GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,
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The spectral dependence of terrestrial gamma-ray flashes on source distance 1
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B. J. Hazelton, B. W. Grefenstette, D. M. Smith, J. R. Dwyer, X.-M. 3
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Shao, S. A. Cummer, T. Chronis, E. H. Lay, and R. H. Holzworth
B. J. Hazelton, Department of Physics and Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064, USA. (
[email protected]) 1
Department of Physics and Santa Cruz
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Lightning flash locations from the World Wide Lightning Location Net-
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work (WWLLN) were used to identify storm locations near 362 Terrestrial
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Gamma-ray Flashes (TGFs) detected by RHESSI from October 2003 to De-
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cember 2005. The combined spectrum of TGFs with lightning flashes within
Institute for Particle Physics, University of California, Santa Cruz, California, USA. 2
Department of Physics and Space
Sciences, Florida Institute of Technology, Florida, USA. 3
Space and Remote Sensing Sciences, Los
Alamos National Laboratory, Los Alamos, New Mexico, USA. 4
Electrical and Computer engineering
Department, Duke University, Durham, North Carolina, USA. 5
Global Hydrology Climate Center,
NASA Marshall Space Flight Center, Huntsville, Alabama, USA. 6
Department of Earth and Space Science,
University of Washington, Washington, USA.
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300 km of the sub-satellite point is found to be much harder than the spec-
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trum of TGFs with more distant lightning flashes. When these data are com-
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pared with simulations of relativistic runaway breakdown, it is found that
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the most likely model has a source altitude of 15 km and a wide beam ge-
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ometry. Four associations of TGFs with individual sferics localized to po-
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sitions more than 300 km from the sub-satellite point are reported and it is
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shown that a narrow beam source at 21 km altitude is unlikely to produce
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the number of observed high energy photons in these TGFs.
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1. Introduction 15
TGFs were first discovered with the BATSE instrument on the Compton Gamma Ray
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Observatory by Fishman et al. [1994] and over 800 have since been observed by the
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RHESSI satellite [Smith et al., 2005]. From their first detection, TGFs have been as-
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sociated with thunderstorms, and some flashes from each satellite have been linked to
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individual lightning flashes [e.g. Inan et al., 1996, 2006; Cummer et al., 2005; Stanley
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et al., 2006]. Localizations of lightning flashes associated with RHESSI TGFs indicate
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that most TGFs occur within ∼300 km of the sub-satellite point [Cummer et al., 2005].
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Relativistic runaway models have been successful in modeling the combined spectrum
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of all RHESSI TGFs [Dwyer and Smith, 2005], but details of source beaming and alti-
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tude cannot be constrained by the combined spectrum because it averages over important
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differences among individual TGFs. One such difference is the horizontal distance from
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the TGF source to the sub-satellite point. As this distance increases, the spectrum of
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photons reaching the satellite is expected to soften (decrease in average photon energy)
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because the Bremsstrahlung radiation is inherently harder along the beam and Compton
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scattering of photons out of the beam also removes energy [Østgaard et al., 2008]. The
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change in the detected TGF spectrum with source distance is model dependent, so the
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spectral differences between TGFs that are detected close and far from the source can
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constrain source geometry and altitude. Unfortunately, the spectra of individual TGFs
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associated with localized sferics cannot be directly fit with model spectra because RHESSI
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TGFs have fewer than 30 counts on average.
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To obtain separate spectra of TGFs with close and distant sources, we used the World
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Wide Lightning Location Network (WWLLN) to identify storm locations around the world
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at the times when TGFs were detected. These storm locations are used to indicate the
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possible locations of TGF sources and to categorize TGFs based on the distance from the
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sub-satellite point to the nearest potential source location. WWLLN is a multi-station
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VLF network that records times and locations of lightning flashes all over the world with
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a mean accuracy of 15 km [Rodger et al., 2008]. Jacobson et al. [2006] showed that despite
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its low detection efficiency for a given flash, WWLLN provides a spatially accurate and
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complete census of storms when averaged over many flashes.
