnetic field distribution, and it is likely typical of solar active regions. The highest null point identified was located
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Magnetic skeleton of the reconstructed magnetic field shortly before the flare and its relation to the flare ribbons. (Left) Perspective view showing the SHARP $B_r$ at 17:48:00 on the base, using the standard colorized HMI color table. (Right) Top view showing flare ribbons in AIA 304 Å. The skeleton is visualized by showing null points as red or blue balls, spine field lines (thick red and blue lines), fan field lines (thin salmon-colored or pale blue lines), and separators (thick yellow lines); see also Figure 10 for greater clarity. Reddish/bluish color identifies positive/negative 3D nulls and their associated field lines. The size of the base is 304 SHARP pixels in both dimensions, making the sides of the base approximately 111 Mm.</figcaption></figure>

9.1 Mm above the base. However, most of the nulls are low lying, with 90% having altitudes below 2.5 Mm, i.e., at heights associated with the chromosphere or photosphere. While the fraction of the null points that are in the corona is therefore relatively small, at 10%, it is significantly larger than the 2% fraction reported for the quiet Sun by S. Régnier et al. (2008), and we attribute the greater null heights in this active region compared to the quiet Sun to the larger scales associated with active region flux distributions. Where null points are found at chromospheric heights, departures from non-force-free (low beta) conditions are likely to change the locations of the null points; however, we believe that the large-scale topology of the active region, which our discussion focuses on, is robust.

Figure 9 shows the full magnetic skeleton from two viewpoints, with HMI SHARP $B_r$ and the AIA 304 Å emission shown on the base. The AIA data were reprojected onto the SHARP patch coordinates using `sunpy`<fnref n="16" />; and the alignment was manually fine-tuned by aligning sunspots in AIA 1700 Å with the corresponding $B_r$ concentrations, which resulted in a translation by a few pixels. Examining Figure 9, a striking topological feature is the large cluster of interconnected nulls that runs along the western edge of the flaring region, most easily seen in the right panel as the network of yellow separators along the western edge of the elliptic ribbon. The flare starts at the southern end of this null cluster network, and it spreads toward the northern end where the NW hot spot is located, as more of the null point network becomes activated. Comparing Figures 3 and 9 shows that the main X-ray source and much of the brightest EUV emission remain at the southern end of the null point network.

The magnetic skeleton of the extrapolated magnetic field explains some of the major visual differences between different parts of the flare ribbons. The S and southeastern parts of the ribbons are narrow and bright, and these coincide with locations where fan surfaces intersect with the base (as is

illustrated by the salmon-colored lines in Figure 9), analogous to the circular ribbon of a simple circular ribbon flare. In contrast, the W and northwestern parts of the elliptical flare ribbon are spread over a larger area with a broken appearance. The extrapolation indicates that this appearance reflects the topological complexity in this part of the active region, with the dispersed ribbons being associated with magnetic footpoints of an extensive cluster of nulls (traced by the thick yellow lines in Figure 9). Finally, we remark that, when comparing the flare ribbons to the magnetic skeleton, it should be borne in mind that AIA 304 Å has a characteristic temperature of $10^{4.7}$ K (J. R. Lemen et al. 2012), which is expected to occur several Mm above the photospheric base. This can produce an offset between the intensity image and the corresponding magnetic field lines, with this effect being largest where the field is highly inclined. The advantage of showing AIA 304 Å instead of 1600 Å or 1700 Å (which form closer to the base) is the availability of a short exposure taken during the flare that avoids saturation and bleeding and, therefore, most clearly shows the flare ribbon structure.

### 5.3.1. Topology of NW Hot Spot Region

The main focus of this paper is the ion-rich particle acceleration of the second γ-ray peak, which the observations indicate is somehow connected with the NW hot spot. We therefore focus now on the magnetic skeleton components related to the magnetic nulls that are near to the NW hot spot, shown in Figure 10. With the rest of the skeleton stripped back, Figure 10 (upper left) shows that the reconstructed magnetic field contains a dome formed of blue fan and red spine field lines, in the NW corner, threaded by a wall comprised of salmon-colored fan and blue spine field lines that arch over the active region, connecting to the photosphere in the SE part of the flare ribbon.

