Characteristics of Late-phase >100 MeV Gamma-Ray Emission in Solar Eruptive Events

The Fermi/LAT (Atwood et al. 2009) has a five-times-larger peak effective area and four-times-larger field of view than the EGRET detector (Nolan et al. 1992) on the Compton Gamma Ray Observatory (CGRO). This provides an order-of-magnitude improvement in sensitivity to solar events over previous high-energy observations. The LAT first detected >100 MeV γ-ray emission on 2010 June 12 (Ackermann et al. 2012a, 2012b) during the impulsive GOES-class M2 solar flare that was associated with a 500 km s⁻¹ CME and a barely detectable solar energetic particle (SEP) event. That paper primarily focused on the Gamma-ray Burst Monitor (GBM) (Meegan et al. 2009) observations of bremsstrahlung and nuclear γ-rays and the LAT >30 MeV observations during the minute-long impulsive flare. The high-energy γ-ray emission was delayed from the impulsive hard X-ray emission, but only by about 10 s, reflecting the time it takes to accelerate particles to tens of MeV. Ackermann et al. (2012a) found no evidence for any late-phase >100 MeV emission in the hours following the flare.

After that first Fermi impulsive flare observation, the LAT team reported detection of three events with late-phase γ-ray emission. The first observation (Allafort et al. 2011a, 2011b) was made just after the impulsive phase of the GOES M3.7 flare on 2011 March 7 that was detected by GBM at energies up to 1 MeV. The second event (Tanaka et al. 2011) followed a GOES M2.5 flare on 2011 June 7 detected in its impulsive phase by both the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and GBM up to 800 keV. The third event (Tanaka et al. 2012) followed impulsive phase emission up to 300 keV detected by GBM from the GOES M8.7 flare on 2012 January 23. Common to all three events was an impulsive flare with >100 keV hard X-ray emission, a >1000 km s⁻¹ CME, and an accompanying SEP event. In an attempt to understand the conditions that are necessary for producing LPGRE, we identify a sample of 95 solar events occurring between 2008 and 2012 having at least one of these characteristics. The relationship between LPGRE occurrence and the properties of this sample is discussed in Appendix B, and relevant results are presented in the body of the paper.

In this paper, we catalog 30 solar eruptive events with late-phase γ-ray emission observed by LAT from 2008 until the end of 2016. We discuss our temporal and spectroscopic studies of the events and relate the measurements to the associated solar flares, radio emissions, coronal mass ejections (CMEs), and SEP events. In Section 2, we discuss how LAT is used as a solar observatory, and in Section 2.1, we describe our method for analyzing LAT data. This method is different than that used by Ackermann et al. (2014) and Ajello et al. (2014) but provides comparable measurements of γ-ray fluxes and spectra. A major advantage is that the Fermi data can be accessed and studied using standard solar data analysis software. In Section 3, we list the 30 events with LPGRE and provide an example of our analysis for one of the events, including details of the observations and time histories of the emission. Similar studies of each of the other 29 events are presented in Appendix C. In Section 4, we describe our methods for analyzing LAT >100 MeV spectra from both the impulsive and late phases of the solar eruption, thus providing information about the protons producing these emissions. We also discuss RHESSI and GBM spectroscopic studies that provide further information on the proton spectra at energies below 300 MeV. In Section 5, we detail what we have learned about the overall characteristics of the late-phase emission and its relationship to the impulsive-phase emission and accompanying CME and SEP event. We summarize the principal characteristics of LPGRE in Section 6.1 and discuss their implications in Section 6.2. The paper includes five appendices that (1) summarize pre-Fermi observations of LPGRE; (2) describe a 4 yr study of the relationship between LPGRE event flares, CMEs, and SEPs; (3) detail the temporal and spectral details of the 30 events; (4) present our estimate of the number of >500 MeV SEP protons; and (5) detail the accompanying radio bursts. This allows us to focus on the scientific results in the body of the paper.

In performing both our temporal and spectral studies, we first accumulated >100 MeV photons with measured locations within 10° of the Sun using standard LAT analysis tools. For reference, we note that about 95% of all 200 MeV solar γ rays have measured locations within this disk of 10° radius (Atwood et al. 2009). We reduced the γ-ray background from the Earth’s atmosphere in these accumulations by restricting events to those with angles <100° from the zenith. All of the accumulated data were then put into a format compatible with SSW IDL software⁸ used by the solar community and operating within IDL.⁹ Therefore, any scientist familiar with OSPEX¹⁰ can study LAT solar data in the same way that they study RHESSI and GBM spectral data. We perform two types of analysis on these data in this paper.

The first is a temporal analysis designed to reveal the presence of solar transients on orbital timescales and determine the time variation of the emission on minutes-to-hours timescales (Sections 2.2 and 3.1). In producing what we call “light-bucket” time profiles, we simply divided the accumulated count rate in each time interval by the default effective area provided in the LAT data products. This provides a simple and fast way to obtain an estimate of the >100 MeV γ-ray flux from within about 10° of the Sun. During solar-quiet times, the flux comes from Galactic, extragalactic, and quiescent solar photons (Abdo et al. 2011). This background flux varies seasonally from ∼3 × 10⁻⁶ γ cm⁻² s⁻¹ in March to ∼4.5 × 10⁻⁵ γ cm⁻² s⁻¹ in mid-December, as the Sun moves along the ecliptic and passes through the Galactic plane.¹¹ Any transient solar flux will therefore appear above this background in the plots. The effective area used to determine the light-bucket fluxes was for a hard celestial background spectrum and not for a softer solar transient spectrum. This affects the accuracy of the plotted flux during a solar transient. For the above reasons, we caution the reader not to use the light-bucket fluxes plotted in the body of the paper and appendices to make quantitative comparisons of solar fluxes. Instead, one should only use the >100 MeV solar fluxes provided in Table 3, derived using spectroscopic studies of background-subtracted data discussed below.

The second type of analysis involves detailed spectroscopic studies of background-subtracted data performed using OSPEX. The >100 MeV background in LAT source-class data from a 10° region around the Sun is relatively constant on timescales of hours (see Figure 3 in Section 2.2 below), as long as data <12° from the Earth’s horizon (i.e., a zenith angle <100°) is excluded. Therefore, as background, we chose LAT observation intervals just before and/or after the LPGRE event with comparable solar exposures. The solar fluxes for the 30 LPGRE events listed in Table 3 were determined by fitting the background-subtracted spectra with plausible solar photon models as described in Section 4.1. As questions have been raised about the accuracy of our solar flux determinations, we compared the fluxes listed in Table 3 with the fluxes from the more sophisticated maximum-likelihood method used by the LAT team (Ackermann et al. 2014, 2017; Ajello et al. 2014) for the same events. We plot a comparison of the fluxes in Figure 2. Even though the solar exposures for the two methods were not always identical, the agreement in flux is generally within the uncertainties and supports the validity of our method.

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In Figure 3, we show an example of the 4 day time histories of >100 MeV solar fluxes observed by LAT that are available for the entire Fermi mission on the RHESSI Browser.¹² The top panel shows the >100 MeV light-bucket fluxes plotted as black data points with ±1σ statistical uncertainties. As discussed in Section 2.1, these fluxes include all photons <10° of the Sun, including background from Galactic, extragalactic, and quiescent solar sources. Although they accurately reveal the temporal variations, these light-bucket fluxes should not be used in quantitative solar studies. When the >100 MeV flux exceeds about 4.2σ above background (∼2 × 10⁻⁵ probability for a random Gaussian distribution), as it did in three exposures separated by 3 hr on 2014 February 25, the plotted points are circled in red, identifying possible >100 MeV solar events. There were significant excesses in five exposures between 2011 November 7 and 11 when the active radio quasar PKS 1510–089 passed near the Sun.

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In the bottom panel of Figure 3, we plot the solar gamma-ray fluxes provided by the Fermi/LAT team using their more sophisticated and sensitive maximum-likelihood method (Ackermann et al. 2014). This technique models and removes the background so that only upper limits (in black) are plotted unless there is a statistically significant solar transient, where the points are plotted with ±1σ errors and circled in red. Both methods also provide information on the LAT solar exposures shown in blue in each plot; the average effective area is given in the top panel, and the effective area × exposure time is in the bottom panel. More information about these plots can be found at http://hesperia.gsfc.nasa.gov/fermi/lat/qlook/LAT_qlook_plots.htm.

We present light-bucket time histories and observational details of each of the 30 events with LPGRE in Appendix C. In Figure 4, we provide an example of one of these time histories. The event occurred on 2011 March 7. It was the first event with LPGRE detected by LAT (Ackermann et al. 2014) and lasted about 14 hr. In the main part of the figure, we plot the >100 MeV γ-ray fluxes (with ±1σ statistical uncertainties) within the 10° accumulation region centered on the Sun¹⁶ for several hours before and after the flare. As discussed in Section 2.1, care must be taken in using these light-bucket fluxes in quantitative solar studies. Absolute solar fluxes for the events are provided in Table 3. It is clear from the main plot that the LPGRE began around the time of the flare and reached a peak about 6 hr after the flare, consistent with the time history presented by Ackermann et al. (2014). The 6 hr delay to the peak of the LPGRE is in stark contrast with the 2 minute delay observed in the 1982 June 3 event (Figure 1). In addition, the associated flare was only an M3.7 GOES-class event, compared to the X8 flare on June 3.

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In the inset of Figure 4, we plot a blowup of data spanning the GOES soft X-ray event (dashed vertical lines). The relative LAT >100 MeV fluxes are plotted at 4 minute time resolution. The horizontal right- and left-pointing arrowheads show the estimated range of CME onset times using linear and quadratic extrapolations given in the CDAW LASCO CME Catalog.¹⁷ We also studied SDO EUV images to visually determine the time when the CME lifted off with a 1–2 minute uncertainty; this time is shown by the downward solid arrow in the inset. The downward dashed arrow shows the estimated onset time of Type II radio emission given in the NOAA Solar Event Reports¹⁸ or derived from studies of the radio spectra. We compare estimates of CME and Type II onset times for the 30 LAT events in Table 2. Unlike the 1982 June 3 flare, where pion-decay γ rays were observed during the impulsive phase, GBM and RHESSI observed impulsive hard X-rays up to only 100–300 keV with no evidence for nuclear-line emission. The combined GBM/RHESSI 100–300 keV time history is plotted as the continuous time series in the inset, and the rate peaks after the onsets of CME and Type II radio emission. The LAT began observing the Sun at about 20:14 UT near the end of the impulsive hard X-ray emission. The >100 MeV fluxes plotted in the inset reveal that the LPGRE began within minutes of the hard X-ray peak. We estimated the range of LPGRE onset times by extrapolating the best linear fit and ±1σ uncertainties, shown by the dashed lines, to background level. It is clear from the rising LPGRE flux that it is due to a distinct particle acceleration phase and is not just the tail of emission from the impulsive phase of the flare.

In Sections 2 and 2.1, we discussed how we processed LAT data to put them into a format for spectral analysis. In Figure 5, we show the background-subtracted count spectrum on 2014 February 25 (Event 28, Table 1, Appendix C.28) from one of the brightest episodes of LPGRE observed by LAT. The spectrum was accumulated over 4 minutes (01:13–01:17 UT) during the peak exposure to the Sun to avoid any instrumental issues near the edge of the field of view. As discussed in Ackermann et al. (2014) and Ajello et al. (2014), LPGRE photon spectra have the shape of a power law with an exponential cutoff varying from several tens of MeV to a few hundred MeV. Such a shape arises naturally from the decay of neutral and charged pions produced when high-energy protons and α-particles interact in the solar chromosphere and photosphere. A computer code developed by Murphy et al. (1987) calculates the yield of neutral and charged pions and the associated γ-ray spectra from neutral pion decay, bremsstrahlung of positrons and electrons from charged-pion decay, and annihilation in flight of positrons from positive pion decay. The calculations are performed assuming that the particles interact isotropically in a cold thick-target region and use nuclear data and models for the p + p and p + ⁴He reactions (and the inverse reaction α + H). Both the accelerated and ambient ⁴He/H abundance ratios are assumed to be 0.1. If the accelerated α/p ratio were 0.2, the pion-decay yield would increase by ∼10%. The pion-decay cross sections for p + heavier-ion interactions are significantly larger, and their threshold energies are lower than for the p–H reaction; however, this is offset by the significantly lower heavy-ion abundances. Only for power-law ion spectra with indices steeper than 6 does the pion-decay gamma-ray yield from p-heavy and heavy-H reactions reach close to 15% of the yield from p–H reactions for assumed coronal abundances (Reames 1995) for both the ambient medium and the accelerated particles. For an impulsive-flare accelerated-particle composition (Reames 1995), the yield would not increase significantly due to Coulomb energy losses of the heavy ions.

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Due to the high >300 MeV proton threshold for pion production, the pions are produced deep in the solar atmosphere. Because of the short pion-decay times, the photons are released at comparable depths. At these depths, scattering effects on the escaping photons are significant, especially for flares observed at heliocentric angles >70°. We calculated the angle-dependent scattering effects on the spectra of the escaping photons from an estimated depth distribution for pion production and using a Monte Carlo N-Particle (MCNP6) photon-propagation code¹⁹ employing a spherical geometry model for the Sun. We isotropically released pion-decay spectra calculated with the Murphy et al. (1987) code and recorded escaping gamma-ray spectra at various angles relative to the normal to the solar surface at the flare site; these angles correspond to flare heliocentric observation angles as observed from Earth. The primary effect is the reduction in the number of photons that escape. Only ∼82% of the 100 MeV pion-decay photons that escape at disk center can escape at a heliocentric angle of 70°. This number drops to ∼47% at 85° and ∼8% at 90°. Attenuation also hardens the spectrum of escaping gamma rays near the solar limb. At a heliocentric angle of 85 degrees the estimated proton power-law index is higher (spectrum is steeper) by about 0.5, compared with the estimate for an event near disk center.

Using the Murphy et al. (1987) code and attenuation corrections, we then calculated pion-decay spectral templates for the location of the associated active region and varied the proton spectral index to obtain the best fit to the LAT spectral data. As an illustration of our LAT spectral analyses, we discuss our fits with these templates to the 2014 February 25 count spectrum plotted in Figure 5. We assumed that the 2014 February 25 emission came from the active region located at a heliocentric angle of 78° and fit the count spectrum with calculated pion-decay templates for unbroken proton power-law spectral indices, s_p. The χ² statistic was used to determine the proton spectral index, and its estimated 1σ uncertainty was determined from the values where χ² increased by unity. The best-fitting spectrum was for a power-law index s_p = 3.45 ± 0.15 (dotted curve). The fit is poor, χ²/dof of 3.7; only 0.2% of random trials with this power-law form would have higher values of χ²/dof. It is clear that the photon spectrum must steepen above ∼1 GeV, implying that the proton spectrum is not an unbroken power law but rolls over at high energies. We found that a power-law proton spectrum with exponential cutoff ((${dN}/{dE}\propto {E}^{-{s}_{p}}{\exp }^{-E/{E}_{0}}$); used by Ellison & Ramaty 1985 in their study of shock acceleration in solar flares) having an index, s_p = 2, and an exponential cutoff, E₀ = 1.3 GeV, provides a good fit to the spectral data (solid curve; 31% of random trials with this power-law exponential form would have higher values of χ²/dof). For the statistics available in most events in our study, fits with pion-decay spectra from protons with spectra following a unbroken power law are adequate. Because of the threshold for pion production, the information derived from these fits is only valid for proton energies above 300 MeV.

From the derived γ-ray flux and proton spectral index, we then applied the results of Murphy et al. (1987) to calculate the number of accelerated protons with energies >500 MeV at the Sun during each LAT exposure. The number of protons >500 MeV is relatively insensitive to uncertainties in spectral index because of the 300 MeV threshold. We also corrected the number of protons for atmospheric attenuation. Because of the limited duty cycle of the LAT observations, our knowledge of the temporal evolution of the LPGRE is limited. For events where only one LAT exposure is available, we estimated the number of accelerated protons by assuming that the flux onset occurred at the end of the previous (null) LAT observation and increased linearly to the observed value that is assumed to be the peak. Similarly, we assumed that the flux decayed linearly from the peak to the beginning of the following (null) LAT observation. If there are higher time cadence LAT data available, as there are for the 2011 March 7 event (see Figure 4), we use them to estimate the onset time by linear extrapolation. For events where more than one exposure is available, we estimated the total number of protons by assuming that the flux changed linearly with time between measurements.

4.1.1. >100 MeV LPGRE Spectra Cannot Be Fit by Primary Electron Bremsstrahlung

As discussed in Section 1 and above, pre-Fermi observations suggested that ions and not primary electrons are responsible for producing the late-phase emission. We quantitatively addressed this question using the observed >100 MeV 2014 February 25 LPGRE spectrum. In Figure 6, we plot the calculated pion-decay photon spectrum (red curve) produced by interactions of protons with a power-law index s_p = 2 and an exponential cutoff, E₀ = 1.3 GeV, that provides a good fit to the LAT count spectrum observed at the peak of the LPGRE on 2014 February 25 (Figure 5). We attempted to find an electron bremsstrahlung spectrum that approximates the same shape. In order to duplicate the flat photon spectral shape at low energies, we chose a power-law electron spectrum with index, s_e = 1. In order to duplicate the rollover in the pion-decay spectrum that fits the data well above a few hundred MeV, we introduced an exponential cutoff, E₀, in the electron spectrum. We varied the cutoff energy to provide the closest fit to the pion-decay spectrum and found that this occurred at about 1 GeV.

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At these high electron energies, it is necessary to take into account the effect that synchrotron losses have on the shape of the resulting bremsstrahlung spectrum. The green curves in Figure 6 show how the bremsstrahlung spectrum changes with increasing magnetic field when the interaction region has a density of 10¹⁶ cm⁻³. Electrons with energies >100 MeV can penetrate to these chromospheric densities. At such densities, bremsstrahlung dominates over synchrotron losses so that even with a magnetic field of 1000 G, the photon spectrum changes only marginally, as can be seen by the two green curves. The fit of this optimized bremsstrahlung spectrum to the LAT spectral data is poor (probability of <10⁻⁵). If the thick target has a lower density, 10¹² cm⁻³, the bremsstrahlung spectrum in a 1 G field has a shape similar to the green curve plotted for 1000 G and 10¹⁶ cm⁻³ density. If we increase the field strength to 1000 G at this lower density, the spectrum rolls over more rapidly at high energies (see blue curve) and is an even worse representation of the best-fit pion-decay spectrum. It is, therefore, clear that primary electron bremsstrahlung fails to reproduce the broad peak near 100 MeV resulting from π⁰ decay. This poor fit of electron bremsstrahlung to the LAT count spectrum is shown by the dashed curve in Figure 5. We conclude that bremsstrahlung from plausible electron spectra cannot fit the shape of the LPGRE in the event on February 25 and that the source of >100 MeV γ-rays is the decay of pions produced by proton interactions.

We made similar comparisons of pion-decay and bremsstrahlung spectral shapes for 16 separate LAT exposures where the >100 MeV LPGRE flux exceeded >10⁻⁴ γ cm⁻² s⁻¹. With >99.9% confidence, the pion-decay shape provided a significantly better fit to each γ-ray spectrum than did any plausible primary electron bremsstrahlung spectrum.

4.1.2. Corrections for Nonisotropic Particle Distributions

4.1.3. Using the Neutron-capture Line for Studying the Spectra of Impulsive- and Late-phase Protons

A clear association of LPGRE events with either impulsive flares, CMEs, or SEP events would provide valuable information about the source of ion acceleration. The associated GOES soft X-ray flares ranged from a C3.7 to an X5.4, with one C-class, 14 M-class, and 16 X-class flares associated with the 31 emission episodes. There is no clear association between the intensity of flare soft X-ray emission and the occurrence of LPGRE events. By contrast, all of the pre-Fermi LPGRE events were associated with X-class flares. This may have just been due to the lower sensitivity of earlier >10 MeV instruments relative to Fermi/LAT. The listed GOES X-ray durations ranged from about 8 to 135 minutes.

All but two of the LPGRE events were associated with CMEs, with speeds ranging from about 600 to 2700 km s⁻¹. In every case where a CME was present, it was either a halo or partial halo event (indicating very wide CMEs). Twenty-four of the 30 events were associated with Type II metric radio emission, and all but two were associated with either the Type II metric or DH emission. SEPs were clearly observed in association with all but eight of the LPGRE events. A stronger preceding SEP event may have masked the particle emission in five or six of the events. The only two LPGRE events with no clear evidence for SEP protons occurred on 2012 October 23 and November 27, the two events when CMEs were not detected. However, AIA movies reveal evidence for the eruption of a magnetic loop in the low corona in both of these events, and Type II metric radio emission, indicating shock formation, was detected following the magnetic eruption on 2012 October 23. This suggests that these LPGRE events may have been accompanied by failed CMEs (Ji et al. 2003). Hard X-ray observations during the impulsive phase are available for 27 of the 30 LPGRE events (28 of the 31 emission episodes), and in each case, photons exceeding 100 keV were observed.

To further investigate this association of fast CMEs and >100 keV flares with LPGRE events, in Appendix B, we analyze a sample of solar eruptive events detected between 2010 and 2012 that have at least one of these characteristics. The sample consists of events that exhibit a wide CME faster than 800 km s⁻¹, SEPs exceeding 1 pfu at 10 MeV at 1 AU, or hard X-rays detected above 100 keV. This results in a list of 95 events, composed of one GOES-class B flare, 23 C flares, 38 M flares, 15 X flares, and 18 events with no flare identification (generally fast CMEs, presumably from events over the limb). Nineteen of the 95 events exhibit both CME speeds above 800 km s⁻¹ and flare emission above 100 keV. Fourteen of these 19 events produced LPGRE, indicating that the combination is not a sufficient condition for producing LPGRE. It is, however, possible that LAT’s limited duty cycle for solar observations (see Section 2), i.e., solar data for 20–40 minutes out of every 90 or 180 minutes, could have resulted in LAT missing LPGRE in these five events (see Appendix B.1) if the duration of >100 MeV emission was less than about 50 minutes. The proximity of some of the five events to the solar limb could also result in diminished >100 MeV fluxes.

