We present a summary of data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) terrestrial gamma ray flash (TGF) catalog. We describe the RHESSI search algorithm and discuss its limitations due to its design emphasis on cleanliness rather than completeness. This search algorithm has identified 820 TGFs between March of 2002 and February of 2008. Radiation damage to the RHESSI detectors has resulted in a decreased sensitivity after early 2006 and a corresponding decrease in the number of identified TGFs in the years 2006–2008. Prior to this, the average rate of occurrence was one TGF every 2.35 days. RHESSI has seen multiple TGFs associated with a single storm system, either in the same orbit or in the subsequent orbit. The X-ray flux in a 100 ms pedestal region surrounding all of the TGFs is (1.3 ± 1.9) × 10−3 times the average peak flux of a TGF. We show that RHESSI was counting at or near its maximum throughput during the peak 50 μs of many of the TGFs and that we do not yet know the maximum possible brightness of a TGF. On short time scales, some TGFs may be much brighter than could be observed by either RHESSI or BATSE. Finally, we show that there is no detectable change in the spectrum of TGFs when they are grouped by brightness, geographic latitude, geomagnetic latitude, or the local day or night.
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 Terrestrial gamma ray flashes (TGFs) are short bursts of X rays and gamma rays observed by satellites. The study of TGFs began with their serendipitous observation by the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) in 1994. The TGFs were immediately correlated with times when the satellite flew over areas of high lightning activity and were thought to be the bremsstrahlung emission from runaway electrons created by electrical discharge [Fishman et al., 1994]. Atmospheric high-energy electrons were first predicted by Wilson , who suggested that electrons could be accelerated to extreme energies by the electric fields in a thunderstorm. These electrons would then produce X rays and gamma rays via bremsstrahlung emission, which could then propagate to space. TGFs are distinguished from cosmic gamma ray bursts (GRBs) by their extremely short durations. While short GRBs typically have peaks that last >300 ms, TGFs generally have peaks that last less than a millisecond. There are a few exceptions which may have a different source mechanism [Dwyer et al., 2008].
 The source of the relativistic electrons has been modeled over the last decade and a half. A number of models are based on the relativistic runaway electron avalanche (RREA) process, which produces a large number of runaway electrons [Gurevich et al., 1992, 1994; Gurevich and Milikh, 1999; Gurevich et al., 2006; Roussel-Dupre and Gurevich, 1996; Taranenko and Roussel-Dupre, 1996; Lehtinen et al., 1999;Inan and Lehtinen, 2005] via avalanche multiplication of a seed population of energetic secondary electrons produced by the extensive air showers from high-energy cosmic rays. In addition, Moss et al.  have developed a Monte Carlo simulation which demonstrates that a seed population of thermal electrons can be accelerated to energies of hundreds of keV, and possibly several MeV, by the extreme electric fields found in streamer tips. Dwyer [2007, 2008] has introduced a process called relativistic breakdown that includes the natural positive feedback due to back-scattered X rays and positrons. The Dwyer model operates on the background population of relativistic atmospheric electrons to drive a self-sustaining runaway electron discharge without requiring a large impulsive injection of energetic electrons from extensive air showers from high-energy cosmic rays. Roussel-Dupre et al.  have recently given a review of the physics of electrical discharges and include a section on runaway electrons that specifically deals with the energy loss of energetic electrons due to the dynamical friction of the atmosphere. All of the above models produce electrons with a mean energy near the minimum of the energy loss for relativistic electrons in air of 1.4 MeV and a distribution of energies that extends to greater than 20 MeV. The difference in the predicted observed spectrum for these models is based on the assumed source location and angular distribution of the source electrons.
 A comparison of different source models to the BATSE data is limited by the lack of spectral information in the data since the only BATSE data mode that has a fine enough time resolution to observe the TGFs only provides four coarse energy channels. Studies of the temporal evolution of subsets of the 78 BATSE TGFs [Nemiroff et al., 1997; Feng et al., 2002] show that the spectrum of the TGFs tends to lower energies over time. This has recently been revisited by Østgaard et al.  with Monte Carlo simulations demonstrating that the temporal evolution of the spectrum is roughly consistent with the expected time delays introduced by the Compton scattering of high-energy bremsstrahlung photons to lower energies in the atmosphere. The predictions of the time delays become more precise once the effect of instrumental dead time is included [Grefenstette et al., 2008].
Smith et al.  presented data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite that demonstrate that the TGFs are more numerous than originally indicated by the BATSE data. While BATSE required an onboard trigger, which was optimized to search for cosmic gamma ray bursts, RHESSI telemeters all of its data to ground, allowing for a postobservation search for TGFs. Since its launch in 2002, 820 TGFs have been identified by the RHESSI search algorithm compared to the 78 observed by BATSE during its decade-long mission. In addition to the increase in the number of events, the RHESSI data also provide much finer spectral resolution and allow for detailed spectroscopic comparison to models. Dwyer and Smith  and Carlson et al.  show that the RHESSI data are consistent with the expected spectrum of the bremsstrahlung of electrons accelerated to relativistic energies deep in the atmosphere (<21 km) near the tops of thunderclouds.