Figure 10 (lower left) shows a view looking into the dome from the NW. During flares, the AIA 1600 and 1700 Å filters

<footnote n="16">¹⁶ https://sunpy.org/</footnote>
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Magnetic skeleton components most relevant to the NW hot spot, visualized as for Figure 9. (Upper left) Side view from the SW showing flare ribbons in AIA 304 Å on the base. Blue fan field lines and red spines form a dome-like structure at the NW corner, while salmon-colored fan field lines and blue spines form a wall that arches over the active region, connecting in the SE ribbon. (Lower left) View from the NW into the blue dome, showing the hot spot emission in AIA 1600 Å. The hot spot coincides with the footpoints of blue spine field lines from negative nulls. (Right) A slightly inclined top-down close-up of the null point chain, where the blue dome and salmon-colored wall intersect. The spine field line that connects most centrally into the NW hot spot belongs to a negative null point that is located at the NW end of the chain of nulls (represented by the red and blue balls).</figcaption></figure>

are dominated by emission from continuum and spectral lines formed at chromospheric and transition region temperatures (P. J. A. Simões et al. 2019), making these AIA images especially well suited for comparing flare ribbons with magnetic topology. The 1600 Å image taken at 17:53:53 UT captures the NW hot spot well, with the hot spot unaffected by the saturation and bleeding that affects other parts of the ribbons; hence, this image is shown on the base in Figure 10 (right). The NW hot spot directly coincides with the footpoints of dark blue spine lines that are connected with negative null points.

The topological structure we have isolated in Figure 10 is similar to the fan and spine skeleton of a single negative null point, with the hot spot situated at the footpoint of a spine field line. The dome and wall structure can be interpreted by considering what happens if a single negative null point splits into a chain of *n* + 1 negative null points and *n* positive nulls, alternating in sign along the chain. In this case, the original spine field line becomes a wall that is bounded by a pair of negative spines, which corresponds well to the structure we have identified. B. M. Williams (2018) provides an extended discussion of topological structures like these and their occurrence in the solar atmosphere.

Figure 10 (right) provides a close-up of the reconstructed null chain, using a slightly inclined (15°) top-down view. The blue spine that connects into the center of the hot spot belongs to the negative null point (blue ball) at the NW end of the null chain. This null point's spine field lines form one edge of the wall of salmon-colored fan field lines. It is likely to be pertinent that the chain of null points runs from SE to NW, which aligns with the direction of the flux rope eruption (Figure 7) and the direction in which the AIA 304 Å wave front propagates (Figure 8). This alignment may be potentially

important for the acceleration. Spines from nulls at the SE end of the null chain connect into a fainter patch of emission, near the bottom edge of the image. Null points in the chain have low altitudes, consistent with the upper chromosphere or transition region, where the relatively large density means that in principle acceleration benefits from a large supply of particles but is impeded by high collisionality. Finally, we do not put too much weight on the precise number or altitude of the null points, which may be subject to uncertainties from the field extrapolation or may change during the dynamics of the eruption and flare; however, we believe that the existence of an extended weak-field region with an SE–NW orientation is robust, as is the large-scale magnetic topology.

The main conclusions from this topological analysis are that the NW hot spot and its conjugate brightening in the SE ribbon are consistent with the particle acceleration occurring in the null cluster at the NW corner of the active region, and that the particles that power the emission of the hot spot precipitate along the spines of the negative nulls (and neighboring field lines). The direction of the null chain suggests that ions may be accelerated by a shock wave passing through this extended weak-field region, which then precipitate at the far end of the null chain. Alternatively, the acceleration may be associated with the onset of reconnection within the null cluster, e.g., in response to stressing of the null points by the flux rope eruption.

