Fermi-LAT Observations of High-energy Behind-the-limb Solar Flares

TL;DR

This paper reports Fermi-LAT observations of high-energy emissions from behind-the-limb solar flares, analyzing their spectra, localization, and acceleration mechanisms, revealing protons accelerated by CMEs impacting the solar surface.

Contribution

It provides detailed multi-wavelength analysis and modeling of behind-the-limb flares, offering new insights into particle acceleration and emission processes in occulted solar events.

Findings

High-energy gamma-ray emission associated with behind-the-limb flares.

Protons accelerated in CME environments precipitate onto the solar surface.

HXR emission from electron bremsstrahlung in coronal loop tops.

Abstract

We report on the Fermi-LAT detection of high-energy emission from the behind-the-limb (BTL) solar flares that occurred on 2013 October 11, and 2014 January 6 and September 1. The Fermi-LAT observations are associated with flares from active regions originating behind both the eastern and western limbs, as determined by STEREO. All three flares are associated with very fast coronal mass ejections (CMEs) and strong solar energetic particle events. We present updated localizations of the >100 MeV photon emission, hard X-ray (HXR)and EUV images, and broadband spectra from 10 keV to 10 GeV, as well as microwave spectra. We also provide a comparison of the BTL flares detected by Fermi-LAT with three on-disk flares and present a study of some of the significant quantities of these flares as an attempt to better understand the acceleration mechanisms at work during these occulted flares. We interpret the HXR emission to be due to electron bremsstrahlung from a coronal thin-target loop top with the accelerated electron spectra steepening at semirelativistic energies. The >100 MeV gamma-rays are best described by a pion-decay model resulting from the interaction of protons (and other ions) in a thick-target photospheric source. The protons are believed to have been accelerated (to energies >10 GeV) in the CME environment and precipitate down to the photosphere from the downstream side of the CME shock and landed on the front side of the Sun, away from the original flare site and the HXR emission.

Tables

Table 1. Table 1 Fermi -LAT Spectral Analysis of the Solar flares considered in this work

Time Interval	TSPL	$\Delta$TSa	Photon Indexb	Cutoff Energyc	Fluxd	Proton Index
(UT)				(MeV)	($\times$10-5 ph cm-2 s-1)
SOL2013-10-11
07:10:00–07:15:00	20	3	$-$2.0$\pm$0.4	-	0.9$\pm$0.1	-
07:15:00–07:18:00	487	43	$-$0.4$\pm$0.4	130$\pm$30	17$\pm$1	4.5$\pm$0.4
07:18:00–07:20:00	846	77	$-$0.1$\pm$0.4	112$\pm$21	49$\pm$2	4.3$\pm$0.2
07:20:00–07:22:00	776	76	$-$0.3$\pm$0.3	128$\pm$23	46$\pm$2	4.4$\pm$0.3
07:22:00–07:24:00	677	58	$-$0.2$\pm$0.4	153$\pm$31	29$\pm$2	3.7$\pm$0.2
07:24:00–07:26:00	345	25	$-$0.9$\pm$0.4	208$\pm$61	21$\pm$2	3.9$\pm$0.3
07:26:00–07:28:00	219	34	0.6$\pm$0.7	86$\pm$22	16$\pm$1	4.5$\pm$0.4
07:28:00–07:40:00	283	29	0.1$\pm$0.7	86$\pm$26	7$\pm$1	5.3$\pm$0.4
SOL2014-01-06
07:55 – 08:15	67	20	$-$2.4$\pm$0.2	-	0.6$\pm$0.1	-
SOL2014-09-01
11:02:00–11:04:00	42	9	$-$2.5$\pm$0.3	-	11$\pm$3	-
11:04:00–11:06:00	321	41	$-$0.2$\pm$0.5	117$\pm$27	117$\pm$10	4.7$\pm$0.4
11:06:00–11:08:00	1070	120	$-$0.5$\pm$0.3	116$\pm$15	360$\pm$17	5.2$\pm$0.2
11:08:00–11:10:00	1549	126	$-$0.9$\pm$0.2	158$\pm$20	477$\pm$19	4.9$\pm$0.2
11:10:00–11:12:00	2549	115	$-$1.2$\pm$0.2	194$\pm$28	565$\pm$21	4.8$\pm$0.2
11:12:00–11:14:00	6394	157	$-$0.8$\pm$0.1	167$\pm$10	522$\pm$20	4.4$\pm$0.1
11:14:00–11:16:00	2430	159	$-$0.6$\pm$0.2	148$\pm$17	540$\pm$22	4.5$\pm$0.2
11:16:00–11:18:00	1069	32	$-$1.9$\pm$0.2	488$\pm$90	465$\pm$23	4.2$\pm$0.2
11:18:00–11:20:00	1047	49	$-$1.0$\pm$0.3	182$\pm$37	396$\pm$27	4.5$\pm$0.2
12:29:00–12:34:00	56	12	$-$2.2$\pm$0.2	-	3$\pm$1	-
12:34:00–12:39:00	133	3	$-$2.3$\pm$0.2	-	3$\pm$1	-
12:39:00–12:44:00	130	5	$-$2.2$\pm$0.2	-	2$\pm$1	-
12:44:00–12:49:00	97	11	$-$2.3$\pm$0.2	-	2$\pm$1	-
12:49:00–12:54:00	84	3	$-$2.4$\pm$0.2	-	2$\pm$1	-

Table 2. Table 2 Comparison between behind-the-limb and on-disk flare quantities

Date	GOESa	CME speedb	AR	Duration	Peak Fluxc	E${}_{\gamma }{}^{}>$100 MeVd	Protone	Ep $>$500 MeVf
(UTC)	class	(km s-1)	position	(minutes)	(10-5 ph cm-2 s-1)	(ergs)	index	(ergs)
2013-10-11	M4.9	1200	N21E103	30	49$\pm$2	1.5$\times$1023	4.3$\pm$0.1	9.8$\times$1024
2014-01-06	X3.5	1400	S8W110	20	0.8$\pm$0.1	4.2$\times$1021	5.3$\pm$0.4g	3.5$\times$1023
2014-09-01	X2.4	2000	N14E126	113	565$\pm$14	1.4$\times$1024	4.7$\pm$0.1	7.0$\times$1025
On-disk flares
2011-03-07	M3.7	2125	N30W48	798	3$\pm$1	5.1$\times$1023	4.7$\pm$0.2	3.6$\times$1025
2011-06-07	M2.5	1255	S22W53	38	3$\pm$1	3.2$\times$1022	5.0 $\pm$0.3	2.5$\times$1024
2012-03-07Ih	X5.4	2684	N16E30	45	417$\pm$13	3.9$\times$1024	3.90$\pm$ 0.02	2.1$\times$1026
2012-03-07Ei	X5.4	2684	N16E30	1068	97$\pm$2	1.4$\times$1025	4.3$\pm$0.1	9.0$\times$1026