 In addition to the correlation between TGF occurrence and the satellite flying over an area of high lightning activity, there has also been an effort to correlate TGFs with individual lightning strikes by observing the atmospheric radio signal (sferic) produced by the lightning strike. Inan et al.  first observed a sferic that occurred within a few milliseconds of a BATSE TGF. Further studies by Cummer et al.  show that the charge moment changes observed from sferics associated with TGFs are much smaller than those observed from sferics associated with sprites. Cohen et al.  show that a large percentage of TGFs can be matched to a sferic given a sufficiently sensitive instrument and that the sferics associated with TGFs often are some of the most intense VLF emissions from lightning in the storm region. Stanley et al.  has found that the sferics associated with TGFs are specifically related to positive intracloud lightning discharges.
 We will leave the comparison of TGFs and lightning, including their geographic distributions and their occurrence rates versus time of day, to a subsequent paper. In this paper, we present a detailed review of the RHESSI TGFs, including a discussion of the search algorithm that selects the TGFs from the RHESSI archival data and an overview of the mission to date.
2. Description of RHESSI Instrument and Data
 RHESSI's nine germanium detectors are cylindrical with a small bore going most of the way up the center leaving one closed end at the front [Smith et al., 2002]. The detectors are divided into front and rear segments by an interruption in the electrical contact on the inner bore. Events collected at the front and rear parts of the inner contact are read out by separate electronics chains. The front segments are primarily used for imaging solar high-energy X rays and detect photons in the energy range from 3 keV to 2.7 MeV, while the rear segments view the entire sky in the energy range from 25 keV to 17 MeV, with reduced sensitivity below 50 keV due to absorption in the aluminum cryostat that houses the detectors. When high-energy photons Compton scatter from one rear segment to another, two counts are observed to occur at the same time in the two detector segments. Because of time jitter in the electronics, these coincidence counts may occur ±1 clock tick from each other. When the energies of coincidence counts are combined to reconstruct the energy of the original photon, energies greater than 20 MeV can be recorded.
 For simplicity, our analysis is restricted to data from the rear segments since they have approximately six times the volume of the front segments and because the front segments are sometimes turned off while the Sun is beneath the horizon. We also ignore data from detector 2. This detectors is operated at low voltage to avoid arcing, so for much of the mission this detector has not been completely depleted of charge carriers. This lack of depletion near the inner bore prevents the detector volume from registering as two separate segments [Smith et al., 2002]. In this mode the electronics become noisy, giving poor energy resolution and a higher low-energy threshold.
 RHESSI continuously records every count (energy deposit in a detector segment) and telemeters the data to ground where archival data are scanned for TGFs. Exceptions to the continuous data mode occur during the periods when the data stream is switched off as RHESSI passes through the South Atlantic Anomaly, a region of the Earth's inner radiation belt populated by energetic protons. Another is when RHESSI passes through regions of high magnetic latitude and the satellite encounters energetic electrons from the outer radiation belt. These electrons result in a significant increase in the count rate below a few hundred keV. To compensate for this, the data are decimated to reduce the load on telemetry. This is characterized by a decimation level, where a level of four indicates that only one in every four counts with energies below a threshold (usually 375 keV) is telemetered to ground. Decimation occurs whenever the satellite enters a geographic region in the northern hemisphere above 20°N latitude and between 190 to 340°E longitude (North America) and a region in the southern hemisphere below 25°S latitude and between 25 to 150°E longitude (southern Indian Ocean and Australia). The decimation state is recorded in diagnostic data and corrections are implemented as required. As of 6 August 2008, the northern decimation region was discontinued to increase the sensitivity of RHESSI to TGFs from North America. Analysis of these new data is ongoing.
Figure 1 shows the effective area of the RHESSI instrument as a function of energy for the eight active rear segments assuming an isotropic angular distribution of photons. This simulates the average response to TGFs hitting the detectors from random directions. Shown are both the effective area for any interaction in the active detector segments and the effective area for the full capture of the gamma ray energy in the active detector segments. Photons that do not leave all of their energy in the active detector segments are observed to “downscatter,” leaving anywhere from most of their energy in the detectors to only a little. To put the spectral response in the context of TGFs, Figure 2 shows the fraction of observed counts at each energy that result from photons depositing all of their energy in the detectors (fraction of counts in the photopeak) for simulated TGFs at three different altitudes and shows that as the intrinsic photon spectrum gets harder (Figure 2, inset), the fraction of counts in the photopeak becomes dramatically lower at all energies. Atmospheric absorption removes real low-energy photons from the incoming spectrum, so the recorded low-energy spectrum is dominated by downscattered photons.
