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Constraining the initial properties of Terrestrial Gamma-ray Flashes Ragnhild Schrøder Nisi Dissertation for the degree of Philosophiae Doctor (PhD) Department of Physics and Technology University of Bergen May 2014 2 Preface ii Preface Contents Preface i List of Figures v List of papers ix Acknowledgements xi 1 Introduction 1 2 Observations 2.1 Satellite observations of TGFs . . . . . . . . . . . . . . . . . . . . . 2.1.1 The Burst and Transient Source Experiment . . . . . . . . . . 2.1.2 The Reuven Ramaty High Energy Solar Spectroscopic Imager 2.1.3 Astrorivelatore Gamma a Immagini Leggero . . . . . . . . . 2.1.4 Fermi Gamma-ray Space Telescope . . . . . . . . . . . . . . 2.2 Airborne and ground observations of TGFs . . . . . . . . . . . . . . 2.2.1 Airborne Detector for Energetic Lightning Emissions . . . . . 2.2.2 Detection from ground . . . . . . . . . . . . . . . . . . . . . 2.2.3 Radio waves from TGFs . . . . . . . . . . . . . . . . . . . . 2.2.4 Observability of TGFs by aircraft and balloon . . . . . . . . . 2.3 Observations of lightning . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Low Frequencies . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 High Frequency and Very High Frequency . . . . . . . . . . . 2.3.3 Satellite measurements . . . . . . . . . . . . . . . . . . . . . 2.4 X-rays from lightning and laboratory sparks . . . . . . . . . . . . . . 2.4.1 X-rays from lightning . . . . . . . . . . . . . . . . . . . . . 2.4.2 X-rays from laboratory sparks . . . . . . . . . . . . . . . . . 3 Theories of production 3.1 Relativistic Runaway Electron Avalanche 3.2 Thunderstorms and lightning . . . . . . . 3.2.1 Initiation of lightning . . . . . . . 3.2.2 Streamer and leader process . . . 3.3 The Thermal runaway theory . . . . . . . 3.4 Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 5 7 7 7 7 8 8 8 9 9 9 9 10 10 10 . . . . . . 13 13 15 16 18 20 21 iv 4 Modeling of TGFs 4.1 Photon transport in air . . . . . . . . . . . . 4.2 The bremsstrahlung process . . . . . . . . . 4.2.1 The Born approximation . . . . . . . 4.2.2 The Sommerfelt-Maue wave function 4.2.3 Use in models . . . . . . . . . . . . . CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 25 26 27 28 29 5 Source properties of TGFs 5.1 Space and time distributions . . . . . . . . . . . . . . . . . . 5.1.1 Geographical distribution . . . . . . . . . . . . . . . . 5.1.2 Distance from satellite nadir . . . . . . . . . . . . . . 5.1.3 Annual and diurnal distributions . . . . . . . . . . . . 5.1.4 Duration of TGFs . . . . . . . . . . . . . . . . . . . . 5.1.5 Timing of TGFs . . . . . . . . . . . . . . . . . . . . 5.2 Number of TGFs . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 TGF/lightning . . . . . . . . . . . . . . . . . . . . . 5.2.2 Total global number of TGFs . . . . . . . . . . . . . . 5.2.3 x-ray/spark . . . . . . . . . . . . . . . . . . . . . . . 5.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Altitude distribution . . . . . . . . . . . . . . . . . . . . . . . 5.5 Emission angles of TGF photons . . . . . . . . . . . . . . . . 5.6 Number of initial photons . . . . . . . . . . . . . . . . . . . . 5.7 Number of electrons . . . . . . . . . . . . . . . . . . . . . . 5.8 How the determination of source properties affects the theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 31 31 32 33 33 35 36 36 38 40 40 40 42 43 45 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Introduction to the papers 47 Bibliography 49 Acronyms 61 Nomenclature 63 Scientific results 67 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters . . . . . . 79 6.3 An altitude and distance correction to the initial fluence distribution of TGFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 List of Figures 2.1 2.2 2.3 2.4 An illustration of the two main detector responses to photons hitting the detector when the detector is dead. The top panel shows the time of the incoming photons, the middle panel shows the response of a nonparalyzable detector, and the lower panel shows the response of a paralyzable detector. The red lines mark the photons that are registrered by the detector. The paralyzable detector start a new dead time for photons hitting the detector within the deadtime of a previous photon. This can make the detector dead for long periods of time if new photons are arriving too short after one another. . . . . . . . . . . . . . . . . . . 4 An illustration of the number of measured counts vs true counts in a paralyzable and a nonparalyzable detector. The ideal detector would measure the true number of photons, but the actual detectors measure less than the actual number when the number of photons are more than a few tens in this example. Note that for the paralyzable detector, the measured number of photons can relate to two different numbers of true photons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The dead time of RHESSI as found from Monte Carlo simulations of a TGF detected on May 2. 2005. The duration of the TGF was 362 µ s and the TGF consisted of 30 measured photons. The gray error bars are calculated from repeating the simulation 100 times. The figure shows that the RHESSI instrumentation is mostly able to detect all photons up to around 15 photons per TGF. For higher fluxes of photons RHESSI will be affected by the dead time, and not all photons detected. For this TGF with 30 measured photons, the true number was probably between 35 and 45 photons. This figure is adapted from Østgaard et al. [2012] (Paper 1 of this thesis). . . . . . . . . . . . . . . . . . . . . . . . . . . 6 X-rays from a triggered lightning reported by Dwyer et al. [2004]. The red diamonds are the recorded data, the black curve is the detector response. This shows several µ s-duration bursts of energetic radiation just before the lightning return stroke (t=0). . . . . . . . . . . . . . . . 10 vi LIST OF FIGURES 2.5 Photos of a positive polarity spark using a camera with very high shutter speed at different points during a spark development. The panel at the bottom show the times of the photos, the voltage across the gap (U), the current on the high voltage electrode (IHV ), the current of the ground electrode (IGND ) and the signal from x-rays as detected by a LaBr-detector. The two arrows in the first photo mark the electrode tip (lower arrow) and the streamers created on the top of the electrode disk. The photos show that the x-rays are created just before the streamers from the two electrodes connect. . . . . . . . . . . . . . . . . . . . . . 12 3.1 Friction force for electrons in air at standard surface pressure. If an electron with energy of εth experience an electric field greater than or equal to E it will accelerate to relativistic energy. Eb and a seed electron of ε ≈ 1 MeV is the weakest electric field that can give a runaway electron. The other electric fields in the figure is explained in the text. Figure adapted from Dwyer et al. [2012a] . . . . . . . . . . . . . . . Illustration of the charge structure of thunderstorms adapted from Stolzenburg et al. [1998]. The cloud has a main negative at around 25 °C and a main positive above that. In addition the screening charges create a basic quadrapole charge structure in the updraft region. In the downpour region more layers are present. . . . . . . . . . . . . . . . Measured electric field (solid curve) and integrated voltage (dashed) for a balloon sounding on August 1. 1984. Approximate altitude and polarity of the charge regions of the cloud are shown at the right. This was inferred using a one-dimensional approximation to Gauss law. The figure is adapted from Marshall and Stolzenburg [2001]. . . . . . . . A simulation of the runaway breakdown process from Dwyer [2005]. A positive region is placed on top of the figure, and a negative on the bottom. If this ambient field is larger than Eb that is the limit for runaway breakdown, some electrons will start accelerating towards the positive region. These accelerating charges will create ionization and hence increase the field in a small region. The field will lead to more acceleration and more ionization and hence the process will escalate. In this figure the black arrows depicts the trajectories of the runaway electrons and the electric field strengths at the 1 atmosphere equivalent are shown in colors. In the white region where the electric field is around 1 MV/m a streamer might form if a hydrometeor is present. . . . . . . . . . . . A schematic drawing of the propagation of positive (a) and negative (b) streamers. In front of both streamers, small avalanches of electrons form. For the positive streamer, these avalanches will be attracted towards the streamer tip and the streamer will expand in an almost constant way. For the negative streamer, the avalanches will be repelled from the streamer tip. When the avalanches has created enough ionization in front of the streamer tip, the streamer will jump to this ionized region and thus expand in a step-wise manner. Image credit: Alexander Skeltved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 3.3 3.4 3.5 . 14 . 16 . 17 . 18 . 19 LIST OF FIGURES 3.6 3.7 3.8 4.1 4.2 5.1 5.2 5.3 5.4 vii An illustration of the tip of the streamer, depicting how the surface charge create a region of strong electric field at the tip of the streamer. This field can be large enough to accelerate low energy electrons to keV energies. Image credit: Alexander Skeltved . . . . . . . . . . . . . . . 20 An illustration of the leader tip with the streamer zone. In the streamer zone electrons of keV energies can accelerate to MeV energies [Mallios et al., 2013]. Image credit: Alexander Skeltved . . . . . . . . . . . . . 21 Simulation of the feedback process in an electric field of 750 MV/m over 150 m. Top panel: t < 0.5 µ s, middle panel: t < 2 µ s, lower panel: t < 10 µ s. Black is electrons (1 per 1000 are drawn) and blue is positrons. Figure adapted from Dwyer [2007]. . . . . . . . . . . . . . . 23 Attenuation cross sections for high energy photons in air. At low energies the photoelectric absorption is dominating, at high energies the pair production is dominating and at intermediate energies the attenuation is dominated by the Compton scattering. . . . . . . . . . . . . . . 26 An illustration of the bremsstrahlung process. An electron with momentum p1 is decelerated in the Coulomb field of a nucleus and exit the field with momentum p2 . The nucleus receives the momentum q in the process and the energy lost by the electron is emitted as a photon with energy and direction k. . . . . . . . . . . . . . . . . . . . . . . . 