Table 3. Table 3 Best-Fitting Spectral Parameters of Fermi -LAT and Fermi -GBM data

Parameter	Value
SOL2013-10-11
Best fit model: PL1+PION
Power-law (1) index	3.2$\pm$0.1
Proton Index	4.1$\pm$0.1
PL1+PL2$\times$EXP+PION
Power-law (1) index	3.4$\pm$0.06
Power-law (2) index	$-$0.9$\pm$0.3
Cutoff energy (MeV)	0.8$\pm$0.1
Proton Index	4.1$\pm$0.1
SOL2014-09-01
Best fit model: PL1$\times$EXP+PION
Power-law (1) index	2.06$\pm$0.01
Cutoff energy (MeV)	90$\pm$7
Proton Index	4.4$\pm$0.1
(PL1+PL2)$\times$EXP+PION
Power-law (1) index	2.18$\pm$0.01
Power-law (2) index	1.4$\pm$0.3
Cutoff energy (MeV)	10$\pm$0.1
Proton Index	4.4$\pm$0.1

Equations

$$T_2(\frac{1}{\beta })=T_1+\frac{\zeta }{c}\times \frac{1}{\beta }$$

$$\begin{gathered} N_{\mathrm{Coul}}=(4\pi r_0^2\ln \Lambda {)}^{-1}(m/m_e){\int }_0^E{\beta }^{2}dE \\ =5\times 10^{22}(m/m_e)E^2/\gamma {\mathrm{cm}}^{-2}, \end{gathered}$$

$$\delta=\left\{\begin{array}[]{ll}\gamma-0.5&\text{non-relativistic case},\\ \gamma&\text{relativistic case}.\end{array}\right.$$

$$\delta=\left\{\begin{array}[]{ll}1.1\alpha+1.36&\text{semi-relativistic case},\\ 2.0\alpha+1&\text{relativistic case}.\end{array}\right.$$

Full text

1. Introduction

Gamma-ray emission from solar flares is generally believed to occur predominantly in compact high-density regions near the photospheric footpoints of magnetic field lines. Observations of gamma-ray emission from flares whose host active regions are located behind the visible solar disk pose interesting questions regarding the acceleration sites and mechanism, the transport and interaction points of the accelerated particles during these rare events.

Three behind-the-limb (BTL) flares with emission up to 100 MeV were observed during solar cycles 21 and 22. The first occulted solar flare whose active region (AR) was estimated to be 15*∘* behind the western limb was observed on 1989 September 29 by the Gamma-Ray Spectrometer (GRS) on-board the Solar Maximum Mission (SMM). Vestrand & Forrest (1993) reported intense gamma-ray line emission in the 1–8 MeV range and a strong 2.223 MeV neutron capture line from this flare. Given the strength of the line emission it was concluded that a spatially extended component was required in order to explain the observations. The second, detected by PHEBUS on GRANAT (Barat et al., 1994) on 1991 June 1, had intense gamma-ray line emission in the 1–8 MeV range but no neutron capture line, indicating that the emission was of coronal origin. The third occulted flare, detected by PHEBUS, BATSE and EGRET on 1991 June 30, was an electron-dominated flare with no detectable line emission but with significant emission up to almost 100 MeV. Vilmer et al. (1999) report that the spectral properties of this flare were similar to those of the flares occurring on the visible disk. Although there was some speculation and some scenarios were put forth (Cliver et al., 1993), no definite explanations were found on how and where the particles responsible for these emissions were accelerated and where the gamma-rays were produced.

Hard X-ray (HXR) emissions from the loop-top of flares originating from ARs located just beyond the limb is often observed by RHESSI (Saldanha et al., 2008). These are referred to as partially occulted flares since only the emission from the loop footpoints are occulted. An unusual such flare was reported by Krucker et al. (2007) where the flare originated 40*∘* behind the limb. This is very similar to the 2014 September 1 flare discussed in this paper.

The Fermi-Large Area Telescope (LAT) (Atwood et al., 2009) observations have doubled the number of occulted flares detected and provided the first detections of emission in the GeV range from such rare events. The Fermi-LAT observations sample flares from active regions originating from behind both the eastern and western limbs, are all associated with very fast Coronal Massive Ejections (CMEs) and strong Solar Energetic Particle (SEP) events. In this paper we present the observations of the first three BTL flares detected by Fermi-LAT together with those from complementary instruments such as STEREO, RHESSI, Konus-Wind (Aptekar et al., 1995), Fermi-GBM (GBM; Meegan et al., 2009) as well as solar observatories in the Radio Solar Telescope Network (RSTN).

In § 2 we present the multiwavelength features including the light curves and localization of the various emissions. Then in §3 we describe a more detailed analysis of the spectral data and compare the properties of the BTL flares with three on-disk flares observed by the Fermi-LAT. In §4 we discuss the associated SEP observations and in §5 we present a brief summary and interpretation of these results.

2. Observations of Fermi-LAT behind-the-limb flares

We have collected all relevant observations of the three BTL flares detected by the Fermi-LAT. In what follows we present these observations. A first analysis of the SOL2013-10-11 flare based on Pass7_REP data was presented in Pesce-Rollins et al. (2015). We have re-analyzed all three of the flares using Pass 8 data. The Pass 8 data benefit111A summary of the Fermi-LAT Pass 8 performance can be found at http://www.slac.stanford.edu/exp/glast/groups/canda/lat_Performance.htm from an improved point-spread function, effective area, and energy reach.