 The time resolution of the RHESSI data is one binary microsecond, or 2−20 s (0.95 μs), while an absolute offset of +1.8 ms has been added to the data to account for an error in the RHESSI clock. This offset was determined from a single set of serendipitous observations by both the Swift and RHESSI satellites of SGR 1806-20 when it produced a giant flare on 27 December 2004 [Palmer et al., 2005; Boggs et al., 2007]. Since we do not know whether this 1.8 ms offset is constant or varies throughout the mission, we assume that there is still an uncertainty in the absolute timing of the RHESSI instrument of 1 or 2 ms.
3. RHESSI Search Algorithm
 The RHESSI TGF search algorithm currently runs daily as data are downloaded from the satellite. The trigger criteria were initially developed to reject specific types of false triggers (such as cosmic ray showers in the detectors, the satellite passing through the South Atlantic Anomaly, etc) so that the catalog of events is as clean as possible rather than complete. The algorithm operates as follows:
 1. Time series data are collected into 1-ms time bins over a range of 300 ms, summing over all eight rear segments. The background is defined as the average number of counts per millisecond (N) over the current block of 300 ms. A typical value for N is 2 . Since we average over such a long (300 ms) sample of the background, this number is statistically well defined and not subject to large Poisson fluctuations.
 2. A millisecond is considered a TGF candidate if it contains at least 12 σ counts over the background, where σ is approximated by . If a candidate event is found, the following second stage of screening is performed on the individual counts (photons) in the event:
 3. We define the event as a “run” of counts where the gap between one count and the next is less than 300 binary microseconds (286 μs).
 4. The duration of the run, defined by taking the time difference between the first and last counts in the run, is longer than 100 binary microseconds (95 μs). This rejects cosmic ray showers which have durations ≪100 μs, but which may be observed in the electronics to last as long as 50 μs because of large energy deposits in the electronics.
 5. Fewer than half of the counts in the run are coincidence events between two detectors; this screen also helps reject cosmic rays. A coincidence event occurs when a photon interacts in one detector and then interacts in a second detector, leaving a fraction of its energy in each detector. This process occurs at the speed of light, so both of these counts are recorded simultaneously. To recover the initial photon energy, we sum together coincidence events in a single count.
 6. After coincidences are combined into single photon counts there are still more than 17 counts in the run.
 7. Fewer than a quarter of the counts occur in a single detector. This rejects false counts caused by high voltage arcing in any one detector.
 8. N is greater than 1 count per ms. This prevents a false trigger from occurring when the background count rate suddenly increases as the data stream is turned back on (for example, when RHESSI exits the SAA).
 9. The signal count rate, defined as the number of counts in the run divided by the duration of the run, is greater than 4 × N.
 We note that conditions 2, 5, and 8 are partly redundant and that, for TGFs that contain the same number of counts, this algorithm favors TGFs with durations of less than a millisecond because of the size of the time bin used in condition 1. We are in the process of developing new search algorithms that will efficiently search the archival database for TGFs on different time scales.
 During the preparation of this paper we have discovered that our search algorithm does not catch a rare error in the raw data packaging that can cause coincident events to occur nonconsecutively. Several TGFs that were originally published on the public list of TGFs (http://scipp. ucsc.edu/∼dsmith/tgf/) only triggered because the search algorithm did not properly combine coincident counts. Once coincident counts were properly combined, these events fell below our 17 count per TGF trigger threshold (Table 1). In addition there are three events that have a total number of counts very close to the 17 count threshold and also have very long durations. These three events (Table 2) also occur in regions where we do not observe any other TGFs. If these events were real TGFs that occurred just above the noise threshold, then they should occur where we see the most TGFs, rather than where we never see TGFs. We will not include these events in our analysis, but data from these events are available as part of the database.
Table 1. TGFs With Data Errors
Time of Occurrence
24 Sep 2005
17 Aug 2006
29 Aug 2006
14 Nov 2006
Table 2. TGFs Near Threshold
Time of Occurrence
3 Apr 2002
9 Feb 2006
4 Dec 2006
4. RHESSI TGF Catalog
4.1. Overview of Data
 We have collected the data into a publicly available RHESSI TGF catalog. The catalog contains data for 820 TGFs that occurred between March of 2002 and February of 2008. A periodically updated version of the data and their description can be obtained by contacting the authors or at http://scipp.ucsc.edu/∼dsmith/tgflib_public/. Figure 3 shows the location of the RHESSI subsatellite point for each TGF. This map is a multiplication of the true distribution of TGFs with the total instrumental sensitivity and exposure for each location. Figure 4 is a map of the combined sensitivity/exposure produced by inserting artificial TGFs through a month of satellite orbits and seeing how many were identified by our algorithm at each location. The map shows the increased exposure time at the highest altitudes as a dark band (e.g., from the Mediterranean through Japan), the lack of data in the South Atlantic Anomaly, and a loss of sensitivity in the northern and southern decimation zones due both to the decimation itself and the higher level of background in these regions. Figure 5 shows the rate of TGF occurrence per month since the start of the mission and the average background count rate per month for the entire mission.