27 The position of The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) nadir at the time of TGFs. The gray areas are the areas within 370 km from the coast. It can be seen that most TGFs occur over land or coastal areas. The figure is adapted from Splitt et al. [2010]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The location of the Fermi nadir and the probable source lightning show that most TGFs are originating from coastal regions even if the satellite is inland or above the ocean. The circles marks the location of the source lightning and the start of the line marks the Fermi nadir. The blue circles are TGFs found from the continuous data collection and the red circles are triggered TGFs. The figure is adapted from Briggs et al. [2013]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The distance between the RHESSI nadir at the time of TGFs and the geolocated lightning from The World Wide Lightning Location Network (WWLLN) for the years 2002-2011. As can be seen the source density is largest close to the satellite nadir. This is as expected as farther distances and more atmosphere between the location of TGF production and the satellite makes more TGFs fall below the detectability threshold of the instrument. . . . . . . . . . . . . . . . . . . . . . . . . . . The diurnal distribution of TGFs from the first RHESSI catalog and the lightning density from LIS/OTD. The boxes indicate the lightning density, the black is oceanic TGFs, the dark gray is inland TGFs and the light gray is the combined land and coastal TGFs. It is clear that at least the land and coastal TGFs follow the same diurnal distribution as lightning. The figure is adapted from Splitt et al. [2010]. . . . . . . . . 32 . 33 . 34 . 35 viii LIST OF FIGURES 5.5 This map is showing how the TGF/lightning ratio, based on RHESSI TGFs, is changing geographically relative to the median ratio. 0 is median ratio, blue is a lower than median TGF/lightning ratio, red is a higher than median ratio. It can be seen that the ratio is significantly higher in America and Asia than in Africa. The full description of the figure can be found in Nisi et al. [2014](Paper 3 of this thesis) . . . . 5.6 Latitudinal difference in tropopause pressure for TGFs occurring in June-July-August and in December-January-February. The lower pressure in DJF is due to a stronger Dobson-Brewer circulation in these months. Figure is from Nisi et al. [2014]. . . . . . . . . . . . . . . . 5.7 Fluence distribution of the first (red) and second (black) RHESSI catalog TGFs. As the new catalog expands the distribution to lower fluences, it is clear that we might just see the tip of the iceberg and are limited by the detection threshold of the instrument. Figure is adapted from Gjesteland et al. [2012]. . . . . . . . . . . . . . . . . . . . . . . 5.8 The measured fluence distribution go the second RHESSI catalog (gray) and the dead-time corrected fluence distribution (black). If the power law shown in the figure is expanded to lower fluxes it is clear that a larger number of events would be expected from the soft (gray) distribution than the hard (black) distribution. Figure is from Østgaard et al. [2012](Paper 1 of this thesis). . . . . . . . . . . . . . . . . . . . 5.9 The photon altitude distribution for a TGF for an initial production altitude of 12 km. The electric field is stretching over an atmospheric depth of 87 g/cm2 which corresponds to around 9.7-12 km at this altitudes. The figure is adapted from Smith et al. [2011a] . . . . . . . . . . . . 5.10 Modeling results of how the angle of observation and the half angle of the emission cone affects the fluence observed at a satellite. a) shows an illustration of the setup, α is the observation angle and θ is the half angle of the emission cone. b) shows the number as a function of the observational angle. The source altitude is put at 15 km. The solid curve is showing how the number change if only considering the reduction in fluence with distance. The dashed-dotted curve is for 60 degrees emission angle, the dashed curve for 40 degrees emission half angle and the dotted curve for 20 degrees emission half angle. It is clear that the number of photons drop significantly (but not to 0) outside the emission cone. All the photons outside the cone is either produced by annihilated positrons or they are Compton scattered away from their initial direction. The figure is adapted from Gjesteland et al. [2011] . 5.11 The fluence distribution of a selection of the second RHESSI catalog TGFs (red) and the fluence distribution of the same selection when corrected for maximum production altitude and distance from the satellite. This shows that the correction change the distribution to a softer distribution, and that it is important to project the fluence back to the source. The figure is adapted from Nisi et al. [2014]. . . . . . . . . . . . . . . . 36 . 37 . 38 . 39 . 42 . 43 . 44 List of papers 1. Østgaard, N., Gjesteland, T., Hansen, R. S., Collier, A. B., and Carlson, B., The true fluence distribution of terrestrial gamma flashes at satellite altitude, Journal of Geophysical Research, 117(A03327), doi:10.1029/2011JA017365, 2012 2. Hansen, R. S., Østgaard, N., Gjesteland, T., and Carlson, B., How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters, Journal of Geophysical Research 118, doi:10.1002/jgra.50143, 2013 3. Nisi, R. S., Østgaard, N., Gjesteland, T., and Collier, A., An altitude and distance correction to the initial fluence distribution of TGFs, Journal of Geophysical Research, 2014 x List of papers Acknowledgements I would like to thank. . . xii Acknowledgements Chapter 1 Introduction In 1991, NASA launched the Compton Gamma Ray Observatory (CGRO) satellite. On board was the Burst and Transient Source Experiment (BATSE), whos goal was to measure cosmic gamma ray bursts. In 1994 Fishman et al. [1994] reported on another phenomenon observed by the instrument. Short bursts of gamma rays with duartions much shorther than the cosmic gamma rays were seen to originate from the Earth. The phenomenon was named Terrestrial Gamma Ray flashes (TGFs). This was the start of the TGF research and 20 years on, the TGFs are still not fully understood. We know that the source of the TGFs are somewhere inside thunderstorms and that they result from a large number of high energy electrons that produce high energy photons through bremsstrahlung. However, we do not know exactly where in the thunderstorm; at what altitude are TGFs produced, and is the production occuring inside or outside of the actual lightning? We do not know how many electrons are actually needed for the production of the TGFs. Furthermore, we do not know the full acceleration process of the electrons. In my work with this PhD, I have mainly worked with establishing the source properties. If we can constrain these further, we will be able to answer more of the questions concerning the production process. One major question is the fluence distribution of the TGFs. Variations in the clouds and in lightning can be expected to create variations in the fluence of TGFs. In paper 1 of this thesis, we investigated how this fluence distribution lookes at satellite altitude. Later, in Paper 3, we adressed how the fluence would change if propagated back to the source. As we do not know the actual source location and altitude of the TGF, this was only possible to do approximately, but the result clearly shows that the fluence change signinficantly when propagated to the source. In Paper 2, we adressed the possibility of doing measurements that would make us able to get more knowlege of the TGF initial properties. We show that measurements made at aircraft and balloon altitudes are heavily affected by the initial source properties, but that care have to be taken to be able to separate the effects of one property change to another. A parallell study that is not yet published is a modelling of the bremsstrahlung process at TGF energies. The bremsstrahlung models that excist are all based on an assumption that we do not know the effect of for TGFs. I want to show how big the error is in order to improve the models and be able to say more about the high energy electrons that creates the TGFs. In this dissertation, I will first present the observations we have of TGFs and connected lightning. Subsequently, I present the two main production theories for TGFs 2 Introduction and explain how they are different. I then present the modelling efforts that I have been involved in before looking closely at the initial source properties of TGFs. I explain what we know and do not know and how new knowledge of the initial source properties will help us solve several of the issues connected to the TGF production. Lastly are my papers and a summary of each of them. Chapter 2 Observations So far, TGFs have mainly been measured by space borne instruments. However, observations have also been made by airborne detectors and more space and airborne instruments are in the planning. The main problem with the data already available, is that almost all the instruments are designed to detect gamma rays from the universe or the sun. These gamma rays have much longer time scales and different energies than TGFs. Very early, a connection between TGFs and lightning was established, which made reliable lightning detection essential. The main measurements and observational methods for TGFs, together with the main instrumentation for lightning detection are presented first in this chapter. In the last section x-rays from lightning and laboratory sparks are discussed. 2.1 Satellite observations of TGFs 2.1.1 The Burst and Transient Source Experiment The Burst and Transient Source Experiment (BATSE) on board the The Compton Gamma-Ray Observatory (CGRO) was the first instrument to detect TGFs [Fishman et al., 1994]. The instrument was designed to study cosmic Gamma-Ray Burst (GRB) and consisted of 8 Sodium Iodide (NaI) detectors of 2000 cm2 each, one on each corner of the satellite. Having the detectors positioned this way allowed for determining the direction of the incoming gamma rays, which is how some gamma rays were found to originate from the Earth. BATSE was sensitive to photon energies between 20 keV and 2 MeV and stored the photons in 4 energy channels (20-50keV, 50-100keV,100300keV and >300keV) [Fishman et al., 1994; Grefenstette et al., 2008]. In the 9 years of the satellites lifetime, it detected 78 TGFs, with each TGF consisting of around 100 photons [Nemiroff et al., 1997]. The large number of photons in each TGF enabled spectral analysis of individual TGFs, which was used to constrain some of the initial conditions of TGFs [Østgaard et al., 2008]. This is described further in Chapter 5. The trigger algorithm had a minimum trigger window of 64 ms, which is much longer than the TGF duration. This means that the instrument only got a significant signal over the background counts for the longest and strongest TGFs [Dwyer et al., 2012a]. As early as in the first paper by Fishman et al. [1994], the connection between TGFs and thunderstorms was established, as TGFs was only detected when the satellite was passing over an area with thunderstorms. 