Terrestrial Gamma-ray Flashes (TGFs) are brief pulses of energetic radiation observed in low-earth orbit. They are associated with thunderstorms and lightning and have been observed both as gamma-ray and electron flashes depending on the position of the spacecraft with respect to the source. While gamma-ray TGFs are detected as short pulses lasting less than 1 ms, most TGFs seen by the Fermi Gamma-ray Burst Monitor (GBM) with durations greater than 1 ms are, instead, the result of electrons traveling from the sources along geomagnetic field lines. We perform spectral analysis of the three brightest electron TGFs detected by GBM and discover strong 511 keV positron annihilation lines, demonstrating that these electron TGFs also contain substantial positron components. This shows that pair production occurs in conjunction with some terrestrial lightning and that most likely all TGFs are injecting electron-positron beams into the near Earth environment.
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 TGFs were unexpectedly discovered with the Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory in the early 1990s [Fishman et al., 1994]. Gamma-rays from TGFs have been observed to 40 MeV and higher [Marisaldi et al., 2010a; Briggs et al., 2010; Marisaldi et al., 2010b]. Since their discovery with BATSE, TGFs have been associated with thunderstorms and lightning, an association that was strongly confirmed with the large sample from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) [Smith et al., 2005]. The microphysics is believed to be well understood: electrons are accelerated to high energies in strong electric fields by the Relativistic Runaway Electron Avalanche (RREA) process, emitting gamma-rays via bremsstrahlung [Gurevich et al., 1992; Dwyer, 2003]. When a spacecraft is located above the source, within a cone of ≈30° half-angle, a gamma-ray TGF may be observed.
 Assuming a high-altitude source, Lehtinen et al.  noted that some energetic electrons should also escape to space. Unlike photons, these charged particles are constrained to follow the geomagnetic field line, traveling helical paths. They predicted that the interactions of the electrons with the atmosphere at the geomagnetic conjugate point of the source would produce gamma-rays observable from a satellite; however, this gamma-ray glow has not yet been observed. Additionally, spectral fits of RHESSI data indicate a lower source altitude [Dwyer and Smith, 2005].
 As the gamma-rays in a TGF propagate up and out of the atmosphere, they produce secondary electrons, mostly via Compton scattering and pair production. Dwyer et al.  proposed that secondary electrons produced ≳40 km should escape into space, a mechanism that should take place regardless of the source altitude. Furthermore they proposed that the electrons could be observed by their directly interacting with an instrument located along the field line from the source. While gamma-rays disperse from the source, the intensity of an “electron TGF” is maintained with distance from the source because the electrons follow the field line; however electron TGFs are infrequently detected because the electron beam has a small diameter [Dwyer et al., 2008; Carlson et al., 2009]. This model additionally predicts that electron TGFs should have longer durations because of velocity dispersion due to the range of helical pitch angles: electrons with low pitch angles have velocities nearly aligned along the field line and arrive at the satellite first. Electrons with high-pitch angles have similar velocity magnitudes but have smaller velocity components along the field and arrive later. Furthermore, if the geomagnetic field at the conjugate point is stronger than at the source, electrons will magnetically mirror above the atmosphere and return along the field line to the satellite.
 BATSE TGF 2221 and the RHESSI TGF of 17 January 2004 showed both signatures in their time histories, lengthening and a second peak [Dwyer et al., 2008], as does Gamma-ray Burst Monitor (GBM) TGF 091214 (Figure 1). All three of these TGFs were detected when the spacecrafts were over the Sahara desert, with the spacecrafts magnetically connected to the region of high thunderstorm activity in southern Africa. These events are identified as electron TGFs based on their time profiles and other characteristics; the detectors are unable to distinguish photons from electrons. The Solar Anomalous Magnetospheric Particle Explorer (SAMPEX) Heavy Ion Large Telescope (HILT) is sensitive to ions and electrons; with it numerous possible electron TGFs have been identified [Carlson et al., 2009]. It is difficult to conclusively establish the nature of these events from the SAMPEX data alone because of the 20 ms resolution of that data. As additional confirmation that some TGFs have been observed via electrons directed along a geomagnetic field line, the associated lightning discharge at the terminus of the field line was observed for the first time for GBM TGF 100515 [Cohen et al., 2010].