 After January of 2006, the rate of TGFs per month decreases significantly. This is due to a decrease in detector sensitivity caused by radiation damage to RHESSI's germanium detectors. Figure 5 (bottom) shows the average monthly background count rate. After early 2006 the background rate also starts to decrease as the detectors lose sensitivity because of the radiation damage. In November of 2007 the detectors were annealed in an attempt to recover some sensitivity. The increase in the background count rate seems to indicate that the annealing was successful, but we have not seen a corresponding recovery in the number of observed TGFs.
 We and the RHESSI team are currently working to understand the detector response both during the 2006–2007 damaged regime and in the postanneal era to understand the change in the spectral response of the detector and in order to reoptimize the search algorithm. Figure 5 (bottom) suggests that the effective area of the instrument decreased by roughly a factor of two during 2006–2007. However, the results of the upcoming detector modeling is necessary for a more accurate estimate of the detector effective area. Until we understand the impact of the radiation damage on the spectral response and overall sensitivity of the instrument, we conservatively restrict our spectroscopic analyses to data from before 1 January 2005 (vertical dashed line in Figure 5) and all other analyses to data obtained before 1 January 2006 (vertical dot-dashed line in Figure 5). This leaves 417 TGFs for spectroscopic analyses and 591 TGFs for all other analyses.
4.2. Frequency of Occurrence of TGFs
 To see if a single storm is capable of producing multiple TGFs, we calculate the time between the 591 TGFs that occurred before 1 January 2006 (Figure 6). As a nominal model for the waiting time between events, we take a homogeneous Poisson distribution of events with the probability of waiting time (T) given by (1) and a rate equivalent to the average waiting time between TGFs (λ = one TGF per 2.35 days, or 3380 min). We can then compare the expected number of events in a given time interval for the Poisson process and the number of TGFs actually observed.
 There are 17 TGFs that occur within 2 min of a previous TGF, while only 0.3 events are predicted by a Poisson process. The probability of randomly observing at least 17 events from a Poisson process with a mean of 0.3 events is 10−23. We also find an enhancement at the 96 min orbital period of the RHESSI satellite with 13 TGFs occurring as the satellite passes over the same geographic region while only 5 TGFs are predicted for the Poisson process (vertical dashed line in Figure 6). The probability of observing 13 events from a Poisson process with a mean of 5 is 7 × 10−3. Since it is not uncommon to have thunderstorms with periods of lightning activity that exceed 90 min, we view this as a confirmation of the conclusion that a single storm is capable of producing multiple TGFs, with the satellite flying over the same storm system during its subsequent orbit. At larger time scales, the waiting time between TGFs is well matched by the Poisson process, as expected.
4.3. Pedestal Emission
 Second- to minute-scale enhancement in X-ray count rates have been observed from balloons, aircraft, and ground based observatories in and around thunderstorms, sometimes starting or ending with a lightning strike [McCarthy and Parks, 1985; Eack et al., 1996a, 1996b, 2000; Torii et al., 2002; Tsuchiya et al., 2007]. We explore whether such “pedestal” emission commonly occurs with every TGF and is observable from orbit in the RHESSI data immediately surrounding a TGF. Since the radiation environment changes as RHESSI progresses through its orbit, we will not be able to discriminate weak minute-scale enhancements in the X-ray count rate due to thunderstorms from natural variations in the background. We estimate the background during the TGF by taking a sample of the RHESSI data integrated from 10 to 50 s before each TGF and from 10 to 50 s after each TGF. Some TGFs have dramatic background variations (due to solar flares, the satellite entering or exiting the SAA, or outer belt electrons) that prevent the background from being modeled by linear, quadratic, or cubic models. These TGFs are discarded from the analysis. For the 537 remaining TGFs, we find that quadratic and cubic models do not improve the fit to the background, so we use only the linear model of the background.
 For the second-scale enhancements in the X-ray count rate, we look for an increase in X-ray flux over the predicted background flux in a 100 ms window centered on the TGF. Each TGF provides a small number of counts, so we combine all of the TGFs into a single observation. We do this by sliding a 250 μs window across each TGF to find the region that has the highest number of counts. We use the leading edge of the peak window in each TGF to align the observations. The data from the aligned TGFs are then combined into a single time histogram and the expected background is subtracted (Figure 7). This process artificially smoothes out any temporal structure in the data; see Grefenstette et al.  for a discussion of the time evolution of the RHESSI TGFs. We average the data over the 100 ms pedestal region with a central 5 ms slice removed (vertical dashed lines in Figure 7). When the statistical errors in the photon counts in the pedestal are combined with the uncertainties in the subtracted background fits, we find that for the combined TGF data the average count rate in the pedestal is (1.3 ± 1.9) × 10−3 of the average count rate in the peak bin.