As noted earlier, the requirement for pion production by interaction of >300 MeV protons with H implies that the pions are produced in high-density regions that must be relatively deep in the solar atmosphere, and in order for the resulting pion-decay photons to be detected, these interactions must be happening on regions of the solar disk visible from Earth. With the detection of the LPGRE events on 2013 October 11 and 2014 September 1 (Pesce-Rollins et al. 2015a; Ackermann et al. 2017) arising from flares with locations ∼10° and ∼40° beyond the limb, it is clear that the protons producing the LPGRE can interact tens of degrees from the flare site. Gamma-ray line emission from a flare ∼15° beyond the limb was also observed by SMM on 1989 September 29 (Vestrand & Forrest 1993). From the study discussed in Appendix B of 70 eruptive events from 2008 to 2012 associated with CMEs with velocities ≳800 km s⁻¹, we find that 35 were on the visible disk and 35 were beyond the limb of the Sun. There were 13 LPGRE events associated with the 35 fast CMEs arising from locations on the visible disk, but there were none associated with the 35 fast CMEs on the far side of the Sun. If we assume that about one-third of all fast CMEs are associated with LPGRE events and that LPGRE can be observed within tens of degrees from the flare location, we would expect to have detected up to seven LPGRE events from the 21 CME events located on the far side of the Sun but within ∼40° of the limb. Since no LPGRE was detected in this sample, we conclude that the source of LPGRE usually lies within about 10 heliocentric degrees of the active region location.

There is one peculiarity in the location of the flares associated with LPGRE: 24 out of the 30 events (∼1% probability for a random distribution) occurred in the northern hemisphere, even though sunspot activity was higher in the southern hemisphere during the same time period. Similarly, 79 of the 95 eruptive events discussed in Appendix B occurred in the northern hemisphere, although this is less surprising, since in the sample period 2010–2012, activity was markedly stronger in the northern hemisphere. We note, however, that such varying north/south asymmetries in solar indices is well known (see, e.g., Verma 1993 and references within). There were roughly equal numbers of LPGRE events in the eastern (17) and western (13) hemispheres.

We provide time histories on minute and hour timescales for all 30 LPGRE events in Appendix C. They are plotted in the same format as Figure 4. Because the 2012 March 7 event (Table 1, event 12; Appendix C.12; Figure 29) has two separate LPGRE eruptions, there are 31 cases to study. For each of the 31 episodes in the appendix, we start by discussing the distinct nature of the LPGRE. In 17 of the 31 LPGRE episodes, the >100 MeV emission began after the impulsive-phase hard X-rays. In four other episodes (events 5, 16, 19, and 30), the >100 MeV LPGRE began during the impulsive hard X-ray peaks but had a time history different from that of the X-ray emission. Each of the remaining 10 LPGRE episodes were observed in only one 20–40 minute LAT solar exposure well after the flare. In seven of these events, there is no evidence for temporal variation during the exposure, suggesting that the measurement may have been made near the peak of the LPGRE. In two of the events (events 26 and 27), there is weak evidence at the 80%–90% confidence level that the emission was falling with time during the exposure, and in one event (event 17), the evidence for a falling flux is stronger. We could not determine if the emission in these three events came from the falling phase of a short LPGRE event or from the tail of the impulsive phase. However, in none of the 31 episodes did we find clear temporal evidence that the emission was the tail of >100 MeV γ rays produced in the impulsive phase. In the following sections, we (1) compare CME, Type II radio, and LPGRE onset times; (2) study the LPGRE onset times and durations; and (3) discuss whether the LPGRE is due to a series of episodic events rather than continuous emission.

5.2.1. CME, Radio, and LPGRE Onset Times

We compared three methods for obtaining the time of rapid acceleration, or onset time, of CMEs: (1) CDAW extrapolations of LASCO coronagraphic observations of CME height versus time, (2) our visual inspection of SDO AIA movies, and (3) the rise in flare soft X-rays (Zhang et al. 2001). We investigated these onset times in a sample of 28 eruptive events, including some in which LPGRE was observed, and we found that the CME onset times estimated from the EUV movies agreed well with the rise time of GOES 1–8 Å emission; the mean difference is less than 0.5 minutes, with a maximum difference of 4 minutes. In contrast, the average of the CME onset times in the CDAW catalog, derived from linear and quadratic extrapolations, differ by as much as 20 minutes from the times based on the EUV movies, with an average difference of just over a minute. We therefore chose to use the CME onset times derived from the EUV movies as the reference time in determining the delays of Type II radio and late-phase γ-ray emission. We list these CME onset times for the 30 LPGRE events in column 3 of Table 2. There were no CMEs reported for the 2012 October 23 (event 17; Appendix C.18, Figure 36) and 2012 November 27 (event 18; Appendix C.19, Figure 37) events, but there is clear evidence for the eruption of magnetic loops in AIA images at 03:15 and 15:56 UT, respectively, along with material moving away from the flare region. We therefore use these times as the eruption onsets for these two events.

Table 2.  Onset Times of CME, Type II Radio, and LPGRE

Event Number	Date	CME Onset	Type II Onset	LPGRE Onset
		UT	UT	UT
(1)	(2)	(3)	(4)	(5)
1	2011 Mar 07	19:45	19:54	$19:{40}_{-00:20}^{+00:22}$
2	2011 Jun 02	07:43	08:00a	<09:40
3	2011 Jun 07	06:16	06:25	<07:48
4	2011 Aug 04	03:46	03:54	<04:56
5	2011 Aug 09	08:02	08:01	08:02:40 ± 00:00:40
6	2011 Sep 06	22:18	22:19	22:20:00 ± 00:00:40
7	2011 Sep 07	22:36	22:38	<23:38:00
8	2011 Sep 24	09:34	09:35	09:40 ± 00:01
9	2012 Jan 23	03:40	04:00a	04:17 ± 00:01
10	2012 Jan 27	18:07	18:10	$19:{31}_{-00:22}^{+00:06}$
11	2012 Mar 05	03:32	04:00a	04:30 ± 00:03
12	2012 Mar 07	00:07	00:17	$00:{20}_{-00:20}^{+00:08}$
		01:01	01:09	$02:{01}_{-00:13}^{+00:07}$
13	2012 Mar 09	03:38	03:43	$04:{00}_{-01:10}^{+00:30}$
14	2012 Mar 10	17:24	17:55a	20:00 ± 01:20
15	2012 May 17	01:27	01:31	<02:15
16	2012 Jun 03	17:53	17:59	$17:{55}_{-00:04}^{+00:01}$
17	2012 Jul 06	23:04	23:09	<23:26
18	2012 Oct 23	03:15b	03:17	<04:16
19	2012 Nov 27	15:56b	⋯	15:55 ± 00:01
20	2013 Apr 11	06:53	07:02	07:11 ± 00:01
21	2013 May 13	01:58	02:10	<04:30
22	2013 May 13	15:48	15:57	$17:{07}_{-00:09}^{+00:07}$
23	2013 May 14	01:04	01:07	01:20 ± 00:03
24	2013 May 15,	01:29	01:37	03:00 ± 01:00
25	2013 Oct 11	07:08	07:11	07:15 ± 00:01
26	2013 Oct 25	07:57	07:59	<08:17
27	2013 Oct 28	15:00	15:10	<15:45
28	2014 Feb 25	00:43	00:56	$00:{55}_{-00:16}^{+00:06}$
29	2014 Sep 01	10:57	11:12a	11:02 ± 00:01
30	2015 Jun 21	02:10	02:24	02:23 ± 00:03

Notes.

^aDH Type II start time in the absence of metric report. ^bNo CME observed; onset time of magnetic eruption.

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Type II radio emission, discussed in Appendix E, is attributed to electrons accelerated at a shock and radiating in its vicinity as it moves through the corona. The onset time of Type II emission is often taken to mark the formation time of the shock as the CME moves outward through decreasing Alfvén speed in the corona and can be compared with the onset times of the CME and LPGRE. In column 4 of Table 2, we list the Type II onset times, primarily derived from metric observations. Where these metric measurements are not available, we list in italics the times derived from interplanetary DH observations. No Type II radio emission was observed from the 2012 November 27 event (event 19), one of the two LPGRE events not accompanied by a CME. On average, we find that metric Type II emission begins about 6 minutes after the CME onset times. Using these delays and the CME linear speeds from the CDAW catalog for the events in the study, we estimate that the shock, on average, was formed at a heliocentric distance of ∼1.7 R_⊙. Using a more sophisticated analysis of CMEs, Gopalswamy et al. (2013) found that the shock formation locations ranged from 1.20 to 1.93 R_⊙, with mean and median values of 1.43 and 1.38 R_⊙, respectively. These timing studies indicate that the CME shocks can form relatively low in the corona.

The LPGRE onset times were derived by visual inspection of the >100 MeV fluxes plotted for the 30 events in Appendix C. In some cases, the onset time can be clearly distinguished with an accuracy of 1 or 2 minutes. In other cases, we fit the time history to estimate the onset and its uncertainty, as we did for the 2011 March 7 LPGRE event plotted in Figure 4 and discussed in Section 3.1. For events for which there was only one solar exposure with detectable >100 MeV emission and no evidence for short-term variability, we used the start time of the exposure as an upper limit on the onset time. Our best estimates of the LPGRE onset times and their uncertainties are listed in column 5 of Table 2.

5.2.2. Study of LPGRE Onset Delays and Durations

We define the LPGRE onset delay as the difference between the LPGRE onset time and the CME onset time listed in column 3 of Table 2. As LAT had limited exposure to the Sun, our estimates of the durations are, in many cases, upper limits based on the time of the first LAT solar exposure with no detectable >100 MeV emission. This uncertainty does not impact the coarse comparisons that we are making. The durations are listed in column 6 of Table 3 for the “LPGRE Total” entries in column 2. In Figure 7, we plot the durations of the LPGRE events versus their onset delays. We separately include the delays and durations of the two post-flare LPGRE episodes on 2012 March 7, each identified by number 12 in the figure. Thus, there are 31 individual points in the plot. We were able to estimate the onset delays based on multiple flux observations for 21 of them (shown by filled circles). For 10 of the events, we only have upper limits on the delays. The measured LPGRE onset delays ranged from minutes to 1 hr or more. Sixteen of the 31 plotted events have onset delays shorter than 30 minutes. Four well-measured delays exceeded 1 hr.

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Table 3.  Spectral Characteristics of LPGRE Events

Date (Event)	Type	Observing	Flux >100 MeV	Proton PL Index	Emission	>500 MeV Protons × 1028
yyyy/mm/dd		Interval, UT	10−4 γ cm−2 s−1	sf	Interval, UT	(Correction Factor)a
(1)	(2)	(3)	(4)	(5)	(6)	(7)
2011 Mar 07 (1)	LPGRE (1)	20:10–20:39	0.17 ± 0.03	3.3 ± 0.45	20:00–20:39	0.1
	LPGRE (2)	23:21–00:03	0.29 ± 0.03	4.1 ± 0.4	20:39–00:03	1.6
	LPGRE (3)	02:32–03:13	0.35 ± 0.03	4.3 ± 0.4	00:03–03:13	2.4
	LPGRE (4)	05:43–06:25	0.14 ± 0.02	6.7 ± 1.4	03:13–06:25	2.0
	LPGRE (5)				06:25–11:00	1.1
	LPGRE Total				20:00–11:00	7.2 ± 2.1 (2.1)a
	M3.7 flare				19:58–20:06	<0.07b
2011 Jun 02 (2)	LPGRE	09:41–10:28	0.07 ± 0.02	4.2 ± 2.0	08:10–12:00	0.03 ± 0.02 (2.2)a
2011 Jun 07 (3)	LPGRE (1)	07:48–08:19	0.29 ± 0.03	4.5 ± 0.6	07:00–08:20	0.5
	LPGRE (2)				08:20–10:00	0.6
	LPGRE Total				07:00–10:00	1.1 ± 0.4 (2.0)a
	M2.5 flare				06:24–06:45	<0.2b
	SEP protons					4.3 ± 2.9
2011 Aug 04 (4)	LPGRE (1)	04:56–05:37	0.28 ± 0.03	4.6 ± 0.6	04:10–05:10	0.4
	LPGRE (2)				05:10–07:10	0.8
	LPGRE Total				04:10–07:10	1.2 ± 0.3 (2.1)a
	M9.3 flare				03:48–04:00	<0.1b
						<0.4 (2.1)a
	SEP protons					7.3 ± 5.0
2011 Aug 09 (5)	LPGRE	08:02:40–08:06:00	2.0 ± 0.2	5.8 ± 0.9	08:02:40–08:06:00	0.4 +- 0.1 (1.4)a
	LPGRE <300 MeV			4.3 ± 0.3c
	X6.9 flare				08:02:00–08:02:20	<0.01 (1.4)a
	X6.9 flare				08:03:40–08:04:00	<0.01 (1.4)a
2011 Sep 06 (6)	LPGRE (1)	22:21–22:28	3.9 ± 0.2	5.3 ± 0.4	22:21–22:28	1.2
	LPGRE (1) <300 MeV	22:21–22:28		<4.0c
	LPGRE (2)	22:28–22:34	4.4 ± 0.2	3.5 ± 0.3	22:28–22:34	0.6
	LPGRE (2) <300 MeV	22:28–22:34		<3.6c
	LPGRE (3)	22:37–22:47	1.5 ± 0.1	3.5 ± 0.2	22:37–22:47	0.4
	LPGRE (3) <300 MeV	22:37–22:44		<3.9c
	LPGRE Total				22:21–23:20	2.2 ± 0.4 (2.3)a
	X2.1 flare		6.6 ± 1.0	>6	22:18–22:20	0.13 ± 0.05(2.3)a
2011 Sep 07 (7)	LPGRE (1)	23:51–00:09	0.07 ± 0.02	4.4 ± 1.4	22:45–00:00	0.1
	LPGRE (2)				00:00–01:10	0.1
	LPGRE Total				22:45–01:10	0.2 ± 0.1 (2.2)a
	X1.8 flare				22:36–22:38	<0.1b
2011 Sep 24 (8)	LPGRE	09:40–09:44	0.3 ± 0.09	3.4 ± 1.4	09:40–09:44	0.03 ± 0.01 (1.7)a
	X1.9 flare				09:35:30–09:37:00	<0.007(1.7)a
2012 Jan 23 (9)	LPGRE (1)	05:46–06:10	0.19 ± 0.02	5.1 ± 0.8	04:20–05:59	0.8
	LPGRE (2)	07:18–07:48	0.16 ± 0.05		05:59–07:34	0.7
	LPGRE (3)	08:58–09:28	0.19 ± 0.03		07:34–09:14	0.8
	LPGRE (4)				09:14–12:00	0.7
	LPGRE Total				04:20–12:00	3.0 ± 0.6 (2.2)a
	M8.7 flare				03:53–04:09	<0.4b
	SEP protons					37 ± 23
2012 Jan 27 (10)	LPGRE (1)	19:36–19:56	0.26 ± 0.05	4.7 ± 0.7	19:00–19:50	0.5
	LPGRE (2)	21:06–21:37	0.05 ± 0.02	3.1 ± 0.6	19:50–21:21	1.1
	LPGRE (3)				21:21–22:00	0.05
	LPGRE Total				19:00–22:00	1.7 ± 1.0 (1.1)a
	SEP protons					100 ± 62
2012 Mar 05 (11)	LPGRE (1)	05:46–06:12	0.10 ± 0.015	4.9 ± 0.9	04:35–05:59	0.12
	LPGRE (2)	07:18–07:56	0.075 ± 0.019	3.6 ± 0.8	05:59–07:36	0.25
	LPGRE (3)				07:36–10:00	0.16
	LPGRE Total				04:30–10:00	0.53 ± 0.15 (2.0)a
	X1.1 flare				03:55–04:35	<0.3b
		04:28–04:35	<0.15		04:28–04:35	<0.04 (2.0)a
2012 Mar 07 (12)	LPGRE (A) Total	00:39–01:24	28.7 ± 0.4	3.6 +- 0.3	00:28–01:24	40 ± 15 (2.2)a
	LPGRE (B1)	02:18–02:48	5.8 ± 0.3	3.5 ± 0.2	02:00–02:34	3
	LPGRE (B1) <300 MeV			<3.3c
	LPGRE (B2)	03:50–04:34	10.0 ± 0.2	3.85 ± 0.1	02:34–04:12	23
	LPGRE (B2) <300 MeV			<3.3c
	LPGRE (B3)	05:34–06:01	8.7 ± 0.4	4.25 ± 0.2	04:12–05:46	30
	LPGRE(B4)	07:02–07:46	6.2 ± 0.2	4.5 ± 0.15	05:46–07:24	27
	LPGRE (B4) <300 MeV			<3.3c
	LPGRE (B5)	08:42–09:12	4.1 ± 0.3	4.8 ± 0.5	07:24–08:48	18
	LPGRE (B5) <300 MeV			<3.7c
	LPGRE (B6)	10:33–10:58	2.5 ± 0.2	5.2 ± 0.4	8:48–10:46	17
	LPGRE (B6) <300 MeV			<3.7c
	LPGRE (B7)	13:23–13:33	0.6 ± 0.2		10:46–13:27	9
	LPGRE (B8)	16:35–16:49	0.22 ± 0.06		13:27–16:41	3
	LPGRE (B9)	19:46–20:14	0.07 ± 0.02		16:41–20:01	1
	LPGRE (B) Total				02:00–20:01	131 ± 15 (2.2)a
	X5.4 flare				00:16–00:28	1.4b
	M7 flare				01:11–01:20	1.1b
	M7 flare				01:12–01:17	<0.4 (2.2)a
	SEP protons					4075 ± 2590
2012 Mar 09 (13)	LPGRE (1)	05:10–05:58	0.06 ± 0.03	>6	04:30–06:00	0.1
	LPGRE (2)	06:46–07:32	0.11 ± 0.03	6 ± 1.5	06:00–07:09	0.3
	LPGRE (3)	08:22–09:08	0.15 ± 0.03	6.7 ± 1.5	07:09–08:46	0.7
	LPGRE (4)				08:46–10:30	0.4
	LPGRE Total				04:30–10:30	1.5 ± 0.6 (2.3)a
	M6.3 flare				03:40–04:14	<0.1 (2.3)a
	M6.3 flare				03:30–04:06	<0.6b
2012 Mar 10 (14)	LPGRE (1)	20:59–21:33	0.02 ± 0.01	≥6	20:00–21:15	0.05
	LPGRE (2)	22:35–23:15	0.043 ± 0.027	≥6	21:15–22:55	0.18
	LPGRE (3)	00:10–00:56	0.038 ± 0.015	≥6	22:55–00:33	0.2
	LPGRE (4)				00:33–02:00	0.09
	LPGRE Total				20:00–02:00	0.5 ± 0.3(2.2)a
	M8.4 flare				17:51–18:11	<0.1 (2.2)a
	M8.4 flare				17:41–18:05	<0.2b
2012 May 17 (15)	LPGRE (1)	02:10–02:48	0.08 ± 0.03	2.6 ± 0.6	02:05–02:29	0.02
	LPGRE (2)	03:46–04:22	0.05 ± 0.025	2.2 ± 1.0	02:29–04:02	0.1
	LPGRE (3)				04:02–05:20	0.03
	LPGRE Total				02:10–05:20	0.15 ± 0.1 (1.4)a
	M5.1 flare				01:40–01:55	<0.6b
	SEP protons					143 ± 92
2012 Jun 03 (16)	LPGRE (1)	17:51–17:53	0.24 ± 0.08	2.5 ${}_{-?}^{+1.5}$	17:51–17:53	0.01?
	LPGRE (2)	17:54–18:02	0.54 ± 0.06	4.3 ± 0.7	17:54–18:02	0.15
	LPGRE (3)				18:02–19:00	0.58
	LPGRE Total				17:54–19:00	0.74 ± 0.35 (2.2)a
	M3.3 flare		3.3 ± 0.4	6.4 ± 1.0	17:53–17:54	0.19 ± 0.05 (2.2)a
2012 Jul 06 (17)	LPGRE (1)	23:27–23:54	0.37 ± 0.04	5.1 ± 0.6	23:14–23:40	0.2
	LPGRE (2)	23:27–23:40		4.7 ± 0.8
	LPGRE (3)	23:40–23:54		>6.0
	LPGRE (4)				23:40–01:00	0.7
	LPGRE Total				23:14–01:00	0.9 ± 0.3 (2.1)a
2012 Oct 23 (18)	LPGRE (1)	04:10–04:40	0.13 ± 0.03	4.6 ± 1.2	03:20–04:25	0.18
	LPGRE (2)				04:25–05:20	0.15
	LPGRE Total				03:20–05:20	0.33 ± 0.2 (1.9)a
	X1.8 flare				03:15–03:17	<0.06b (1.9)a
2012 Nov 27 (19)	LPGRE Total	15:55–16:11	0.13 ± 0.03	2.9 ± 0.6	15:55–16:11	0.04 ± 0.02(1.4)a
	M1.6 flare				15:55:40–15:56:44	<0.002 (1.4)a
2013 Apr 11 (20)	LPGRE (1)	07:10–07:14	1.0 ± 0.1	5.8 ± 0.8	7:10–07:14	0.21
	LPGRE (1) <300 MeV	07:10–07:30		<4.5c
	LPGRE (2)	07:14–07:20	1.1 ± 0.09	5.2 ± 0.5	07:14–07:20	0.30
	LPGRE (3)	07:20–07:30	0.53 ± 0.06	5.0 ± 0.7	07:20–07:30	0.23
	LPGRE Total				07:10–07:30	0.74 ± 0.3 (2.3)a
	M6.5 flare				07:07–07:11	<0.03 (2.3)a
	SEP protons					41 ± 25
2013 May 13 (21)	LPGRE Total	04:30–05:15	0.10 ± 0.02	6.0 ± 2.0	02:30–06:00	2.2 ± 1.5 (1.0)a
2013 May 13 (22)	LPGRE (1)	17:15–17:28	0.11 ± 0.05	4 ± 2	17:00–17:22	0.06
	LPGRE (2)	17:41–17:59	0.25 ± 0.05	2.9 ± 0.6	17:22–17:50	0.2
	LPGRE (3)	20:25–21:10	0.2 ± 0.04	6.2 ± 1.0	17:50–20:45	2.0
	LPGRE (4)				20:45–23:00	1.0
	LPGRE Total				17:00–23:00	3.3 ± 1.8 (1.3)a
	X2.8 flare				16:00–16:07	<0.6b
2013 May 14 (23)	LPGRE (1)	01:30–01:47	0.06 ± 0.02	6 ± 2	01:20–01:40	0.05
	LPGRE (2)	02:58–03:23	0.42 ± 0.03	5.0 ± 0.5	01:40–03:10	1.3
	LPGRE (3)	04:20–05:06	0.26 ± 0.03	6.6 ± 0.9	03:10–04:43	2.1
	LPGRE (4)	06:01–06:41	0.08 ± 0.02	>6.5	04:43–06:20	1.2
	LPGRE (5)				06:20–07:00	0.1
	LPGRE Total				01:20–07:00	4.8 ± 2.0 (1.4)a
	X3.2 flare				01:06–01:16	<0.2b
2013 May 15 (24)	LPGRE (1)	02:37–03:23	0.02 ± 0.01	4.5 ± 2	02:00–03:00	0.02
	LPGRE (2)	04:13–04:58	0.06 ± 0.02	5 ± 1.5	03:00–04:35	0.15
	LPGRE (3)	05:52–06:34	0.03 ± 0.01	<2.5	04:35–06:13	0.12
	LPGRE (4)	07:33–08:09	0.03 ± 0.01	<2.5	06:13–07:51	0.12
	LPGRE (5)				07:51–09:00	0.04
	LPGRE Total				02:00–09:00	0.45 ± 0.25 (1.3)a
	X1.2 flare				01:36–01:46	<0.01 (1.3)a
	X1.2 flare				01:30–01:55	<0.36b
2013 Oct 11 (25)	LPGRE Total	07:14–07:30	2.6 ± 0.2	4.3 ± 0.2	07:14–07:30	3.0 ± 1.7e (1.0)a
	LPGRE <300 MeV	07:14–07:30		<4.2c,e
2013 Oct 25 (26)	LPGRE (1)	08:14–08.59	0.13 ± 0.02	5.6 ± 1.4	08:02–08:30	0.11
	LPGRE (2)				08:30–09:30	0.21
	LPGRE Total				08:02–09:30	0.32 ± 0.15 (1.5)a
	X1.7 flare				07:58–08:02	<0.32b
2013 Oct 28 (27)	LPGRE (1)	15:46–16:06	0.07 ± 0.02	2.5 ± 0.5	15:20–15:55	0.014
	LPGRE (2)				15:55–17:00	0.026
	LPGRE Total				15:20–17:00	0.04 ± 0.02 (2.2)a
2014 Feb 25 (28)	LPGRE (1)	01:13–01:17	14.1 ± 0.5	∼3.5d	00:55–01:15	6
	LPGRE (1) <300 MeV	01:10–01:26		<3.5c
	LPGRE (2)	04:21–04:40	3.5 ± 0.2	∼7	01:15–04:30	73
	LPGRE (2) <300 MeV	04:21–04:40		<3.8c
	LPGRE (3)				04:30–05:30	9
	LPGRE Total				00:50–05:30	88 ± 40 (1.3)a
	X4.9 flare				00:43–00:52	3 ± 1.5b
	SEP protons					30,600 ± 22,700
2014 Sep 01 (29)	LPGRE (1)	11:06–11:12	40 ± 2	4.75 ± 0.2	11:06–11:12	20
	LPGRE (2)	11:12–11:20	50 ± 2	4.35 ± 0.15	11:12–11:20	29
	LPGRE <300 MeV	11:04–11:30		<3.4c,e
	LPGRE (3)	12:26–12:58	0.30 ± 0.03	3.65 ± 0.3	11:20–12:42	149
	LPGRE (4)				12:42–15:52	1
	LPGRE Total				11:02–15:52	199 ± 90e (1.0)a
2015 Jun 21 (30)	LPGRE (1)	02:20–02:41	0.12 ± 0.04	?	02:20–02:41	0.07
	LPGRE (2)	05:20–05:53	0.13 ± 0.03	3.2 ± 0.7	02:41–05:37	0.57
	LPGRE (3)	08:30–09:02	0.09 ± 0.02	2.7 ± 0.7	05:37–08:46	0.38
	LPGRE (4)	11:41–12:14	0.07 ± 0.02	3.3 ± 1.3	08:46–11:56	0.27
	LPGRE (5)				11:56–14:00	0.08
	LPGRE Total				02:20–14:00	1.4 ± 0.7 (2.3)a
	M2.6 flare				02:11–02:20	<0.2 (2.3)a
	M2.6 flare				02:09–02:25	<0.6b