2. Data and Analysis 44
We consider 362 TGFs detected by RHESSI between October 2003 and December 2005
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for which concurrent WWLLN data are available. This time range is chosen to start
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after the time of group arrival (TOGA) algorithm was implemented in WWLLN [Rodger
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et al., 2005] and to end before radiation damage to the RHESSI detectors affected the
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spectral quality too much (Grefenstette et al., 2008b, in preparation). For each TGF, all
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WWLLN lightning flashes within ± 20 minutes of the TGF time were accumulated to
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locate lightning producing storms. The TGFs were divided into two categories: those that
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had lightning flashes within 300 km of the sub-satellite point (316 TGFs), and those that
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did not (46 TGFs). To evaluate the spectral differences between TGFs in each category,
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the combined spectrum for each category was divided by the combined spectrum of all
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362 TGFs in the sample. The spectrum of TGFs with only distant lightning flashes is
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much softer than the spectrum of TGFs with closer ones (Figure 1).
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3. Runaway Breakdown Models 56
A Monte Carlo simulation of runaway breakdown in air similar to the one used in Dwyer
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and Smith [2005] was used to calculate the spectra of TGFs originating more than and
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less than 300 km from the sub-satellite point. The simulation includes, in an accurate
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form, all the important interactions of energetic electrons, positrons and photons in air.
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A detailed description of the included physics is in Dwyer [2007].
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In the first phase of the simulation, the runaway avalanche was allowed to develop in a
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region with a uniform vertical electric field. Outside this region the field was set to zero.
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The runaway electrons were propagated until they left the avalanche region and came to a
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stop. The solid angle distribution of the photons produced in this phase of the simulation
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(Figure 2a) shows that the photons are beamed upward, with the higher energy photons
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in a narrower cone than the lower energy photons. The photons were then propagated
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through the atmosphere using GEANT, a standard high-energy particle transport code
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used in particle physics and astrophysics [GEANT Team, 1993].
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We also considered a wider beam that might result from divergence in the electric field
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in the avalanche region. The wider distribution is generated by convolving the original
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distribution with a gaussian in solid angle. This convolution widens the beam while
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preserving the energy structure of the original beam (Figure 2b).
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To compare the models with data, it is important to consider the intensity threshold
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for detecting the events. As the photons propagate through the atmosphere they are
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sometimes Compton scattered to very large angles. These Compton scattered photons
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have a much softer spectrum than the photons in the main part of the beam, so they
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can have a significant effect on the model spectrum. Because they are scattered into a
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large solid angle, the satellite is more likely to fly into the path of the Compton scattered
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photons than the main beam. The flux of Comptonized photons is much lower than the
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flux in the beam, however, so the search algorithm is less likely to identify them as a
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TGF. In Dwyer and Smith [2005] the model spectra only included emission into angles
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at which the flash would appear at least half as bright to the satellite as a flash directly
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below it. This threshold was based on the range of observed fluences in RHESSI TGFs
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and the assumption that all TGFs have the same intrinsic brightness, so the observed
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fluence depended only on source distance. A more sophisticated threshold was developed
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for this paper using the knowledge of source distance provided by WWLLN.
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First, the number of counts detected by RHESSI from the total of all 362 TGFs was
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calculated as a function of distance from the sub-satellite point using the distance from the
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sub-satellite point to the nearest lightning flash for each TGF. Next, the model photons
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were binned by horizontal distance from the source and the spectrum from each distance
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bin was convolved with the instrument response to generate the count spectrum that
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would be detected by RHESSI. Finally, the number of model counts in each distance bin
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was re-normalized to the number of counts actually detected by RHESSI in that distance
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bin. One major advantage of this method is that any deadtime effect on the number
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of detected counts versus distance is duplicated in the models (see section 5). There is
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some systematic bias in this re-normalization method for placing the source too near the
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RHESSI sub-satellite point because the horizontal distance to the nearest lightning flash
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was used for the source distance. The result of this bias is that the calculated model
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spectra are harder than they would be if the actual source distances were known.