4.4. Distribution of TGF Intensity
Figure 8 shows the distribution of the number of observed counts in the TGFs. We integrate over a region ±5 ms from each TGF as “source” counts and subtract the number of counts expected from the local background as described above to obtain the integrated intensity of the TGF (hereafter, intensity). The minimum intensity is 10.2 counts, the maximum intensity is 86.8 counts, the mean intensity is 27.2 counts, and the median intensity is 24.9 counts. We note that while an event must have 17 counts in the run in order to trigger the search algorithm, some of these counts may be attributed to the background, resulting in a net minimum intensity of less than 17 counts. Events that occur just above the trigger level are more likely to contain a positive statistical fluctuation in the background that allows an event that would normally fall below the trigger threshold to trigger the search algorithm.
 It has been previously suggested that this distribution of events is missing a large number of low-intensity events because of the low sensitivity of RHESSI and the number of counts required to trigger an “event” [Smith et al., 2005]. The distribution of high-intensity events has previously been considered to be representative of the actual distribution of TGF intensities. We no longer consider this to be accurate. From our analysis of dead time (see Appendix A), it is clear that the RHESSI electronics suffer from dead time during the peak emission of a TGF and we do not yet know the maximum possible brightness of a TGF.
5. Statistical Analysis of TGF Spectroscopy
5.1. Inter-TGF Variability
 An easily posed question of the TGF spectroscopy is whether all TGFs are drawn from the same spectrum. If this were true, then the only variation between TGFs would be caused by the undersampling of a single, intrinsic spectrum. The combination of all of the TGFs into an “average” TGF spectrum should then reproduce the underlying spectrum. To explore this, we perform a simple Monte Carlo “bootstrap” in which the number of counts for each TGF is drawn from the combined spectrum of all TGFs. This process is repeated a large number of times, with the mean energy of the counts in each simulated TGF recorded. Figure 9 shows the distributions of the mean energies of both the real TGFs and the simulation. The excess variability among TGFs demonstrates that the spectrum of individual TGFs is more variable than what is obtained by simply undersampling the average TGF spectrum. This is, of course, not surprising since all of the models of TGF production result in a source of bremsstrahlung photons that Compton scatter in the atmosphere and produce spectra that vary with the distance to the source, the depth of the source, and the angular distribution of photons at the source [Østgaard et al., 2008; Hazelton et al., 2009].
5.2. Statistical Variability Among Observables
 Each RHESSI TGF only contributes an average of 27.2 counts, so large numbers of TGFs must be combined to obtain better counting statistics when making comparisons to models. This necessarily results in averaging over many parameters that may affect the spectrum. While some of these are related to the source (e.g., the intrinsic brightness of a TGF and the orientation and geometry of the TGF beam) and some require external sources of information (e.g., the distance from the TGF source to the satellite location), there are some parameters that are already known. Here, we investigate the possible dependence of the TGF spectrum on the observed intensity of a TGF, the geomagnetic and geographic latitude of the satellite while observing the TGF, and the local day or night. In these analyses, we will use only the TGFs that occurred before 1 January 2005 and for which we are able to obtain a good background fit (410 TGFs).
5.2.1. Variation of Spectrum With Intensity
 If all TGFs are identical, then the observed intensity of the TGF should primarily depend on the distance between the satellite and the TGF. We could expect dimmer (distant) TGFs to have a different spectral shape than brighter (closer) TGFs because of the angular dependence of the bremsstrahlung (which tends to lower energies at larger angles from the beaming axis) and because of an increase in the amount of Compton scattering of high-energy photons to lower energies in the atmosphere. Figure 8 shows the distribution of the observed counts in the RHESSI TGFs. We break the data up into “bright” and “dim” sets that each contain roughly half of the TGFs using the median intensity of 24.9 counts per TGF to discriminate between the two sets. Figure 10 presents the spectrum of each set and the difference between the two. The spectrum produced by bremsstrahlung is smooth and lacks any small-scale variability, so any spectral dependence on viewing angle or distance to the source should appear as a systematic change in the spectral shape rather than any point-by-point variability. We use a two-sample chi-square statistic to compare the two spectra and find that there is no statistical difference between them (χ2 of 36.6 with 36 degrees of freedom, reduced χ2 of 1.01, and random probability of obtaining at least the quoted χ2 of 44%). We have run Monte Carlo simulations to test the ability of the two-sample chi-square statistic to distinguish between simulated power laws with slightly different power law indices given the spectral bins that we use and with the counting statistics available in the data. We find that the two-sample chi-square statistic is able to reliably distinguish between changes in the power law index of greater than 0.15. We leave a more detailed analysis of the change in spectrum with distance to another paper [see Hazelton et al., 2009].