4 Observations Grefenstette et al. [2008] showed that BATSE was heavily affected by dead time. Dead time is the time after a photon hit that the instrument is dead to new photons due to the processing of the first photon. If the time between individual photons are larger than the dead time, the instrument will be able to detect all photons, but if the next photon hit the detector within the dead time, the photon will not be registrerd. In Figure 2.1 the two main types of dead time is illustrated. The top panel shows the time of the incoming photons as red lines. The second panel shows the response of an unparalyzable detector. The black boxes illustrate the dead time, while the red lines are the registrerd photons. In a unparalyzable detector, a photon hitting within the dead time is not counted, but also not affecting the ongoing dead time. The lower panel illustrates a paralyzable detector. A photon that hit the detector within the dead time of this detector will start a new dead time. This may lead to a situation where no new photons can be detected before the time between photons are reduced to a time longer than the dead time. Incomming photons Time Nonparalyzable Dead Live Time Paralyzable Dead Live Time Figure 2.1: An illustration of the two main detector responses to photons hitting the detector when the detector is dead. The top panel shows the time of the incoming photons, the middle panel shows the response of a nonparalyzable detector, and the lower panel shows the response of a paralyzable detector. The red lines mark the photons that are registrered by the detector. The paralyzable detector start a new dead time for photons hitting the detector within the deadtime of a previous photon. This can make the detector dead for long periods of time if new photons are arriving too short after one another. In a nonparalyzable detector, the total dead time is proportional to the measured counts (m), and the number of measured counts is related to the actual counts (n) as n follows: m = 1+n τ , where τ is the dead time [Knoll, 2000, Chap. 4.7]. For a paralyzable detector, the number of measured counts are proportional to the number of true counts and are found to be: m = n × exp(−nτ ) [Knoll, 2000, Chap. 4.7]. An example of measured vs actual counts in a paralyzable and a nonparalyzable detector is shown in Figure 2.2. The figure also shows how, for the paralyzable detector, one measured number of photons can be produced by two different numbers of true photons. BATSE is a paralyzable detector, with high energy photons creating longer dead times than low energy photons [Grefenstette et al., 2008]. Grefenstette et al. [2008] investigated the preflight data of BATSE and found that the dead time can be expressed k as: τ = α ln( k0p ), where α =0.75 µ s is the signal decay time, k p is the energy of the incoming photon and k0 =5.5 keV is the reset level of the detector. This equation shows 5 Id ea l 2.1 Satellite observations of TGFs Nonparalyzable Paralyzable n1 n2 Figure 2.2: An illustration of the number of measured counts vs true counts in a paralyzable and a nonparalyzable detector. The ideal detector would measure the true number of photons, but the actual detectors measure less than the actual number when the number of photons are more than a few tens in this example. Note that for the paralyzable detector, the measured number of photons can relate to two different numbers of true photons. that a TGF with a hard spectrum (many high energy photons) will be most affected by the instrument dead time. 2.1.2 The Reuven Ramaty High Energy Solar Spectroscopic Imager The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite was launched in 2002 to investigate solar flares, and is still operating. The satellite was launched into a low Earth orbit at around 500 km altitude and with an inclination of 38 degrees. This means that the satellite cover most of the tropics and subtropics, excluding most of South America where the back ground radiation is very high due to the South Atlantic Anomaly. The effective area of RHESSI to photons above ∼100 keV was initially ∼200-300 cm2 , but the sensitivity was significantly reduced after radiation damage to the instrument in 2005/2006 [Grefenstette et al., 2009]. Even the original sensitivity is significantly smaller than BATSE, and RHESSI measures typically less than 30 photons per event [Gjesteland et al., 2012]. RHESSI is sensitive to photons with energies from 30 keV to 20 MeV and transmits the data of all individual photons to ground [Smith, 2002]. Because of the transmission of all photon data, there exists two catalogs of RHESSI TGFs from ground search using two different search algorithms. The first was made by Grefenstette et al. [2009] and consists of about 900 TGFs between 2002 and 2011, the second catalog by Gjesteland et al. [2012] use a reduced significance level for a signal to be considered a TGF and consists of ∼2500 6 Observations TGFs from the same period. This means that Gjesteland et al. [2012] get more of the weak TGFs, but at the expense of a higher probability for counting statistical fluctuations as TGFs. The limit that Gjesteland et al. [2012] use is a probability of 10−11 that the signal is a statistical fluctuation and not a TGF. With 1011 search bins per year, this gives one expected false TGF per year. The RHESSI satellite also suffers from dead time. RHESSI is a semi paralyzable detector that is paralyzable if the photons are less than 0.84 µ s apart, and nonparalyzable for photons arriving more than 5.6 µ s and less than 9.6 µ s apart [Grefenstette et al., 2009]. This means that the satellite is paralyzable, but only for fluxes not known to excist in TGFs. Since the RHESSI detectors has a much smaller area than BATSE, RHESSI are rarely paralyzed even if the dead time for paralyzation of RHESSI is longer than for BATSE. Østgaard et al. [2012] did a Monte Carlo simulation of the RHESSI dead time for a TGF detected by RHESSI on May 2. 2005, and found that for up to 15 counts, RHESSI are mostly able to count all photons, while for higher count rates some photons were not registrerd. Figure 2.3 shows the results of the MC modeling by Østgaard et al. [2012], the duration of the TGF was 361 µ s and it consisted of 30 photons. The gray areas are error bars, found by repeating the same simulation 100 times. For this TGF with 30 measured photons, the true number was probably between 35 and 45 photons hitting the detector. Østgaard et al. [2012] is Paper 1 of this thesis. Figure 2.3: The dead time of RHESSI as found from Monte Carlo simulations of a TGF detected on May 2. 2005. The duration of the TGF was 362 µ s and the TGF consisted of 30 measured photons. The gray error bars are calculated from repeating the simulation 100 times. The figure shows that the RHESSI instrumentation is mostly able to detect all photons up to around 15 photons per TGF. For higher fluxes of photons RHESSI will be affected by the dead time, and not all photons detected. For this TGF with 30 measured photons, the true number was probably between 35 and 45 photons. This figure is adapted from Østgaard et al. [2012] (Paper 1 of this thesis). 2.2 Airborne and ground observations of TGFs 7 2.1.3 Astrorivelatore Gamma a Immagini Leggero The Astrorivelatore Gamma a Immagini Leggero (AGILE) is an Italian mission designed to measure gamma rays from the universe. The satellite was launched into a low-Earth orbit with an inclination of only 2.5 degrees, which means that it has a very good cover of the equatorial region. The Mini-Calorimeter (MCAL) measure photons from 350 keV to 100 MeV and have a effective area of around 500 cm2 [Marisaldi et al., 2010a]. This area is aboth 2 times as large as RHESSI, but significantly smaller than BATSE. Between March 2009 and July 2012, AGILE detected 308 TGFs with photon energies up to 30 MeV, each TGF consisting of a few tens of photons [Marisaldi et al., 2014]. It has also been reported signals with individual photon energies up to 100 MeV, but it is unclear if this is from TGFs [Tavani et al., 2011]. 2.1.4 Fermi Gamma-ray Space Telescope The Fermi Gamma-ray Space Telescope (Fermi) is a NASA satellite launched in 2008. The main instrument for detecting TGFs is The Gamma-ray Burst Monitor (GBM). This instrument consists of 2 Bismuth Germanate (BGO) detectors of 200 cm2 each and 12 NaI detectors of about 100 cm2 each and can detect photons between 8 keV and 40 MeV [Meegan et al., 2009]. The TGFs consists of ∼50 or more photons, making spectral analysis of single TGFs possible [Briggs et al., 2013]. During the first years of data collection, Fermi was triggered by a significant increase in the NaI detectors only [Briggs et al., 2010], but later the BGO was also included in the trigger algorithm [Fishman et al., 2011]. This significantly increased the number of TGFs detected as the NaI detectors only measure photons up to a few hundreds of keV and the background is significantly higher for the NaI detectors than for the BGO detectors [Briggs et al., 2013; Fishman et al., 2011]. The Fermi use a trigger window of 16 ms. This is significantly less than BATSE (64 ms), but still 20-100 times larger than the duration of typical TGFs [Briggs et al., 2013]. In 2010 Fermi started downloading continuous data for times and locations known to have a high number of TGFs. Between July 2010 and August 2011, 1036.7 hours of data was transmitted to ground. From a ground search of the data, 423 TGFs were detected [Briggs et al., 2013]. The large number of TGFs with high count rates makes this the most extensive set of TGF measurements so far. 2.2 Airborne and ground observations of TGFs 2.2.1 Airborne Detector for Energetic Lightning Emissions The Airborne Detector for Energetic Lightning Emissions (ADELE) is the only instrument that has detected TGFs from low altitudes. The instrument was mounted on The Gulfstream V jet (GV) operated by The National Center for Atmospheric Research (NCAR). And it was flown for about 37 hours at around 14 km altitude above thunderstorms in Florida and Montana in August-September 2009. During these flights it detected one TGF, and passed closer than 10 km from 1213 individual lightning flashes [Smith et al., 2011a,b]. The significance of these results are discussed in connection to the number of TGFs in section 5.2. 