Notes.

^aMultiplicative factor to correct number for a downward isotropic angular distribution. ^bFrom 2.223 MeV line flux, assuming that protons follow a power-law spectrum with index s = 4 above ∼30 MeV that steepens to an index of 5 at >300 MeV; see Section 4.1.3. ^cThe 95% confidence limit on index between 30 and 300 MeV based on comparing 2.223 MeV line flux upper limit and >100 MeV γ-ray flux; see Section 4.1.3. ^dBetter fit E⁻²*exp-(E/1300 MeV). ^eAssuming a heliocentric angle of 85°. ^f>300 MeV unless noted in column 2.

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The estimated LPGRE durations were as short as about 10 minutes and as long as ∼20 hr, with a mean duration of about 4.5 hr. As some of the longest-lasting LPGRE events also had large onset delays, the durations and delays of the measured events (filled circles) exhibit a weak correlation (correlation coefficient 0.24). We also studied the approximate rise times of the LPGRE events (onset to estimated peak). They range from as short as a few minutes to as long as 6 hr.

We found no correlation between CME speed and LPGRE onset delay and only a weak correlation (correlation coefficient 0.3) between CME speed and LPGRE duration. We also compared the durations of 10 >100 MeV SEP proton events observed by GOES that were magnetically well-connected to the flare site with the durations of the associated LPGRE events. The SEP duration was estimated from the time of onset to the time that the flux dropped to ∼10% of its peak value. The SEP and LPGRE durations plotted in Figure 8(a)) are correlated (correlation coefficient 0.93), with the SEP events lasting an average of about five times longer. For comparison, in Figure 8(b)), we compare LPGRE durations with the durations of tails observed in soft X-rays from extended heating of the corona following flares (e.g., Ryan et al. 2013). We defined the duration of the soft X-ray emission to be from the time of the peak GOES 1–8 Å flux to the time at which the flux had fallen back to the pre-flare background level. Small flares that occurred during this decay did not affect this study because of the relatively smooth exponential decay of the SXR emission from the flare of interest. There is a large scatter in the data points leading to a weaker correlation (correlation coefficient 0.32).

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5.2.3. Search for Short-term Temporal Variations in LPGRE Events

In this section, we summarize the Fermi/LAT spectroscopic measurements of >100 MeV γ rays observed in the 30 LPGRE events and the related RHESSI and GBM observations in the nuclear γ-ray-line energy range. These include observations made during both the impulsive and late phases of the events. Details of our analysis techniques are presented in Section 4. They are based on theoretical studies of pion-decay emission for an assumed isotropic ion distribution (Murphy et al. 1987). Because the angular distribution of the ions producing the pion-decay emission is likely to be anisotropic, we discuss how our results need to be modified for such distributions. We detail the results of these spectroscopic studies in Table 3 in Section 5.3.1. In Section 5.3.2, we discuss the inferred power-law indices of >300 MeV protons producing the LPGRE for all 30 events, and in Section 5.3.3 we discuss the indices of <300 MeV protons for seven intense events in Section 5.3.3.

5.3.1. Table of Spectral Characteristics of LPGRE in Solar Eruptive Events

5.3.2. Spectral Indices of >300 MeV Protons Producing LPGRE

In this section, we review the properties of the spectra and variability of >300 MeV protons producing LPGRE. We assume that the >300 MeV protons interact in a thick target and have an unbroken power-law spectrum, even though there is evidence that the spectra in the most intense events steepen above about 1 GeV. The derived power-law spectral indices and uncertainties are listed for each LAT solar exposure in column 5 of Table 3 and plotted in Figure 9 by event number. These were calculated for an assumed isotropic proton angular distribution. As discussed in Section 4.1.2, for a downward isotropic angular distribution of protons, the proton spectral indices for events near disk center will be smaller by as much as unity (harder spectra) than those listed in the table and plotted in the figure. There is not enough information given in Mandzhavidze & Ramaty (1992) to provide event-by-event correction factors. Recall that there are two LPGRE episodes associated with the two flares on 2012 March 7 (event 12). For events where there is more than one LAT solar exposure and statistics are sufficient, we plot the derived spectral index and error for both the first (filled circles) and last (unfilled circles) exposures. The values of the event-averaged proton power-law index have a large scatter relative to the uncertainties and range from ∼2.5 to 6.0, with a mean index of 4.5 for an isotropic angular distribution of protons. We would expect the average index to be harder for a downward isotropic distribution of protons.

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One of the hardest of the LPGRE proton spectra is associated with the 2012 May 17 ground-level enhancement (GLE; event 14). The proton spectral index measured between 02:10 and 02:48 UT had a value of 2.6 ± 0.6. As this event was close to the solar limb, we do not expect the calculated index to be significantly different for a downward isotropic angular distribution. Over a 0.3–1 GeV energy range, this differential power-law index in energy is equivalent to a differential rigidity index of 3.4. Neutron monitors recorded rigidity indices ranging from 2.1 to 3.8 from 01:40 to 03:30 UT in this event (Plainaki et al. 2014), consistent with that implied by the γ-ray measurement.

There are six events in which there appears to be significant variation in proton spectral index with time. Four of these showed spectral softening with time: 2011 March 7 (event 1), 2012 March 7 (2nd episode event 12), 2013 May 13 (event 22), and 2014 February 25 (event 28). All of these events had durations longer than 4 hr. As can be seen in Table 3, the spectrum of the second 2012 March 7 event gradually softened from an index of ∼3.5 to an index of ∼5.2 over a 9 hr period. This is consistent with the observations of Ackermann et al. (2014). The second event on 2013 May 13 (event 21), associated with the flare at 16 UT, also showed clear evidence of softening between 17:50 UT, when the power-law index was ∼3, and 20:50 UT, when the index was ∼6. A similar spectral softening from a power-law index of ∼3 to an index of ∼6 also occurred over a 3 hr period in the event on 2014 February 25.

There are two events that showed evidence for spectral hardening: 2011 September 6 (event 6) and 2014 September 1 (event 29). These two events were of shorter duration than the four discussed above. The September 6 event had a duration of less than 1 hr and a much softer proton spectrum, power-law index 5.3, during the rise to maximum than it did during the decaying phase, when the index was 3.5. A similar but less significant spectral variation was observed during the behind-the-limb 2014 September 1 event, where the proton spectrum hardened from an index of 4.75 ± 0.20 during the 6 minute rise phase to 4.35 ± 0.15 during the 8 minute decline phase. The protons producing weak emission 1 hr later also appeared to have a harder index, 3.65 ± 0.3.

We studied other LPGRE events with durations shorter than 1 hr in a search for spectral hardening with time. As shown in Figure 22(d), there are two 20 s LAT exposures at the peak of the 6–10 minute >100 MeV LPGRE event on 2011 August 9 (event 5). The spectrum of the first exposure appears to be softer than the second one. The spectral evolution of the first LPGRE event on 2012 March 7 (first point; event 12 in Figure 9) following the X5.7 flare (see inset of Figure 29) is complicated because there were only a few measurements before the peak. The proton spectrum from 00:39 to 00:44 UT, in what appears to be the rising phase of the emission, is harder than the spectrum during the falling phase before the M7 flare, but the statistical significance is not compelling (see also Table 1 in Ajello et al. 2014). The event on 2012 November 27 (event 19) exhibits a clear rise and fall, but the measured spectra during those times are both consistent with power laws with indices of ∼3. The event on 2013 April 11 (event 20) also showed a clear rise and fall, and there is a suggestion that the proton spectrum hardened after the peak flux, but it is not statistically significant. There was no evidence for spectral hardening from the rise to the fall of the behind-the-limb event on 2013 October 11 (event 25), with the power-law indices both being consistent with an index of 3.7 ± 0.2. Thus, there is no clear pattern of spectral hardening with time in LPGRE events with durations shorter than about 1 hr.

5.3.3. Information on LPGRE Proton Spectra <300 MeV

We estimate the number of >500 MeV protons in the LPGRE events using techniques discussed in Sections 4.1 and 4.1.3 and list the number in each 20–40 minute LAT exposure for the 30 events in column 7 of Table 3. The total number of protons at the Sun responsible for the LPGRE events ranges from ∼2 × 10²⁶ to 1.5 × 10³⁰, assuming that the protons have an isotropic angular distribution. For a downward isotropic particle distribution, the number of protons increases from a factor of unity for events near the solar limb to about 2.3 near disk center (Section 4.1.2). We list this heliocentric angle–dependent factor in parentheses for each event in Table 3.

It is of interest to determine whether the number of LPGRE protons is correlated with other event parameters, such as CME speed and peak GOES soft X-ray power. In Figure 10, we plot the number of >500 MeV protons for a downward isotropic angular distribution versus CME speed in panel (a) and peak GOES power in panel (b). The scatter is large, and there is no clear correlation of proton number with either CME speed or X-ray power, with the exception of the three largest LPGRE events on 2012 March 7, 2014 February 25, and 2014 September 1 that had large associated CME speeds and X-ray powers. This may just be a manifestation of what Kahler (1982) called “the Big Flare Syndrome” (BFS); statistically, energetic flare phenomena are more intense in larger flares, regardless of the detailed physics.

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In Section 5.4.1, we compare the number of >500 MeV protons producing the late-phase γ-ray emission with the number of protons producing pion-decay radiation in the impulsive phase of the flare. In Section 5.4.2, we compare the number of LPGRE protons with the number of >500 MeV protons in space inferred from SEP observations.

5.4.1. Comparison of Number of Protons in the LPGRE and Impulsive Flare

In this section, we compare the number of >500 MeV protons that produce LPGRE with the number in the impulsive phase of the flare. In making this comparison, we assume that the protons follow the same angular distribution in both phases. Our sample includes the 19 events for which there was near-complete exposure to the impulsive phase with either LAT observations >100 MeV (eight events) or RHESSI or GBM measurement of the 2.223 MeV neutron-capture line (11 events). In Section 4.1.3, we discussed how we obtain estimates of the number of impulsive >500 MeV protons from 2.223 MeV line measurements. The measured impulsive-phase proton numbers or upper limits are given in column 7 of Table 3 in the row listing the GOES X-ray class. We plot the derived impulsive-/late-phase proton number ratios versus event number in Figure 11. The red and blue symbols give the ratios for events where LAT and 2.223 MeV line impulsive-phase observations were used, respectively. In most instances, we only have 95% upper limits on the ratios, and only one of them is >0.2.

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Impulsive-phase >100 MeV emission was observed by LAT on 2011 September 6 (event 6; Appendix C.6) and 2012 June 3 (event 16; Appendix C.16). The LPGRE in the hour following the flare on 2011 September 6 was produced by ∼15 times the number of protons responsible for the impulsive emission. The number of protons producing LPGRE on June 3 was ∼4 times higher than the number in the impulsive phase. The 2.223 MeV neutron-capture line was detected by the SPI detector on INTEGRAL (Zhang et al. 2012) during the the X5.4 and M7 flares on 2012 March 7 (event 12; Appendix C.12, Figure 29). From these observations, we estimate that there were 1.4 and 1.1 × 10²⁸ protons with energies >500 MeV in the X5.4 and M7 flares on 2012 March 7, respectively. We note that the number derived for the M7 flare is consistent with the upper limit of 0.9 × 10²⁸ obtained from LAT observations. There was a 45 minute LPGRE event following the X5.4 flare produced by ∼50 times the number of impulsive-phase protons and a second 18 hr LPGRE that began within 1 hr of the flares. We summed the proton numbers in the two impulsive flares and the numbers in the two LPGRE events to estimate the ratio plotted in the figure. The neutron-capture line was detected by GBM during the impulsive phase on 2014 February 25 (event 28; Appendix C.28), and for that event, the number of protons in the LPGRE was ∼40 times larger.

Overall, most of the observations suggest that the number of >500 MeV protons producing the LPGRE is at least a factor of 10 larger than the number producing impulsive-phase >100 MeV γ-ray emission.

5.4.2. Comparison of Number of Protons in the LPGRE and the Associated SEP Event

Most SEP measurements are made at energies below 100 MeV. Satellite experiments such as PAMELA (Adriani et al. 2015) and AMS (Aguilar et al. 2013) provide sensitive observations >100 MeV, but results on the total number of protons in space are not yet available. Determination of the total number of particles in an SEP event requires knowledge of the spatial distribution of high-energy SEPs. Using data from the GOES HEPAD experiment and neutron monitors, Tylka et al. (2014) developed a method to estimate the total number of >500 MeV SEP protons in space for some of the LPGRE events. We update this study in Appendix D and provide estimates of the number of protons in eight SEP events with emission that can be studied above 100 MeV. There are systematic uncertainties in the numbers listed in column 7 in Table 3 and the rows labeled SEP protons in column 2 that are not reflected in the quoted errors. This is due to the estimate in the transport, or crossing correction. We have used neutron-monitor data to infer that the >500 MeV crossing correction is ∼2. Values as large as eight are inferred from Monte Carlo calculations (Chollet et al. 2010) that would reduce the estimated number of SEP protons. However, these larger factors also imply significantly more interplanetary scattering, producing a radial dependence in SEP flux that falls faster than the r⁻² dependence assumed. The estimated number of interplanetary protons would then increase.

With these uncertainties in mind, we plot the number of >500 MeV LPGRE protons versus the number observed in eight accompanying SEP events in Figure 12. In estimating the number of LPGRE protons, we have assumed that the protons followed a downward isotropic angular distribution. Even though the two largest SEP events are associated with the two largest LPGRE events, the overall probability that LPGRE and SEP proton numbers are correlated is small (correlation coefficient 0.3). The LPGRE/SEP proton number ratio ranges from 0.0015 to 0.5 with an average of 0.14. Systematic uncertainties, primarily due to the transport correction, could increase these ratios by as much as a factor of five.

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Detection of >100 MeV LPGRE from behind-the-limb events on 2013 October 11 (event 25) and 2014 September 1 (event 29; Pesce-Rollins et al. 2015a, 2015b; Ackermann et al. 2017) demonstrates that this emission can be produced by protons interacting far from the flare site. Plotnikov et al. (2017) detailed the characteristics of these events and showed that the onsets of the LPGRE are consistent with the times when CME shock-accelerated protons interacted at locations visible from Earth after transport on magnetic fields returning to the Sun.

We plot the time histories of these two behind-the-limb events in Figures 42 and 46 and discuss the detailed observations in Appendices C.25 and C.29. Before the onset of LPGRE, the NaI detectors on GBM observed hard X-rays from high coronal sources associated with both flares after they appeared over the solar limb. Direct on-disk observations of the flares themselves were made by the Solar Assembly for X-rays (SAX) instrument on MESSENGER (Schlemm et al. 2007). The LPGRE on 2013 October 11 began about 7 minutes after the 50–100 keV coronal source rose above the solar limb, lasted 15 minutes, and showed no evidence for spectral evolution. The >100 MeV γ-ray spectrum is consistent with the decay of pions produced by >300 MeV protons with a power-law spectral index s = 4.3 ± 0.2 throughout the observation (Table 3). Because the emission came from close to the solar limb, the spectrum is not significantly different for isotropic, downward isotropic, or fan-beam angular distributions of protons.

The most intense portion of the LPGRE on 2014 September 1 lasted about 30 minutes, and its peak flux was about 10 times larger than that of the 2013 October 11 event. It was one of the most intense LPGRE events observed by LAT, even though the active region was more than 30° beyond the solar limb. Our studies summarized in Table 3 and Section 5.3.2 provide evidence that the proton spectrum producing the pions hardened from a power-law index ∼4.5 to ∼3.7 from 11 to 13 UT. During the peak emission time, we also found that the proton power-law spectrum steepened from one with an index harder than 3.4 between 20 and 300 MeV to one with an index of ∼4.5 above 300 MeV.

What is significantly different about the 2014 September 1 event is that the >100 MeV LPGRE was accompanied by hard X-ray emission extending to energies above 10 MeV that began within 1 minute of the >100 MeV emission and peaked about 5 minutes earlier (see Figure 46 in Appendix C.29). The 60–910 keV spectra from three solar facing GBM NaI detectors from 11:06 to 11:15 UT were acceptably fit by broken power-law electron spectra interacting in both thin and thick targets. For the thick target model, the electron power-law index above the ∼330 keV break energy was 3.2 ± 0.1. For the thin target model, the index above the ∼240 keV break energy was 2.15 ± 0.1. We obtained the same power-law indices when we fit GBM/BGO 0.2 to 34 MeV spectra over the same time intervals, indicating that the electron emission extended to several tens of MeV. There is no evidence for spectral variability over the full time interval of the event. Ackermann et al. (2017) showed that the hard X-ray and microwave time histories match one another and that the electrons producing the >1 GHz emission had a power-law index of ∼3.1, the same value we found for electrons producing the bremsstrahlung in thick target bremsstrahlung. At face value, this would suggest a thick target origin for the bremsstrahlung. Although Ackermann et al. (2017) focused most of their discussion on a thin target origin from a source high in the corona (they obtained the same power-law index as we do), they leave open the possibility that the emission could be due to thick target bremsstrahlung in the chromosphere.

There is evidence that the hard X-ray source may have been extended over tens of heliographic degrees. After emerging from the South Atlantic Anomaly (SAA) radiation belts at 11:11 UT, RHESSI detected >20 keV X-rays from the Sun. RHESSI derives spatial information from the modulation of the photon flux in grids sensitive to different spatial scales as the satellite rotates. RHESSI detected a sufficient number of photons to yield an image of the source in this case (Hurford et al. 2002), but the only modulation observed was derived by taking the differences in the fields of view parallel and perpendicular to the slit axis. This localized the source to the northeast quadrant of the Sun, consistent with the LAT centroid (Ackermann et al. 2017), but no image could be made. The absence of rotational modulation in RHESSI detector 9, which has the coarsest grids, implies that the source size had to be larger than 300″. This indicates that the >20 keV hard X-ray emission was distributed over a broad region and not confined to the relatively small (<50″) loop-top source imaged in the 6–12 keV range by Ackermann et al. (2017). If the association of this electron bremsstrahlung with the LPGRE is valid, then these measurements provide evidence that the protons producing the emission can be distributed over tens of heliographic degrees in some events. Additional evidence for a distributed source comes from the LAT observation of the westward shift by tens of degrees in the location of the LPGRE late in the 2012 March 7 event (event 12; Ajello et al. 2014).

We did not observe late-phase bremsstrahlung during the LPGRE from the behind-the-limb flare on 2013 October 11, where the peak pion-decay γ-ray flux was about 20 times lower than that on 2014 September 1. The SEP 0.7–4.0 MeV electron flux on October 11 was between 50 and 100 times lower than it was on September 1. Bremsstrahlung from an electron flux two orders of magnitude smaller than that observed on September 1 would not have been detectable above the background by GBM. The LPGRE events on 2012 March 7 (Appendix C.12) and 2014 February 25 (Appendix C.28) were of an intensity comparable to the 2014 September 1 event, but we did not detect any evidence for late-phase bremsstrahlung emission. However, flare-related and instrumental background could have affected the GBM sensitivity to late-phase bremsstrahlung. We estimate the expected late-phase bremsstrahlung flux from these events by assuming that the (peak LPGRE)/(peak late-phase bremsstrahlung) ratio was the same as that measured in the 2014 September event, modified by the relative SEP proton/electron ratio measured in space. For the first LPGRE event on 2012 March 7, the estimated second-phase bremsstrahlung flux was about a factor of six lower than the upper limit that could be set from the background at that time. For the second event on March 7, the estimated bremsstrahlung flux was about the same as the upper limit based on the background. In contrast, we estimate that the late-phase bremsstrahlung during the peak of the LPGRE on 2014 February 24 should have exceeded the upper limit set by the background by a factor of five. Thus, we have evidence for late-phase bremsstrahlung emission only during the peak of the LPGRE on 2014 September 1, and there is one event where we might have expected to detect the bremsstrahlung but did not.