2.1. Light Curves

SOL2013-10-11: On 2013 October 11 (Oct13) between 07:05:51 and 07:10:51 UT STEREO-B detected a solar flare with an AR located at N21E103. GOES detected an M1.5 class flare starting at around the same time as STEREO-B. However, based on the STEREO-B 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ emission and the method described in Nitta et al. (2013) we estimate that the GOES class of this flare if the active region had not been occulted would have been M4.9 with an uncertainty within a factor of three. This method utilizes the pre-flare background subtracted, full-disk integrated EUV intensity, as shown in Figure 1b. A fast CME was observed by LASCO with a reported first appearance by the white light coronagraph C2 (imaging from 2-6 solar radii) at 07:24:10 UT and a linear speed of 1200 km s*-1*.

Fermi coverage started at 07:08:00 UT and continued for more than 30 minutes. The Fermi-LAT detected $>$100 MeV emission for $\sim$30 min with the maximum of the flux occurring between 07:20:00–07:25:00 UT222From the re-analysis of this flare with Pass 8 data we gain 5 minutes of additional emission with respect to our previous work (Pesce-Rollins et al., 2015).. The Fermi-GBM detection of HXRs began a few minutes before the Fermi-LAT and peaked earlier ($\sim$07:10 above 50 keV). RHESSI coverage was from 07:08:00–07:16:40 UT, overlapping with Fermi for 9 min. Konus-Wind, located at Lagrangian point L1, detected emission in the 20-78 keV and 78-310 keV energy bands simultaneously with RHESSI and Fermi-GBM. This flare was also observed in radio by the Radio Solar Telescope Network (RSTN) and the Nobeyama radio polarimeter (Nakajima et al., 1994) at frequencies up to 9 GHz (see Section 3.4).

The light curves (LCs) for the GOES, STEREO-B, RHESSI, Fermi-GBM, Konus-Wind and Fermi-LAT are shown in Figure 1. The microwave (MW) emission is compared with the HXR light curve from Konus-Wind in Figure 2.

SOL2014-01-06: On 2014 January 6 (Jan14) between 07:35:46 and 07:45:46 UT a solar flare erupted from an AR located at S8W110. Both STEREO spacecrafts had a full view of the AR and detected a large filament eruption from the AR at approximately 07:50:00 UT. The tip of this filament was seen from the visible solar disk by SDO/AIA. There is a hint of detection by GOES of a smaller-than-C-class flare. However, the peak rate of 2.5$\times$105 photons s*-1* detected by STEREO-B in its 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ channel indicates that the flare would have been classified as a GOES X3.5 if it had not been occulted (Nitta et al., 2013). LASCO detected a halo CME with a first C2 appearance at 08:00:05 UT with a linear speed of 1400 km s*-1*.

Upon exiting the South Atlantic Anomaly (SAA)333Both detectors on-board Fermi are turned off while the spacecraft is in the SAA. at 07:55:00 UT both instruments on-board Fermi detected emission associated with this flare. The Fermi-LAT detected $>$100 MeV emission for approximately 20 minutes (with no evidence of temporally extended emission after 08:15:00 UT.), and the Fermi-GBM detected emission in the tens of keV range. RHESSI detected emission starting at $\sim$08:18:00 UT (upon exiting spacecraft night) also in the tens of keV energy range for over 40 minutes. Konus-Wind had a full view of the flare and detected emission only in the softest energy band, 20–78 keV, starting at 07:43:00 UT. Radio data above 1.3 GHz from RSTN for this flare did not indicate a detection. The GOES, RHESSI, Konus-Wind, Fermi-GBM and Fermi-LAT light curves for this flare are shown in Figure 3.

SOL2014-09-01: On 2014 September 1 (Sep14) between 10:55:56 and 11:00:56 UT a bright solar flare occurred in an AR located at N14E126. There was no GOES signal but STEREO-B had an unblocked view of the entire flare and detected a maximum rate of 1.7$\times$107 photons s*-1* in its 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ channel, indicating an un-occulted GOES X2.4 class (Nitta et al., 2013). LASCO detected a halo CME with first C2 appearance at 11:12:05 UT with a linear speed of 1900 km s*-1*. A Type II radio burst with an estimated velocity of 2079 km s*-1* was reported by NOAA Space Weather Alerts in association with this flare. SDO/AIA reported a coronal wave from this AR starting during 10:45:35–12:21:35 UT. This wave was seen to propagate along the limb and over onto the visible disk444as reported by Nitta on http://www.lmsal.com/isolsearch.

The Fermi-LAT detected emission from this flare for $\sim$2 hours, peaking between 11:10:00–11:15:00 UT555Thanks to improvements provided by the new Fermi-LAT event selection we gained 10 extra minutes of coverage with respect to Pass7_REP.. The GBM detected emission up to a few MeV in temporal coincidence with the Fermi-LAT emission in both the BGO and NaI detectors. RHESSI was in the SAA from 10:55:00 to 11:11:00; upon exiting the SAA it detected emission up to 30 keV. Konus-Wind detected emission in all three energy bands: 20–78 keV, 78–310 keV and 310–1180 keV in temporal coincidence with Fermi-GBM. A significant radio flux at frequencies up to 16 GHz was detected by the San Vito station of the RSTN simultaneously with the HXR emission peak detected by both Fermi-GBM and Konus-Wind. Figure 4 shows the light curves from GOES, STEREO, RHESSI, Fermi-GBM, Konus-Wind and Fermi-LAT. The light curves of the microwave emission (MW) are compared with the HXR light curve from Konus-Wind in Figure 5. The MW intensity distribution with frequency has a maximum at about 1 GHz (see Section 3.4). Thus we show the time profile of only this one frequency for this flare. As evident from Figure 5 there is good agreement between these light curves.

2.2. Localization of the Emission

We present composite images of the Sun as seen by STEREO and SDO and, whenever available, the position of HXR emission based on RHESSI and $>100$ MeV gamma-ray emission centroid based on Fermi-LAT data. We used the FITS World Coordinate System software package (Thompson & Wei, 2010) to co-register the locations of the flares between STEREO and SDO images. We applied the CLEAN imaging algorithm (Hurford et al., 2002) to RHESSI data using the detectors 3–9 to reconstruct the X-ray images. The centroid for the $>$100 MeV gamma-ray emission is determined using the gtfindsrc tool, which performs a likelihood analysis of the average position in the time integrated data set.