8 Observations 2.2.2 Detection from ground Due to the density of the atmosphere at low altitudes, gamma rays can only travel for very short distances before being attenuated by the air. This means that detectors have to be positioned close to the lightning to detect TGFs on ground. Dwyer [2004] and Dwyer et al. [2012b] report on one TGF each, that is observed from ground. In Dwyer [2004], the source lightning was a rocket triggered lightning. The TGF lasted for about 300 µ s and consisted of 227 photons with individual energies of up to 11 MeV. The gamma rays were observed during the initial stage of the triggered lightning, about 40 ms into the triggering. The timing of the gamma rays made Dwyer [2004] conclude that the gamma rays originated from the inside of the cloud at an altitude of a few km. The TGF recorded by Dwyer et al. [2012b] was from a natural lightning. The TGF consisted of 19 gamma photons, the most energetic photon had an energy of at least 20 MeV. The TGF lasted only 52.7 µ s and occurred during the return stroke of the lightning. The energy spectrum and duration of these two TGFs is what distinguish them from x-rays commonly observed from lightning. 2.2.3 Radio waves from TGFs As the TGFs are produced by a large amount of high energy electrons, these will create a current that emits a electromagnetic pulse. Connaughton et al. [2013] estimated the radiated effect from TGFs and found that especially short TGFs would radiate enough energy to be measured by Very Low Frequency (VLF) receivers. For longer events, they argued that the combined radiated effect from TGFs and lightning might make the probability for observing TGF-producing lightning greater that non-TGF-producing lightning. About the same time as this was published, Østgaard et al. [2013] investigated a RHESSI TGF above Lake Maracaibo and found that the detected VLF signal could probably be related to the TGF electrons. This analysis was made possible by the fact that the TGF producing lightning was detected by an optical signal in addition to VLF. In the next section we will see that also lightning detection is made by radio waves and one have to be extra carful when assigning observed radiowaves to the lightning as it may be produced by the TGF itself. 2.2.4 Observability of TGFs by aircraft and balloon Hansen et al. [2013] (Paper 2 of this thesis) investigated the observability of the TGFs by balloons and aircrafts. The photons from TGFs were modeled by using the Monte Carlo model of photon transport that will be described in section 4.1. The expected measurements from a balloon or aircraft was then estimated by placing a detector area at balloon (35 km) and aircraft (14-20 km) altitudes and at different horizontal distances from the source. At all altitudes, the expected observation was very sensitive to the horizontal distance from the source, the initial altitude and the initial number of source photons. For low observational altitudes, the expected fluence was also very sensitive to the distribution in initial altitude and direction of the initial photons. This result might be useful in the planning of new missions as well as in the analysis of the future observations. 2.3 Observations of lightning 9 2.3 Observations of lightning Lightning creates a large current that emits a powerful electromagnetic pulse that can be used to measure lightning. From ground, this is widely used. From space, large areas can be observed by one single satellite, this is utilized to look for the optical signals from lightning. All the different observational methods have limitations, but can complement each other. 2.3.1 Low Frequencies Electromagnetic waves in the Very Low Frequency (VLF) and Extreme Low Frequency (ELF) range is the ones mainly used for lightning detection. This is because these waves can travel for long distances in the atmosphere with little or no absorption due to the wave guide created between the conducting Earth and the conducting ionosphere. Even at long distances from the lightning, VLF and ELF receivers can detect the electromagnetic wave with little or no distortion. As long as more than three receivers detect the same lightning, the location of the lightning can be determined through triangulation. The World Wide Lightning Location Network (WWLLN) is a global network, covering most of the geographic areas with large numbers of lightning. WWLLN had an overall global efficiency of around 2 % in 2007, increasing to about 6 % in 2009, but with large local variation [Abarca et al., 2010]. The detection efficiency is about two times higher for lightning to the ground than for lightning occurring inside the clouds and the efficiency is much higher for large current discharges than for low current discharges [Abarca et al., 2010; Collier et al., 2011; Connaughton et al., 2010]. Other networks include The National Lightning Detection Network (NLDN) and The Atmospheric Weather Electromagnetic System for Observation, Modeling, and Education (AWESOME) and a detector at Duke University [Cohen et al., 2010a,b; Cummer, 2005; Cummer et al., 2011; Kulak et al., 2012]. Due to the low frequency and long distances, the low frequency networks are not able to determine the altitude of the lightning discharge or the polarity of the lightning. This is possible with higher frequency networks. 2.3.2 High Frequency and Very High Frequency High Frequency (HF) and Very High Frequency (VHF) waves from lightning can only travel short distances in the atmosphere before they are attenuated, but they are less distorted when detected by the receiver. This enables a fairly accurate estimation of the position, current direction, current magnitude and current moment of the lightning. The Los Alamos Spheric Array (LASA) and The Lightning Mapping Array (LMA) have been extensively used for TGF research [Lu et al., 2010; Shao et al., 2010; Stanley et al., 2006]. As the receiver has to be close to the actual lightning, only a very small part of the total amount of lightning is detected by HF-receivers. 2.3.3 Satellite measurements The Lightning Imaging Sensor (LIS) on board The Tropical Rainfall Measuring Mission (TRMM) and The Optical Transient Detector (OTD), which preceded LIS, are 10 Observations optical satellite-carried lightning detectors. Within their field of view these instruments have very good detection efficiency. LIS and OTD can give time, position, duration and approximate intensity of the lightning, but can not say anything about the current direction or magnitude due to the large distance from the lightning [Boccippio et al., 2000; Christian, 2003]. 2.4 X-rays from lightning and laboratory sparks 2.4.1 X-rays from lightning Dwyer et al. [2003] were the first to reliably confirm x-rays from lightning. Before this, for instance Moore et al. [2001] had also measured x-rays coincident with lightnings, but they were not able to fully confirm the lightning as the source of the x-rays. Figure 2.4 shows the x-rays from a lightning reported by Dwyer et al. [2004]. The time 0, is the time of the start of the optical return stroke. The red diamonds are the recorded data, the black line is the detector response. This shows several bursts of x-rays with energies of more than 100 keV, lasting on the order of 1 µ s. The last few pulses before the return stroke saturated the detector, probably because the source of these bursts were closer to the detector [Dwyer et al., 2004]. Figure 2.4: X-rays from a triggered lightning reported by Dwyer et al. [2004]. The red diamonds are the recorded data, the black curve is the detector response. This shows several µ s-duration bursts of energetic radiation just before the lightning return stroke (t=0). Since this discovery, this type of x-rays have been shown to be connected to the stepping process during the initial part of the lightning. It has also been seen to be colocated with the streamer tip ?his will be further discussed when looking at the lightning process in section 3.2.2. 2.4.2 X-rays from laboratory sparks In 2005, Dwyer et al. [2005] discovered that also large laboratory sparks produce short x-ray bursts. They had a 1.5 MV Marx circuit and produced discharges between 1.5 and 2 m long in air at 1 atmosphere pressure. All of the 14 discharges they investigated produced x-rays with energies between 30 and 150 keV. Dwyer et al. [2008] used the same experimental setup and investigated more than 200 sparks. They measured x-rays 2.4 X-rays from lightning and laboratory sparks 11 with individual photon energies of up to 300 keV, in around 70 % of the sparks of negative polarity and in around 10 % of the sparks of positive polarity. Using spherical electrodes with diameters of 12 cm they also excluded the possibility of the electric fields of the electrodes influencing the x-ray production. Later, Kochkin et al. [2012] used a camera with very high shutter speeds to investigate how the spark looked when x-rays were emitted. Figure 2.5 shows photos of a positive polarity spark at different times, together with the x-ray signal from a LaBr detector. The figure shows how the x-rays are created just before the streamers from the two electrodes connect. This is probably because this is the location and time when the electric field is largest. The theory behind the acceleration process will be discussed in section 3.2.2 and 3.3. In these experiments Kochkin et al. [2012] used a Marx generator that could produce up to 1 MeV potential across a gap of approximately 1 m. They measured x-rays with single photon energies of about 200 keV. In a total of almost 1000 sparks they also showed a significant dependence on location of the LaBr detector. In one position they measured x-rays in all the sparks, while in another position the detection rate was down to about 25 %. This experimental setup at Eindhoven University of Technology has also been use to investigate if all sparks create x-rays. This might be important in order to establish the total number of TGFs and will be further discussed in section 5.2. 