Below, we list the primary results of our study of LPGRE properties.

• 1.  
  The spectra of >100 MeV LPGRE can be fit by the shape expected from the decay of neutral and charged pions produced by protons interacting in a thick target and having a power-law spectrum in energy (Section 4.1). However, there is evidence in the most intense events that the >300 MeV proton spectrum steepens from an unbroken power law near 1 GeV. The LPGRE >100 MeV spectra (Section 4.1.1) cannot be fit by bremsstrahlung from high-energy primary electrons with synchrotron losses.
• 2.  
  In all 27 LPGRE events for which there were available hard X-ray measurements of the accompanying impulsive phase, hard X-rays with energies in excess of 100 keV were detected (Section 5.1). This suggests that accompanying flare emission reaching energies above about 100 keV is a necessary condition for LPGRE.
• 3.  
  Accompanying 28 of the 30 LPGRE events were ≳800 km s⁻¹ CMEs that were either full or partial halo events. No CMEs were observed in the two remaining events, but there is evidence for magnetic eruptions, suggesting that they were failed CMEs. Thus, a fast-broad CME is not a necessary condition for LPGRE (Section 5.1).
• 4.  
  Neither an accompanying flare with detectable >100 keV hard X-rays nor an accompanying fast CME is a sufficient condition for LAT detection of LPGRE. However, this conclusion may be influenced by the limited duty cycle of LAT observations.
• 5.  
  The LPGRE from behind-the-limb flares (Ackermann et al. 2017) indicates that LPGRE can extend up to a few tens of degrees from the active region. However, a study of solar eruptive events with >800 km s⁻¹ CMEs on the near and far sides of the Sun suggests that >100 MeV emission over such a spatial extent is not common (Section 5.1).
• 6.  
  The LAT LPGRE time histories are incomplete due to its limited duty cycle for solar observations. However, it is clear that LPGRE begins after the impulsive-phase hard X-ray emission (17 of 21 eruptions; two on 2012 March 7) and/or has a time profile distinctly different from or extended well beyond the impulsive-phase emission. None of the LPGRE events have a time history that clearly represents the decay of impulsive-phase flare emission (Section 5.2). There is no evidence that LPGRE is due to a series of episodic short-duration high-energy outbursts masquerading as steady emission (Section 5.2.3).
• 7.  
  The LPGRE begins as early as the onset of the CME and as late as about 2 hr after CME onset (Section 5.2.2). The rise times range from a few minutes to 6 hr. The duration of the emission ranges from about 5 minutes to 20 hr. There is no correlation between onset delay and duration.
• 8.  
  The LPGRE durations appear to be correlated with the durations of the accompanying >100 MeV SEP proton events, but the SEP durations are, on average, five times longer (Section 5.2.2).
• 9.  
  The average power-law index of >300 MeV protons producing LPGRE is 4.5 for an assumed isotropic proton distribution, but there is a large statistically significant flare-to-flare scatter in index with an rms value of 1.8 (Section 5.3.2). For downward isotropic and fan-beam proton distributions near disk center, the proton spectra are significantly harder.
• 10.  
  Analysis of nuclear lines in the γ-ray spectra of LPGRE events indicates that the proton spectrum between 20 and 300 MeV tends to be flatter than it is above 300 MeV (Section 5.3.2).
• 11.  
  The spectral index of the >300 MeV protons producing LPGRE associated with the GLE on 2012 May 17 is consistent with the spectrum determined from neutron-monitor data (Section 5.3.2).
• 12.  
  The spectrum of LPGRE softened with time in four of the events with durations >4 hr and hardened in two events with shorter durations (Section 5.3.2).
• 13.  
  The number of >500 MeV protons producing LPGRE is typically about an order of magnitude larger than the number producing any impulsive γ-ray emission during the associated flare (Section 5.4.1).
• 14.  
  Type II metric or DH radio emission, indicating the presence of a shock, accompanied all of the LPGRE events except the 2012 November 27 event, which also did not have an associated CME (see Appendix E).
• 15.  
  Type III metric or DH radio emission, indicating that flare electrons reached open field lines, accompanied all of the LPGRE events except the two events that did not have associated CMEs (see Appendix E).
• 16.  
  From all LPGRE events that were accompanied by a CME and for which the proton flux was not masked by the remnants of a previous SEP event, SEP protons were observed.
• 17.  
  The number of >500 MeV protons needed to produce LPGRE ranges from 0.1% to 50% of the number of protons observed in SEPs in interplanetary space (Section 5.4.2). There are significant systematic uncertainties in the SEP estimates, however.
• 18.  
  There is evidence that late-phase emission electrons with energies in excess of 10 MeV producing bremsstrahlung in a thick target were accelerated along with the protons producing the >100 MeV LPGRE on 2014 September 1 (Section 5.5). RHESSI imaging studies indicate that the bremsstrahlung was distributed over tens of degrees in heliographic longitude (Section 5.1), suggesting that the LPGRE was similarly distributed.

Fermi/LAT’s high sensitivity to >100 MeV γ-ray emission allows the study of significantly weaker late-phase emission than was possible with previous instruments. In contrast to pre-Fermi LPGRE events, which were all associated with X-class flares, only about 50% of the events observed by Fermi are associated with such intense flares. Studies of LPGRE events made prior to Fermi and discussed by Ryan (2000) and Chupp & Ryan (2009; see also Appendix A) indicated that the emission came primarily from ion interactions. Spectra of intense >100 MeV LPGRE events observed by LAT are consistent with pion-decay emission and are not compatible with any plausible spectrum from primary electron bremsstrahlung. One of the limitations of LAT, however, is its limited duty cycle for solar observations. Here we discuss the constraints imposed by the characteristics summarized in the previous section on models for the late-phase emission (e.g., Ryan 2000; Chupp & Ryan 2009). The two critical issues are the nature of the mechanism that can accelerate protons to GeV energies and the long duration of >100 MeV emission compared with most flare properties (we note that all known LPGRE events have flare associations).

One early model can be described as a magnetic trap: it invoked delayed precipitation into the chromosphere of high-energy particles that were accelerated in the impulsive phase of the flare and then stored in magnetic structures high in the corona (e.g., Ryan 1986). The nature of impulsive-phase acceleration is still under debate, but γ-ray observations confirm that it can accelerate protons to high energies within seconds of the electrons producing bremsstrahlung (e.g., Ackermann et al. 2012b). The trapping mechanism could be magnetic mirroring in a large loop combined with very slow pitch-angle diffusion (i.e., weak wave turbulence), or perhaps very strong wave turbulence that inhibits proton escape by imposing a slow random-walk process on propagation. The difficulty with this model is that it does not provide a natural way to explain the LPGRE events displaying a distinct increase in >100 MeV flux beginning after the impulsive phase. Such a passive trap also cannot explain the much larger number of late-phase protons than impulsive-phase protons inferred from the pion-decay γ-ray observations.

What is required is a mechanism that can accelerate particles after the impulsive phase is over. Ryan & Lee (1991) studied a model in which particles are injected into a large loop (10⁵ km) that is dominated by magnetic hydrodynamic turbulence. These particles diffuse and precipitate to the footpoints producing the impulsive-phase emission with intensities depending on where along the loop they were injected. The turbulence also accelerates the particles by the second-order Fermi process to energies high enough to produce pion-decay emission over a longer timescale. The parameters of the loop and turbulence can be adjusted to account for the time profiles of the impulsive- and late-phase emission observed on 1982 June 3. More recently, Ryan et al. (2015) applied this model to some of the events observed by Fermi. With enough turbulent energy in the loop, the model can account for the factor of 10 increase in the number of >500 MeV protons in the late-phase emission over that found in the impulsive phase. However, this model requires a very high level of turbulence filling a large volume for a long period of time. It is not clear what the source of such a high-energy density of turbulence is. The mean free path due to turbulent scattering needed in the Ryan & Lee (1991) model to precipitate impulsively injected particles and accelerate the protons producing late-phase emission is 2 × 10⁴ times smaller than that in magnetic-loop models for impulsive-phase electron bremsstrahlung and nuclear γ-ray line emission (Hua et al. 1989; Miller & Ramaty 1989; Murphy et al. 1997). The long loops in the Ryan & Lee (1991) model can account for detection of LPGRE far from the flare site in behind-the-limb events and smooth time profiles but may not be able to explain emission that is spatially extended over tens of heliographic degrees.

As initially conceived, this high-turbulence loop model is not dependent on the presence of a CME. However, one of the features of the LPGRE events is their association with fast CMEs and SEP production. All but two of the 30 events are associated with fast wide CMEs. Because the energy carried by a CME is comparable to or larger than that of the flare-accelerated particles (Emslie et al. 2012), and because CME-driven shocks are generally believed to produce SEPs, CMEs are clearly candidates for the energy source for the >300 MeV protons that produce LPGRE. An accompanying CME is not necessary to produce late-phase emission in the Ryan & Lee (1991) model, but it is possible that the passing CME could impart additional magnetic turbulence to the large loops and enhance the acceleration of the protons to the high energies necessary to produce the observed pion-decay radiation. The eruption of a fast CME also naturally provides two other mechanisms for accelerating particles to high energies (e.g., Ryan 2000).

The first mechanism is acceleration by the strong electric fields in the current sheet formed behind the receding CME. Akimov et al. (1996) suggested that the late-phase γ-ray emission observed by the GAMMA satellite on 1991 June 15 was due to particles accelerated in the current sheet behind the receding 1100 km s⁻² CME. Such a mechanism could also account for the extended duration of the events, but it would have difficulty explaining the longer onset delays of hours or more, since we expect the current sheet to form once the CME launches. The mechanism might account for LPGRE far from the flare site in behind-the-limb events but may not be able to explain emission that is spatially extended over tens of heliographic degrees. It is also not clear whether electric fields in the current sheet would be strong enough to accelerate protons to hundreds of MeV.

The second mechanism is acceleration of particles by the shock produced by a fast CME. Type II radio emission indicating the presence of such a coronal shock was observed in all but one of the 30 LPGRE events (the 2012 November 27 event without an accompanying CME). Solar energetic particles were detected in all of the LPGRE events that were accompanied by fast CMEs, except for those where the SEPs were masked by particles from a previous event. The correlation between the duration of LPGRE events and the duration of SEP events observed above 100 MeV also suggests a common CME-shock origin, even though the LPGRE durations are, on average, about five times shorter than those of the SEPs. Thus, a plausible scenario for production of LPGRE is shock acceleration of seed particles onto magnetic field lines that reach the visible disk and precipitation of these particles into the chromosphere.

A shock origin for the LPGRE explains other characteristics of LPGRE events. Particle acceleration across a wide fast CME can account for the variations in observed arrival times and spectra of SEPs at widely separated spacecraft (Rouillard et al. 2012). It can, therefore, explain how >300 MeV protons interacted at the Sun to produce the first LAT LPGRE event on 2011 March 7 while the energies of the SEP protons measured in space barely exceeded 100 MeV. In addition, Plotnikov et al. (2017) and Jin et al. (2018) explained LPGRE from behind-the-limb flares by the passage of a CME shock that accelerates protons onto front-side-connected field lines. A CME-shock model also addresses the wide range of delays observed in LPGRE onset times: short LPGRE onset delays represent shock acceleration low in the corona (e.g., Gopalswamy et al. 2013), while long LPGRE onset delays indicate that the CME had to expand over several solar radii before accelerating >300 MeV protons that could return to the Sun. Deposition of shock-accelerated particles onto field lines returning to the Sun may have difficulty explaining the smooth time histories of the LPGRE events lasting several hours because it implies that the shock continues to accelerate protons to energies >300 MeV at several tenths of an astronomical unit from the Sun and that these particles were able to return to the Sun. Such long-duration events can be explained by precipitation of particles that are magnetically trapped in a reservoir (Reames 2013) behind the expanding CME.

One of the main difficulties with this model is transporting the protons back to the Sun against the magnetic mirror force, well after the flare, when the CME is many solar radii above the surface with magnetic field strengths much lower than at the solar surface. Quantitative estimates indicate that only a very small fraction of accelerated protons can return to interact in the chromosphere (e.g., Hudson 2018). The way around this objection is to assume that there is significant MHD turbulence on the field lines connecting the CME to the Sun, such as required in the model of Ryan & Lee (1991). Kocharov et al. (2015) presented a shock-wave model to estimate the ratio of the number of protons that return to the Sun and interact to the number that escape into interplanetary space. They estimated that the ratio for >100 MeV protons ranges from about 0.2% to 10%, depending on the amount of turbulence in the corona. This range is consistent with the 0.1%–50% range that we estimate in our comparison of the number of >500 MeV protons producing LPGRE and those detected as SEPs in space.

A variant on the magnetic trap model was proposed by Hudson (2018) and called the “lasso” model. In this case, the SEP particle accelerator crosses both open (SEP) and closed (LPGRE) field lines, leaving energetic protons on both. The closed field region can be large, perhaps extending out to several R_⊙, and rather than requiring that the protons themselves find their way back to the solar surface, Hudson (2018) suggested that instead, the loop structure holding the protons contracts back downward toward the solar surface as the corona recovers from the launch of a CME. The contraction of the closed field lines leads to an increase in magnetic field strength that eases the problem of magnetic mirroring, as well as possibly supplying additional acceleration of the protons.

The fact that two LPGRE events were observed without accompanying CMEs presents a problem for the CME-shock magnetic field scenario. Neither the event on 2012 October 23 (event 17; Figure 36, Appendix C.18) nor the event on 2012 November 27 (event 18; Figure 37, Appendix C.19) had an accompanying CME or detectable SEP event. The GOES soft X-ray durations for these events were two of the three shortest in our sample of 30 LPGRE events, and such short-duration soft X-ray flares are less likely to have CMEs (Sheeley et al. 1983). It is unlikely that the flares were directly responsible for the LPGRE because the numbers of protons required to produce the October 23 and November 27 LPGRE were 5 and 20 times larger, respectively, than the upper limits on the number of protons accelerated during the flare impulsive phase. Movies from AIA reveal evidence for the eruption of a magnetic loop in both events, at the times denoted by the downward arrows in the inset of Figures 36 and 37. In addition, Type II metric radio emission, indicative of shock formation, was detected following the magnetic eruption on 2012 October 23. This suggests that the two LPGRE events may have been accompanied by failed CMEs (Ji et al. 2003). Such events can still accelerate protons, but presumably only for a short period of time while the mass is still moving outward, and then only onto field lines in the relatively low corona. The LPGRE event on 2012 October 23²⁰ requires that the protons be stored in the low corona for over 1 hr after the flare.

There is one feature of the LPGRE events that is puzzling: the observation of impulsive-flare hard X-rays with energies greater than ≳100 keV in every LPGRE event for which there were flare measurements. Such an association may simply be a manifestation of the BFS (Kahler 1982), but there may also be a physical explanation that we offer here. Detection of >100 keV X-ray emission indicates the presence of hundreds of keV electrons in the flare, but it also may indicate the presence of sub-MeV ions. This follows by analogy because nuclear de-excitation–line γ-rays, produced by >1 MeV protons, are detected with high probability in flares only when the accompanying electron bremsstrahlung exceeds 300 keV (e.g., Vestrand et al. 1999; Share & Murphy 2000; Shih et al. 2009). Such sub-MeV to MeV flare protons can provide the seed population for further acceleration in the Ryan & Lee (1991) loop model. To provide a seed population for subsequent acceleration by a CME shock, the protons must escape from the flare site. Electrons can escape from the flare site, as evidenced by their presence in radio plumes containing both open and closed field lines (Fleishman et al. 2017) and their large number higher in the corona and further from the hard X-ray footpoints than previously detected (Gary et al. 2018), as well as by the fact that they have been shown to be the source of heating of a CME (Glesener et al. 2013). The presence of electrons on open field lines is also inferred in 27 of the 30 LPGRE events by the accompanying Type III radio emission. In addition, acceleration of flare-produced electrons by CME shocks was suggested by Petrosian (2016) to explain the harder electron spectra in the associated SEP events. Thus, it is possible that hundreds of keV flare electrons accelerated to MeV energies by the CME shock onto field lines returning to the visible disk produced the observed late-phase ∼MeV bremsstrahlung emission in the 2014 September 1 behind-the-limb flare. In like manner, flare-accelerated sub-MeV ions, which do not produce detectable γ rays, may provide the seed population for further acceleration in one of the scenarios discussed above to produce the LPGRE. This would explain the LPGRE association with >100 keV hard X-rays from flares. We discuss other aspects of this association in Appendix B, including observation of significantly higher SEP protons fluxes when >100 keV hard X-rays were observed in the accompanying flare.

It is possible that such a seed population of sub-MeV ions accelerated in the flare may also in part explain the delay in the onset of the LPGRE because of the time it would take them to catch up to the CME shock, where they can be further accelerated. If we assume that the protons are ejected into space at the time of the midpoint of flare 100–300 keV X-ray emission, we can estimate the energy they would require in order to reach the shock by the time of the onset of the LPGRE. From a comparison of CME and LPGRE onsets and hard X-ray time profiles in 18 events where the LPGRE onset was determined, we estimate that these protons would need to have an energy of ∼75 keV. This energy would be even higher if the LPGRE onset delay were in part due to the time it takes both for the shock-accelerated particles to reach a magnetic field line returning to the Sun and to accelerate the protons to energies >300 MeV.

Due to the broad range of LPGRE characteristics, we deem it unlikely that any one of the mechanisms discussed above alone will be able to account for the emission in all of the observed events. The acceleration and transport process is complicated and will require detailed modeling that will need to draw upon those and other processes to explain the emission and its relationship to flares, CMEs, and SEP events.

If the dual requirements, ≳800 km s⁻¹ CME speed and impulsive >100 keV hard X-ray emission, are physically related to the production of LPGRE, we need to explain the five events (black numbers in bold: A15, A24, A44, A70, and A75) in Table 4 meeting these requirements that did not exhibit LPGRE. The first question to address is whether there is any difference between the average characteristics of the 14 LAT events (red numbers in bold) with observed LPGRE and these five events. We use median values to compare these characteristics because of the small number of events in the samples. Events associated with LPGRE had a higher median GOES X-ray class (X1.1 versus M3.5), comparable median CME speeds (1582 versus 1407 km s⁻¹) and peak SEP proton fluxes (61 versus 75 pfu), and median heliographic longitudes closer to disk center (47° versus 68°) than events with no LPGRE. The higher GOES class for LPGRE events might be just a manifestation of the BFS.

The higher heliographic longitude of the five events with no detectable LPGRE can be explained by the detectability of γ rays near the solar limb. The transmission of >100 MeV γ rays from the lower chromosphere and photosphere through the overlying solar atmosphere decreases from about 95% at 45° to 82% at 70° and 15% at 89° relative to disk center. In addition, if the LPGRE does not all come from the flare site but is distributed over tens of degrees in heliographic angle, then γ-ray fluxes from events near the solar limb may be weaker due to attenuation and occultation.

The lack of an LAT detection of >100 MeV emission in the five events might also just be due to the limited duty cycle for good LAT solar exposures: 20–40 minutes every 90 or 180 minutes. The LAT would have a higher probability of missing a short, 30 minute transient than one that lasted several hours. Below, we plot and discuss the LAT, GBM, and RHESSI observations of the five events to determine whether these duty-cycle considerations could have played a role in the failure to detect LPGRE. We identify the event by its date, the standard naming convention for the accompanying flare (Leibacher et al. 2010), and its number in the table.

2011 February 24, SOL2011-02-24T07:23, Event A15.

Why might the LPGRE have been missed? There was good solar exposure for LAT that ended just before the impulsive phase, and no >100 MeV emission was detected at that time. Any LPGRE with a duration less than 1 hr following the impulsive phase would not have been detected because the next solar exposure began at 08:35 UT. The flare was near the solar limb (E84); thus, some of the emission might have been beyond the solar limb or attenuated by at least a factor of two in the overlying atmosphere.

Details. Event A15 is plotted in Figure 13. It is an M3.5-class flare at E84 (limb flare) lasting ∼20 minutes. It has an ∼1200 km s⁻¹ CME with onset ∼5 minutes before the 100–300 keV X-ray onset, M (metric) and DH Type II emissions observed with the M onset about 12 minutes after the CME onset, marginal evidence for solar energetic protons, and impulsive γ-ray emission up to 1 MeV observed by GBM (100–300 keV rates plotted in inset) and RHESSI, with no evidence for a 2.223 MeV neutron-capture line, as is expected for such a location near the limb. There is good LAT solar exposure at 07:05–07:35 UT that overlaps the early part of the impulsive phase; however, LAT solar exposure ends just before the rise of the hard X-rays. There is no evidence for >100 MeV emission at 08:35–09:10 UT, 1 hr after the impulsive phase, and no additional LAT solar exposure until 14 UT. Both the 2.223 MeV line and >100 MeV emissions would be strongly absorbed if produced at the flare site.

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2011 May 29, SOL2011-05-29T21:04, Event A24.

Why might the LPGRE have been missed? There was poor solar exposure to the impulsive phase for LAT, and the first good Fermi solar exposure was at 22:54 UT (see Figure 14); therefore, we have no information about the presence of >100 MeV emission from about 21:04 to 22:54 UT, about 2 hr after the impulsive peak. The active region was also relatively close to the solar limb (E75), with consequences for attenuation and missed radiation behind the solar limb if the late-phase gamma rays were broadly distributed. We also note that there was only a weak (6 pfu) SEP observed by the magnetically well-connected STEREO B.

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Details. Event A24 is plotted in Figure 14. It is a C8.7-class flare at E75 lasting ∼39 minutes and has an ∼1400 km s⁻¹ CME with an estimated onset within minutes of the soft X-ray rise. The GBM entered sunlight at 21:07 UT, revealing 100–300 keV emission (plotted in inset); M and DH Type II emissions are observed with the M onset ∼10 minutes after the CME launch; and there is a small flux of solar energetic protons up to energies >40 MeV at STEREO B for which the flare site was well connected. There is poor LAT solar exposure at 21:14–21:40 UT after the hard X-ray peak, with no evidence for >100 MeV emission. There is good LAT exposure at 22:54–23:36 UT but no evidence for >100 MeV emission. We cannot rule out >100 MeV emission up until 22:54 UT.