## 6. Interpretation

### 6.1. *The Impulsive Phase*

From the magnetic configuration presented in Section 5.2, one possible scenario that could explain the impulsive phase of this flare is illustrated in Figure 11. The particle acceleration
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Geometry of the magnetic field including two fan surfaces and three null points, one surface delimiting the flare ribbon (large pink dome) and one surrounding the NW ribbon (smaller blue dome). The labels represent three key features tied to the particle acceleration during this event. Label 1 indicates the region where the particle acceleration leading to the first peak is believed to occur, label 2 shows the EUV bright loops associated with the erupting flux rope driven shock, and label 3 is the location of the cluster of magnetic nulls near the NW hot spot. The right panel shows the AIA 171 Å image of the elliptical ribbon with the three regions indicated.</figcaption></figure>

leading to the first peak appears to occur during the main flare phase in the vicinity of the J-shaped flare ribbons labeled “1” in the figure. This is supported by the similarities in the time profiles between γ-rays and emissions in HXRs and radio waves (shown in Figure 1), as well as the RHESSI footpoints shown in Figure 3. The predominant emission of ions in the second peak is a strong argument for an acceleration process at a different place and possibly of a different nature from the one accelerating the electrons and ions in the first peak. The change of location of the associated energy release is supported by the temporal association between the γ-ray peak and the distinct EUV brightening on the northwestern side of the elliptical flare ribbon. The change of the dynamic spectrum in the 500–100 MHz range, with the time coincidence of a series of type J bursts with the main HXR and microwave peak, together with the first γ-ray peak, and the absence of these bursts during the second γ-ray peak, further supports this idea. This is not the first case where accelerated electrons and ions displayed distinct and separate phases during a flare. J. Kiener et al. (2006), for example, reported significant changes in the time evolution of the nuclear line emission with respect to the bremsstrahlung emission during the flare of 2003 October 28. However, this is the first time that such distinct phases are observed for >100 MeV emission and that the location of the energy release and the acceleration process for the second γ-ray peak are identified as being separate from the first one.

## 6.2. Acceleration Mechanisms

The time evolution of the second γ-ray peak is impulsive, like the first one, and the coincidence with the rise of the EUV intensity confirms the similarity with impulsive acceleration processes. The particle acceleration in this part of the flare is unusually ion rich, and it coincides with the eruption of a fast magnetic flux rope (gray line anchored in the J-shaped flare ribbons in Figure 11). The topological analysis of the magnetic field in Section 5.3.1 indicates that particles producing the NW hot spot are accelerated in a cluster of magnetic null points that are interconnected by magnetic separators. Here, we consider two main types of explanation: acceleration by reconnection

(by DC and Fermi mechanisms, at the reconnection site labeled 3 in Figure 11), and acceleration involving a shock driven by the eruption (shown by the green arc in Figure 11). It is also possible that mechanisms of both types could work together, with one mechanism providing the initial injection of energetic particles and another process further continuing the acceleration energization.

When the flux rope erupts beneath the “magnetic wall” identified in Section 5.3.1, the magnetic field in the vicinity of the null cluster will naturally be stressed by the eruption, which we would expect to form intense parallel currents along the separators. This raises the possibility of acceleration by at least two reconnection mechanisms. First, if parallel currents concentrated at the separators have an associated parallel electric field, e.g., due to resistivity, then particles can be accelerated by a DC mechanism. J. Threlfall et al. (2016) and A. Borissov et al. (2020) have recently modeled this process using MHD simulations and test particles, obtaining proof-of-principle that this mechanism may accelerate particles into the MeV to GeV range, especially given a stronger current density and longer separators. The main objection to DC acceleration is that it cannot explain preferential ion energization. In fact, a hypothesis of acceleration by DC electric fields implies that electrons should also be accelerated to greater than 100 MeV, which we do not see evidence for.

The second reconnection mechanism that we consider is Fermi acceleration. It is well established that thin current layers fragment by tearing instabilities; see for example P. F. Wyper & D. I. Pontin (2014) for a simulation of nonlinear tearing of a current sheet at a 3D null point. The nonlinear development following the instability produces conditions favorable to acceleration by Fermi processes. J. F. Drake et al. (2009) and J. F. Drake & M. Swisdak (2014) have argued that ions are preferentially energized during reconnection because ions gain an immediate kick of the order $m_i V_A^2$ when they enter a reconnection exhaust (whereas electrons gain much less energy in this initial step), and subsequent acceleration within merging flux ropes causes particles to gain energy at a rate proportional to the particle energy (J. F. Drake et al. 2006, 2013). The ions therefore run
farther ahead in energy space, and the electrons never catch up. This scenario has been validated in 2D simulations (e.g., Z. Yin et al. 2024) and 3D simulations (e.g., J. T. Dahlin et al. 2014, 2017; Q. Zhang et al. 2021; L. Comisso & L. Sironi 2022).