12 Observations Figure 2.5: Photos of a positive polarity spark using a camera with very high shutter speed at different points during a spark development. The panel at the bottom show the times of the photos, the voltage across the gap (U), the current on the high voltage electrode (IHV ), the current of the ground electrode (IGND ) and the signal from x-rays as detected by a LaBr-detector. The two arrows in the first photo mark the electrode tip (lower arrow) and the streamers created on the top of the electrode disk. The photos show that the x-rays are created just before the streamers from the two electrodes connect. Chapter 3 Theories of production TGFs are recognized as being bremsstrahlung photons produced by relativistic electrons. And it is widely accepted that the electrons are accelerated in an electric field related to thunderclouds. For an electron to create a photon of tens of MeV energy the electron have to be accelerated in an electric field with a potential of at least several tens of MV. In this chapter, a description of the acceleration process will be given, before an overview of thunderstorms and lightning will be presented. Next, the two leading theories of TGF production is introduced. The main differences between the two theories are the location of the accelerating electric field and the origin of the initial electrons. Finally, a discussion of the bremsstrahlung process will be presented. Bremsstrahlung is the process in which the electron decelerate and emits a photon. 3.1 Relativistic Runaway Electron Avalanche The Relativistic Runaway Electron Avalanche (RREA) process is a result of the the friction force in the air changing with energy in combination with electron-electron (Møller) scattering. Figure 3.1 shows the friction force for electrons in air at standard atmospheric pressure. The friction force is increasing with energy up to about 100 eV, before decreasing with energy. This means that if an electron with initial energy εth that is higher than around 100 eV, which is the energy corresponding to the maximum friction force, experience an electric field higher than the corresponding field E, the electron can accelerate to relativistic energies. The initial high energy electron is usually referred to as a seed electron. This process was first described by Wilson [1924] and are known as the Wilson runaway. If a runaway electron collides with another electron, the second electron can receive enough energy to also be in the runaway energy range (ε >εth ) and accelerate to high energies. If this is allowed to continue it will result in an avalanche of relativistic electrons with the number growing exponentially with time. This has been named Relativistic Runaway Electron Avalanche (RREA) and has been extensively discussed by Babich et al. [2007], Dwyer and Smith [2005], Roussel-Dupré et al. [1994] and Roussel-Dupré and Gurevich [1996] among others. The number of electrons accelerated in a uniform field can be expressed as: FRREA = F0 exp(z/λ ) (3.1) 14 Theories of production eEc eE eEk eEst- eEst+ eEth eEb εth Figure 3.1: Friction force for electrons in air at standard surface pressure. If an electron with energy of εth experience an electric field greater than or equal to E it will accelerate to relativistic energy. Eb and a seed electron of ε ≈ 1 MeV is the weakest electric field that can give a runaway electron. The other electric fields in the figure is explained in the text. Figure adapted from Dwyer et al. [2012a] where F0 is the initial number of seed electrons, z is the distance from the start of the avalanche and λ is the avalanche length. Over the entire avalanche region, the number of electrons will become: FRREA = F0 exp(L/λ ) (3.2) where L is the total size of the avalanche region. λ is defined as where the number of initial photons have increased by a factor e [Dwyer et al., 2012a]. Empirically from models, we have λ = 7.3MeV eE−Fd , where Fd is the average energy loss rate for the electrons in the direction of the avalanche [Dwyer, 2003]. The electric field Eb ≈ 2 × 105 V/m in Figure 3.1 is the weakest electric field that can give a runaway electron. To get a RREA the electric field has to be at least Et h= 2.8 × 105 V/m. This is due to the electrons giving off energy to the secondary electrons in the Møller scattering process. When the avalanche has been allowed to work for several avalanche lengths, the energy spectrum of the electrons (runaway electrons per unit energy) in a RREA is given as dF FRREA −ε fre = = exp (3.3) dε 7.3MeV 7.3MeV where ε is the energy of the electron [Dwyer et al., 2012a]. Note that this means that the average energy of the electrons will be 7.3 MeV. 3.2 Thunderstorms and lightning 15 If the electric field is higher than the critical electric field Ec on Figure 3.1, all electrons independent on initial energy can be accelerated to relativistic energies by the electric field. Ec has a sea equivalent value of about 26 MV/m [Moss et al., 2006]. This electric field is much larger than the electric field required to create a breakdown and can thus only exist in a small localized region. 3.2 Thunderstorms and lightning Already in the first report on TGFs by Fishman et al. [1994], the connection to thunderstorms was established . Thunderstorm electrification is a result of strong convection of warm air causing ice crystals present in the cloud to collide with groupels [Saunders, 2008]. In this collision process, water present on the surface of the grouple freeze onto the ice crystal. Due to different growth rate of the particles one of the particles will carry more negative surface charge than the other. In the collision the charge present in the point of contact will distribute equally between the two particles, resulting in the two types of particles carrying a net charge. Which particle that grows fastest and that has the most negative surface charges is depending on the temperature and water content of the air. The transition between the two is about ??. Due to the need for warm and moist air, most lightning occur over land, over regions where there is no desert and in the afternoon local solar time. The main charge configuration in a thundercloud is often described as a tripole with a main positive charged region on top, a main negative charged region below and a small positive region at the bottom. Due to the charge transfer between ice and groupels changing with temperature, the main negative region is usually where the temperature is between -5 °C and -25 °C [Saunders, 2008]. The exact location is determined by the liquid water content of the air. The main positive and main negative charge regions are a direct result of the collisions between the ice and groupels, while the lower positive charge region is a screening layer that develops between the main negative charged region and the neutral atmosphere. An illustration from Stolzenburg et al. [1998] is presented in Figure 3.2, showing that the commonly measured charge structure is much more complex than the simple tripole. Generally, the updraft region has a quadrapole structure with an extra negative screening layer on top in addition to the basic tripole structure, and the downpour region have more layers [Stolzenburg and Marshall, 2008; Stolzenburg et al., 1998]. The measurements of electric fields in thunderstorm are mainly obtained by balloons or aircrafts flying through a thunderstorm. A typical balloon sounding of the electric field and voltage is shown in Figure 3.3. This sounding was reported by Marshall and Stolzenburg [2001]. Using a one-dimensional approximation to Gauss law they also estimated the altitude and polarity of the charge regions, shown on the right side of the figure. The strongest electric fields in a thundercloud is usually around 15×105 V/m and commonly stretches over a couple of km vertically [Stolzenburg and Marshall, 2008; Williams, 2006]. The typical measured potential between the main positive and the main negative region is around 60-80 MV, and a maximum measured potential around 100 MV [Marshall and Stolzenburg, 2001]. The estimated maximum potential available for intra cloud lightning is shown to be slightly higher, at around 130 MV [Marshall and Stolzenburg, 2001]. The maximum available potential for intra- 16 Theories of production Figure 3.2: Illustration of the charge structure of thunderstorms adapted from Stolzenburg et al. [1998]. The cloud has a main negative at around -25 °C and a main positive above that. In addition the screening charges create a basic quadrapole charge structure in the updraft region. In the downpour region more layers are present. cloud lightning is considered to be the potential difference between the nearest relative maxima and minima voltage within the cloud. There are two main types of lightning. The Intra Cloud (IC) lightning is a discharge between charged regions in the cloud or between one cloud and another. The Cloud to Ground (CG) lightning is transferring charge between the thundercloud and the ground. A negative lightning is defined as a breakdown process bringing negative charge downward, positive lightning will bring negative charge upwards. 3.2.1 Initiation of lightning Very little is known about the actual initiation of lightning. The requirement is a region where the electric field is strong enough to ionize the air at a higher rate than the attachment processes for the electrons. This required field is known as the conventional breakdown electric field Ek and has a value of ≈3 MV/m at 1 atmosphere pressure, see Figure 3.1. However, the maximum electric field in a thunderstorm is usually an order of magnitude lower than this, suggesting that other processes are involved as well. The first element of a lightning is the streamer, which is a filamentary discharge propagating as an ionizing wave that represent a common electrical breakdown process at ground level atmospheric pressure [Celestin and Pasko, 2011]. A streamer need an electric field of Ek to be initiated, but the field can be very small in size. All the main lightning initiation theories include the role of the hydrometeors (water droplets and ice crystals). Hydrometeors have a large dielectric constant making them act as conductors in the electric field of a thundercloud, and the hydrometeors will become polarized. The role of water droplets was investigated by Griffiths and Latham [1972], who found that an ambient electric field of about Ek /3 was needed in order to initiate a streamer. 3.2 Thunderstorms and lightning 17 Figure 3.3: Measured electric field (solid curve) and integrated voltage (dashed) for a balloon sounding on August 1. 