2011 September 24, SOL2011-09-24T12:33, Event A44.

Why might the LPGRE have been missed? There was good solar exposure for LAT at the beginning of the impulsive phase between 12:37 and 13:00 UT and poor exposure near the end between 14:10 and 14:30 UT. There is no evidence for LPGRE in both source-class and solar flare transient–class data in these time intervals. The next good solar exposure was 1 hr later, and no LPGRE was observed. Any LPGRE during the flare from 13:10 to 14:10 UT and for about 1 hr after the flare would have been missed by LAT.

Details. Event A44 is plotted in Figure 15. It is an M7.1-class flare at E61 lasting ∼37 minutes. The CME speed was ∼1936 km s⁻¹, with an estimated onset about 14 minutes before the first intense 100–300 keV X-ray peak. There was only DH Type II emission, and only an upper limit on the SEP proton flux was obtained because of the large event on September 22. The GBM observed emission up to 100–300 keV from the beginning of the flare until nighttime at 13:05 (time history plotted in the inset). There was good solar exposure for LAT at 12:37–13:00 UT, poor exposure at 14:10–14:30 UT, and good exposure at 15:30–16:10 UT. There is no evidence for >100 MeV emission in the source-class data in any of these intervals. The source-class data in the first two exposures were compromised because of high ACD rates. We therefore plot the solar flare transient–class >100 MeV fluxes during these time periods in the inset. There is no evidence for LPGRE in any of the exposures.

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2012 March 4, SOL2012-03-04T10:29, Event A70.

Why might the LPGRE have been missed? There was limited exposure for the LAT during the impulsive phase, ending near the rise of the impulsive X-ray peak, and there is no evidence for impulsive emission in our plots of source-class and LAT low-energy (LLE) data. The ability to search for >100 MeV emission following the impulsive phase was compromised by the shortened solar exposure split by an SAA passage beginning about an hour after the impulsive phase, and again during the next orbit.

Details. Event A70 is plotted in Figure 28 in Appendix C.11, where both the full plot and inset used Pass8 source-class data in hopes of improving sensitivity and detecting weak LPGRE; there was no significant improvement over Pass7. It is an M2.0 class flare at W68 lasting ∼107 minutes. It has an ∼1300 km s⁻¹ CME with onset coincident with the GBM 50–100 keV X-ray rise (plotted in the inset in lieu of the 100–300 keV band) and no Type II radio emission. It is a moderate solar energetic proton event with emission observed >60 MeV and impulsive hard X-ray emission up to 100–300 keV (RHESSI, GBM), with no evidence for the 2.223 MeV neutron-capture line. The LAT peak solar exposure from 10:40 to 11:10 UT is only 50% of the exposure of the adjacent orbits. The exposure is very small at the time of the 100–300 keV impulsive peak at 11:05 UT. There is no reported impulsive >100 MeV (Ackermann et al. 2014) emission or any observed in our study of the Pass8 solar flare transient–class data. LAT exposures from 12:10–12:20 UT, 12:40–12:50 UT and from 13:50–13:57 UT were truncated by passage through the South Atlantic Anomaly (SAA) causing large uncertainties in the flux. There is no clear evidence for LPGRE during these exposures.

2012 March 13, SOL2012-03-13T17:12, Event A75.

Why might the LPGRE have been missed? This event was the most likely of the five to have produced LPGRE because of its association with a 1900 km s⁻¹ CME and 271 pfu SEP event. Unfortunately, the first good LAT solar exposure occurred about 90 minutes after the impulsive phase. Thus, it is possible that any LPGRE lasted less than 90 minutes. There is an alternative explanation, assuming that the particles responsible for the LPGRE are produced along with SEPs. Because of different shock and magnetic field geometries (Rouillard et al. 2012), it is possible that the protons on field lines reaching the Sun may not have been accelerated to energies sufficient to produce pions, even though the protons observed in space reached energies >100 MeV. This same process might also explain why >300 MeV protons reached the Sun during the 2011 March 7 LAT event (event 1 in Table 1, A16 in Table 4) while few SEP protons were observed in space with energies >100 MeV.

Details. Event A75 is plotted in Figure 16. It is an M7.9-class flare at W59 lasting ∼73 minutes. It has an ∼1600 km s⁻¹ CME with an estimated onset ∼2 minutes after the GOES start time and 6 minutes before GBM hard X-ray data become available, as well as M and DH Type II emissions observed with the M onset within 1 minute of the CME launch. It is a strong SEP event with emission >100 MeV that appeared to steepen at higher energy because it was not observed in the GOES HEPAD data, and impulsive hard X-ray emission was observed up to 1 MeV by GBM (100–300 keV time history plotted in inset). There was no LAT solar exposure during the flare. Good LAT solar exposures were only made every other orbit: 19:08–19:30, 22:17–23:00, and 01:28–02:12. There is no evidence for LPGRE at a flux level in excess of 3 × 10⁻⁶ γ cm⁻² s⁻¹ about 90 minutes after the flare and in the ensuing hours. However, it is possible that there was time-extended >100 MeV emission during the 90 minutes between the time of the hard X-ray peak and first LAT observation at 19:08 UT. The GBM spectrum during the impulsive hard X-ray peak can be fit by bremsstrahlung from the sum of two power-law populations of electrons >200 keV: one containing about 2.6 × 10³⁵ electrons having an index of 5.3 and the second containing about 1.4 × 10³⁴ electrons having an index of 3.2. The 5.3 index of the soft component is the same as that derived by Kaufmann et al. (2013) in their paper discussing the discovery of 30 THz emission that has a time history somewhat broader than that observed in the hard X-rays. Kaufmann et al. (2013) pointed out that the softer spectrum of electrons cannot penetrate to depths where the THz emission can be produced. The fact that there may be a harder spectrum of electrons that is suggested by our fits may provide a source that could penetrate to the depths needed. However, the time history of the 30 THz emission is significantly more extended in time than the γ-ray emission observed by GBM. There is weak evidence (95% statistical confidence) for the 2.223 MeV neutron-capture line in the GBM impulsive-phase spectrum, but this could be due to the strong background line. There is also structure in the spectrum that Trottet et al. (2015) attributed to nuclear lines, but the features do not appear at the energies of the expected nuclear lines.

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Distinct nature of the LPGRE. The >100 MeV flux began sometime during or after the impulsive phase and lasted several hours. The LPGRE is clearly not the decay of the impulsive-phase emission. The estimated number of >500 MeV protons in the LPGRE is at least an order of magnitude higher than in the impulsive phase.

Details. The event is plotted in Figure 17. This was the first late-phase emission event detected by the LAT. Additional details are given in Section 3.1 and in Ackermann et al. (2014). It is an M3.7-class flare at W47 lasting 15 minutes. It has an ∼2100 km s⁻¹ CME, with onset determined from SDO/AIA 171 and 211 Å images consistent with the rise in 100–300 keV X-rays, ∼15 minutes before its intense peak and about 9 minutes before the onset of metric Type ll emission. It is a moderate SEP event with proton energies barely exceeding 100 MeV and impulsive γ-ray emission up to 1 MeV with no evidence for a 2.223 MeV neutron-capture line (the limit on line flux is used to estimate a limit on the number of >500 MeV protons during the impulsive phase of the flare). Note that the CME onset time derived from AIA is about 7 minutes earlier than the CDAW onset times. In plotting the 100–300 keV time history, we used RHESSI data from the onset of the flare until 20:08, when the satellite entered the radiation belts of the SAA, and normalized GBM 100–300 keV fluxes after ∼20:02 UT, when Fermi entered sunlight.

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There was good LAT solar exposure between 20:10 and 20:40 UT following the impulsive phase; >100 MeV emission appears to increase to a peak flux of ∼3.5 × 10⁻⁵ γ cm⁻² s⁻¹ near 03:00 UT (consistent with Ackermann et al. 2014) and was observable until about 13:00 UT on March 8. The fluxes plotted in the figure and inset used source-class data; we confirmed the fluxes measured just after the flare using solar flare transient–class data. The celestial background level ∼3 × 10⁻⁶ γ cm⁻² s⁻¹ in March was low and is about 50% higher than the quiescent solar flux from cosmic-ray interactions (Abdo et al. 2011). From our extrapolations, the LPGRE onset appears to have occurred before 20:05 UT. The best-fitting pion-decay spectra suggest that the >300 MeV proton spectra soften during the duration of the event (Table 3). The number of protons >500 MeV in the LPGRE exceeds the number in the impulsive phase, determined by the upper limit on the 2.223 MeV line flux, by at least a factor of 10. We note that the SEP proton energies only reached 100 MeV, significantly below the threshold for producing the pion-decay photons observed by LAT.

Distinct nature of the LPGRE. The >100 MeV γ rays were only weakly observed in one split exposure 2 hr after the flare; there is no evidence for flux variability. We have no information about the onset of the emission; however, it lasted significantly longer than the impulsive hard X-ray emission.

Details. The event is plotted in Figure 18. It is a C3.7-class flare at E22 lasting ∼35 minutes. It has an ∼1000 km s⁻¹ CME with a CDAW projected onset at ∼07:43 UT, consistent with measurements of SDO/AIA movies. Only DH Type II emission was detected; and solar energetic protons with energies up to 35 MeV were barely detected. The GBM did not observe the flare, and RHESSI only observed the flare up until 07:36 UT, thus missing the peak of the soft X-ray emission and time of CME onset. This is confirmed by plotting the derivative of the soft X-ray emission that is a proxy for the hard X-ray emission. The derivative shows two peaks, one from about 07:20 to 07:33 UT and another from 07:33 to 07:48 UT. The latter one peaks at about 07:43 UT, the time of the CME onset. It is likely, then, that any high-energy impulsive hard X-ray emission occurred during the second peak, where there were no available RHESSI observations. This is a weak LAT event that is only identified at just over 3σ significance in the Pass8 source-class data, not in our earlier search of Pass7 data. It was also listed as an event in Ackermann et al. (2014). Weak >100 MeV emission was only observed in the first LAT exposure from 09:40 to 10:25 UT, 2 hr after the impulsive phase. There is no evidence for time variability and thus no information on when the LPGRE began. The flare would not have been identified as having the potential for >100 MeV emission because no hard X-ray measurements were available during most of the flare. Our estimate of the number of >500 MeV protons at the Sun in Table 3 was made by assuming that the emission began just after the impulsive phase, peaked at 10 UT, and fell to zero by 12 UT. We could not estimate the number of protons in the impulsive phase.

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Distinct nature of the LPGRE. The >100 MeV γ rays were only observed during one ∼30 minute exposure 1 hr after the impulsive hard X-ray emission; there was no evidence for flux variability. The upper limit on the number of protons in the impulsive phase was a factor of five smaller than that observed in the LPGRE. Therefore, it is unlikely that the LPGRE was the tail of the impulsive emission.

Details. The event is plotted in Figure 19 (additional details in Ackermann et al. 2014). It is an M2.5-class flare at W54 lasting ∼40 minutes. It has an ∼1200 km s⁻¹ CME with onset ∼7 minutes before the 100–300 keV X-ray onset and M and DH Type II emissions observed with the M onset ∼9 minutes after the CME launch. It is a moderate solar energetic proton event with emission observed >100 MeV and impulsive hard X-ray emission up to 300–800 keV observed by both GBM (100–300 keV time history plotted in inset) and RHESSI, with no evidence for the 2.223 MeV neutron-capture line (the limit on line flux is used to estimate a limit on the number of >500 MeV protons during the impulsive phase of the flare). There was no LAT solar exposure during the impulsive phase; the first good LAT solar exposure flare was at 07:48–08:22 UT, 1 hr after the flare. There is a significant flux of >100 MeV emission during this interval, with no evidence for temporal variability; the peak flux in Table 3 is consistent with that reported by Ackermann et al. (2014) in their Table 2. During this time interval, prominence material was observed to fall back to the solar surface. There is no evidence for >100 MeV during the next LAT exposure 3 hr later. The best-fitting pion-decay spectra suggest that the >300 MeV proton followed a power law with an index of ∼4.5 (Table 3); this is consistent with that measured by Ackermann et al. (2014). As LAT had no exposure to the impulsive phase, we used upper limits on the 2.223 neutron-capture line observed in the front RHESSI detectors to estimate the number of impulsive protons. The number of protons >500 MeV in the LPGRE exceeded the number in the impulsive phase by at least a factor of five, but could be up to ∼50% of the number of >500 MeV protons observed in space (Table 3). The LPGRE lasted no more than about 3 hr; in contrast, the >100 MeV proton event at Earth that lasted close to 2 days.

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Distinct nature of the LPGRE. The LAT detected >100 MeV emission 1 hr after the impulsive phase, and there was no clear temporal variation; no emission was observed in the next exposure 3 hr later. The estimated upper limit on the number of protons in the impulsive phase was a factor of 10 smaller than that observed in the late phase. Therefore, it is unlikely that the γ-ray emission was the tail of the impulsive phase.

Details. The event is plotted in Figure 20. It is an M9.3-class flare at W46 lasting ∼25 minutes. It has an ∼1300 km s⁻¹ CME with estimated onset ∼4 minutes before the 100–300 keV X-ray onset observed by GBM (plotted in the inset) and M and DH Type II emissions observed with the M onset ∼8 minutes after the CME launch. It is a moderate solar energetic proton event with emission observed >100 MeV and impulsive hard X-ray emission observed up to ∼400 keV by GBM with no evidence for the 2.223 MeV neutron-capture line. The LAT solar exposure between 03:30 and 03:50 UT during the impulsive phase was poor, and Ackermann et al. (2014) only classified this as a LPGRE event with no impulsive component observable using their LLE data. The recently released Pass8 solar impulsive-class data had only marginal exposure to the rising phase of the hard X-ray emission between 03:43 and 03:49 UT, and only upper limits on the >100 MeV could be estimated during that interval. The first good LAT solar exposure was between 04:56 and 05:38 UT, about 90 minutes after the flare. The measured >100 MeV flux during this interval (see Table 3, consistent with Ackermann et al. 2014) had no evidence for temporal variability. There was no evidence for >100 MeV during the next good LAT exposure 3 hr later. We estimated a limit on the number of >500 MeV protons during the impulsive phase in two ways. First, we obtained an upper limit using the limit on >100 MeV emission observed between 03:43 and 03:49 UT scaled to the entirety of the observed hard X-ray time history. This gave a limit of 0.4 × 10²⁸ protons >500 MeV. From a limit on the neutron-capture line obtained by GBM, we obtained a proton limit about four times lower with 95% confidence. We find that the number of protons >500 MeV in the LPGRE exceeds the number in the impulsive phase by at least a factor of 10, but it is only ∼20% of the number of >500 MeV protons observed in space (Table 3). The event at the Sun lasted no more than about 4 hr; in contrast, the >100 MeV proton event at Earth lasted close to 20 hr.

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Distinct nature of the LPGRE. The event had an impulsive phase dominated by two hard X-ray peaks, with nuclear-line emission detected by GBM and RHESSI and >100 MeV γ-ray emission observed by LAT in both LLE and solar flare transient–class data. As >100 MeV emission was detected within 1 minute of the hard X-ray peaks, the event was classified by Ackermann et al. (2014) as impulsive. On closer inspection of the time history, we believe that there are two distinct phases of emission. This is seen in the inset of Figure 21, where the >100 MeV flux measured in the solar flare transient–class data appears to rise just after the hard X-ray peak and reaches a maximum about 1 minute later. The ∼1 minute high-energy delay from the first hard X-ray peaks contrasts with the shorter ∼10 s delays observed in the nuclear and >100 MeV emission observed in the impulsive 2010 June 12 flare (Event 3 in Table 4; Ackermann et al. 2012a, 2012b). The distinct components of the 2011 August 9 flare are revealed in Figure 22, where the impulsive component is reflected in the two peaks at about 08:02:10 and 08:03:50 UT visible in a few hundred keV hard X-rays and in the nuclear emission. The two peaks appear to be of comparable strength, with higher-energy electrons producing the bremsstrahlung (panel (b)) and tens of MeV protons producing the γ-ray lines (panel (c)). There is an additional temporal component in the γ-ray-line time profile that rose just after the first peak and lasted for about 2 minutes. This rise and duration is similar to that observed in the >100 MeV flux plotted in panel (d)), obtained from spectral fits to the LLE data. It is interesting to note that the CME and Type II radio emission onsets occurred within about 1 minute of each other and near the time of the first hard X-ray peak, suggesting the formation of a shock deep in the corona that could be responsible for this distinct component of tens to hundreds of MeV protons. Even though this event lasts only a few minutes, we include it in our list of LPGRE events because of its distinct temporal history. There is no evidence for LPGRE in the two good LAT exposures at 09:20–09:45 and 10:58–11:20 UT following the flare.

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Details. The event is plotted in Figure 21. It is an X6.9-class flare at W70 lasting ∼20 minutes. It has an ∼1600 km s⁻¹ CME with onset coincident with the rise of the 100–300 keV X-ray emission and M and DH Type II emissions observed with the M onset within 1 minute of the CME launch. It is a small solar energetic proton event with emission observed >100 MeV. The >100 MeV γ-ray emission was observed in LAT solar flare transient–class data plotted at 1 minute resolution in the inset of the figure beginning just after the prominent hard X-ray peak. The GBM spectrum showed clear evidence for the 2.223 MeV neutron-capture line and nuclear de-excitation lines between 08:00 and 08:08 UT. The event was classified by Ackermann et al. (2014) as impulsive, but on closer inspection, there are two distinct phases of emission, as can be seen in the inset of Figure 21, where the >100 MeV flux appears to rise just after the hard X-ray peak and reaches a maximum about 1 minute later. This behavior is different than that observed in the impulsive 2010 June 12 flare (Event 3 in Table 4; Ackermann et al. 2012a, 2012b), where the hard X-ray and γ-ray time histories follow one another closely.

Comparing the flux observed in nuclear lines with that observed in pion-decay emission from 08:02:40 to 08:06:00 UT (after removing the contribution from the second impulsive peak), we estimate that the proton spectrum between 5 and 300 MeV was consistent with a power law having an index of 4.3 ± 0.3. This compares with a much steeper proton spectrum above 300 MeV, a power-law index of 5.8 ± 0.9 that we measured from LLE spectral fits. Thus, the proton spectrum of the LPGRE steepened significantly above a few hundred MeV. There is no evidence for LPGRE in the two good LAT exposures between 09:20–09:45 and 10:58–11:20 UT following the flare. We have also compared the upper limit on >100 MeV emission with that observed in nuclear lines during the impulsive phase peaks and conclude that the proton spectrum between 5 and 300 MeV during the flare was steeper than a power law with an index of 4.2. It is interesting that the peak SEP flux is about a factor of 10 smaller than what we might expect for such a fast CME that was preceded by a broad CME a few hours earlier (Gopalswamy et al. 2004).

Distinct nature of the LPGRE. The >100 MeV emission was only observed in one ∼30 minute exposure during and just after the associated impulsive phase. Because of possible saturation effects, we used LLE data to obtain the 1 minute >100 MeV time history shown in the upper inset of the figure up until 22:34 UT; after this time, we used Pass7 source-class data. The >100 MeV time history plotted in the insets reveals two peaks: one delayed by about 8 s from the peak in 100–300 keV hard X-rays and a second with onset within 1 minute following the >100 MeV impulsive peak that reached a maximum at about 22:27 UT and then gradually fell until the end of the LAT solar exposure. Thus, both impulsive- and late-phase >100 MeV γ rays were observed in this event.

Details. The event is plotted in Figure 23. It is an X2.1-class flare at W18 lasting ∼12 minutes. It has an ∼575 km s⁻¹ CME in the CDAW catalog but is listed as ∼1000 km s⁻¹ for both STEREO A and B in the CACTUS catalog, with onset coincident with the rise of 100–300 keV X-rays. It has only M Type II emission, with an onset time within about 1 minute of CME onset. It is a small solar energetic proton event but has emission observed >100 MeV; both RHESSI and GBM (100–300 keV time history plotted in top inset) observed the impulsive phase of the flare up to energies in excess of 1 MeV, with evidence for nuclear-line emission between about 22:18 and 22:20 UT.

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The LAT had good solar exposure between 22:12 and 22:46 UT, covering the entire impulsive phase. There is clear evidence for >100 MeV emission in the source-class data, but the measured flux was compromised because of the high rates in the ACD. We fit the publicly available LLE data for this flare to obtain the 1 minute >100 MeV time history plotted in the upper inset up until 22:34 UT; after this time, we fit the source-class data. The LLE time history plotted in the top inset reveals a sharp peak during the latter part of the impulsive phase. Studying the LLE emission >80 MeV at higher time resolution, we find that it peaks about 8 s after the peak in the broader 100–300 keV X-ray time history (see bottom inset) and lasts only about 10s. The >100 MeV LPGRE flux plotted in the top inset of Figure 23 rose after 20:20 UT, peaking about at 22:27 UT and then falling until the end of the exposure. We have also studied the time history of this event using the recently available solar flare transient–class data. The time history of the extended-phase emission agrees well with the LLE data plotted in the figure. There is no evidence for >100 MeV emission during the next good solar exposure beginning on September 7 at 01:23 UT. We have fit LAT/LLE LPGRE photon spectra after 22:21 UT during the rise to and fall from the peak (Table 3). The fitted proton spectrum before the peak is significantly softer (power-law index 5.3) than the spectrum after the peak (power-law index 3.5). Our fits to the source-class data after 22:37 UT indicate that the proton spectrum also followed a power law with an index of about 3.5. We have obtained information on the LPGRE proton spectrum below 300 MeV by searching for the neutron-capture line in the GBM spectrum accumulated between 22:21 and 22:47 UT. Comparing the 95% confidence upper limit 2.223 MeV flux with the average flux observed >100 MeV by LAT enables us to determine that the proton spectrum from 20 to 300 MeV was harder than a power law with index ∼4.0 during the rising portion of the emission. As the measured spectral index above 300 MeV was 5.3 ± 0.4, the proton spectrum steepened above 300 MeV.