Alternatively, the second γ-ray peak coincides with the eruption of a magnetic flux rope. Because of its high speed, it may drive a shock wave, especially in the restricted region of weak magnetic field around the null points. First-order Fermi acceleration at shocks is a well-established mechanism that has been proposed to accelerate particles during solar flares (e.g., E. W. Cliver et al. 1993; G. Rank et al. 2001; G. H. Share et al. 2018; M. Ajello et al. 2021; M. Pesce-Rollins et al. 2022). The limited duration of the shock could in principle explain the short duration of the γ-ray peak, the spatially localized NW hot spot in EUV and its stable position, and the correlated EUV-brightenings of the northwestern and south-eastern ribbons (yellow and red rectangles in Figure 5), which support instead a scenario of localized energy release on field lines connecting the conjugate locations.

In this scenario, the duration of the second γ-ray peak should be similar to the time it takes for the shock to transit the weak-field region. In the plane-of-the-sky approximation, the length of the null cluster is about 5000 km, and the EUV wave that is later seen propagating away from the NW hot spot travels at around 2000 km s⁻¹ (Section 4.4), implying that the rise time should be approximately 2.5 s. This timescale is consistent with the rapid increase in the Fermi-LAT > 100 MeV flux at the onset of the second peak, seen in Figure 1.

In this hypothesis, particles would be accelerated by repeated reflections as the shock passes through the weak-field region associated with the NW hot spot, which acts as a magnetic trap. Here, we envisage a shock advancing NW along the chain of null points visualized in Figure 10, right. Particles that are trapped within the weak-field region bounce back and forth between the magnetic mirror at the NW end of the chain and the shock, equivalent to alternate reflections between a static mirror and a moving mirror. When particles reflect from the shock (the moving mirror), their speed normal to the shock increases by twice the speed of the shock.

This mechanism is, however, inefficient because the energy gain is along the direction of the magnetic field and leads to a rapid escape from the trap. The relative energy gain is comparable to the magnetic mirror ratio, and stays well below the 300 MeV required for the γ-ray emission. Scattering back to the shock therefore needs the development of upstream turbulence, which is advocated in numerical models of diffusive shock acceleration (e.g., A. Afanasiev et al. 2018). It is uncertain that such a process can develop on the short timescales imposed by the observations.

### 6.3. The Delayed Phase

The radiation observed by LAT shows a steady decline from about 17:54. This time behavior is consistent within errors with an exponential decay, ~e⁻¹/τ with the decay timescale τ ≈ 350 s. A simple interpretation suggests itself. Some of the ions accelerated by the events of the flare remain trapped on closed field lines, in a low-density region where they lose energy and radiate negligibly. They escape gradually to the chromosphere and photosphere where they stop promptly, emitting γ-rays in the process. In a first approximation, the observed decay time of γ-radiation will be identical with τ. We can test the plausibility of this idea.

Let N(E, t) be the distribution in energy (GeV⁻¹) of accelerated protons of the energy E at the time t in this reservoir. Neglecting in the first instance any energy-dependence of τ, we have

$$N(E, t) = N_0(E)E^{-t/\tau} \quad (5)$$

for some energy distribution N₀(E), to be determined from the γ-ray spectrum. The flux of protons into the dense atmosphere at the time t is given by N(E, t)/τ.

We find that the LAT data in the period 17:54:01–18:02:11 UT are best fit assuming (2.08 ± 0.23) × 10²⁷ protons above 0.5 GeV, with a PL energy distribution of the energy spectral index δ = 4.4 ± 0.5. In this 480 s period, 0.75 of the initial proton population has escaped to emit γ-rays. Thus,

$$N_0(E) = A \left(\frac{E}{0.5}\right)^{-4.4} \quad (6)$$

where A = 1.81 × 10²⁸ GeV⁻¹.

Define

$$n_0(E) = \frac{1}{V} \int_E^\infty N_0(E')dE' \quad (7)$$

where V is the total volume of the trapping region, with n₀(E) as the average density of accelerated ions of the energy E or greater. Scenarios in which n₀ is not implausibly large are preferred.