Figure 6 displays the composite image for the Oct13 flare showing the STEREO-B 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ image of the AR located about 10*∘* behind the limb, the SDO/AIA 193 $\buildrel{}_{\circ}\over{\mathrm{A}}$ emission peaking above the limb, a contour of the RHESSI image and results from re-analysis of the flare with Pass 8 data. The new emission centroid is located in heliocentric coordinates [-880$\arcsec$, 290$\arcsec$], about 200$\arcsec$ closer to the RHESSI centroid, and with a 68% error radius of 190$\arcsec$, which is $\sim$20% smaller than the value we reported in Pesce-Rollins et al. (2015) using Pass7_REP data. In addition, in the Pass 8 data set, the total number of $>$1 GeV events measured from this flare increased from 4 to 7. The highest-energy photon detected from this flare was 3.4 GeV and the arrival was 07:19:00 UT.

For the Jan14 flare the Fermi-LAT photon statistics were not sufficient to provide an emission localization error circle smaller than 0.5*∘*. However, we can still conclude that the emission detected by the Fermi-LAT was consistent with the position of the Sun. In Figure 7 we show the STEREO-A and SDO images of this event at two different times. The top panels of Figure 7 present SDO 171 $\buildrel{}_{\circ}\over{\mathrm{A}}$ (left) and STEREO-A 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ (right) at 07:55:46 UT and show the filament eruption, while the bottom panels show the SDO 193 $\buildrel{}_{\circ}\over{\mathrm{A}}$ (left) and STEREO-A 195 $\buildrel{}_{\circ}\over{\mathrm{A}}$ (right) at 08:25:46 UT with the RHESSI 6-12 and 25-50 keV contours of this flare.

The Fermi-LAT $>$100 MeV emission centroid of Sep14 is located at heliocentric coordinates [-720*′′,610′′] with a 68% error radius of 100′′. RHESSI imaging shows a 6–12 keV source located above the visible limb slightly offset from the Fermi-LAT centroid, both shown in Figure 8. If the RHESSI source is the loop-top of the behind-the-limb flare then the minimum height needed for this source to be visible from $\sim$40∘* behind-the-limb would be $\sim$1010 cm. HXR loop-top emission from a flare located $\sim$40*∘* behind the limb has been detected before by RHESSI (Krucker et al., 2007). The Fermi-LAT measured 17 photons with energies $>$1 GeV; 15 of these (including a 3.5 GeV photon with an arrival time of 11:16:01 UT) arrived during the first 20 minutes of Fermi-LAT detection.

3. Spectral analysis

3.1. Gamma-ray spectra

We performed an unbinned likelihood analysis of the Fermi-LAT data with the gtlike program distributed with the Fermi ScienceTools666We used the version 10-01-00 available from the Fermi Science Support Center http://fermi.gsfc.nasa.gov/ssc/. We selected Pass 8 Source class events from a 10*∘* circular region centered on the Sun and within 100*∘* from the local zenith (to reduce contamination from the Earth limb).

We fit three models to the Fermi-LAT gamma-ray spectral data. The first two, a pure power law (PL) and a power-law with an exponential cut-off (PLEXP) are phenomenological functions that may describe bremsstrahlung emission from relativistic electrons. The third model uses templates based on a detailed study of the gamma rays produced from decay of pions originating from accelerated protons with an isotropic pitch angle distribution in a thick-target model (updated from Murphy et al., 1987).

We rely on the likelihood ratio test and the associated test statistic TS (Mattox et al., 1996) to estimate the significance of the detection. The TS is defined as twice the increment of the logarithm of the likelihood obtained by fitting the data with the source and background model components simultaneously. Because the null hypothesis (i.e. the model without an additional source) is the same for the PL and PLEXP models, the increment of the TS ($\Delta$TS=TSPLEXP-TSPL) is equivalent to the corresponding difference of maximum likelihoods computed between the two models. Note that the significance in $\sigma$ can be roughly approximated as $\sqrt{\rm TS}$ for 2 degrees of freedom.

In Table 1 we list the TSPL, $\Delta{\rm TS}$, $\Gamma$ the photon index for the best-fit model (PL when $\Delta{\rm TS}<25$ or PLEXP when $\Delta{\rm TS}\geq 25$) and PLEXP cut-off energy. For several intervals $\Delta{\rm TS}>$25, indicating that PLEXP provides a significantly better fit than PL. For these intervals we fit the pion-decay models to the data to determine the best proton spectral index following the same procedure described in Ajello et al. (2014). In particular, we performed a series of fits with the pion-decay template models calculated for a range of proton spectral indices. We then fit the resulting profile of the log-likelihood with a parabolic function of the proton index. The minimum gives the most likely index for the pion-decay model. Note that the TS values for PLEXP and pion-decay fits cannot be directly compared (Wilks, 1938) because they are not nested models. However the PLEXP approximates the shape of the pion-decay spectrum; thus we expect the pion-decay models to provide a similarly acceptable fit.

The main contributions to the systematic uncertainties are uncertainties in the effective area; in the energy range 100 MeV to $\sim$100 GeV these are of the order of $\pm$5%.This uncertainty applies directly to the flux values and from our previous studies on LAT-detected solar flares (Ajello et al., 2014) we find that the systematic uncertainties on the cut-off energy and photon index are also of the order of $\pm$5%777A more detailed description of the systematic uncertainties tied to the effective area of the LAT can be found here http://fermi.gsfc.nasa.gov/ssc/data/analysis/LAT_caveats.html..

3.1.1 Comparison of BTL and Disk flare Characteristics

We compare the characteristics of the $>100$ MeV emission associated with the three BTL flares with three disk flares with similar GOES classifications and temporally extended emissions and are described in Ackermann et al. (2014) and Ajello et al. (2014). In addition to spectral parameters we also compare the total $>100$ MeV emitted energies and the total energy released by protons with energy $>500$ MeV needed to produce the detected gamma-ray emission, as based on the templates of Murphy et al. (updated from 1987). We present these numbers along with the date, estimated GOES class, CME speed, AR position and the Fermi-LAT detection duration in Table 2. The proton indexes are very similar whereas the on-disk flares appear to have more energy; this is most likely because we observed the on-disk flares over longer time scales. Peak fluxes and the total energy released by protons with E$>$500 MeV for Sep14 and the impulsive phase of SOL2012-03-07 are comparable.