We also obtained spectral information during the impulsive phase of the flare, 22:18–22:20 UT, using both GBM and LLE data. Nuclear-line emission was distributed over this full time interval, while >100 MeV emission was mostly concentrated between 22:19:00 and 22:19:30 UT, as seen by the solid line plotted in the lower inset, with a sharp peak delayed from about 8 s from a peak in the 100–300 keV X-rays (dashed line). Our spectral fit to the >100 MeV LLE data yields a very soft accelerated proton spectrum >300 MeV with a power-law index steeper than ∼6, much softer than that observed in the LPGRE. Our fits also rule out a power-law bremsstrahlung origin for the impulsive emission with a confidence of 95%. We have fit GBM spectra over the same 22:18–22:20 UT time interval and detected nuclear de-excitation lines and the neutron-capture line. By comparing the measured pion-decay, neutron-capture line, and de-excitation line fluxes, we estimate proton power-law spectral indices from ∼4.0 between 5 and 40 MeV to ∼4.2 between 40 and 300 MeV, assuming a downward isotropic distribution for the protons. Thus, the impulsive-phase proton spectrum steepened rapidly above 300 MeV.

We have estimated the numbers of protons >500 MeV during the impulsive and time-extended phases of the event. We see from Table 3 that the number of impulsive-phase protons >500 MeV was less than 10% of the number in the time-extended phase. This fact, along with the vastly different spectra of protons >300 MeV, indicates that the impulsive phase could not have been the major energy source for the LPGRE. There is only an upper limit of the number of >500 MeV protons in space.

Distinct nature of the LPGRE. The >100 MeV γ rays were observed in only one LAT exposure about 1 hr after the impulsive phase. There is no evidence for flux variability during that time interval, suggesting that the measurement may have been made at the peak of the emission. Thus, the onset of the LPGRE was within 1 hr of the impulsive phase of the associated flare, and the emission lasted at least 1.5 hr after the hard X-rays. As discussed below, the upper limit on the number of protons in the impulsive phase was within a factor of two of the number in the LPGRE. Therefore, it is not possible on energetic grounds to rule out the tail of the impulsive phase as the source of LPGRE.

Details. The event is plotted in Figure 24. It is an X1.8-class flare at W32 lasting ∼12 minutes. It has an ∼800 km s⁻¹ CME with an estimated onset coincident with the 100–300 keV hard X-ray rise and only M Type II emission observed ∼2 minutes after the CME launch. There is no evidence for solar energetic protons. It has impulsive hard X-ray emission up to at least 1 MeV observed by GBM (100–300 keV time history plotted in inset). There is no LAT solar exposure during the impulsive phase; the first good LAT solar exposures at 23:36 (1 minute duration) and 23:52–00:10 UT (4 minute resolution) were during a ToO 1 hr after the flare. The >100 MeV flux is consistent with that of Ackermann et al. (2014), with no evidence for temporal variability. There was no evidence for >100 MeV during the next LAT exposure 90 minutes later. There is weak evidence for both nuclear de-excitation and 2.223 MeV line emission observed by GBM during the impulsive phase of the flare. We obtained a limit on the number of >500 MeV protons at the Sun during the flare from the 95% confidence limit on the 2.223 MeV flux, assuming a proton spectra >40 MeV that follows an unbroken power law with an index of 4.5. The limit on the number of protons during the flare is a factor of two smaller than the number of LPGRE protons (Table 3).

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Distinct nature of the LPGRE. The LAT had good solar exposure between 09:18 and 09:45 UT, covering the entire flare. Weak γ-ray emission >100 MeV appears to have begun about 6 minutes after the 100–300 keV impulsive hard X-ray peak and lasted about 4 minutes.

Details. The event is plotted in Figure 25. It is an X1.9-class flare at E61 lasting ∼27 minutes. The CME speed is uncertain, although the CDAW catalog lists it as ∼1936 km s⁻¹ (both CACTUS and DONKI list lower speeds) with an onset ∼1 minute before the 100–300 keV X-ray narrow peak. There is questionable M Type II emission with an onset ∼1 minute after the CME launch; only an upper limit on the SEP proton flux was obtained because of the large particle event on September 22. Both RHESSI and GBM observed emission up to about 10 MeV during the impulsive phase, with evidence for nuclear de-excitation and neutron-capture lines. The LAT had good solar exposure between 09:18 and 09:45 UT, covering the entire impulsive phase. The GBM 100–300 keV time history is plotted in the top inset, along with the >100 MeV flux derived solar flare transient–class data. The >100 MeV fluxes derived from source-class data were affected by the high ACD rates during the flare. This can be seen in the difference between the open-circle (solar flare transient–class data) and filled-circle (source-class data) fluxes. There is no clear evidence for >100 MeV emission during the impulsive X-ray peak. The LPGRE began about 6 minutes later and lasted only about 5 minutes. The LAT had poor solar exposure between 10:58 and 11:18 UT and good exposure between 12:37 and 13:00 UT, and no LPGRE was observed during those time intervals. The spectrum of the LPGRE is consistent with emission from pion decay produced by protons following a power-law index of 3.4 ± 1.4. The 95% confidence upper limit on the number of >500 MeV protons during the impulsive peak is less than 25% of the number observed in the LPGRE.

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As shown in the bottom inset, LAT/LLE data reveal a striking peak in ∼10–60 MeV γ-ray emission delayed by about 8 s from the 100–300 keV hard X-ray peak in the impulsive phase. This delay is similar to that observed by LAT in the impulsive event on 2010 June 12 (event A3; Ackermann et al. 2012a, 2012b), but in this case, the emission is clearly dominated by electron bremsstrahlung; thus, the delay measures the time to accelerate electrons to energies >10 MeV and is not due to delays associated with accelerating ions to hundreds of MeV, as may have been the case for the 2010 June 12 flare. Ackermann et al. (2014) also reported this event as impulsive. The LAT LLE photon spectrum appears to follow a power law in energy visible up to just above 100 MeV with index ∼4.8; there is only marginal evidence for pion-decay emission at the 67% confidence level. If this steep bremsstrahlung spectrum extended to energies below 10 MeV, it should have been detectable by GBM; but our studies indicate that it was not detected. The GBM measured 2.223 MeV and de-excitation line fluxes indicating that the 4–40 MeV proton spectrum in the impulsive phase had an index of about 4.5. If this proton spectrum extended without steepening to energies of 300 MeV, the >100 MeV pion-decay flux would have been about a factor of two higher than the limits on emission that we set. This indicates that the impulsive proton spectrum steepened above ∼40 MeV.

Distinct nature of the LPGRE. The LAT began observing the Sun late in the flare and may have detected a weak decreasing impulsive >100 MeV flux and the onset of late-phase emission 15 minutes after the impulsive hard X-ray peak. The flux in the next orbit is at least five times higher, and the emission lasted for 8 hr.

Details. The event is plotted in Figure 26. It is an M8.7-class flare at W21 lasting ∼55 minutes. It has an ∼2000 km s⁻¹ CME with onset about the time of the soft X-ray event, before Fermi entered sunlight at 03:53 UT, and only DH Type II emission. It is an intense solar energetic proton event with emission observed >100 MeV and impulsive hard X-ray emission up to 100–300 keV observed by GBM (time history plotted in inset), with no evidence for the 2.223 MeV neutron-capture line. The LAT had good source-class data exposures to the Sun at ∼04:08–04:36 and 05:46–06:10 UT, in response to an autonomous repoint to the Sun, and at 07:18–07:48, 08:58–09:28, and 10:48–11:00 UT (truncated by the SAA). The >100 MeV emission was observed in each of these intervals. The source-class data plotted at 4 minute resolution in the inset suggest that there were >100 MeV γ rays associated with the impulsive hard X-rays and that the LPGRE began at ∼04:20 UT, ∼15 minutes after the observed hard X-ray peak. This variation is due to the solar flux and not to modulation (<20%) of the weaker celestial background by the varying solar exposure. We reach the same conclusion using the solar flare transient–class data. Ackermann et al. (2014) reported a >100 MeV flux of (0.8 ± 0.1) × 10⁻⁵ γ cm⁻² s⁻¹ that is consistent with our measurement between 04:08 and 04:34 UT. We have fit the background-subtracted γ-ray spectra between 05:46 and 09:29 UT assuming that the emission is due to pion-decay radiation. The results of these fits are given in Table 3. Our best-fitting >100 MeV γ-ray fluxes are consistent with those listed by Ackermann et al. (2014), with the possible exception of the 07:18–07:48 UT interval that had relatively poor solar exposure and large flux uncertainty. The data between 05:46 and 06:10 UT were good enough to provide an estimate of the accelerated proton power-law spectral index, 5.1. Power-law spectra with indices of ∼5 also fit the weaker fluxes in the next two intervals reasonably well and were used in our determination of the numbers of protons. Based on these spectral fits, we estimate that there were 3 × 10²⁸ > 500 MeV protons accelerated at the Sun during the 6 hr period of the LPGRE. As RHESSI was not operating at the time, and GBM missed the most intense portion of the flare, we have no information on the number of protons in the impulsive phase of the flare from neutron-capture line observations.

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Distinct nature of the LPGRE. There is evidence for a rising >100 MeV γ-ray flux about 1 hr after the impulsive phase. Much of the impulsive phase was not observed because Fermi was in the SAA. The LPGRE event appears to have lasted about 3 hr.

Details. The event is plotted in Figure 27 using Pass8 data. It is an X1.7-class flare at about W81 lasting 79 minutes. It has an ∼2500 km s⁻¹ CME with an estimated onset coincident with the 100–300 keV X-ray rise and M and DH Type II emissions observed with the M onset ∼5 minutes after the CME launch. It is a strong SEP event with proton energies not exceeding 100 MeV. Fermi was in SAA between 18:15 and 18:34 UT, and 100–300 keV hard X-rays were observed by GBM at beginning and end of the impulsive phase (see time history plotted in inset). Poor GBM exposure and large background after the SAA prevent estimates of the neutron-capture line flux during the impulsive phase, although any line emission would have been strongly attenuated because the flare was near the limb. RHESSI was not operating at that time. Using solar flare transient–class data, we found no evidence for >100 MeV emission during the first part of the flare from 18:10 to 18:15 UT. Because the flare was at a heliocentric angle of ∼81°, the >100 MeV flux at that location would have been attenuated by about 40% relative to disk center.

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The LPGRE was observed during the next two exposures, 19:36–19:56 and 21:06–21:37 UT. Within the large uncertainties, the γ-ray fluxes, determined using Pass8 data and listed in Table 3, are consistent with those reported by Ackermann et al. (2014). The increasing fluxes with time (98% confidence), plotted in the inset of Figure 27, suggest that the onset of the LPGRE occurred about 1 hr after the impulsive phase. The derived LPGRE proton spectrum during the first exposure followed a power law with index 4.7 ± 0.7, while the spectrum taken 90 minutes later appears to be a much harder power-law index, 3.1 ± 0.6. We have estimated the number of >500 protons producing the LPGRE, assuming that they interact at the location of the flare (Table 3). The number of >500 MeV protons in space was about 50X larger than those producing the LPGRE event (Table 3). Due to the limited exposure of GBM and LAT, we have no information on the number of >500 MeV protons at the Sun during the flare.

Distinct nature of the LPGRE. The latter part of the impulsive phase of this event was well observed by LAT. Spectral fits to background-subtracted solar flare transient–class data were used to obtain the 1 minute resolution time history plotted in the right inset of Figure 28. There is no evidence for impulsive >100 MeV emission associated with the hard X-ray peak that followed the main phase of the flare. The late-phase γ-ray emission appears to have begun within about 5 minutes of the hard X-ray peak and was observed for about 5 hr.

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Details. The event is plotted in Figure 28. It is an X1.1-class flare at E54 lasting ∼210 minutes. It has an ∼1500 km s⁻¹ CME with onset 1 hr after the GOES start time and ∼17 minutes before GBM hard X-ray data become available (note that this was the last of a series of three CMEs occurring over a 3 hr period; Colaninno & Vourlidas 2015). It has only DH Type II emission and only an upper limit on solar energetic proton flux was possible due to the preceding March 4 SEP event. Impulsive hard X-ray emission is observed up to 100–300 keV by GBM (see time history in right inset) after 03:55 UT, when Fermi moved into daylight; this initiated an autonomous repoint to the Sun that lasted until 06:15 UT. There is no evidence for the 2.223 MeV neutron-capture line in GBM spectra. The LAT solar exposures in Pass7 source-class data are 02:35–03:04, 04:06–04:38, 05:46–06:12, 07:18–07:56, and 08:56–09:26 UT. There is clear evidence in Figure 28 for LPGRE in the two orbits following the flare, beginning at 05:46 UT. The >100 MeV fluxes that we derived for these two orbits are consistent with those reported by Ackermann et al. (2014). Our fits also suggest that the proton spectrum may have hardened with time, although the uncertainties are large.

The right inset shows the time history of >100 MeV emission around the time of the late hard X-ray peak near 04:30 UT that we derive using spectral fits to the solar flare transient–class data. There is no evidence for >100 MeV γ rays during the hard X-ray peak between 04:28 and 04:35 UT with a upper limit of 1.5 × 10⁻⁵ γ cm⁻² s⁻¹. There is evidence for an increase (85% confidence) in flux after that time, with a peak of ∼5 × 10⁻⁶ γ cm⁻² s⁻¹, that is likely the onset of the LPGRE. As the solar exposure was increasing during this time period, the increase was not due to modulation of the celestial background. Because GBM missed the most intense portion of hard X-ray emission between 03:30 and 04:00 UT, we have no information on the number of >500 MeV protons at the Sun during the impulsive phase. We have no estimate of the number in space because of a preceding SEP event.

Distinct nature of the LPGRE. There are two intense late-phase emission events associated with two flares within about 1 hr of each other. The LLE data (Ajello et al. 2014) reveal >100 emission about 20 minutes after the first flare, a GOES-class X5.4 that lasted for at least 1 hr. Our study of Pass8 solar flare transient–class data, plotted in the upper right inset, reveals that this is a short LPGRE event similar to the one observed on 2011 September 6. The longer LPGRE event shown in the lower left inset began about 02 UT, 45 minutes after an M7 flare, and lasted about 16 hr.

Details. The event is plotted in Figure 29. It consists of X5.4- and M7²⁷ -class flares at E27 lasting ∼38 and 18 minutes, respectively. It has ∼2700 and 1800 km s⁻¹ CMEs with onsets several minutes before hard X-ray peaks and M and DH Type II emissions observed with M onsets delayed by ∼17 and 8 minutes after the respective CME launches. It is an intense solar energetic proton event with emission >100 MeV and has impulsive hard X-ray and γ-ray emission from both flares observed to MeV energies (Zhang et al. 2012). Detailed temporal, spectroscopic, and location studies of this event are discussed by Ajello et al. (2014). The >100 keV time history in the upper right inset was derived from the INTEGRAL/SPI ACD (Zhang et al. 2012) and covers the entire period of the two flares. The LPGRE from both episodes was observed for up to 18 hr. Because the fluxes from this event were so large, it was possible to make LAT observations every orbit, even when the peak solar exposure was about 20% of the maximum. Fermi came into sunlight at 00:30 UT, and GBM observed the decay of the X5.4 and most of the M7 flare. Due to the high hard X-ray rates, there were no source-class data during the flares, but there were LLE data from 00:35 to 01:25 UT analyzed by Ajello et al. (2014). We have analyzed data from the new solar flare transient–class data and plot >100 MeV flux histories in the upper right inset at 1 minute resolution. The plot shows that the flux peaked at 00:44 UT, suggesting that this emission was not from the impulsive phase but from a short LPGRE event similar to that observed on 2011 September 6 (event 6). Good LAT source-class exposures were obtained in several time intervals: 02:18–02:48, 04:06–04:34, 05:34–06:01, 07:02–07:46, 08:42–09:12, 10:33–10:58, 13:23–13:33, 16:35–16:49, and 19:46–20:14 UT. The fluxes for these observations were derived from Pass8 source-class data. The rising flux between 02:18 and 02:45 UT, plotted along with an extrapolation to earlier times, suggests that the onset of the 16 hr LPGRE began about 02:00 UT, about 45 minutes after the peak of the M7 flare.

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Table 3 presents the results of our spectroscopic analysis of the LAT data. As discussed above, there were two discrete LPGRE episodes: LPGRE (A) began ∼20 minutes after the hard X-ray peak associated with the X5.4 flare and lasted through the M7-class flare, and LPGRE (B) began about 45 minutes after the M7-class flare. Assuming that LPGRE (A) began at 00:28 UT, we estimate that there are 4.0 × 10²⁹ >500 MeV protons producing the emission. In contrast, there were 1.3 × 10³⁰ protons >500 MeV responsible for producing LPGRE (B). These numbers were obtained assuming that the proton angular distribution is isotropic. For a downward isotropic distribution, the number should be about two times larger. We confirm the finding of Ajello et al. (2014) that the spectrum of protons producing the pion-decay γ rays appeared to be variable from 00:39 to 01:21 UT. The spectrum initially softened from an index s_p ≃ 3.6 to ≃3.9 at about 01:00 UT and then hardened to an index s_p ≃ 3.3 about the time of the M7 flare. This hardening might have been caused by protons from the M7 flare. The γ-ray fluxes and proton spectral indices derived for LPGRE (B) are consistent with those reported by Ajello et al. (2014). The >300 MeV proton spectrum exhibited spectral softening through at least the first 8 hr of the event.

We estimated the number of protons >500 MeV during the X5.4 and M7 flares using the neutron-capture line fluences of 85 and 65 γ cm⁻², respectively, measured by the INTEGRAL high-resolution gamma-ray spectrometer (Zhang et al. 2012). We estimate that both flares accelerated less than 1% of the number of >500 MeV protons produced in LPGRE (A) and LPGRE (B) (Table 3) for a downward isotropic distribution. We can also estimate the number of >500 MeV protons accelerated during the M7 flare by estimating the excess >100 MeV γ-ray flux over the decay emission from LPGRE (A). The excess is only significant at the 1σ level. The 95% confidence limit in the number of protons for a downward isotropic flux, 0.9 × 10²⁸, is about the same as that inferred from neutron-capture line measurement. The number of >500 MeV protons in space was about 10 times the number producing the two LPGRE events.

When the LPGRE fluxes exceed ∼1.0 × 10⁻⁴ γ cm⁻² s⁻¹, it is possible to use measurements of the 2.223 MeV neutron-capture line to constrain the proton spectrum below 300 MeV during these exposures. We were able to use RHESSI rear-detector observations of the neutron-capture line because the flare occurred just after an anneal of the detectors, when the spectral resolution was about 20 keV FWHM at 2.223 MeV. We obtained background-corrected spectra on orbital time frames using background ±15 orbits when the environmental conditions were comparable to those during the observing period. We found no evidence for a significant flux in the neutron-capture line in any exposure. We then estimated limits on the index of the power-law proton spectrum between about 40 and 300 MeV using our 95% confidence limits on the 2.223 MeV line flux from RHESSI compared with the Fermi/LAT measured >100 MeV γ-ray flux. The upper limits on the power indices between 40 and 300 MeV are shown in Table 3 in the row below the indices measured above 300 MeV. All of the limits on the 40–300 MeV index from 02:20 to 11:00 UT are smaller than those measured above 300 MeV, indicating that the proton spectrum producing the LPGRE events steepened above about 300 MeV.

Distinct nature of the LPGRE. The γ-ray emission has a clear onset within 1 hr of the flare; it peaked about 4 hr later and had a relatively short decay phase. As shown in the inset, there is no evidence for impulsive >100 MeV emission, and the number of protons in the LPGRE is at least an order of magnitude higher than in the impulsive phase.

Details. The event is plotted in Figure 30. It is an M6.3-class flare at W02 lasting ∼56 minutes. It has an ∼850 km s⁻¹ CME with onset ∼8 minutes after start of the 100–300 keV emission and M and DH Type II emissions observed with the M onset ∼3 minutes after the CME launch. There is only an upper limit on solar energetic proton flux due to the continuing March 7 event. Impulsive hard X-ray emission only weakly observed up to >100 keV by GBM (we plot the GBM 50–100 keV time history in the inset), and there is no evidence for the 2.223 MeV neutron-capture line in GBM spectra. There are good LAT exposures in each orbit due to a ToO in response to the March 7 SEP event. An LAT solar exposure occurred during the impulsive phase of the flare, but there were no source-class data due to high ACD rates; no LLE data are publicly available, but Ackermann et al. (2014) indicated that no >100 MeV emission was detected. We have analyzed the solar flare transient–class data to study the >100 MeV time history during the impulsive phase. Because of the higher background in the impulsive class of data, we have normalized the fluxes to the LAT source-class background rate. This time history is plotted in the inset. There is no evidence for impulsive >100 MeV emission associated with the hard X-ray peaks. There is also no evidence for modulation of the celestial background caused by the factor of two increase in the solar exposure function during this time period. Other LAT exposures were at 05:10–05:58, 06:46–07:32, and 08:22–09:08 UT. The LPGRE commenced about 04:00 UT, after the impulsive phase and consistent with the delayed nature of the event reported by Ackermann et al. (2014), and lasted until about 10:30 UT. The LPGRE fluxes in the three exposures are consistent with those of Ackermann et al. (2014; Table 3); the spectra of the protons producing pion-decay radiation in the exposures appear to be steep, with power-law indices ≥6. We estimate that 1.5 × 10²⁸ > 500 MeV produced the LPGRE and that there were fewer than 10% of this number during the impulsive phase. Due to a large SEP event on March 7, we have no estimate of the number of protons in space.

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Distinct nature of the LPGRE. The γ-ray onset occurred within about 2 hr of the associated flare, and emission lasted about 6 hr. The time profile was similar to that observed in the LPGRE event on March 9, but the flux was weaker.

Details. The event is plotted in Figure 31. It is an M8.4-class flare at W26 lasting ∼75 minutes. It has an ∼1300 km s⁻¹ CME with onset ∼8 minutes after the GOES start time and 15 minutes before GBM hard X-ray data became available. Only DH Type II emission was detected, and there is only an upper limit on the solar energetic proton flux due to the background from earlier events. Impulsive hard X-ray emission was observed up to 100–300 keV by GBM after entering daylight (see time history in inset), and there is no evidence for the 2.223 MeV neutron-capture line in the GBM spectra. There are good LAT exposures each orbit due the continuing ToO in response to the March 7 event. An LAT exposure occurred during the impulsive phase of the flare, but there were no source-class data due to high ACD rates. No LLE data are publicly available, but Ackermann et al. (2014) indicated that no >100 MeV emission was detected during the flare. We analyzed the solar flare transient–class data to study the >100 MeV time history during the impulsive phase. Because of the higher background in the solar flare transient–class data, we have normalized the fluxes to the LAT source-class background rate. We plot the time history in the inset. There is no evidence for >100 MeV emission associated with the hard X-ray peaks. There is also no evidence for modulation of the celestial background caused by an increase in the solar exposure function during this time period. Other LAT exposures were 19:24–19:52, 21:02–21:34, 22:34–23:14, and 00:10–00:55 (with data gap) UT. The LPGRE was weak, had an uncertain onset time, and lasted about 6 hr. Our spectral fits suggest weak 2σ detections in each of three orbits with >300 MeV proton spectra having power-law indices steeper than 6 (Table 3). We estimate that ∼0.5 × 10²⁸ >500 MeV protons were responsible for the LPGRE. We obtained a limit on the number of protons during the impulsive phase from a limit on the number of 2.223 MeV photons observed by RHESSI at the end of the impulsive phase. This limit is less than the number observed in the LPGRE. We also searched for impulsive >100 MeV γ-ray emission using the solar flare transient–class data in four 5 minute intervals starting at 17:51 UT (see inset of figure). There is no evidence for emission, and we set a limit of 0.03 × 10²⁸ >500 MeV protons. As this observation only covers about 60% of the impulsive phase, we list the upper limit as 0.1 × 10²⁸ in the table but we do not include it in Figure 11. Due to the large SEP event on March 7, we only obtained an upper limit on the number of >500 MeV protons.