The flare seen in 1600 Å and 1700 Å AIA channels has a characteristic scale of ~45'' once its morphology stabilizes. Supposing, e.g., that the fast ion reservoir is a hemisphere of the radius 22'' leads to a volume of 8.5 × 10²⁷ cm³. The density of fast ions is highly sensitive to the value of the lowest energy for which the PL energy distribution still holds, a quantity that is only poorly constrained by observation. Studies of deexcitation lines often use a value of 30 MeV (e.g., R. J. Murphy & R. Ramaty 1984) while 1 MeV has been used for estimates of the flare energy budget (A. G. Emslie et al. 2005). The former case, which is compatible with the limit to the flux in the GBM energy range (Section 2.2), leads to n₀(.03) = 4500 cm⁻³, a plausible value, but n₀(0.001) = 4.7 × 10⁸ cm⁻³. The latter value is probably too close to the total ambient density in the low corona to be acceptable. We conclude that this gradual escape model is plausible as long as the energetic ion distribution flattens below 30 MeV, or the relevant volume is greater than assumed here.

## 7. Conclusions

In this work, we have presented multiwavelength observations of SOL2012-06-03 with particular attention to the >100 MeV γ-ray peaks during the impulsive phase. As outlined in Section 6, the data strongly suggest that there are multiple acceleration sites and that the first impulsive peak is a flare-related event coincident with the radio and HXR emissions. Whereas the particle acceleration during the predominately ion-rich second γ-ray peak can be due to an impulsive burst of reconnection, or a flux rope driven shock that moves through the weak-field region (although it is uncertain whether this process can develop over very short times scales). The delayed emission observed in γ-rays following the impulsive phase can be explained by the trapping of ions in closed field lines and precipitation. This flare represents the first time that two distinct phases are observed for >100 MeV emission and that these phases clearly indicate separate acceleration process and locations of the energy releases of the accelerated particles.
Acknowledgments

The Fermi-LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as the scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/ Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France. M.P.R. and N.O. are members of the LAT collaboration.

SDO data were supplied courtesy of the SDO/HMI and SDO/AIA consortia. SDO is the first mission to be launched for NASA's Living With a Star (LWS) Program. This work was performed in part under DOE Contract DE-AC02-76SF00515.

We are grateful for radio data of the Bleien (Switzerland) and Birr Castle (Ireland) instruments of the e-CALLISTO network and of the POEMAS radio polarimeters of the Centro de Rádio-Astronomia e Astrofísica Mackenzie (Brazil) operated at the CASLEO observatory in Argentina (data provided by G. Giménez de Castro).

T.W. acknowledges DLR grant 50 OC 2301. A.R. and C.P. acknowledge support from STFC grants ST/S000402/1 and ST/W001195/1. H.H. is grateful for hospitality at the University of Glasgow. This research used version 6.0.2 (The SunPy Community et al. 2020) of the SunPy open-source software package (S. J. Mumford et al. 2024).

N.V.N. acknowledges NASA grants 80NSSC23K0408 and 80NSSC24K0175.

Appendix
Fermi-LAT Time Resolved Spectral Analysis

In this appendix, we report the Fermi-LAT time resolved spectral analysis results in Table 2.