 The Fermi Gamma-ray Space Telescope is in orbit at ≈560 km altitude and 25.6° inclination. Fermi consists of two instruments, the Large Area Telescope (LAT), a pair conversion telescope for observing above 20 MeV [Atwood et al., 2009], and the Gamma-ray Burst Monitor. GBM consists of 14 detectors of two types arranged to view the unocculted sky: twelve sodium iodide (NaI) scintillator detectors cover the energy range ≈8 keV to 1 MeV, while two bismuth germanate (BGO) scintillator detectors cover the energy range ≈200 keV to ≈40 MeV [Meegan et al., 2009]. These scintillation detectors record energy deposited by high-energy particles such as photons, protons and electrons; they do not distinguish among particle types. Even though TGFs originate from the Earth's atmosphere near the nadir, the radiation from TGFs is so penetrating that signals are typically produced in most of the GBM detectors. The GBM BGO detectors are well suited for TGF observations due their large volumes, high efficiency for detecting gamma-rays and good ability to measure the full energy of MeV gamma-rays. The improved sensitivity and absolute timing accuracy of GBM have already provided new results on TGFs. The time profiles are observed to be symmetric or to have faster rises than falls; one TGF had a rise time of only ≈7 μs. GBM has observed TGFs with partially overlapping pulses [Briggs et al., 2010]. Thirteen GBM TGFs were found to be simultaneous to within ≈40 μs with radio-detected lightning discharges; clusters of lighting indicative of storms were found for additional TGFs [Connaughton et al., 2010]. Properties of the first 50 GBM TGFs are summarized by Fishman et al. (Temporal properties of terrestrial gamma-ray flashes (tgfs) from the gamma-ray burst monitor on the fermi observatory, submitted to Journal of Geophysical Research, 2010).
2. Sample and Analysis
 GBM detected 77 TGFs between 2008 July 11 and 2010 July 1. Figure 2 shows the duration distribution of these TGFs, using the t90 duration measure [Koshut et al., 1996]. Most of the TGFs have t90 durations from 0.1 to 1.0 ms, with a small fraction contributing a tail to the distribution extending to 25 ms. Two of the eight TGFs with t90 > 1 ms consist of multiple separated short pulses – these two are gamma-ray TGFs. Based upon the velocity dispersion effect producing longer durations for electron TGFs the remaining six long TGFs are probably electron TGFs.
 Here we investigate the spectra of the three brightest TGFs from this sub-sample of six TGFs (Table 1). These three TGFs, 080807, 090813 and 091214, were already identified as very likely electron TGFs [Briggs et al., 2010; Connaughton et al., 2010] based on several unusual characteristics that they share: they are unusually long, their spectra have maximum energies of ≈10 MeV compared to ≳30 MeV for most TGFs and using the World Wide Lightning Location Network (WWLLN), a network of VLF radio receivers [Rodger et al., 2009], lightning discharges were observed within 50 km of one of the termini of the magnetic field lines through Fermi, but not underneath Fermi. The duration and two peaks of TGF 091214 are compellingly explained by charged particles arriving on the geomagnetic field line through Fermi (Figure 1), strongly supporting the “electron” nature of this TGF. Mirror peaks were neither observed nor expected for TGFs 080807 and 090813. For these two TGFs, at equal altitudes, the magnetic field is weaker at the conjugate location so that particles penetrate farther into the atmosphere and are absorbed before they reach a field strong enough to cause mirroring.
Table 1. Properties of the Three Brightest GBM Electron TGFs
Calculated using the 11th Generation International Geomagnetic Reference Field (IGRF-11) (http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html) and a 30 km altitude. The source region for the electrons and positrons extends above this altitude along the field line.
Sum over all 14 GBM detectors of all counts within the t90 interval, except for TGF 080807, for which only the detectors on the +X side of the spacecraft are included.
Relative to the trigger time.
A gain correction factor less than one increases the gain of the model by scaling the energy edges of the channels when the model counts are binned, implying that the observed annihilation line is at a higher than expected energy.
Improvement of C-Stat for the electron + positron fit relative to the electron-only fit.
The counts used for the spectral fits: sum of all counts in BGO 0 in the time interval and energy channel range used for the fits.