1984. Approximate altitude and polarity of the charge regions of the cloud are shown at the right. This was inferred using a one-dimensional approximation to Gauss law. The figure is adapted from Marshall and Stolzenburg [2001]. Later, Petersen et al. [2006] showed that ice crystals seems to be more important than the water droplets. Ice crystals can grow much longer than water droplets without breaking up and Foster and Hallett [2002] showed that the ice crystals align with the electric field of the clouds. In this way, the ambient electric field can be much weaker and still initiate streamers. The altitude of lightning initiation also match well with the area with large ice growth, further supporting this theory [Petersen et al., 2006]. After RREA was established, Gurevich et al. [1992] suggested that the secondary ionization of cosmic-ray air showers accelerated through the RREA process could create a small electric field with field strengths above Ek and initiate a streamer. This theory was further developed and discussed by Gurevich et al. [1997] and Gurevich et al. [1999]. The two main problems with this theory is the relative rarity of powerful enough cosmic-ray air showers and the required size of the avalanche to initiate a streamer. Dwyer [2005] proposed yet another theory for the initiation of the streamer. As soon as the electric field in the thundercloud exceeds Eb , some electrons will start to accelerate and create secondary electrons locally. This might then further increase the electric field and hence the acceleration of new electrons. This process was named the runaway breakdown as the process is seen from models to be able to discharge the electric field without optical lightning. Figure 3.4 is adapted from Dwyer [2005] and shows how the process is developing in models. A negative charge region is placed at 18 Theories of production the bottom of the figure, a positive on the top. The black arrows shows the trajectories of runaway electrons. After a period on the order of seconds from the start of the process, the electric field on can reach a field strength of Ek /3. On Figure 3.4 the field on the tip has reached a value of 450 kv/m which corresponds to Ek /3 or 1000 kv/m at 1 atmosphere pressure. This means that in a presence of a hydrometeor, this could initiate a streamer. This was further investigated by Dwyer [2012] and Liu and Dwyer [2013]. Figure 3.4: A simulation of the runaway breakdown process from Dwyer [2005]. A positive region is placed on top of the figure, and a negative on the bottom. If this ambient field is larger than Eb that is the limit for runaway breakdown, some electrons will start accelerating towards the positive region. These accelerating charges will create ionization and hence increase the field in a small region. The field will lead to more acceleration and more ionization and hence the process will escalate. In this figure the black arrows depicts the trajectories of the runaway electrons and the electric field strengths at the 1 atmosphere equivalent are shown in colors. In the white region where the electric field is around 1 MV/m a streamer might form if a hydrometeor is present. 3.2.2 Streamer and leader process After the first initiation of a streamer, the ionizing wave can then propagate in i much smaller field than the initial field needed. This is because the charges accumulating on the streamer tip creates an electric field in front of the streamer, increasing the ionization in this region and leading to a propagation of the ionizing wave. A positive streamer (from a positive charge region) and a negative streamer will propagate differently in the ambient electric field. The processes are illustrated in Figure 3.5 based on 3.2 Thunderstorms and lightning 19 figures from Cooray [2003, Chap. 3.7]. For the positive streamer (a), new avalanches form in the region in front of the streamer tip. Since the streamer tip is positive, the new avalanches will be attracted towards the streamer tip. When the avalanches attach to the streamer tip, the streamer expands. For a negative streamer (b), the new avalanches that form will be repelled away from the streamer tip. First when the new avalanches has created enough ionization in front of the streamer tip, the streamer will attach to the ionized region. In this way the negative streamer propagates in steps and requires a larger ambient electric field in order to propagate. The electric field required for positive streamer propagation is Est+ ≈440 kV/m, while the negative streamer needs an electric field of Est− ≈1200 kV/m to propagate [Moss et al., 2006]. + + + + + + + + + + - + + + -+++++++a) ++ ++ -+- Streamer head ------+ ++ ------+ + + + ++ + ----+++ ++ + +-+ -+ + +--+ ++++++ +-+- ++++--+++ + +++++ + ++-+ ++++ +- +++ + ++ ++ + +++-++ + ++ + + ++ + -+++++ + +++ + +++++ - +++++ ++ + ++ ++ + + -- ---+ ----- + ++++ - ++ + + -----+ ++ -- ++ -----++ + + - -- + -- ++ + -++ +++- ++ ++ ++ + Ea - - - - - - - - - - - - - - - - - - - b) Streamer head - - -+ - ++ -- + - -- + -+ - -- - - -+ - + - -- - -+- -+ - ---- -- ++-+ - +- --------- - + +++ + ++---------- New avalanches Ea Weak conducting channel Expanding streamer + + ++ + + +++ ---+ - - ++ --- + --- -- + + + + + + + + + + Figure 3.5: A schematic drawing of the propagation of positive (a) and negative (b) streamers. In front of both streamers, small avalanches of electrons form. For the positive streamer, these avalanches will be attracted towards the streamer tip and the streamer will expand in an almost constant way. For the negative streamer, the avalanches will be repelled from the streamer tip. When the avalanches has created enough ionization in front of the streamer tip, the streamer will jump to this ionized region and thus expand in a step-wise manner. Image credit: Alexander Skeltved If the streamer channel gets warm enough or if several streamers heat the area, a channel with high conductivity will develop. This is called the leader. In the leader, the conductivity is high enough for electrons to go large distances and more charge can accumulate in the leader head. Because of the much higher charge of the leader head, a leader can propagate in even lower ambient fields than the streamers. The propagation 20 Theories of production of the leader has the same main properties as the streamer, but where the streamers take the same role as the small avalanches as described in connection to streamers. An area in front of the leader will have high enough electric field to sustain streamer propagation and when the streamers create enough conductivity in front, the leader propagate. Since negative leaders repel the streamers, a negative leader will propagate in steps, the same way as for streamers. The leader can propagate over large distances to connect the different charge regions of the clouds and create a breakdown. 3.3 The Thermal runaway theory The Thermal runaway theory is one of the two main theories of TGF production. Thermal runaway is the process in which thermal electrons are accelerated to relativistic runaway electrons. This happens when the electric field is higher than the critical electric field Ec as shown in Figure 3.1. As this field is much larger than the classical breakdown electric field, such electric fields can only exist in a very localized area. Such an area is shown in models to exist just in front of the streamer tips [Moss et al., 2006]. Here, the field can get up to at least 32 MV/m, which is slightly higher than Ec [Moss et al., 2006]. This is illustrated in Figure 3.6. The surface charge on the streamer tip will create a small region with a very strong electric field. Ionisation region +++++ ++ +++ + + + Es Es I l r Figure 3.6: An illustration of the tip of the streamer, depicting how the surface charge create a region of strong electric field at the tip of the streamer. This field can be large enough to accelerate low energy electrons to keV energies. Image credit: Alexander Skeltved Celestin and Pasko [2011] showed that this field could accelerate electrons to energies of tens of keVs. As seen from the friction curve in Figure 3.1, the continued acceleration of the electrons can then be sustained by an electric field on the order of 0.5-1 MV/m. This is on the same order as the electric field needed for the propagation of streamers and are present in the streamer zone around the leader tip. This is illustrated in Figure 3.7. In the streamer zone, the electric field is larger than 1.2 MV/m for a negative leader/streamer. The streamer zone has an available potential of up to 300 MV [Mallios et al., 2013] and can hence accelerate the electrons to energies on the order of what is observed in TGFs. The acceleration and multiplication of electrons 3.4 Feedback 21 through the RREA can continue in the ambient field of the thunderstorm if this field is larger than Eb . In simulations made by Celestin and Pasko [2011], the streamer and leader fields seems to be able to produce the required number and energies of initial electrons without further acceleration and multiplication. E<Ecr Streamer zone E>Ecr Ecr E Expanding leader E ++ + + -+ -+ + + ++- + -+ - + + -+ + ++ + ++- Leader channel Figure 3.7: An illustration of the leader tip with the streamer zone. In the streamer zone electrons of keV energies can accelerate to MeV energies [Mallios et al., 2013]. Image credit: Alexander Skeltved This theory then creates the TGFs from thermal electrons already present in the air and only requires a discharge to develop without any further external input. Laboratory x-rays and x-rays from the stepping process of lightning, seems to be produced by thermal runaway. The negative leader will have the most charged accumulated on the tip just before the stepping occur, which corresponds well with the timing and energies of x-rays observed from lightning Dwyer et al. [2004]. The x-rays from sparks reported by Kochkin et al. [2012], is shown to occur just before the positive and negative streamers connect. At this time, a large potential is squeezed between the two streamers, making this a probable timing for the x-rays to occur. 