Figure 9 shows the proton index as a function of time for the Oct13 and Sep14 BTL flares. We fit a constant (red dashed line) and a first-degree polynomial (blue dashed line) to the data. In the case of the constant fit we list the best-fit value in the upper left corner, whereas for the straight-line fit we list the value of the slope. The temporal variation over tens of minutes is not sufficient to conclude whether a softening or hardening is present for these BTL flares. In Ajello et al. (2014) we found that for the on-disk flare SOL2012-03-07 the spectrum softened with a time scale of a few hours.

3.2. X-ray spectra

As described above we have HXR data from three instruments: RHESSI, Fermi-GBM and Konus-Wind. Konus-Wind was in waiting mode during the Jan14 and Sep14 flares; therefore these events were detected in only three broad energy channels, namely $\sim$20–78, 78–310 and 310–1180 keV with 2.944 s time resolution. RHESSI provides only a limited coverage of these flares. For the Oct13 flare there is some overlap with Fermi-GBM during the rise of the impulsive phase. As shown in Pesce-Rollins et al. (2015) the HXR spectra of RHESSI and Fermi-GBM agree well. Fermi-GBM was in the SAA and RHESSI was in spacecraft night during the impulsive phase of the Jan14 flare and detected the flare during the decay phase in only two low-energy channels. Thus, we do not have sufficient data for a spectral fit. For the Sep14 flare RHESSI gives information only on the decay phase of the flares. In the following we show results from analysis of Fermi-GBM data for the Oct13 and Sep14 flares.

3.3. Combined Spectroscopic Studies

For both Oct13 and Sep14 we performed a combined Fermi-GBM/LAT fit using the XSPEC package (Arnaud, 1996). The spectral fits were done by minimizing the PGSTAT. PGSTAT is a profile likelihood statistic that takes into account Poisson error on the total count spectrum and Gaussian error on the background. In order to obtain the background-subtracted spectra of the Fermi-GBM data for Sep14 we used both Fermi-GBM-NaI and Fermi-GBM-BGO spectra accumulated before the flare (from 10:54 UT to 10:57 UT), and after the flare (from 11:42 - 11:50 UT). For Oct13, because there was a minor on-disk flare whose onset time was 7:01 UT, we used the procedure described in Pesce-Rollins et al. (2015), which consists of using the background estimation tool developed in Fitzpatrick et al. (2012) with an additional 5% systematic error. For the LAT, we follow the procedure used in Ajello et al. (2014) and Pesce-Rollins et al. (2015) that consists of deriving the background spectrum directly from the model of the background used in the standard LAT likelihood analysis (using first gtlike and then gtbkg), and obtaining the response of the LAT using gtrspgen (all of these tools are available in the Fermi ScienceTools). The combined spectral energy distribution (SED) derived from the Fermi-GBM and Fermi-LAT data extending from 30 keV to 10 GeV for these flares is shown in Figures 10 and 11, respectively, and the parameters for the spectral fit for both solar flares are listed in Table 3.

The Oct13 flare had a very weak signal in the BGO, and the best-fit model (M0) consisted of a single power law and the pion-decay templates to describe the bremsstrahlung and $>$60 MeV emission detected by the Fermi-GBM and Fermi-LAT, respectively. For the Sep14 flare, the best-fit model (M0) consisted of a single power law with an exponential cut off at high energies to describe the bremsstrahlung emission, and the pion-decay templates to describe the $>$60 MeV emission detected by the Fermi-LAT, similar to what was done for the 12 June 2010 Fermi flare (Ackermann et al., 2012). We also tested the statistical significance of an extra power law with a high-energy cut off (model M1). To this end we performed Monte Carlo simulations (using XSPEC fakeit) by generating a spectrum described by the best fit model (M0). We then re-optimized the parameters of M0 by fitting it to the simulated data. We finally compared the improvement of PGSTAT when fitting the simulated data with the model M1. The improvement of PGSTAT for the Oct13 and Sep14 flares is $\Delta_{\texttt{PGSTAT}}\approx$408 and $\approx$109, respectively. Despite these high values of $\Delta_{\texttt{PGSTAT}}$, dedicated Monte Carlo simulations indicate that they correspond to significances of 2.5 and 2.0 $\sigma$, respectively.

We then checked whether the addition of the 2.223 MeV line (on top of model M0) significantly improved the fit. For the Oct13 flare the improvement is negligible (\Delta_{\texttt{PGSTAT}}$$\approx0), while for the Sep14 the improvement is (\Delta_{\texttt{PGSTAT}}$$\approx25), corresponding to a significance of 2.0 $\sigma$, estimated from Monte Carlo simulations. We tested whether adding nuclear de-excitation narrow lines and continua provided an improvement to the fit for both flares and found that it was not significant. The nuclear line and continua templates used here are based on a detailed study of the nuclear gamma-ray production from accelerated ion interactions with elements found in the solar atmosphere (Murphy et al., 2009).

3.4. Radio Spectra

The radio spectra obtained at the peaks of the Oct13 and Sep14 events are shown in Figure 12. The spectrum was obtained by using the RSTN 1-s resolution fluxes. The spectra were background subtracted and the fluxes were integrated within the selected time intervals for each frequency. For each spectrum we detected the frequency where the maximum flux was observed. The spectra of the Oct13 and Sep14 flares are similar to those expected from the gyro-synchrotron (GS) mechanism, with peaks that separate the optically thin and thick parts (for GS spectrum properties see, for example, Dulk, 1985). The values for the microwave photon spectral index, $\alpha$, for both flares are shown in Figure 12. Unfortunately, the RSTN data for the time period of the Jan14 flare are not sufficient to obtain radio spectra.