5.2.2. Variation With Local Day/Night
 If the TGFs are produced high in the atmosphere (≈50 km), then we might expect to see some spectral variability that corresponds to the change in the ionosphere that occurs between the local day and night. We use the local time reported in the RHESSI catalog to divide the TGFs up into those that occur in the local day (0600–1800 local time, 151 TGFs) and those that occur in the local night (1800–0600 local time, 259 TGFs) and compare the spectra (Figure 11). We find that the spectra are statistically consistent (χ2 of 31.1 with 36 degrees of freedom, reduced χ2 of 0.86, and random probability of occurrence of 70%) and there is no systematic difference between the two spectra.
5.2.3. Variation With Geographic Latitude
 All models of bremsstrahlung production in the atmosphere produce different expected spectra based on the depth of the source region [Dwyer and Smith, 2005; Carlson et al., 2007; Østgaard et al., 2008]. Williams et al.  suggested that the altitude of the tropopause may be a good proxy for the altitude of TGF production since the tropopause represents the maximum vertical extent of most thunderstorms. The height of the tropopause varies with latitude, so we could expect a spectral dependence on latitude. Figure 12 shows the geographic latitude of the RHESSI subsatellite point for all of the TGFs. We break the distribution of TGFs into tropical (<23° latitude, 368 TGFs) and extratropical sets (42 TGFs). Figure 13 shows the spectrum of each set. There is again no systematic difference between the spectra and only a marginal statistical difference (χ2 of 40.1 with 36 degrees of freedom, reduced χ2 of 1.11, and a random probability of occurrence of 29%).
5.2.4. Variation With Geomagnetic Latitude
 If TGFs are high-altitude events (>30 km), then we should expect the electrons producing the bremmstrahlung to spiral around the local geomagnetic field line [Gurevich et al., 1996]. The electromagnetic pulse driven model of TGFs proposed by Inan and Lehtinen  occurs at such altitudes. If this were the case, then the bremsstrahlung would be beamed along the spiral path of the electrons. Much of the bremsstrahlung would then be emitted sideways or downward, with some Compton-scattered back upward to space, softening the spectrum. The resulting spectrum would depend on the dip angle of the magnetic field, and therefore on geomagnetic latitude. For each TGF, we convert the geographic latitude and longitude into a geomagnetic latitude and longitude (Figure 14) and sort the TGFs into an equatorial set (magnetic latitude < 15°, 228 TGFs) and a midlatitude set (182 TGFs) and compare their spectra (Figure 15). We find that there is no statistical difference between the spectra of the two sets (χ2 of 21.4 with 36 degrees of freedom, reduced χ2 of 0.59, and random probability of obtaining at least the quoted χ2 of 97%).
6. Summary and Discussion
 820 TGFs have been identified in the RHESSI archival data by the current search algorithm from March 2002 through February of 2008 (section 4.1). Radiation damage to the detectors resulted in a decrease in the energy resolution after early 2005 and a decrease in the overall sensitivity of the instrument after early 2006. Prior to this, TGFs have been identified from the data at a rate of one every 2.35 days. Work has begun on new algorithms that will search for events on multiple time scales (the first step of the current algorithm). Statistical analyses are separately performed over durations of 100 μs, 300 μs, 1, 3, 10, 30, and 100 ms, with a set of cuts similar to those described earlier but less redundant. Preliminary results for one such search algorithm are shown in Figure 16 for a year's worth of archival data. A significant number of new events are found with positions that correlate to locations where TGFs commonly occur. There are some new events that do not correlate to areas where TGFs are known to occur (for example, the events in Figure 16 that occur at high latitudes) and are probably due to statistical fluctuations in the background. Work on the new algorithms is ongoing.
 Multiple TGFs are observed from the same geographic region, with the second TGF observed either within a few minutes of the first TGF or when the satellite flies over the same region during its subsequent orbit (section 4.2). This provides an interesting implication. The maximum separation between TGFs that occur within a few minutes of each other is 560 km. If we assume that a typical thunderstorm has a cell size on the order of 10 km and that both TGFs are observed from the same storm cell, then we can conclude that most TGFs are observed within 255 km of the thunderstorm and conversely that RHESSI must be able to observe TGFs at a distance of at least 255 km. This is grossly consistent with the findings of Cummer et al.  who found that, when a radio sferic associated with a lightning strike is correlated in time with a TGF, the distance between the location of the sferic and the RHESSI subsatellite point is usually less than 300 km. For the TGFs that occur one orbit after a previous TGF, we find that the minimum distance between the satellite locations when observing each TGF is 705 km, the mean distance is 1780 km, and the maximum distance is 2600 km.