<table><caption>**Table 2**
Results for the Time Resolved Likelihood Analysis of the LAT Data</caption><thead><tr><th>Time Window</th><th>Flux<sub>0.1-1.0 GeV</sub><br>(10<sup>-5</sup> cm<sup>-2</sup> s<sup>-1</sup>)</th><th>Power-law Index</th><th>TS<sub>Sun</sub></th></tr></thead><tbody><tr><td>17:53:10-17:53:18</td><td>16 ± 5</td><td>-2.4 ± 0.4</td><td>80</td></tr><tr><td>17:53:18-17:53:21</td><td>43 ± 14</td><td>-2.6 ± 0.4</td><td>84</td></tr><tr><td>17:53:21-17:53:24</td><td>38 ± 12</td><td>-2.9 ± 0.4</td><td>122</td></tr><tr><td>17:53:24-17:53:28</td><td>29 ± 9</td><td>-2.4 ± 0.4</td><td>85</td></tr><tr><td>17:53:28-17:53:32</td><td>30 ± 11</td><td>-2.5 ± 0.4</td><td>80</td></tr><tr><td>17:53:32-17:53:34</td><td>98 ± 27</td><td>-2.20 ± 0.30</td><td>121</td></tr><tr><td>17:53:34-17:53:36</td><td>60 ± 19</td><td>-2.5 ± 0.4</td><td>83</td></tr><tr><td>17:53:36-17:53:37</td><td>104 ± 31</td><td>-2.4 ± 0.4</td><td>130</td></tr><tr><td>17:53:37-17:53:40</td><td>48 ± 16</td><td>-2.9 ± 0.5</td><td>88</td></tr><tr><td>17:53:40-17:53:41</td><td>83 ± 24</td><td>-2.4 ± 0.4</td><td>132</td></tr><tr><td>17:53:41-17:53:46</td><td>26 ± 7</td><td>-2.13 ± 0.31</td><td>94</td></tr><tr><td>17:53:46-17:54:01</td><td>7.6 ± 2.5</td><td>-2.8 ± 0.5</td><td>70</td></tr><tr><td>17:54:01-17:54:18</td><td>5.6 ± 2.1</td><td>-1.86 ± 0.33</td><td>51</td></tr><tr><td>17:54:18-17:54:40</td><td>5.2 ± 1.8</td><td>-2.3 ± 0.4</td><td>36</td></tr><tr><td>17:54:40-17:55:04</td><td>4.7 ± 1.6</td><td>-2.01 ± 0.32</td><td>48</td></tr><tr><td>17:55:04-17:55:34</td><td>3.3 ± 1.2</td><td>-2.6 ± 0.5</td><td>37</td></tr><tr><td>17:55:34-17:55:53</td><td>5.0 ± 1.8</td><td>-2.5 ± 0.4</td><td>42</td></tr><tr><td>17:55:53-17:56:28</td><td>3.2 ± 1.1</td><td>-1.85 ± 0.28</td><td>45</td></tr><tr><td>17:56:28-17:56:55</td><td>3.0 ± 1.3</td><td>-3.1 ± 0.6</td><td>28</td></tr><tr><td>17:56:55-17:57:35</td><td>2.2 ± 0.8</td><td>-2.7 ± 0.5</td><td>27</td></tr><tr><td>17:57:35-17:58:09</td><td>2.7 ± 1.0</td><td>-2.8 ± 0.5</td><td>30</td></tr><tr><td>17:58:09-17:58:39</td><td>3.4 ± 1.2</td><td>-2.6 ± 0.4</td><td>38</td></tr><tr><td>17:58:39-17:58:58</td><td>5.1 ± 1.9</td><td>-2.3 ± 0.4</td><td>31</td></tr><tr><td>17:58:58-17:59:36</td><td>2.3 ± 0.9</td><td>-2.02 ± 0.35</td><td>23</td></tr><tr><td>17:59:36-18:00:18</td><td>2.4 ± 0.9</td><td>-2.5 ± 0.4</td><td>33</td></tr><tr><td>18:00:18-18:01:21</td><td>1.2 ± 0.5</td><td>-2.1 ± 0.4</td><td>17</td></tr><tr><td>18:01:21-18:02:11</td><td>1.6 ± 0.7</td><td>-2.2 ± 0.4</td><td>19</td></tr></tbody></table>

Note. In each interval, we report the time window for the analysis, the photon flux between 100 MeV and 1 GeV (in 10<sup>-5</sup> cm<sup>-2</sup> s<sup>-1</sup>), the photon power-law index from the fit, and the test statistic, TS, from the fit (significance = √TS).
ORCID iDs

Melissa Pesce-Rollins https://orcid.org/0000-0003-1790-8018

Alexander MacKinnon https://orcid.org/0000-0002-3558-4806

Alexander J. B. Russell https://orcid.org/0000-0001-5690-2351

Hugh Hudson https://orcid.org/0000-0001-5685-1283

Alexander Warmuth https://orcid.org/0000-0003-1439-3610

Thomas Wiegelmann https://orcid.org/0000-0001-6238-0721

Sophie Masson https://orcid.org/0000-0002-6376-1144

Clare Parnell https://orcid.org/0000-0002-5694-9069

Nariaki V. Nitta https://orcid.org/0000-0001-6119-0221

Nicola Omodei https://orcid.org/0000-0002-5448-7577

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