4. Solar Energetic Particles (SEP)

Interpretation of the origin of SEPs is more complicated than studying photons, since they move with different velocities along curved magnetic field lines and are detected only when the field lines are connected to the instrument. Moreover, they may be scattered by turbulence with energy-dependent mean free path. The GOES proton fluxes did not show a significant increase for the Oct13 event (which occurred behind the eastern limb). However, STEREO-B, positioned behind the limb and with better magnetic connectivity, detected an increase of SEP proton intensity starting roughly 2 hours after the detection of an electromagnetic signal from this flare. Whereas the Sep14 flare, which was located roughly 40*∘* behind the eastern limb, was associated with an increase in the proton fluxes detected both by STEREO-B (which had a front view of the flare) and GOES (starting roughly 9 hours after the flare).

The Jan14 flare, originating in an AR 20*∘* behind the western limb, produced no significant increase in the proton flux at STEREO, had better magnetic connectivity to the Earth and was associated with a very strong SEP event with neutrons detected on ground by the South Pole neutron monitors.

The arrival time $T_{2}$ (Debrunner et al., 1988) at the Earth of a particle with velocity $v=\beta c$ released from the Sun at time $T_{1}$, is:

[TABLE]

where $\zeta$ is the distance traveled by the SEP from the acceleration region to the Earth. Assuming scatter-free propagation for the first-arriving particles, $\zeta$ will be independent of particle energy or velocity and will be equal to the path length along a Parker spiral magnetic field line from the Sun to the Earth (usually assumed to be 1.2 AU). If all the particles are accelerated at the same place and time, then the intercept of the line fitting $T_{2}$ to $1/\beta$ would give $T_{1}$, the time at which SEPs are released and is known as the Solar Particle Release (SPR) time. The slope of this line, $\zeta/c$ will be of the order of 600 s.

Since we do not have high energy resolution SEP data we obtain the SEP onset times using two methods depending on the energy range of the particles. For the GOES SEPs with energies $<$200 MeV we apply a median filter to the intensity profile and define the onset time as when the profile reached 5% of the maximum. For the higher-energy SEPs we apply a Fast Fourier Transform (FFT) filter to the intensity profile and evaluate the time when the second derivative is maximum as the onset time. To estimate of the uncertainty on the onset time we performed a scan over a series of values for the median and FFT filter windows and take the difference in onset times as the error.

The onset times as a function of $\frac{1}{\beta}$ for the GOES SEP protons associated with Jan14 are shown in Figure 13. Fitting the data to Equation 1, we estimate the SPR time to be $T_{1}=$07:55 $\pm$ 0:05 UT and path length of $\zeta\sim 1.3\pm 0.2$ A.U.

The value for $T_{1}$ is consistent with the estimated SPR time, 07:47 UT, reported by Thakur et al. (2014) but is somewhat later than the start of the flare activity at the Sun. Since Fermi was in the SAA and RHESSI was in orbital night, the most accurate time of the initiation of the flare was obtained from Konus-Wind and STEREO data. Konus-Wind detected emission in the 21–78 keV energy range starting at 07:43 UT, implying an emission time at the Sun of 07:35 UT, roughly 12 minutes prior to the SPR time. Assuming that the CME was released at this latter time the acceleration of SEPs started when the CME was at a height of 1.5 R⊙ $(v_{\rm CME}/$1400 km s${}^{-1})$.

Unfortunately the high-energy SEP data were not sufficient to estimate the SPR time for the other two BTL flares occurred on Oct13 and Sep14.

5. Summary and Discussion

We have presented the analysis of Fermi-LAT data from three BTL solar flares, whose location is determined by STEREO observations. We also presented analyses of data from RHESSI, Fermi-GBM, Konus-Wind in the HXR range, SDO in EUV, RSTN in radio wavelengths, some SEP observations, GOES and South Pole Neutron Monitors. We found several results:

The HXR LCs measured by the three instruments (in overlapping energy ranges) are in good agreement with each other and with the high-frequency radio LCs. The Fermi-LAT emission, in general, commences several minutes after the HXRs, peaks at a later time and lasts longer. 2. 2.

We are able to obtain RHESSI images in soft HXRs for flares just over the limb, indicating a loop-top emission from loops with heights above the photosphere ranging from $0.2\times 10^{10}$ to $2\times 10^{10}$ cm. SDO detected UV emission is detected for Oct13, and possibly Jan14, but not the Sep14 flare. Jan14 flare was too weak to permit localization of the gamma-ray source but localizations of the Fermi-LAT emission with Pass 8 data for the other two flares situates the centroid locations near the solar limb and about 50$\arcsec$ (Oct13) and 300$\arcsec$ (Sep14) from the RHESSI centroid. 3. 3.

The LCs (available only for Oct13 and Sep14 flares) show good agreement between the HXR spectra measured by Fermi-GBM, RHESSI (whenever contemporaneous data are available) and Konus-Wind below a few 100 keV. The Fermi-LAT spectra can be fitted with a relatively hard PLEXP phenomenological model (possibly due to relativistic electron bremsstrahlung) or to a pion decay model with proton indexes around 4. We note that production of photons of about $\sim$3 GeV detected here requires $>15$ GeV protons or $>6$ GeV electrons. These energies are greater than any other reported for solar particles. 4. 4.

We compare several spectral properties of $>100$ MeV radiation from the BTL flares with those of three on-disk flares previously analyzed. As evident from Table 2 and Figure 9, in general, these flares have similar characteristics. Similar GOES class flares have similar peak photon fluxes, surprisingly, regardless of limb occultation. The higher total gamma-ray energy of on-disk flares is most likely results from their having been observed over longer timescales. Thus, the underlying acceleration and emission processes are most likely similar, but the transport paths of the radiating particles (presumably protons) from the acceleration to the emission site must be different. That is, for BTL flares, protons must travel greater distances to land on the front side of the Sun to produce the detected gamma-rays. 5. 5.

We find that the proton index does not vary significantly during the 30-minute observation time windows for the BTL flares. This is similar to that found for the on-disk flares for the same time frames, but some on-disk flares are detected over longer time intervals (up to 20 hours) during which the proton index increases gradually.

We now present our interpretation of these results with the goal of constraining the emission and acceleration mechanisms and sites.