 We have examined maps of lightning activity from the World Wide Lightning Location Network (WWLLN) [Rodger et al., 2006] for a time period of ±20 min from the TGFs separated both by a few minutes and by an orbit. We find that the TGFs that are observed within a few minutes of each other are typically located near an isolated storm system or when a geographically extended region of lightning activity coincides with the orbital path of the spacecraft. For the TGFs that are observed during two successive orbits of the spacecraft, we find that these events are generally observed when the spacecraft overflies two different lightning producing regions (e.g., two active regions of larger system or two independent thunderstorms). We thus adopt the view that TGFs observed within a few minutes of each other are produced by both isolated storms and by extended systems, while the TGFs that are observed during the subsequent orbit are probably produced by large (e.g., mesoscale) systems or are coincidentally observed from independent thunderstorms.
 The background-subtracted pedestal emission has an average value in the 100 ms surrounding a TGF of (1.3 ± 1.9) × 10−3 times the peak emission in the TGF (section 4.3). This suggests that the pedestal emission must be much more than two orders of magnitude below the TGF emission when observed from orbit. Previous instruments that were able to observe pedestal emission from balloons, aircraft, or on the ground may simply have saturated while observing the TGF. Unfortunately, we cannot easily discriminate between multiminute enhancements in X-ray flux due to thunderstorms and variations in the RHESSI background.
 As can be seen in Figure 8, RHESSI TGFs are, on average, isolated events. A majority of the counts in the combined TGF time histogram are contained in the central bin (250 μs) and nearly all of the emission is contained in the central three bins (750 μs). This is in direct contrast to the TGFs observed by BATSE, which frequently either contain several peaks separated by a few milliseconds or have a longer duration. We note that the current RHESSI search algorithm may be missing such events. However, the RHESSI search algorithm will only miss a multiple-peaked event if all of the peaks in the TGF are below the RHESSI trigger threshold. A new RHESSI algorithm that searches for TGFs on multiple time scales may identify a population of fainter BATSE-like events in the RHESSI data.
 The RHESSI electronics are counting at or near their maximum throughput during the peak 50 μs of many of the TGFs (section 4.4 and Appendix A). This implies that we do not yet know the maximum brightness of a TGF or the intrinsic distribution of TGF intensities. An independent measure of the distribution of TGF brightnesses is required to understand the full impact of the dead time. It is clear that neither BATSE nor RHESSI were able to observe the entire dynamic range of TGF brightness. We can imagine that there are two classes of events that RHESSI is unable to trigger on: a dim type as previously mentioned whose incident count rate is not high enough to saturate the electronics; and a short bright type that pushes the RHESSI electronics at maximum throughput (see Figure A3), but with a duration that is too short (<100 μs) to generate enough counts for RHESSI to trigger. Other instruments such as the gamma ray detectors currently flying on the Fermi Gamma ray Space Telescope and AGILE satellites and the detectors proposed to be flown on the SPRITE-SAT, ASIM, and TARANIS satellites may be able to identify the maximum possible brightness of the TGFs, while the upcoming Airborne Detector of Energetic Lightning Emission (ADELE) may be flexible enough to observe the entire dynamic range of TGF emission from an airplane platform.
 The distribution of mean energies of the RHESSI TGFs is more variable than predicted by simply undersampling the average TGF spectrum (section 5.1). This is not surprising, since all models of TGF production predict variations in the TGF spectrum based on both viewing conditions and intrinsic variation in the TGF source parameters.
 There is no systematic or statistical difference between the average spectrum of dim TGFs (integrated intensity less than the median of 24.9 counts per TGF) and the average spectrum of bright TGFs (section 5.2.1). We note that the effect of the dead time is to compress the apparent dynamic range of intensities, so it is possible that a TGF that occurs near the spacecraft may have the same apparent intensity as a TGF that occurs far from the spacecraft. Alternatively, there may be some intrinsic variation in the intensities of TGFs so that there are intrinsically dim TGFs that occur near the spacecraft and extremely bright TGFs that occur far away from the spacecraft. Either or both of these situations are consistent with a lack of systematic variation in the TGF spectrum when sorted by intensity. We will address the variation of the TGF spectrum with distance in another paper [Hazelton et al., 2009].
 There is no systematic or statistical difference between TGFs that are grouped into those that occur during the local day and those that occur during the local night (section 5.2.2). We conclude that the source mechanism for TGFs does not depend on the condition of the ionosphere, which varies dramatically between the local day and local night.
 There is no systematic difference between the spectra of TGFs that are grouped into sets of those near the geomagnetic equator (<15°) and those at geomagnetic midlatitudes (section 5.2.4). This rules out any spectral variation based on the direction of the local geomagnetic field. This is consistent with a low-altitude source of Dwyer and Smith  where the electrons do not spiral around the local geomagnetic field line.
 There is no systematic difference and only a marginal statistical difference between the spectra of TGFs grouped into tropical (<23°) and extratropical TGFs (section 5.2.3). However, Hoinka  has shown that the tropopause varies by geographic location and by season; often the tropopause remains relatively constant in the summer hemisphere up to 30° of latitude. Consequently, we may be comparing TGFs that all occur in regions where the height of the tropopause is the same. We may also find that high-latitude TGFs may be originating from anomalously high thunderstorms. In a future paper we will compare the change in the TGF spectrum with the seasonal variation of the tropopause as well as with an independent measure of the cloud height as measured by other satellites, such as MODIS, AVHRR, or TRMM.