 Using lightning locations from WWLLN, the largest observed offset of a source of a GBM gamma-ray TGF from the sub-Fermi point is 300 km [Briggs et al., 2010; Connaughton et al., 2010]. (We use the GBM results for source/sub-satellite offsets in case there is an instrumental dependence.) The sources of these three TGFs (Table 1) range from 520 to 4300 km from Fermi so that Fermi should be outside of the gamma-ray beam and only charged particles are expected to be detected. We simulate the response of GBM to incident particles using GRESS [Kippen et al., 2007], obtaining model count spectra. Separate simulations of 5 × 108 particles are made for each TGF and for electrons and positrons, and for various continuum spectra for the electrons and positrons. We find for the continuum spectra that an empirical model of an exponential shape, Aexp(−E/E0), matches the data well when the E-folding energy, E0, is optimized. The simulation directs particles at Fermi from the direction of the magnetic field line from the source, using the field direction at the location of Fermi and assuming that all particle velocities are parallel to the field. Mixtures of these simulated count spectra are fit to the observed counts. (Details of the fitting method are in the auxiliary material.)
 A surprising result is that the fits show the presence of both an electron component and a substantial positron component (Table 1). The positron component manifests itself as a strong 511 keV gamma-ray line (Figure 3) produced when positrons annihilate with Fermi. Incident continuum photon spectra produce 511 keV lines from pair production in Fermi, but the lines are much weaker than those observed (Figure S1 of the auxiliary material). Pure electron spectra should produce a 511 keV line from pair production from bremsstrahlung photons, however this feature is negligible in the model spectra (Figure S2 of the auxiliary material). Positron fractions, N(e+)/(N(e−) + N(e+)), range from ≈0.1 to ≈0.3. The values of the E-folding energy, E0, of the continua range from 2.3 to 4.6 MeV (Table 1, Figure S3 of the auxiliary material) – the electron/positron spectra of TGFs have lower exponential energies and lower maximum energies than the gamma-ray spectra [Dwyer and Smith, 2005; Briggs et al., 2010; Marisaldi et al., 2010a]. The 511 keV positron annihilation line and the lower maximum energy are visible in the raw data (Figure S4 of the auxiliary material).
Table 1 lists the improvements in the fitting statistic, Δ (C-Stat), from adding positrons to electrons-only fits. We conducted simulations to demonstrate that these improvements are extremely unlikely by chance if only electrons are reaching Fermi and that therefore the detections of positrons are statistically significant. For each TGF, 25000 simulated spectra were created and then each of these simulated spectra were fit twice, with the electrons-only model and with the electrons+positrons model. (Further details on the simulations procedure are in the auxiliary material.) The C-Stat improvements from adding a positron component were always smaller in the simulations than for the real data, showing that the positron components have significances of at least 99.996% (Gaussian equivalent to 3.9σ). Furthermore, the three TGFs represent independent detections of positron components.
 The detection of positrons arriving at Fermi from TGFs is direct evidence for a relativistic phenomenon occurring in conjunction with terrestrial lightning: pair production. These positrons are expected from interactions of the TGF gamma-rays propagating upwards, but the positron fraction is higher than anticipated by Dwyer et al. . Monte Carlo simulations now give values of ≈11%, depending on location in the beam, which is broadly consistent with the fitted values (Table 1). The discovery is strong confirmation that some TGFs are detected from electrons and positrons beamed along geomagnetic field lines from distant sources to the spacecraft, rather than from gamma-rays from sources beneath the spacecraft. The finding of high positron fractions, ≳10%, in the three brightest electron TGFs detected by GBM suggests that all TGFs emit substantial numbers of positrons to space. Whether TGFs make an important contribution of electrons and positrons to the inner radiation belt depends on both the poorly known intensity distribution of TGFs and on the degree of scattering from the electron/positron beams. Without scattering, most of the particles will be absorbed into the atmosphere after one or, if mirroring occurs, two inter-hemispherical passages [Lehtinen et al., 2000, 2001].
 The future TGF missions Firefly and TARANIS include instruments with the capability to distinguish between photons and electrons, with TARANIS also including a high-energy electron instrument.
 We thank the anonymous reviewers for their insightful comments. The Fermi GBM Collaboration acknowledges support for GBM development, operations, and data analysis from NASA in the United States and from BMWi/DLR in Germany.