5.1. SEP onset times

Since the spectral information available for the Jan14 flare is limited we cannot constrain the acceleration, transport or radiation processes. However this flare is remarkable because the AR being located beyond the western limb provided good magnetic connection with the Earth and as a result it was associated with a very strong SEP event and increased the neutron flux in the South Pole neutron monitor. As presented in Figure 13, the acceleration time at the Sun for the SEP protons is 07:55 $\pm$ 0:05 UT which is in agreement with the SPR time of 07:47 $\pm$ 0:08 UT reported by Thakur et al. (2014). Unfortunately, the Fermi-LAT was in the SAA at the SPR time and exited at 07:55 UT. Therefore we can only provide an upper limit on the time of acceleration of gamma-ray producing particles (presumably protons) at the Sun. However, Konus-Wind detected emission in the 20–78 keV band starting at 07:43 UT implying that the electrons were accelerated at the Sun at 07:35 UT, roughly 12 minutes prior to the SPR.

Due to the location of the AR the other two flares were not magnetically well connected to the Earth. For the Sep14 flare the GOES proton fluxes begin to increase roughly 9 hours after the flare start time. STEREO-B observed the flare in its entirety but provides proton fluxes only in three energy bands, which is not sufficient to estimate the acceleration time at the Sun as we did for Jan14. Thus, we do not have reliable SEP data to test whether the onset times of the SEP and gamma-rays coincide, however we can compare the height of the CME at the time of the gamma-ray onset with the CME height at SPR found for Jan14. Based on the 2nd order fit of height as a function of time (from the LASCO CME online catalog) we estimated that the CME was at $\sim$2.5R⊙ at the onset time of the Fermi-LAT emission. We found a similar value for Oct13. These heights are significantly smaller than the predicted values reported in Thakur et al. (2014) for the CME heights at SPR as a function of source longitudes from Solar Cycle-23. To test whether these CME heights are compatible with the gamma-ray emission detected from the BTL flares, it would require detailed simulations on particle transport in the solar magnetic field. This study is beyond the scope of this paper and will be addressed in a future work.

5.2. Spatial Distributions

The RHESSI images show that the 20 to 50 keV HXRs, due to electron bremsstrahlung, are emitted from $\approx$30$\arcsec$ ($L\sim 2\times 10^{9}$ cm) and $\approx$50$\arcsec$ ($L\sim 3.5\times 10^{9}$ cm) sources from top of loops extending to heights of $\sim 4\times 10^{9}$ and $\sim 2\times 10^{10}$ cm above the photosphere for Oct13 and Sep14 flares, respectively. The column depth required for a particle of mass $m$ and kinetic energy $E$ (in units of $mc^{2}$), or Lorentz factor $\gamma=E+1=(1-\beta^{2})^{-1/2}$, to lose all its energy via Coulomb interactions is

[TABLE]

where $r_{0}$ is the classical electron radius and $\ln\Lambda\sim 20$ is the Coulomb logarithm. From Equation 2 we find that the column depth required to stop the $>50$ keV electrons that produce the HXRs detected by RHESSI is $\sim 5\times 10^{20}$cm*-2*. Assuming a density of $n<10^{10}$ cm*-3*, the sizes of the loop-top sources imply a column depth of $N_{\rm LT}<2$ and $3.5\times 10^{19}$ cm*-2* for the two HXR sources, respectively. This means that the energy loss time $\tau_{\rm Coul}\sim 2N_{\rm Coul}/(vn)$ is more than 10 times longer than the crossing time $\tau_{\rm cross}\,\equiv L/v=N_{\rm LT}/(vn)$. These values, together with the results reported in Chen & Petrosian (2013) suggest that the HXR emission from these two BTL flares are thin target sources.

If these loop-top sources were to be produced in a thick-target, which can come about in two ways under extreme conditions not likely to be the case here. The first is in the strong diffusion limit, i.e., if the electrons are trapped because the scattering time, $\tau_{sc}$, is smaller than the crossing time, $\tau_{cross}$. Note that because $\tau_{\rm Coul}>\tau_{\rm cross}\,$, the scattering cannot be due to Coulomb interactions but it could be due to turbulence. The second possibility is in the weak diffusion limit $\tau_{\rm sc}\,>\tau_{\rm cross}\,$, where trapping can occur if the field lines converge strongly. In this case we need $\tau_{\rm sc}\,>\tau_{\rm Coul}/\eta$ 888According to Malyshkin & Kulsrud (2001) $\eta\sim\ln(B_{0}/B_{L})$, the log of the ratio of magnetic field strengths at the middle and ends of the magnetic bottle. (with proportionality constant $\eta$ increasing with increasing field convergence (Petrosian, in press)). These are somewhat extreme conditions requiring either a very high density (therefore increasing the scattering, presumably turbulence) or a somewhat strong field convergence and a “clean” loop with low density and low level of turbulence.

Thus, the HXR emission is most likely due to electron bremsstrahlung from a thin-target loop-top source.

Based on the positions of the Fermi-LAT $>$100 MeV emission centroids alone we cannot exclude that the gamma rays come from the loop-top source. In order to investigate this possibility we rely on Equation 2 to find the column depth required to stop $>350$ MeV protons (that produce $>100$ MeV photons) and find $N_{\rm Coul}(350{\rm MeV})\sim 10^{25}$ cm*-2*. This is much larger than the loop-top column depth $N_{\rm LT}\sim 2-3.5\times 10^{19}$ cm*-2* so that, in the absence of trapping, we are again dealing with a thin target loop-top source and a small energy loss compared to what would be the case for emission from a thick target photospheric source. Consequently, we would need much larger energies of accelerated protons than those given in Table 2 assuming a thick target scenario. The condition for proton trapping in the loop-top (or any coronal trap region, for that matter) is also more extreme than that described above for electrons and we would need escape times $10^{5}$ times longer than the crossing time. Thus, the emission detected by the Fermi-LAT is most likely due to decay of pions produced by energetic protons interacting in a thick-target photospheric source.