Appendix A:: RHESSI Dead Time
 The RHESSI electronics operate as follows. If the time between two counts in a detector is less than 0.84 μs, then the electronics cannot discriminate between the two counts and a single count is recorded with an energy that corresponds to the sum of the energy of the two original counts. This is typically referred to as “pileup.” If the time between two counts is greater than the pileup window but is less than 5.6μs, then the arrival of the second count contaminates the processing of the first count and both counts are vetoed. It is this double veto that makes the response of the RHESSI electronics differ from traditional paralyzable and nonparalyzable circuits. Finally, if the time between two counts is greater than 5.6 μs but less than 9.6 μs, then the first count is recorded but the second count is vetoed. Figure A1 shows a simulation of the average throughput achieved for a Poisson process with a given incident count rate.
 In operation, the status of the electronics is monitored by a live time counter, which samples the analog electronics at 1 MHz to see whether the electronics are available to process a new count. In post processing, an additional correction to the live time is included that takes into account the double-veto effect. Since RHESSI was designed to observe solar flares that have long durations of high count rates, the accumulated live time is only read out once every second or at a higher cadence when there is a sustained, high count rate in the electronics. To check the validity of our model of the electronics, we have calculated the distribution of waiting times between counts in each detector for an electron precipitation event that has a corrected live time of 48% and compared this to the expected results from our simulation with the same live time (Figure A2).
 We have previously shown that TGFs are bright enough over a short enough period of time that they saturate the BATSE electronics [Grefenstette et al., 2008]. At that time we argued that the RHESSI data are probably not saturated since the waiting time distribution does not contain the signature expected of electronics with a purely nonparalyzable dead time operating at maximum throughput. Our detailed simulation demonstrates that the RHESSI electronics do not, in fact, behave like a purely nonparalyzable system. Unfortunately, the millisecond time scale of TGFs is too short to generate the fast live time record and the 1-s live time average is not useful. Instead, we compare the RHESSI TGFs to the electron precipitation event, in which we know that the RHESSI electronics were operating near their maximum throughput. Figure A3 shows the distribution of peak count rates (in ) during a 50 μs window for the TGF data, the electron precipitation data, and our model of the electronics with 48% live time. The 50 μs windows are selected to maximize the number of counts in the window, which produces count rates higher than the average throughput shown in Figure A1 since it preferentially selects regions with positive fluctuations caused by Poisson statistics. For the TGFs, the peak 50 μs of each flash was chosen, while for the electron precipitation event and simulation the peak 50 μs of each 100 μs interval was chosen. When we normalize all of the curves so that the highest bins (>30 ) match, we find that only 20% of the RHESSI TGFs have peak count rates that are lower than what is expected from the electronics operating at maximum throughput.
 We conclude that during their peak 50 μs most of the RHESSI TGFs provide a higher count rate than the RHESSI electronics are able to process. Because we do not have a measure of the live time, we cannot reconstruct the incident count rate for individual TGFs or the distribution of incident TGF count rates. We do not yet know the maximum possible brightness of a TGF.
 The spectroscopic impact of the instrumental dead time does not appear to be significant. We take a time-dependent simulation of a TGF observed at a moderate distance (150 km) from the TGF and that tracks the change in the modeled spectrum with time due to Compton scattering. We then apply a Monte Carlo that takes into account the spectroscopic effect of the pileup and veto processes. Figure A4 shows the simulated spectrum after it has been convolved with the detector response for peak emission that corresponds to 100% (black), 50% (red), and 25% (blue) live time. Here we are interested in the change in the spectral shape due to the instrumental effects rather than the overall normalization of each of the simulations. As can be seen, there is a slight hardening in the spectrum, with a decrease of a few percent at low energies (below about 500 keV) and an increase of a few percent at high energies (above 2 MeV) for the 50% and 25% live time spectra relative to the 100% live time spectrum. Spectroscopic analyses of averages of many TGFs (such as those in section 5 of this paper) will average over a large range of possible live times, so this effect will be smoothed out in the average spectrum. Conversely, it is extremely unlikely that this effect could mask a real change in the spectrum, since Nature would have to conspire very precisely for this to happen.
 The authors would like to thank Stephen Mende for the suggestion to look for changes in the TGF spectrum that correspond to variations in the ionosphere. We would also like to thank Morris Cohen and Umran Inan for their assistance in finding the raw data error that was causing the TGFs in Table 1 to trigger. The authors would like to thank Joe Dwyer for many useful conversations. We would also like to thank the referees for many helpful and insightful comments.
 Wolfgang Baumjohann thanks Mark McConnell and another reviewer for their assistance in evaluating this paper.