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Three source altitudes (13 km, 15 km, and 21 km) and two types of beaming (narrow and
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wide) were considered. The models that best fit the combined spectra of all 362 TGFs are
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the 21 km narrow model and 15 km wide model, as in Dwyer and Smith [2005], except that
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the wide beam used in that paper was isotropic in a 45◦ half-angle cone. To compare the
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models with the TGFs separated by source distance, the distance-binned model spectra
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were binned further to make two spectra for each model: one for TGFs within 300 km of
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the source and one for TGFs further from the source (Figure 3). The TGFs with close
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and distant sources are best fit by the 21 km narrow and 21 km wide models respectively;
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the 15 km wide model is the second-best fit to both categories. Unfortunately, no single
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model fits all the data perfectly, but the 15 km wide model comes the closest, particularly
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if all the models are a little too hard as a result of the distance bias mentioned above.
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To quantify the effect of this bias, the same re-normalizing procedure was carried out,
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except that the source distance was defined for each TGF using a randomly selected
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lightning flash that occurred within 20 minutes and 600 km of the TGF, rather than
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the nearest one. This procedure was performed many times and the results provide an
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upper limit on how much the models might change if the actual source locations were
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known, since randomly selecting a lightning flash as the source location will generally
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overestimate the source distance. This algorithm produced models that were all softer
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than when the nearest lightning flashes were used, with the largest changes occurring in
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the narrow models in Figure 3a. The 15 km wide beam model was the best fit for the TGFs
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with close and distant sources, and it was the second best fit for the combined spectrum
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of all the TGFs, after the 13 km wide model. We conclude that the bias introduced by
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using the nearest lightning flash affects the narrow models the most and that the effect
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of removing the bias would be to make the 15 km wide beam model an even better fit to
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all the data.
4. TGFs with Distant Sferic Localizations 125
We report here on four sferics associated with TGFs and localized to positions more
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than 300 km from the sub-satellite point (listed in Table 1). Three of these sferics were
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detected and localized by the Los Alamos Sferic Array (LASA) following the analysis
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procedures outlined in Stanley et al. [2006] and the fourth was detected and localized
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both by the Zeus network [Chronis and Anagnostou, 2003] and by magnetic field sensors
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at Duke University [after Cummer et al., 2005]. The highest energy gamma-rays in these
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distant localized TGFs provide a useful check on the viability of narrow beam models.
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A bootstrap Monte Carlo method was used to compare the number of high energy counts
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observed in each TGF with the number that would be expected from a narrow beam source
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at 21 km. First, model spectra were generated in 100 km wide distance bins and convolved
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with the instrument response. Then for each localized TGF, the model spectrum for the
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appropriate distance bin was combined with the background spectrum for that TGF taken
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from the RHESSI TGF Catalog (Grefenstette et al., 2008b, in preparation) to generate
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an expected observed spectrum for the bootstrap Monte Carlo. An energy threshold that
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contained only the top 5% of model counts was selected and the number of counts in the
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real TGF with energies above this threshold was compared with the number of above
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threshold counts in ten million simulated TGFs. The probability of detecting a TGF with
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at least as many high energy counts as were observed if the source was a narrow beam
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at 21 km is shown in Table 1. Also shown in Table 1 is the joint probability of detecting
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at least the number of observed high energy counts in all four localized TGFs. From the
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probabilities in the table, the likelihood that the 21 km narrow model represents the true
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source for all TGFs is very low.
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The radiation damage to the RHESSI detectors has degraded the spectral resolution
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and decreased the average energy of detected counts in RHESSI TGFs over time. The
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instrument response used in this analysis is therefore not the true RHESSI response for
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the last three TGFs in Table 1. The decrease in average TGF count energy with time
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means that the bootstrap Monte Carlo actually overestimates the probability of detecting
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high energy counts from the 21 km narrow model, so the true observation probabilities
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for these TGFs are even lower than reported in Table 1.
5. Discussion 154
Estimating TGF source locations using sferic data has proved a powerful tool to ex-
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amine models of TGF production. The distance from the estimated source location to
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the sub-satellite point effectively sorts TGFs into categories with very different spectra,
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something no other parameter has ever been observed to do (Grefenstette et al., 2008b, in
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preparation). Information about the source distance for TGFs increases the constraints
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on the models and provides an improved model threshold algorithm. The results of the
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modeling are broadly consistent with Dwyer and Smith [2005] and suggest that the 15 km
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wide beam model is the most likely source geometry, but none of the models considered
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here are completely successful. The failure of any of the models to fully explain the spec-
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tra of both TGFs with close sources and TGFs with distant sources suggests that more
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complicated models, perhaps with non-vertical beams, will need to be considered in the
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future.