5.3. Spectral Distributions

As shown in Lin & Hudson (1971) and McTiernan & Petrosian (1990) in a thin target scenario the relation between the HXR spectral index, $\gamma$, and the number index of the energy spectrum of the emitting electrons999This should not be confused with electron flux, $F(E)=vN(E),$ index, which in non relativistic limit is $\delta\ln F(E)/d\ln E=\gamma-1.0$ used commonly. In the relativistic regime these indexes are equal and as stated in Equation 3 $\delta=\gamma$. through bremsstrahlung processes, $\delta$, is

[TABLE]

For optically thin synchrotron radiation, the relation between $\delta$ and the microwave photon spectral index, $\alpha$, can be describe by the following relations for the relativistic (e.g. Rybicki & Lightman, 1979) and semi-relativistic (e.g. Dulk, 1985) cases

[TABLE]

We will use these relations in the following for the interpretation of the detected emission from the two brightest behind-the-limb flares reported in this work. The spectra of the two flares in the 30 keV to 10 MeV energy range are somewhat different so we discuss them separately.

Oct13: As already shown in Pesce-Rollins et al. (2015), both RHESSI and Fermi-GBM detect HXR spectra for Oct13 flare that are relatively steep (best-fit value of power-law photon index $\gamma=3.2\pm 0.1$). However, as shown in Figure 10 there is a tentative indication that the spectrum may harden into a nearly flat part in the 1–10 MeV range requiring either a similar hardening of the spectrum of the accelerated electrons, as e.g. described in Park et al. (1997), or a contribution from de-excitation nuclear lines. We found that the inclusion of a 2.223 MeV broad neutron capture line and the nuclear de-excitation lines did not improve the fit significantly and that the best-fit model for the emission observed by Fermi-GBM is a single power law.

As described in Section 5.2 the thin target is most likely, in which case following Equation 3 for the non-relativistic case ($<$100 keV) the index of the electron number density $\delta\sim 2.7$. The radio spectrum observed by RSTN, shown in Figure 12, indicates microwave flux of 60 solar flux units ($6\times 10^{5}$ Jy) that peaks at frequency $\nu\sim 5$ GHz and declines as $\nu^{-\alpha}$ with the index $\alpha\sim 2$ above this frequency. Based on the relations described in Equation 4 we find that the required power-law index for the number density of electrons to be $\delta\sim 5$ or $\delta\sim 3.5$ in the relativistic or semi-relativistic regime, respectively.

These values are steeper than the index $\delta\sim 2.7$ required in the non-relativistic HXR range, indicating a steepening of the electron spectrum above 1 MeV. We therefore conclude that the GBM flux in the energy range 300 keV - 10 MeV is probably not due to the accelerated electrons and no extra component is expected.

Sep14: The best-fit model for the combined HXR Fermi-GBM gamma-ray emission from the Sep14 flare is a single power law with an exponential decay with photon index 2.06$\pm$0.01 and a cut-off energy of 90$\pm$7 MeV. This is an extremely hard spectrum for a solar flare and if it is produced by a thin-target electron-bremsstrahlung model as described above, it would require an electron number spectrum with index $\delta\sim 1.5$ in the non-relativistic range steepening to an index $\delta\sim 2$ in the relativistic range. However, as noted above inclusion of the 2.223 MeV line improves the fit slightly, indicating a possible contribution from nuclear de-excitation lines so the steepening of the electron spectrum could be larger.

The radio spectrum of this flare, shown in Figure 12 is also harder. The emission detected by the San Vito station has an index $\alpha\sim 1$ above 1 GHz. Again assuming optically thin synchrotron emission would require semi-relativistic electrons with electron power-law index $\delta\sim 2.5$ indicating a slightly larger steepening at high energies. If the magnetic field is lower, which could be the case because of the larger loop, the steepening would be even larger ($\delta\sim 3$). *Thus, for the Sep14 flare a power-law spectrum, steepening at higher energies, is required to explain the HXR and microwave observations from the loop-top region. This plus a pion decay component provides an acceptable fit to the Fermi data from 30 keV to several GeV. *

5.4. Acceleration Site and Mechanism

The above interpretation of the HXR and microwave emissions indicates that the electrons responsible for these emissions are most likely accelerated in the reconnection region above the loop-top source either by turbulence (Petrosian, 2012) or in merging islands manifested in the particle-in-cell simulations (Drake & Swisdak, 2012). The electrons are trapped in the loop-top region long enough (longer than the crossing time of a fraction of second) to produce detectable bremsstrahlung and synchrotron radiation, but most of their energy is lost in thick-target footpoints hidden from near Earth instruments because of high optical depths (Pesce-Rollins et al., 2015). This scenario can also explain the HXR emission from a BTL flare reported by Krucker et al. (2007). The steepening of the electron spectrum in the semi-relativistic regime is due to a decrease in the acceleration rate and not to transport or energy loss effects.

If the Fermi-LAT emission is from a thick-target photospheric site, then this emission site is located on the visible part of the disk. It can not come from the occulted AR. The fact that accelerated protons reach the on-disk emission site provides strong evidence that the acceleration site is the CME environment, as suggested by Cliver et al. (1993) and Pesce-Rollins et al. (2015). They would diffuse across a wide range of magnetic fields, some connected to the AR behind the limb and some to the visible side of the Sun. These ions will most likely come from the down-stream region of the CME shock while SEPs escape the upstream region. This can account for the differences in their spectral and temporal characteristics. It is then possible that the discrepancy between the spectral characteristics in 1–10 MeV for the GBM and radio observations can be explained by lower-energy 1–100 MeV protons or electrons precipitating to the visible disk side from the down-stream region and producing the 1–10 MeV nuclear de-excitation line or bremsstrahlung emission below the chromosphere. These and other possibilities, for example, production of the Fermi-LAT emission by relativistic electrons either in the CME shock, in reconnection regions on current sheets behind the CME or trapped in a large loop with strong convergence, will be discussed in future papers.

The $Fermi$ LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged. W.L. was supported by NASA HGI grant NNX16AF78G and LWS grant NNX14AJ49G. V.P, W.L and F.R.d.C are supported by NASA grants NNX14AG03G, NNX13AF79G and NNX12AO70G. Val. P and L.K. thanks the RFBR grant 15-02-03717 We thank Nariaka Nitta and Meng Jin for friutful discussions on SEPs and magnetic connectivity.