3.4 Feedback The feedback process was first described in connection to TGFs by Dwyer [2003] and is a development of the RREA. The high energy electrons produced in a RREA creates photons via bremsstrahlung. In the photons interaction with the air, some of the photons go through pair production creating one electron and one positron. If this occurs inside the electric field, the positron will accelerate in the opposite direction of the electrons. If this positron collides with an electron further down in the electric field, the electron can acquire enough energy to become a seed electron, starting a new RREA. This is known as positron feedback. The photons created by the bremsstrahlung can also contribute more directly to the feedback. If the photon is Compton scattered through interaction with the air, it 22 Theories of production might change direction with more than 90 degrees from the direction of the electrons creating it. The photon will then travel backwards in the electric field. If the photon gets absorbed by an electron through photo-absorption, the additional energy acquired by the electron might be enough to make this a new seed electron. If this happens, a new RREA can develop. This is known as photon feedback. Hence the feedback process is a multiplication of RREAs. Generally, the number of relativistic electrons when the feedback process is included is given as: 1 − γn Ff b = FRREA 1−γ (3.4) where FRREA is the number of relativistic electrons created by a single RREA, n is the number of avalanches, and γ is the number of new avalanches created by each avalanche. γ is known as the feedback factor. n is often given as t/τ where t is the time since the start of the feedback process and τ is the time it takes for one photon/positron to go around and start a new avalanche. For E > 350 kV/m, τ is found to be less than 10 µ s, and for E > 500 kV/m, τ is less than 3 µ s [Dwyer, 2003]. From equation 3.4, we see that the equation behave very differently for γ <1 than RREA for γ >1. For γ <1 the number of electrons will converge to Ff b = F1− γ when n → ∞. This means that as long as γ is less than 1, the feedback will add significantly to the number of electrons, but the process will eventually stop even if the electric field is always above the field required for RREA. If γ =1, the equation will give Ff b = nFRREA . This means that the number of electrons will reach a form of steady state where one avalanche create one new avalanche. As long as the electric field stay above Et h as required for the RREA, the number of electrons will increase at a constant rate. γ >1, will lead to an exponential growth of the number of electrons when n → ∞. The number is given as Ff b = FRREA γ n , where the feedback will quickly dominate the process. The value of γ is determined by the strength and size of the electric field. Especially the photon feedback is increasing significantly with larger horizontal size of the electric field [Dwyer et al., 2012a]. This is due to the probability for Compton shattering decreasing with angle, making it much more probable that a photon will shatter to an angle of just over 90 degrees than to shatter to an angle of 180 degrees relative to the vertical. This means that the probability for this photon to be absorbed by an electron inside the electric field is much greater when the horizontal size is large. Figure 3.8 is adapted from Dwyer [2007] and shows a Monte Carlo simulation of the feedback process in an electric field of 750 MV/m over 150 m (approximately 100 MV potential). The top panel is after 0.5 µ s (∼ 1τ ), the second panel is after 2 µ s and the lower panel is after 10 µ s. The black lines are electrons (1 line per 1000 electrons) and the blue lines are positrons. The photons are not drawn on this figure. This shows how quickly the multiplication increase if the electric field is large enough. The only thing that will bring the exponential growth of avalanches to an end is that the electric field is reduced to a level where γ <1. As the avalanches themselves are representing a current and a lot of low energy photons are produced from ionization creating an even larger current, the RREA and feedback process will quickly reduce the electric field back to a stable situation. This discharge of the electric field will produce 3.4 Feedback 23 Figure 3.8: Simulation of the feedback process in an electric field of 750 MV/m over 150 m. Top panel: t < 0.5 µ s, middle panel: t < 2 µ s, lower panel: t < 10 µ s. Black is electrons (1 per 1000 are drawn) and blue is positrons. Figure adapted from Dwyer [2007]. little or no light as no hot channel is present, and has thus been suggested as a form of "dark lightning" [Dwyer and Cummer, 2013]. Models indicate that the time it takes for the feedback process itself to reduce the field so that γ <1 is consistent with the observed durations of TGFs [Dwyer, 2007]. The fact the process is reducing the field also puts a limit on the size/strength of the electric field that can exist in the atmosphere over time [Dwyer, 2003]. The proposed origin of the seed electrons for this process is extensive air showers of cosmic particles from space. The feedback process increases the multiplication of electrons so that fewer seed electrons are required to get the number of photons observed in a TGF. This indicates that the electric field accelerating the electrons is the ambient electric field of the thundercloud and that the seed electrons can be any seed electrons. 24 Theories of production Chapter 4 Modeling of TGFs Direct measurements of the TGFs are hard to acquire, and the production process almost impossible to evaluate without models. The main aim of the models is to use known physical processes to get the same TGF signals as we observe. Because so many different processes are involved and because of the large number of elements to model, most models are only addressing a small part of the full process. Dwyer [2007] has put together many of the elements to a full simulation where the acceleration of electrons are through feedback process. In my work I have used a model for photon transport in air, this model has made us able to understand several features of the TGF observations that are caused by the photon transport through air. This chapter start with the basics of this model, before addressing why the bremsstrahlung process is so important to model correctly and the challenges in doing so. The development of a bremsstrahlung model suitable for TGF modeling is work in progress, and will hopefully give useful insight into TGFs. 4.1 Photon transport in air High energy photons in the air gets attenuated but three main processes: photoelectric absorption, Compton scattering and pair production. Figure 4.1 is a plot of the interaction cross sections for the three processes including the total attenuation cross section. The attenuation is dominated by the photoelectric absorption at low energies, by the pair production at high energies and by Compton scattering at intermediate energies. In photoelectric absorption the photon energy in absorbed by the atoms of the air. In Compton scattering, the photon is experiencing what can be seen as an elastic collision with the atoms. The photon loose some energy to the atom and is continuing with a lower energy and in a different direction. In pair production, the energy of the photon creates one electron and one positron in the interaction with air. The excess energy after the production of the two particles is conserved as kinetic energy of the two particles. The positron will eventually interact with another electron and annihilate. Our code is a Monte Carlo (MC) code, and is described in Østgaard et al. [2008]. A MC code use the probability function for a process to determine if an interaction occur. In our code, we use the attenuation cross sections presented in Figure 4.1 and evaluate the probability in length steps along the photon path. If photoelectric absorption occur, the photon is removed from the simulation. If Compton scattering occur, another MC evaluation is performed to determine the new energy and direction. The new direction 26 Modeling of TGFs Figure 4.1: Attenuation cross sections for high energy photons in air. At low energies the photoelectric absorption is dominating, at high energies the pair production is dominating and at intermediate energies the attenuation is dominated by the Compton scattering. of the photon is highly dependent on the energy transferred to the electron. A small energy loss, generally give a small change in direction, while a large energy loss might give a large change in direction. If pair production occur, the photon is removed from the simulation and replaced by a 511 keV photon, representing the energy released by the annihilation of the positron. The positron is assumed to annihilate at the same position as the pair production and with no time delay. The code was shown to be in good correspondence with results from the GEANT3 package, that is a much used simulation tool developed for high energy physics [Østgaard et al., 2008]. The cross section for attenuation is decreasing with the atmospheric decrees in density at higher altitudes. In the MC-code the attenuation is set to 0 for altitudes above 100 km. This means that when modeling the expected signal at a space craft, no interactions occur above 100 km and the photon will continue with the same direction and energy. This means that from 100 km altitude the photon density will decrease with 1/r2 , where r is the radial distance. The input to the model is between 105 and 107 photons with a position, energy and direction distribution. In paper 2 of this thesis, the energy distribution was kept constant at a 1/energy distribution for all simulations. This is the hardest spectrum that the bremsstrahlung process can produce. Both the directional distributions and the initial positions of the photons was changed between simulations and caused very different results. This is described more in section 5 and in paper 2. 4.2 The bremsstrahlung process The bremsstrahlung process is a very important process in the production of TGFs. In this process, energy from decelerating electrons are emitted as photons. It is the elementary process where the energy from the electric field ultimately end up as gamma rays and TGFs, and for both the suggested theories it is important to describe the process correctly. It is important that the models are able to get both the energy of the photons and electrons right, as well as the direction of the photon and outgoing electron. If the energy and direction of photons are not correct, the input to the modeling of 4.2 The bremsstrahlung process 27 photon transport will be wrong. If the electron energies and direction is not right, further acceleration of the secondary electrons will be wrong. To get the bremsstrahlung process modeled correctly is also important to establish how many high energy photons each high energy electron produce. This will make us able to more accurately estimate the number of high energy electrons that are needed to produce a TGF. This is further described in section 5.7. Bremsstrahlung is a quantum-mechanical process where an electron interacts with the electric field of a nucleus or another electron. The incoming electron is decelerated and loose energy, and the excess energy is emitted as light. The situation is illustrated in Figure 4.2.For relativistic energies, the process is fully described by the Dirac equation (the relativistic wave equation), and the differential cross section (number of interactions per unit time per unit flux of incident particles) is expressed as: d 3σ α ε1 ε2 p2 k = |M|2 4 dk dΩk dΩ p2 (2π ) p1 (4.1) in units of m = c = h̄ = 1. Here, α ≈ 1/137 is the fine structure constant, k is the energy of the photon produced in the process, Ω is the solid angle, p1 and p2 is the momentum of the incoming and outgoing electrons respectively, and ε1 and ε2 is the energy of the incoming and outgoing electrons. |M| is the matrix element for the electron transition 1→2 of the Hamiltonian of the electron in the interaction of a radiation field. This matrix element depends on the two wave functions of the incoming and outgoing electrons, the distance the electron pass from the charge, the polarization vector, and the Pauli spin matrix [Haug and Nakel, 2004]. Also, note that the directions of the photon and the outgoing electron is not restricted by the kinematics as the nucleus can take any recoil momentum even if the received energy is usually neglectable [Haug and Nakel, 2004]. This makes the cross section a triple differential over the photon energy, the photon direction and the direction of the outgoing electron. When including the incoming electron energy, it becomes a quadruple differential. p1 k q p2 Figure 4.2: An illustration of the bremsstrahlung process. An electron with momentum p1 is decelerated in the Coulomb field of a nucleus and exit the field with momentum p2 . The nucleus receives the momentum q in the process and the energy lost by the electron is emitted as a photon with energy and direction k. This equation is not possible to solve in a closed form and one or more assumptions has to be made in order to solve the equation. 