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Distinct nature of the LPGRE. There is no clear evidence for temporal variability >100 MeV in the first exposure taken about 30 minutes after the last hard X-ray peak. As the flux in the next exposure was not significantly lower, it is likely that the gamma-ray emission peaked between the two exposures, suggesting that the LPGRE began less than 30 minutes after the last impulsive phase peak. The event lasted about 4 hr. As discussed below, the upper limit on the number of protons in the impulsive phase was a factor of four larger than the observed number of protons responsible for the observed emission after the flare. Therefore, it is not possible on energetic grounds to rule out the tail of the flare as the source of the >100 MeV γ rays.

Details. The event is plotted in Figure 32. It is an M5.1-class flare at W77 lasting ∼50 minutes. It has an ∼1600 km s⁻¹ CME with onset ∼2 minutes after the GOES start time and 10 minutes before RHESSI hard X-ray data became available. It has M and DH Type II emissions observed with the M onset ∼4 minutes after the CME launch and is a strong SEP event with proton emission >100 MeV and observed as the first ground-level enhancement (GLE) of Cycle 24. Impulsive hard X-rays are observed by RHESSI up to 100–300 keV after entering daylight (see the 50–100 keV time history plotted in inset), and there is no evidence for a 2.223 MeV line in the RHESSI spectrum during the flare.

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There were good LAT solar exposures every orbit, including one just before the flare at 00:34–01:10 and at 02:10–02:48, 03:46–04:22, and 05:22–05:56 UT. There was significant LPGRE in the first two exposures after the flare. The measured flux (Table 3) in the first exposure is consistent with that reported by Ackermann et al. ( 2014). It is not clear why they classified this event as being both impulsive and sustained, as there are no >100 MeV observations during the flare. The γ-ray flux just after the flare is plotted at 4 minute resolution in the inset of the figure and shows no clear evidence for variation in time. Therefore, there is no clear evidence for onset of LPGRE, but assuming that the >100 MeV came from a distinct late phase, the onset had to be <30 minutes after the hard X-ray peak. It is also possible that the falling flux observed in the two orbits after the flare could be due to the decay of the impulsive phase. The proton spectrum producing the π-decay emission was one of the hardest observed in any LPGRE. The number of >500 MeV protons producing the LPGRE is less than the upper limit on the number during the impulsive phase derived from the limit on the solar 2.223 MeV line. What is surprising is that the >100 MeV flux is so weak that the inferred number of protons in the LPGRE is about 1000 times less than that observed in SEPs in space. These comparisons of proton numbers suggest that a significant fraction of the LPGRE may have been radiated behind the west limb of the Sun.

Distinct nature of the LPGRE. Solar flare transient–class data, plotted in the inset, reveal a 1 minute >100 MeV peak flux coincident with the impulsive hard X-ray peak near 17:53:30 UT and emission following the peak until the end of the exposure at 18:02 UT. The >100 MeV spectrum during the 1 minute impulsive phase is steep and can be fit by pion decay produced by protons following a power-law spectrum with index 6.5 ± 1.0 (see Table 3). In contrast, the protons producing what appears to be the 8 minute late-phase emission following the X-ray peak have an average power-law index of 4.3 ± 0.7. There is evidence that the proton spectrum softened during this 8 minute period because the power-law index was 3.6 ± 0.9 between 17:54 and 17:55 UT, just after the flare peak. The significant spectral difference between the protons producing the flare and those producing the time-extended emission suggests an additional acceleration process.

Details. The event is plotted in Figure 33. It is an M3.3-class flare at E38 lasting ∼9 minutes. It has an ∼605 km s⁻¹ CME with an estimated onset coincident with the 100–300 keV X-ray rise, and only M Type II emission is observed, with onset ∼6 minutes after the CME launch. It is a weak SEP event, and impulsive hard X-rays are observed up to 300–800 keV by RHESSI and GBM (100–300 keV time history plotted in the inset). This event would not have been included in our 4 yr study because of the low CDAW CME speed, but this may have been due to its viewing angle, as CACTUS reported a maximum speed of 892 km s⁻¹ observed from STEREO B. Gamma-ray emission was detected in our automated search of source-class data during a single solar exposure (17:38–18:03 UT) and listed by Ackermann et al. (2014) as both an impulsive and a sustained event; our 1 minute resolution plot of solar flare transient–class >100 MeV fluxes in the inset of the figure clearly shows both characteristics. We note that the time profile derived from source-class data is similar, although the fluxes are lower due to ACD live-time effects from the high rate of impulsive hard X-rays. The solar exposure was relatively constant during the observation, varying by at most 25%; thus, background modulation is not significant. There is no evidence for >100 MeV γ-ray emission during the next LAT exposure between 20:50 and 21:26 UT.

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There is weak evidence for enhanced >100 MeV emission between 17:51 and 17:53 UT in both source- and solar flare transient–class data, suggesting that the LPGRE may have began as early as 2 minutes before the impulsive hard X-ray peak. We fit the flare (17:53–17:54 UT) and post-flare (17:54–18:02 UT) solar flare transient–class data using pion-decay templates. The proton spectrum during the flare is significantly softer than that during the LPGRE, with a power-law index of 6.5 versus 4.3, respectively. The average flux from this study from 17:50 to 18:02 UT is 30% higher than that reported by Ackermann et al. (2014). We estimated the number of protons in the LPGRE by assuming that the emission lasted until 19:00 UT. If this is the case, then the LPGRE was produced by about four times the number of >500 MeV protons as those in the impulsive phase. We have no information on the number of protons in space. There is no evidence for the neutron-capture line or nuclear de-excitation lines in the GBM spectrum during the 1 minute impulsive phase of the flare. Comparing these limits with the observed >100 MeV flux, we estimate that the spectrum of flare-accelerated protons between about 10 and 300 MeV is consistent with a power law with an index of 4 or harder. This indicates that the flare proton spectrum may have steepened above a few hundred MeV.

In Figure 34, we compare the GBM 100–300 keV and >80 MeV LLE rates during the flare. There are two peaks visible >80 MeV. The first peak is coincident with the hard X-ray peak. The γ-ray emission is not delayed by about 10 s from the hard X-ray emission, as has been found in other studies of impulsive flares on 2010 June 12 (Ackermann et al. 2012a, 2012b), 2011 September 6 (Appendix C.6), and 2011 September 24 (Appendix C.8). The second γ-ray peak is delayed by about 20 s but with no accompanying hard X-ray emission.

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Distinct nature of the LPGRE. Neither RHESSI nor GBM observed the Sun during the impulsive phase, although burst data are available from the Konus instrument on Wind (Aptekar et al. 1995), which revealed the presence of >500 keV emission. There is only one LAT exposure in which >100 MeV emission was observed; this began about 15 minutes after the impulsive phase, and our 4 minute resolution plot in the inset indicates that the flux was falling during this time period. Thus, we cannot tell whether the emission came from a separate delayed phase beginning in the 15 minutes after the hard X-ray peak or whether it was the tail of the impulsive-phase emission. As there were no γ-ray observations during the flare, we have no comparison of the relative numbers of protons in the impulsive- and late-phase emission.

Details. The event is plotted in Figure 35. It is an X1.1-class flare at W52 lasting ∼13 minutes. It has an ∼1800 km s⁻¹ CME with onset coincident with the rise of the GOES 0.5–4 Å power plotted in the inset. There were no hard X-ray observations during the peak of the flare, as both RHESSI and Fermi were in nighttime (in lieu of a 100–300 keV X-ray time history, we plot the GOES 0.5–4 Å time history). Hard X-ray emission >500 keV was observed by Konus during the rise of the impulsive emission, and M and DH Type II emissions were observed with the M onset ∼5 minutes after the CME launch. It is a moderate SEP event with emission >100 MeV. It was listed by Ackermann et al. (2014) as both an impulsive and LPGRE event, but there were no >100 MeV observations during the impulsive phase. There are good LAT solar exposures each orbit due to the Crab Nebula ToO. The >100 MeV γ rays were observed during the 23:27–23:54 UT solar exposure with a flux (Table 3) that is consistent with that listed by Ackermann et al. (2014). The inset of the Figure shows the >100 MeV emission accumulated in 4 minute intervals over this time period; the flux appears to be falling. This suggests that the emission may be the decay phase of the impulsive flare, but it could also be a separate component with an onset time in the 15 minutes after the impulsive peak. The best-fitting pion-decay spectrum over the full 27 minute exposure is consistent with a proton spectrum with index 5.1, but the spectrum appears to have softened in time, with an index of 4.7 ± 0.8 from 23:27 to 23:40 UT, and an index steeper than 6.0 from 23:40 to 23:54 UT. There were ∼1 × 10²⁸ protons >500 MeV producing the LPGRE assuming an onset just after the impulsive phase; we only have an upper limit on the number of protons in the SEP event (Table 3).

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Distinct nature of the LPGRE. The LAT observed γ-ray emission during a single 30 minute exposure about 50 minutes after the 5 minute impulsive phase on 2012 October 23. There is no evidence for variability in the flux during the exposure. We only know that the emission began before this time. The flare itself was observed by both RHESSI and GBM, and the right inset of Figure 36 a shows a high time resolution plot of the impulsive phase in two GBM energy channels, 100–300 keV (dashed) and >9 MeV (solid), revealing two peaks separated by ∼15 s. The spectrum of the first peak can be fit by bremsstrahlung from the sum of two power-law electron spectra, one having a steep index 5.1 and the second a hard index of 3; only bremsstrahlung from a steep electron spectrum could fit the second peak. Although the Sun had just left the LAT aperture, γ rays from the first peak scattered in the spacecraft and were detected in LLE data up to ∼50 MeV. The spectrum was relatively steep. This suggests that the impulsive phase was dominated by electron bremsstrahlung and that it was not the source of the delayed emission. Thus, it is not likely that the there were a sufficient number of impulsive-phase protons to account for the emission. This event differed from all of the previous events in that it was not accompanied by a CME. As discussed below, the upper limit on the number of protons in the impulsive phase was smaller than the number in the LPGRE. Therefore, it is not likely that the tail of the flare was the source of the >100 MeV γ rays.

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Details. The event is plotted in Figure 36. It is an X1.8-class flare at E57 lasting 8 minutes. No CME or SEP event is detected, but M Type II radio emission is observed. Impulsive hard X-ray and γ-ray emission is observed to >9 MeV (see the 100–300 keV time history in the left inset). There is evidence for the eruption of a magnetic loop in AIA 94 and 131 Å images at 03:15 UT (time denoted by the downward arrow in the left inset) along with material moving away from the flare region suggesting that this might have been a failed CME (Ji et al. 2003). The LPGRE event was only revealed in the Pass8 source-class data; it only appeared at 2σ significance in the Pass7 source-class data. The LAT had good solar exposures each orbit: 02:34–03:12 (just before the impulsive peak), 04:10–04:40, and 05:45–06:22 UT. The LPGRE was only observed between 04:10 and 04:40 UT, and there is no clear evidence for variability during 4 minute integrations. The onset delay of the >100 MeV emission was estimated from the time of the erupting magnetic loop. The right inset shows a high time resolution plot of the impulsive phase in two GBM energy channels, 100–300 keV (dashed) and >9 MeV (solid), that reveals two peaks separated by ∼15 s. The first peak can be fit by the sum of an electron spectrum made up of two power-law components, one having a steep spectral index, ∼5, and the second a harder spectral index, ∼3; only the steep spectral component of electrons was observed in the second peak, and there is no evidence for emission >9 MeV. Although the Sun had just left the aperture of LAT, scattered radiation from the hard first flare peak was observed in LLE data up to about 50 MeV. Thus, the emission in the impulsive phase was dominated by electron bremsstrahlung. We estimated the number of >500 MeV protons in the LPGRE assuming that it began just after the impulsive phase and peaked in intensity between 04:10 and 04:40 UT. We estimated the number of protons in the impulsive phase by using the upper limit on the 2.223 MeV capture line. The results of this study are presented in Table 3 and indicate that the number of >500 MeV protons in the flare was only about 20% of the number producing the LPGRE, but the uncertainties are large.

Distinct nature of the LPGRE. The LAT had good exposure throughout the impulsive phase, which was not accompanied by a CME. The >100 MeV emission was observed only during this exposure, and the fluxes are plotted at 4 minute resolution in the inset along with GBM 100–300 keV rates. Plots at higher resolution indicate that the late-phase emission began within 1 minute of the narrow impulsive peak observed in hard X-rays. It lasted for at least 16 minutes, suggesting that it was produced by a distinctly different acceleration process than the flare. The flare spectrum can be fit with bremsstrahlung from a power-law electron spectrum with a break near 1 MeV. The upper limit on the number of protons in the flare was more than a factor of 10 less than the number in the LPGRE based on pion-decay fits to the LAT spectrum. Therefore, it is not likely that protons accelerated in the flare were the source of the >100 MeV γ rays.

Details. The event is plotted in Figure 37. It is an M1.6-class flare at W73 lasting ∼35 minutes. There is no CME, Type II emission, or SEP event observed. A 1 minute long impulsive hard X-ray peak reaching energies >300 keV is observed by GBM, and 100–300 keV rates are plotted in the inset. There is evidence for the eruption (time denoted by downward arrow in the inset) of a magnetic loop in AIA 171 Å at 15:55:50 UT, along with material moving away from the flare region, suggesting that this was a failed CME (Ji et al. 2003). The Sun was in LAT’s field of view during the impulsive phase of the flare. The solar exposure varied by less than 25% from 15:55 to 16:30 UT. Source-class data could be used for the study because the rates in the ACD from hard X-rays were not too high. The LPGRE flux between 04:10 and 04:40 UT measured using the solar flare transient–class data is consistent with the flux derived using the source-class data. We plot the >100 MeV γ rays at 4 minute resolution in the inset to improve the statistical significance of each point. Plots at 1 and 2 minute resolution indicate that the LPGRE began within 1 minute of the X-ray peak and that there was no peak in >100 MeV γ rays coincident with the X-rays. The LPGRE lasted about 16 minutes with marginal evidence for more rapid time variations when plotted at 1 and 2 minute resolution. The >100 MeV emission appears to have been produced by an acceleration process distinctly different from the flare. Our fits to the spectra indicate that the protons producing the LPGRE followed a power law with index ∼3 that was constant over the observation period. In contrast, the spectrum of electrons producing the flare bremsstrahlung, observed up to 800 keV, followed a power law with index ∼3.7. There is no evidence for either nuclear de-excitation or 2.223 MeV neutron-capture γ rays during the flare in the GBM data. The number of protons >500 MeV in the LPGRE was the smallest observed by LAT but still exceeded the upper limit on the number of protons in the impulsive phase by at least a factor of 10. The onset delay of the >100 MeV emission for this event is estimated from the time of the erupting magnetic loop.

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Distinct nature of the LPGRE. The LAT had a good exposure to most of the impulsive phase. There is no evidence for >100 MeV γ-ray emission during the 4 minute impulsive X-ray peak. The onset of the LPGRE was clearly observed at 07:10 UT, about 1 minute after this peak. It reached a maximum about 3 minutes later and lasted only about 20 minutes. The estimated number of >500 MeV protons in the LPGRE is at least 25 times more than in the impulsive phase.

Details. The event is plotted in Figure 38. It is an M6.5-class flare at W13 lasting ∼34 minutes. It has an ∼850 km s⁻¹ CME with onset ∼15 minutes before the main peak in 100–300 keV flux observed by GBM (plotted in the inset) and M and DH Type II emissions observed with the M onset ∼9 minutes after the CME launch. It is a strong SEP event with emission >60 MeV. The Sun was in LAT’s field of view during most of the flare, but source-class data are only available between 07:21 and 07:40 UT due to high rates in the ACD. However, solar flare transient–class data are available beginning at 07:00 UT. The >100 MeV fluxes derived from fits to background-subtracted spectra at 1 minute resolution show no detectable γ-ray emission during the prominent X-ray peak. The LPGRE began about 1 minute later, peaked 3 minutes after onset, and lasted ∼20 minutes. From fits to spectra in three time intervals during the event, we estimate that ∼0.7 × 10²⁸ >500 MeV protons produced the LPGRE. The proton spectrum >300 MeV had an average power-law index of ∼5.5 and may have hardened during the event (see Table 3). Comparing the 0.05 γ cm⁻² s⁻¹ upper limit on the flux in the 2.223 MeV line from 07:10 to 07:30 UT with the observed flux >100 MeV, we estimate that the 40–300 MeV LPGRE protons followed a power law with an index harder than 4.5. This suggests that the LPGRE proton spectrum steepened above 300 MeV. An upper limit on the flux of 2.223 MeV γ rays during the impulsive phase of the flare provided a limit on the number of >500 MeV protons that is a factor of 10 below the number in the LPGRE. An even more constraining limit comes from the upper limit on the >100 MeV flux during the hard X-ray peak listed in Table 3. The number of >500 MeV protons in the SEP event was about 50 times larger than the number at the Sun.

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Distinct nature of the LPGRE. The LAT had no exposure to the impulsive phase, and it only observed >100 MeV emission during its first solar exposure 2 hr later. We found no evidence for time variation in the flux during this exposure, suggesting that the observation may have been made near the peak of the emission. We note that if the γ rays came from the footpoints of the flare at 89E, the flux would have been attenuated by about a factor of 6. Due to the flare’s location near the solar limb, we could not use the 2.223 MeV line to estimate the number of protons in the impulsive phase that could be compared with the number producing the LPGRE.

Details. The event is plotted in Figure 39. It is an X1.7-class flare at E89 lasting ∼39 minutes. It has an ∼1300 km s⁻¹ CME with onset ∼coincident with the 50–100 keV X-ray rise and 10 minutes before the 100–300 keV X-ray rise observed by RHESSI and GBM. The M and DH Type II emissions were observed with the M onset ∼12 minutes after the CME launch. It is a small SEP event with emission >60 MeV and 100–300 keV hard X-ray emission observed by RHESSI (left inset of the figure). A good LAT exposure ended about the start time of the X-class flare; the next exposure was 04:30–05:15 UT, 2 hr after the flare, and weak >100 MeV flux was observed with a flux of ∼1 × 10⁻⁵ cm⁻² s⁻¹ produced by a proton spectrum with power-law index ∼6 (Table 3). There was no observable flux variability during the exposure. If the emission came from the active region, it would have been attenuated by about a factor of 6. Due to the extreme attenuation of the neutron-capture line at E89, we cannot obtain a limit on the number of protons at the Sun during the impulsive phase of the flare.

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Distinct nature of the LPGRE. The LAT had no exposure to the impulsive phase, but it did observe >100 MeV emission in its first solar exposure after the flare. The clearly increasing flux in this exposure measured at 4 minute resolution and plotted in the right inset indicates that the LPGRE began about 1 hr after the impulsive phase. The emission lasted for up to 6 hr.

Details. The event is plotted in Figure 39. It is an X2.8-class flare at E80 lasting ∼28 minutes. It has an ∼1500 km s⁻¹ CME with an estimated onset ∼10 minutes before the 100–300 keV X-ray peaks and M and DH Type II emissions observed with the M onset ∼12 minutes after the CME launch. It is a strong SEP event with emission >60 MeV and hard X-ray and γ-ray emission observed >1 MeV by RHESSI (RHESSI 100–300 keV time history plotted in right inset). Good LAT solar exposures were obtained every other orbit, with >100 MeV γ-ray emission observed during the first orbit after the impulsive phase, between 17:15–17:28 and 17:41–17:59 UT (with comparable solar exposures broken by an SAA passage), and during the third orbit between 20:25 and 21:10 UT. The emission appears to be rising during the first exposure (see right inset of figure) with an apparent onset time near 17:00 UT, about 1 hr after the impulsive phase. The emission lasted at most 5 hr. Fits to the LAT spectra with pion-decay models indicate that the proton spectrum softened between 17:50 and 20:30 UT. About 4 × 10²⁹ >500 MeV protons would have been needed to produce the γ rays if the interactions took place at a heliocentric angle of 80°. RHESSI had the best exposure to the impulsive phase, while GBM began observations in the middle of the flare when its MeV spectrum was dominated by SAA-produced radioactivity. Only the RHESSI front detectors could be used to search for line radiation (below 2.4 MeV) because of radiation damage in its rear detectors; the front detector spectral resolution was ∼30 keV FWHM at 2 MeV. The impulsive bremsstrahlung spectrum had a spectral index of 2.8 and extended to above 1 MeV; there was also evidence for nuclear de-excitation line emission with 6σ significance but no evidence for the neutron-capture line with a 95% confidence upper limit on the flux of 0.035 γ cm⁻² s⁻¹. From this 2.223 MeV line limit, the number of protons was at least a factor of five below the number observed during the LPGRE, assuming they all interacted at a heliocentric angle of 80° (Table 3). This also assumed that the proton spectrum followed a power law with index 4.5 > 40 MeV. However, the proton spectrum was likely to be steeper than that because the power-law index between 4 and 40 MeV, determined by comparing the nuclear de-excitation and 2.223 MeV line, was steeper than 5.

Distinct nature of the LPGRE. The >100 MeV LPGRE clearly began about 5 minutes after the impulsive 100–300 keV X-ray peak. The LPGRE peaked in about 1 hr and had a gradual 4–5 hr decay. The estimated number of >500 MeV protons in the LPGRE exceeded the number in the impulsive phase by more than a factor of 10.