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The viability of models with vertical narrow beams can be constrained by the number of
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high energy photons in individual TGFs with associated localized sferics that have source
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distances greater than 300 km. We find that a 21 km altitude source with the beam profile
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shown in Figure 2a is unlikely to produce the number of high energy counts observed in
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the four such TGFs examined here, so models considered in the literature [e.g Carlson
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et al., 2007; Østgaard et al., 2008] with even narrower beams and higher altitudes are
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unlikely to produce distant TGFs with the number of observed high energy gamma-rays.
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It was recently discovered (Grefenstette et al., 2008b, in preparation) that the brightest
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RHESSI TGFs are likely to be suffering from saturation effects. There are two saturation
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effects that will change the detected spectrum of TGFs with close sources: deadtime and
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pileup. Deadtime occurs when a photon enters a RHESSI detector less than 9 µs after
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a previous one and is not counted because the electronics have not finished processing
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the previous count [Smith et al., 2002]. Deadtime does not directly change the observed
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spectrum, but because the brightest part of the TGF is also the hardest [see Grefenstette
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et al., 2008], the detected spectrum for TGFs affected by deadtime will be softer than
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the true spectrum. Pileup occurs when two photons enter a RHESSI detector less than
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1 µs apart and the detector sees only one event with an energy equal to the sum of the
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energies of the two photons, making the observed spectrum harder. To quantify the spec-
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tral effects of deadtime and pileup, we ran extensive Monte Carlo simulations similar to
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those discussed in section 3 with typical TGF time profiles and 50% peak deadtime and
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compared the resulting spectra to the spectra without saturation effects. We find that
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above 5 MeV, deadtime results in a 5% decrease in the number of observed counts, while
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pileup causes a 20% increase, for a net increase in high energy counts of about 15% due
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to saturation effects. By contrast, the difference between the two best models in Figure
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3a is more than 30%. The analysis in section 4 and the data in Figure 3b are unlikely to
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be affected by deadtime or pileup because TGFs with distant sources are expected to be
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the least saturated.
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Acknowledgments. We wish to thank Craig Rodger for very useful conversations.
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Table 1.
TGFs with sferic localizations more than 300 km from the sub-satellite point.
The last column is the probability of observing a TGF with at least the observed number of high energy counts if the source was a narrow beam at 21 km. The last row shows the joint probability for all four TGFs (see text for details).
Date August 4, 2004
Detection Network
Source Total High Energy Observation Distance (km) Counts Counts Probability
Duke & Zeus
535
18
2
0.22
September 11, 2006
LASA
371
22
5
0.0034
June 11, 2007
LASA
319
22
2
0.28
LASA
374
19
2
0.23
June 16, 2007
4.8 × 10−5
All Events
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Figure 1.
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Ratios of the spectra of TGFs with close lightning flashes (red) and TGFs with no
lightning flashes within 300 km (blue) to the combined spectrum of all 362 TGFs in the sample. The black line indicates the combined spectrum of all TGFs in the sample. TGFs with only distant lightning flashes have a much softer spectrum than TGFs with close lightning flashes.
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Figure 2.
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(a) Intrinsic beam shape from relativistic runaway simulations. Note the energy
structure of the beam, with the high energy photons concentrated in a narrower emission cone than the low energy photons. (b) Wide beam shape from the convolution of the intrinsic beam shape with a gaussian in solid angle. The energy structure of the intrinsic beam is preserved.
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Figure 3.
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(a) The ratio of the spectrum of TGFs with close lightning flashes (316 TGFs) to
the combined spectrum of all 362 TGFs plotted with the runaway breakdown models for close sources. The 21 km narrow model is the best fit, followed by the 15 km wide model. (b) The ratio of the spectrum of TGFs with only distant lightning flashes (46 TGFs) to the combined spectrum of all 362 TGFs plotted with the runaway breakdown models for distant sources. The 21 km wide model is the best fit to the data, followed by the 15 km wide model.
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