Details. The event is plotted in Figure 40. It is an X3.2-class flare at E77 lasting ∼80 minutes (strongest emission began after 01:00 UT and lasted 20 minutes). It has an ∼2600 km s⁻¹ CME with an estimated onset about 1 minute before the hard X-ray peak observed by GBM and M and DH Type II emissions observed with the M onset ∼3 minutes after the CME launch. It is a strong SEP event with emission >60 MeV and hard X-ray emission >1000 keV observed by GBM; the inset shows the 100–300 keV time history (weak impulsive emission barely visible in the plot continued until 02:00 UT). There were good LAT solar exposures each orbit in response to a ToO on May 13 and even better exposure for two orbits due to an ARR solar pointing in response to the flare. Pass7 source-class data were originally available from 01:10 to 01:47 UT, but later versions of it and Pass8 data only began after 01:30 due to concerns about ACD rates. However, these rates do not appear to be high enough to have seriously affected LAT time histories after 01:15 UT. The >100 MeV flux in the Pass7 data appears to be rising after 01:15 UT (95% confidence). The >100 MeV fluxes in the Pass8 source-class data after 01:30 UT show the same increase. Solar flare transient–class data are available after 01:11 UT. We found no evidence for >100 MeV emission between 01:11 and 01:16 UT just after the large X-ray peak. Other solar exposures were made at 02:58–03:23, 04:20–05:06, and 06:01–06:41 UT. The LPGRE peaked in the exposure from 02:58 to 03:23 UT, as evidenced by the relatively constant 4 minute resolution fluxes in that exposure. Our 4 minute resolution plots clearly show that the flux was falling in the next exposure between 04:40 and 05:06 UT. From the weak flux observed between 06:01 and 06:41 UT, we infer that the emission lasted until about 07:00 UT. Fits to the background-subtracted spectra suggest that the spectrum of protons producing the LPGRE had a steep power-law spectrum (Table 3). For an interaction site at 77°, it required about 5 × 10²⁸ >500 MeV protons to produce the LPGRE. The impulsive-phase spectrum measured by GBM can be fit by a power-law with index ∼2.5 and a weak contribution from nuclear lines. There is only an upper limit on the neutron-capture line flux of 0.01 γ cm⁻² s⁻¹; this value suggests that the number of >500 MeV protons at the Sun during the impulsive phase was at most a few percent of the number in the LPGRE.

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Distinct nature of the LPGRE. The LPGRE was relatively weak and below the 4.2σ threshold in our light-bucket analysis; it was identified in the LAT team’s more sensitive maximum-likelihood study and lasted up to 7 hr. The time history in the main plot suggests that the LPGRE began no more than 1 hr after the hard X-ray peak. The estimated number of >500 MeV protons in the LPGRE exceeded the number in the impulsive phase by more than a factor of 10.

Details. The event is plotted in Figure 41. It is an X1.2-class flare at E65 lasting ∼33 minutes. It has an ∼1350 km s⁻¹ CME with an estimated onset ∼15 minutes before the hard X-ray peak and M and DH Type II emissions observed with the M onset ∼8 minutes after the CME launch. It has an upper limit on SEP protons due to an ongoing event from a previous eruption, and hard X-ray emission reached 100–300 keV in RHESSI and GBM (time history in the inset). There were good LAT solar exposures each orbit due to ongoing ToO, and the source-class solar exposure at 01:01–01:33 UT was truncated before the flare due to a high ACD rate. There were good source-class exposures at 02:37–03:23, 04:13–04:58, 05:52–06:34, and 07:33–08:09 UT. This marginal event was noted in the LAT team’s maximum-likelihood study plotted in the RHESSI Browser and was not significant enough to be noted in the light-bucket study, even using the Pass8 source-class data. As plotted in Figure 41, the LPGRE was relatively weak and appears to last about 6 hr. The >100 MeV emission appears to have begun before 02:40 UT, and there is no evidence for temporal variability during that observing period. A fit to the background-subtracted spectra for the four observations spanning 02:37–08:09 UT with pion-decay spectral templates (Table 3) indicates significant flux levels above 3σ in three time intervals; the proton spectra are typically harder than power laws with indices of −5. The total number of protons producing the LPGRE was ∼5 × 10²⁷. The upper limit on the number of protons during the impulsive phase derived from the limit on the neutron-capture line is comparable to this. With solar flare transient–class data, we obtained an upper limit on the >100 MeV flux covering the impulsive phase from 01:36 to 01:46 UT and a limit on the number of protons >500 MeV fewer than 5% of that producing the LPGRE.

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Distinct nature of the LPGRE. This was the first LPGRE event detected from a flare behind the solar limb (Pesce-Rollins et al. 2015a; Ackermann et al. 2017). The hard X-rays from the flare at E103 peaked about 3 minutes before the onset of the LPGRE. This can be seen in Figure 42 by comparing the hard X-ray time profile (green solid line) estimated from the derivative of the soft X-ray rates observed by MESSENGER (green dashed line) and the >100 MeV flux observed by LAT (data points with uncertainties). There is no evidence for an increase in the 100–300 keV rates observed by the GBM NaI detector at the time of >100 MeV onset.

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Details. The event is plotted in Figure 42. It is an estimated (Pesce-Rollins et al. 2015a, 2015b) M4.9-class flare beyond the limb at E106 lasting ∼44 minutes. It has an ∼1200 km s⁻¹ CME with an onset within 2 minutes of the rise of hard X-rays observed by GBM and M and DH Type II emissions observed with the M onset ∼3 minutes after the CME launch. It is a strong SEP event extending to energies >60 MeV, and hard X-ray emission is only observed to 50–100 keV. There are good LAT solar exposures every other orbit: 06:58–0740 and 10:16–10:50 UT. Emission >100 MeV was only observed during the first orbit. The 50–100 keV GBM time history (also observed by RHESSI) plotted in the inset of the figure shows an abrupt increase at about 07:08 UT followed by a slower decay lasting until about 07:35 UT. The dashed green line plotted at 3.5 minute resolution follows the 1–4 keV time history observed by the SAX instrument on MESSENGER (Schlemm et al. 2007) that directly observed the flare site. This emission preceded the occulted soft X-ray emission observed by GOES (dashed black trace) by ∼2–3 minutes. The derivative of the SAX 1–4 keV emission (solid green line) reflects the hard X-ray time history of the flare and has an onset near 07:00 UT. The sharp rise in hard X-rays observed by GBM at 07:08 UT may be due to the emission region rising above the solar limb. RHESSI hard X-ray images up to 50 keV indicate that the source of the emission was above the Sun’s limb (Pesce-Rollins et al. 2015a; Ackermann et al. 2017). The background-subtracted hard X-ray spectrum observed by GBM from 38 to 200 keV between 07:09 and 07:12 UT, before the start of the LPGRE, can be fit acceptably (probability 10%) by an electron spectrum with power-law index 5.0 ± 0.1 interacting in a thick target or by an electron spectrum with index 3.3 ± 0.06 interacting in a thin target. We note that there is an artifact in the GBM NaI spectrum that prevents us from fitting <38 keV.

The time profile of the >100 MeV γ-ray flux, plotted at 1 minute resolution, reveals an increase beginning at 07:15 UT that peaks in 5 minutes and falls back to background by about 07:35 UT. The γ-ray onset occurred about 15 minutes after the inferred onset of hard X-ray emission observed by MESSENGER SAX. There is no evidence for this onset in the 100–300 keV rates. This difference in temporal structure suggests that the protons producing the >100 MeV emission were accelerated by a second process. Plotnikov et al. (2017) studied the timing in detail and concluded that the γ-ray onset occurred just after protons accelerated by the CME shock reached magnetic field lines that reached the visible disk of the Sun. The centroid of the >100 MeV emission by LAT is consistent with a location near the east limb of the Sun at N03E62 with a 1σ range in longitude from E39 to just above the eastern limb (Pesce-Rollins et al. 2015a). The background-subtracted γ-ray spectrum from 07:14 to 07:30 UT can be fit with a pion-decay template for a power-law proton spectrum with an index of ∼4.3 (Table 3) with no evidence for spectral variation during the rising and falling phases. There is evidence that a better fit would be achieved with a proton spectrum rolling over at energies above 500 MeV. Assuming that the protons impacted at E85, we estimate that the their total number was ∼3 × 10²⁸; because we do not know the true interaction location, this number is probably uncertain by a factor of 5. As the flare site was beyond the limb, we have no estimate of the number of protons during the impulsive phase. There is also no evidence for the presence of a solar 2.223 MeV neutron-capture line in GBM spectra between 07:15 and 07:30 UT. Because the γ rays in this line would be highly attenuated near the solar limb, we could not obtain information on the proton spectrum below 300 MeV.

Distinct nature of the LPGRE. The LAT had good solar exposure beginning about 15 minutes after the impulsive hard X-ray peak, and significant >100 MeV emission was detected. There is a suggestion (90% confidence) that the >100 MeV flux, plotted at 4 minute resolution, was decreasing during that time interval, and there is no evidence for emission in the next good exposure 3 hr later. We are, therefore, not able to determine whether the observed emission comes from the tail of the impulsive phase or from LPGRE beginning after the flare. The 95% confidence limit on the number of impulsive-phase protons >500 MeV is comparable to the number protons in the LPGRE. Therefore, there is no significant constraint on whether the impulsive phase was the primary source of the LPGRE.

Details. The event is plotted in Figure 43. It is an X1.7-class flare at E71 lasting ∼16 minutes. It has a relatively slow ∼590 km s⁻¹ halo CME with an onset coincident with the rise in 100–300 keV X-rays and M and DH Type II emissions observed with the M onset ∼2 minutes after the CME launch. It is a moderate SEP event extending to energies >60 MeV, and hard X-ray emission was observed up to in excess of 800 keV by RHESSI (the 100–300 keV time history plotted in the inset). There were good LAT solar exposures every other orbit, at 08:14–08.59 and 11:26–12:10 UT, with a weak <20% exposure at 10:00–10:24 UT. Emission >100 MeV was only observed during the first solar exposure, beginning ∼15 minutes after the hard X-ray peak; 4 minute accumulations of LAT source-class data suggest (95% confidence) that the >100 MeV emission was decreasing during the 08:14–08.59 UT exposure. Therefore, it is not clear whether the emission is just the tail of flare or an associated event beginning after the impulsive hard X-rays. Modulation of the celestial background flux by the solar exposure is not a significant fraction of the observed variation. The spectrum of protons producing the pion-decay γ rays was relatively steep with a power-law index between 4 and 7 (Table 3). We estimate that ∼3 × 10²⁷ >500 MeV protons were required to produce the LPGRE, assuming that it began just after the impulsive phase and lasted until 09:30 UT. RHESSI front detectors were used to study the impulsive phase (note that due to radiation damage, the spectral resolution was ∼20 keV at 511 keV); emission was observed up to about 1500 keV. There is a hint of nuclear-line emission in the spectrum with about 70% confidence and only an upper limit on the neutron-capture line flux. This 95% limit was used to set an upper limit on the number of >500 MeV protons that is comparable to the number observed in the LPGRE.

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Distinct nature of the LPGRE. The LAT had good exposure about 30 minutes after the impulsive phase, and significant >100 MeV emission was detected. There is a weak suggestion (80% confidence) that the >100 MeV flux, plotted at 4 minute resolution, was decreasing during that time interval, and there is no evidence for emission in the next good exposure 90 minutes later. We are therefore not able to determine whether the observed emission is just the tail of impulsive-phase radiation or a distinct late-phase component. We have no information on the number of flare-produced protons that could constrain the flare contribution to the LPGRE proton numbers.

Details. The event is plotted in Figure 44. It is an M4.4-class flare at E28 lasting ∼14 minutes and preceded by a weaker flare. It has an ∼800 km s⁻¹ CME with an onset ∼7 minutes before the rise of the prominent 50–100 keV X-ray peak observed by RHESSI and GBM. It has M and DH Type II emissions observed with the M onset ∼10 minutes after the CME launch and weak SEP radiation. Hard X-ray emission was observed up to just above 100 keV by RHESSI (the RHESSI 50–100 keV time history plotted in the inset). Fermi was performing a solar ToO, but the exposures were shortened by SAA passages; there were good solar exposures between 15:46 and 16:06 UT and 17:21 and 17:40 UT. Emission >100 MeV was only observed during the first exposure, beginning ∼35 minutes after the hard X-ray peak associated with the second M-class flare. The inset shows 4 minute >100 MeV accumulations with evidence that the flux was falling (80% confidence). A fit to the time-integrated γ-ray spectrum indicates that the accelerated proton spectrum was hard (Table 3). We estimated the number of >500 MeV protons at the Sun by assuming that the LPGRE flux peaked at the time of the observation and decreased after that time. The RHESSI hard X-ray spectrum follows a power law up to about 140 keV. The poor quality of the γ-ray spectrum due to radiation damage prevented measurement of the neutron-capture line flux and the ability to place a constraint on the number of protons during the impulsive phase. Therefore, we have no information on the number of flare-produced protons that could constrain the flare contribution to the LPGRE proton numbers. We note that there was an impulsive flare on the same day beginning at 01:41 UT with hard X-ray emission extending up to about 1 MeV, but it was not associated with any LPGRE.

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Distinct nature of the LPGRE. The LAT began observing intense >100 MeV solar γ-ray emission ∼20 minutes after the impulsive phase. The emission had an onset before 01:00 UT and increased to a maximum near 01:22 UT, after which time it began to fall. The fluxes during the next exposure 3 hr later continued to decrease. There were 25 times more >500 MeV protons in the LPGRE than in the impulsive phase.

Details. The event is plotted in Figure 45. It is an X4.9-class flare at E78 lasting ∼24 minutes. It has an ∼2150 km s⁻¹ halo CME with an onset coincident with the rise of 100–300 keV X-ray emission and M and DH Type II emissions observed with the M onset ∼13 minutes after the CME launch. It is a strong SEP event extending to energies >700 MeV, and hard X-ray/γ-ray line emission was observed into the MeV range by both RHESSI (the 100–300 keV time history plotted in the inset) and GBM. Fermi came into daylight at about 00:39 UT. Both GBM and RHESSI observed the entire impulsive phase of the flare. The LAT was observing the Galactic center at the time of the flare but had a good solar exposure from 01:11 to 01:30 UT. It also had a good exposure 3 hr later from 04:21 to 04:40 UT. The LAT observed emission >100 MeV during both of these exposures, but not 3 hr later. For both the 01:25 and 04:36 UT observations, the exposure rapidly increased as Fermi slewed from the Galactic center to its normal rocking position, peaked for about 2 minutes, and then decreased over the next 10–15 minutes as the Sun left the field of view. The upper inset shows the 100–300 keV time history observed by RHESSI and 1 minute resolution time history observed by LAT. The >100 MeV emission rose to a peak near 01:25 UT. The lower inset shows the falling >100 MeV intensity during the exposure beginning at 04:20 UT. In Section 4.1, we discussed fits to the background-subtracted spectrum >100 MeV at the peak of the LAT exposure from 01:13:30 to 01:17:30, where instrumental effects are minimum. We showed that the data require a pion-decay spectrum produced by a power-law proton spectrum with a break at about 1.3 GeV. We used this fit and a single power-law fit to the data between the peak exposure between 04:24 and 04:30 UT to estimate the number of >500 MeV protons at the Sun (Table 3). The spectrum softened significantly in the 3 hr between the observations.

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The GBM observed clear γ-ray lines above 2 MeV, including the neutron-capture, carbon, and oxygen lines. The nuclear spectrum dropped precipitously above 7.5 MeV, and there was no evidence for any emission above 10 MeV. We fit the background-subtracted GBM spectrum with a power law and exponentiated power law, along with 2.2 and 0.511 MeV lines, narrow and broad nuclear lines, and pion-decay templates. It concerns us that the fitted width of the solar 2.2 MeV line is ∼85 keV. From the measured 2.2 MeV flux of 0.14 γ cm⁻² s⁻¹, we estimate that there were 3 × 10²⁸ >500 MeV protons at the Sun during the impulsive phase, assuming the proton spectrum followed a power law with index 4.5 above 50 MeV. This value is less than 10% of the number in the LPGRE.

Distinct nature of the LPGRE. The >100 MeV emission began about 7 minutes after the onset of hard X-rays from the flare located nearly 40° beyond the east limb of the Sun (Pesce-Rollins et al. 2015b). The emission continued for about 6 hr.

Details. The event is plotted in Figure 46. It is an estimated X2.1 GOES soft X-ray class flare (Ackermann et al. 2017) at E126 that was observed by the SAX instrument on MESSENGER (Schlemm et al. 2007) and lasted ∼40 minutes (dashed green curve in inset of figure). It has an ∼1500 km s⁻¹ CME with an estimated onset time of 10:57 UT from SDO 193 and 211 Å images just at the rise of the inferred flare hard X-ray emission, plotted as the solid green line in the inset (estimated by taking the derivative of the SAX soft X-ray time history). The M and DH Type II emissions were observed with the late-M onset at 11:13 UT, likely the time when the shock was first visible from Earth. It is a very intense SEP event with comparable peak fluxes of 0.7–4.0 MeV electrons and >13 MeV protons consistent with what has been observed in other CME/shock gradual SEP events.

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The LAT had good solar exposures every other orbit on September 1 and exposures four times smaller in the intervening orbits. Such a 25% exposure occurred between 11:06 and 11:20 UT during the behind-the-limb flare when the Sun was at a large angle with respect to the LAT telescope axis. Source-class data could be used to study >100 MeV γ-ray emission because the intense hard X-ray emission from the flare did not reach Fermi. At these large solar viewing angles, the detector response is small and not as accurately determined. There were also two good exposures between 12:26–12:58 and 15:36–16:08 UT, during which LAT had significantly higher sensitivity to search for late high-energy emission. The >100 MeV flux just after the flare was the largest observed by LAT, with the exception of the first peak observed on 2012 March 7 just after the X5.6 flare. The hourly fluxes are plotted logarithmically in the figure in order to reveal the large range in intensity of LPGRE that lasted up to 6 hr. In the inset, we plot >100 MeV fluxes at 1 minute resolution along with 100–300 keV rates observed by GBM. Both the γ-ray and 100–300 keV X-ray emissions, as viewed from Earth, appear to rise at ∼11:04 UT, about 7 minutes after the onset of the hard X-ray emission observed from the flare as viewed by MESSENGER. The hard X-rays observed by GBM peaked by 11:08 UT, while the >100 MeV γ-ray flux peaked about 5 minutes later.

We have fit the background-subtracted >100 MeV γ-ray spectrum with a pion-decay spectrum produced by >300 MeV protons following a differential power-law spectrum and interacting in a thick target. Our fits indicate that the spectrum hardened over the duration of the event with spectral indices of 4.25 ± 0.15, 3.85 ± 0.1, and 3.45 ± 0.35 at 11:06–11:12, 11:12–11:20, and 12:26–12:58 UT, respectively.

The NaI detectors on GBM observed an increase in 10–25 keV flux (solid black trace) about 2 minutes after the hard X-ray onset detected by SAX on MESSENGER. This may be due to the appearance of the flare’s coronal hard X-ray source 2 × 10⁵ km above the solar limb. Higher-energy emission observed into the MeV range began as the 10–25 keV X-ray emission from the flare decreased in intensity. We fit the spectra between 60 and 910 keV of three GBM NaI detectors with the best views of the Sun between 11:06 to 11:15 UT with SSW OSPEX Thick2 and Thin2 target electron bremsstrahlung routines. We assumed that the electron spectra followed a broken power law. All six fits were acceptable; 1–12% of Gaussian distributed data around the model would have larger values of “chi2” than the fitted data. For the thick target model, the electron power-law index above the ∼330 keV break energy was 3.2 ± 0.1. For the thin target model, the electron power-law index above the ∼240 keV break energy was 2.15 ± 0.1. We obtained the same power-law indices when we fit GBM/BGO 0.2 to 34 MeV spectra over the same time intervals. There is no evidence for spectral variability over the full time interval of the event.

There is no evidence for the presence of a 2.23 MeV line in the background-subtracted GBM spectrum from 11:04 to 11:30 UT with a 95% confidence upper limit of 0.016 γ cm⁻² s⁻¹. Three of the rear RHESSI detectors had moderate spectral resolution at that time due to a recent anneal, allowing us to search for solar nuclear de-excitation and neutron-capture lines. Because of contamination from a preceding SAA passage, we could not perform a sensitive search for the de-excitation lines, but we were able to set a 95% confidence upper limit of 0.028 cm⁻² s⁻¹ from 11:11 to 11:31 UT on the flux in the neutron-capture line, consistent with the GBM result. Comparing the >100 MeV γ-ray fluence with the upper limit on the 2.223 MeV line fluence, we estimate with 95% confidence that the proton power-law spectral index between 40 and 300 MeV was harder than 3.4, assuming that the protons interacted at a heliocentric angle of 85°. For smaller heliocentric angles, the index would be even harder. Because the spectral index for protons >300 MeV was ∼4.5 in the same time interval, we conclude that the LPGRE proton spectrum steepened above a few hundred MeV. Our estimate of the number of >500 MeV protons was also made assuming that the interactions occurred at 85°. As there are no measurements of γ rays during the flare, we cannot compare this number with the number of protons at the flare site.

Distinct nature of the LPGRE. The LPGRE began after the most intense portion of the impulsive phase and lasted 10 hr. There were at least five times more >500 MeV protons in the LPGRE than in the impulsive phase.

Details. The event is plotted in Figure 47. It is an M2.6-class flare at E16 lasting ∼72 minutes. It has an ∼1500 km s⁻¹ halo CME with an estimated onset time of 02:10 UT based on SDO 211 Å images coincident with the peak in 100–300 keV X-rays. The M Type II emission was observed with onset ∼14 minutes after the CME launch but there are no data on DH emission. It is a slowly rising SEP event not observable above 50 MeV by GOES. The LAT had a good exposure to the Sun between 02:11 and 02:41 UT, overlapping much of the impulsive phase. The main plot shows Pass8 source-class data. As the Sun was near the Crab Nebula in mid-June, the celestial background is high. The LPGRE was detected during the next good LAT solar exposures at 05:22–05:52, 08:32–09:03, and 11:42–12:14 UT. The LAT source-class data during the impulsive phase were compromised by the hard X-ray flux in the ACD at that time. We have fit the solar flare transient–class spectra accumulated in 3 minute intervals to obtain the time history of the >100 MeV emission during the flare. This is shown in the inset of the figure and reveals an increase near the end of the impulsive hard X-ray peaks in the 50–100 keV time history from GBM (solid trace). The >100 MeV spectral data between 02:20 and 02:41 UT were not sufficient to determine a proton power-law index. We estimated the number of >500 MeV protons at the Sun in the LPGRE using the four exposures. We also obtained upper limits on the number of >500 MeV protons in the impulsive phase using two different methods. We first obtained an upper limit on the neutron-capture line flux in the RHESSI front detectors (15 keV FWHM resolution at 1275 keV at that time in the mission) after 02:08 UT. From this limit, we estimated that there were no more than half the number of protons found in the LPGRE. Integrating the LAT flux observed in the solar flare transient–class data after 02:11 UT, including what appears to be LPGRE, we obtained a more constraining upper limit of 20% of the number in the LPGRE.

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