4.2.1 The Born approximation The most common assumption is the Born approximation. When applying this approximation one includes only the interaction between the wave function of the incoming 28 Modeling of TGFs electron and the nuclear field of the particle [Nakel, 1994]. For a first order perturbation in a Coulomb field this results in the Bethe-Heitler formula: α Z 2 r02 p2 d 3 σb = dk dΩk dΩ p2 π 2 kp1 q4 {( )2 2ε2 2ε1 p1 × k − p2 × k D1 D2 ( ) } p2 × k 2 2k2 2 p1 × k 2 −q − + (q × k) (4.2) D1 D2 D1 D2 where Z is the atomic number of the target nucleus, D1 = 2(ε1 k − p1 · k, D2 = 2(ε2 k − p2 · k and q is the recoil momentum. The Born approximation is valid for αβZ ≪ 1 and αβZ ≪ 1, where β1 and β2 are the 1 2 velocities of the incoming and outgoing electrons in units of the light velocity [Haug and Nakel, 2004]. This condition is satisfied for low atomic numbers, and as long as both the incoming and outgoing electrons are relativistic. However, the condition is not satisfied at the short wave limit where almost all the energy of the electron is transferred into the photon and the energy of the outgoing electron get close to 0. From equation 4.2, we see that the cross section goes to 0 as p2 → 0 when using the Born approximation. But the exact point-Coulomb wave function included in the Dirac equation is −1/2 not finite and diverges as p2 as p2 → 0, leading to a finite cross section [Haug and Nakel, 2004]. A correction factor, named the Elwert factor, was introduced by Elwert [1939]: a2 1 − exp(−2π a1 ) FE = (4.3) a1 1 − exp(−2π a2 where a1 = αβZ and a2 = αβZ . On the short wave limit, where p1 ≈ p2 , FE ≈1, while the 1 2 factor a2 compensate for p2 when p2 → 0. Commonly other correction factors are added to the Bethe-Heitler formula to account for the screening by the electrons around the nucleus Haug and Nakel [2004]; Koch and Motz [1959]. Both the screening and the ad-hoc solution to the problem with the high energy limit are important factors for TGF modeling. Especially the problems at high energies. If the cross section used in models are too low at the high energy limit, the model will suggest that TGFs require more high energy electrons that what is true. If the cross section is too high, the model will give too few high energy electrons. As this numbers are important to differentiate between the two theories, more focus should be put on the bremsstrahlung modeling. 4.2.2 The Sommerfelt-Maue wave function Another approach to solve the Dirac equation is the Sommerfelt-Maue wave function Elwert and Haug [1969]. This allows for applying more than one of the Matrix elements of equation 4.1 [Roche et al., 1972], and is valid at all energies for low atomic numbers where α Z ≪ 1 [Haug, 2008]. Haug [2008], brought this one step further by including the full screening. As the Coulomb and the screening is independent of each other and hence additive Olsen et al. [1957], the true screened cross section can be 4.2 The bremsstrahlung process 29 written as: ( d 2σ dk dΩk )screened exact ( d 2σ ≈ dk dΩk )unscreened [( 2 )screened ( 2 )unscreened ] d σ d σ + − dk dΩk Born dk dΩk Born exact (4.4) where the unscreened, exact cross section is the cross section from Roche et al. [1972], the Born approximated cross sections are from Fronsdal and Uberall [1958]. The same additive property is valid for d σ /dk [Haug, 2008]. Haug [2008] give the full triple cross section, which is possible to integrate numerically. For TGF research, this will be a much more accurate approach, avoiding the problems at the high energy limit. To do an implementation of this, to use for TGF modeling is work in progress and will hopefully give interesting and important results. 4.2.3 Use in models Seltzer and Berger [1985] and Seltzer and Berger [1986] used many of the available formulas at the time and made a big matrix of cross sections. The cross sections that are valid for different energies and atomic numbers were calculated and an interpolation was made where no formulas were valid. For relativistic energies and low atomic numbers, they used the Davies, Bethe, Maximon and Olsen (DBMO) function, the Bethe-Heitler and other formulas, all using the Born approximation, and included the short wave limit corrections by Elwert [1939] and several screening corrections. Dwyer [2007] made a full simulation of the TGF process. To calculate the bremsstrahlung cross sections, he used a standard Born approximation with a form function to account for screening and a high energy limit correction. Lehtinen et al. [1996] also used the Born approximation to calculate the bremsstrahlung in his Monte Carlo simulation. Both the Bethe-Heitler and the Sommerfelt-Maue wave functions are triple differential equations and are assuming that no energy is transferred to the nucleus. It is differentiated in photon energy, direction of photon and direction of outgoing electron. The double and single differentials are usually found by numerical integration. Köhn and Ebert [2014] found an analytical expression for the double and single differential of the Bethe-Heitler equation. Seltzer and Berger [1985] only give the single differential and in a model their matrix will have to be differentiated twice to acquire the electron and photon direction after interaction. 30 Modeling of TGFs Chapter 5 Source properties of TGFs Ever since the first discovery of TGFs, establishing the source properties of TGFs has been one of the basic questions. Some constraints on the properties are established, but to confine it even further is limited by the number of measurements. One problem is that changes in several different properties might give the same expected measurement. For instance, the seemingly wide beam configuration showing in the accumulated RHESSI spectrum, might equally well be a result of an accumulation of beamed TGFs with different initial angle to the vertical. To establish the initial properties are very important in order to constrain the production theories. In the streamer/leader theory, every lightning should be producing a TGF even if some of the TGFs are too weak to reach our satellites in space. According to the feedback theory, only the thunderstorms with the highest electric fields are producing TGFs. This means that establishing the ratio of TGF to lighting might differentiate between the two theories. The three papers included in this thesis are all addressing the source properties of the TGFs. Paper 1, looks at how the fluence distribution is at satellite altitude and use this to address the question on the ratio of TGF to lightning. Paper 2 estimate the number of photons in a average RHESSI TGF and use this to look at how balloons and aircraft observations can be utilized to constrain the source properties further. Paper 3, is a development of paper 1. This paper look at how the fluence distribution at the source is different from the fluence distribution at satellite altitude. In this chapter I present the known constraints on the source properties of TGFs. At the end of the chapter I will also discuss how the determination of the initial source properties affect the theories presented in chapter 3. 5.1 Space and time distributions 5.1.1 Geographical distribution Already in the first report on TGFs by Fishman et al. [1994], the close similarity between the geographical distributions of lightning and of TGFs were noted. Later observations from RHESSI, AGILE and Fermi have all confirmed this Briggs et al. [2013]; Fuschino et al. [2011]; Gjesteland et al. [2012]; Smith et al. [2005]. This means that most lightning happen over land or coastal areas where the convective energy is high and thunderstorms more easily develop. Figure 5.1 is adapted from Splitt et al. [2010] and shows the location of the satellite nadir for TGFs between 2002 and 2007 from the 32 Source properties of TGFs first RHESSI catalog by Grefenstette et al. [2008]. The figure depicts the coastal areas in gray, coastal areas are defined as areas within 370 km from any shoreline. Figure 5.1: The position of RHESSI nadir at the time of TGFs. The gray areas are the areas within 370 km from the coast. It can be seen that most TGFs occur over land or coastal areas. The figure is adapted from Splitt et al. [2010]. When using WWLLN to geolocate the lightning that are the probable source of the TGF, it is also clear that the source lightning is often shifted towards coastal areas relative to the satellite nadir especially in America and Asia [Briggs et al., 2013; Nisi et al., 2014]. This is shown in Figure 5.2, which is adapted from Briggs et al. [2013]. The figure shows the WWLLN located spheric of the probable TGF source lightning as circles and the start of the lines mark the location of Fermi nadir. 5.1.2 Distance from satellite nadir Due to BATSEs ability to determine the direction of the TGFs, the position of these events could be found directly. With all the other instruments, another method is required to locate the source. The method mainly used is to locate the lightning most closely connected in time and space using VLF or HF wave signals from lightning. As the VLF networks have a low detection rate (<10 % globally [Abarca et al., 2010; Collier et al., 2011; Connaughton et al., 2010]) and the satellite spend very little time above HF networks, only about 20-35 % of TGFs have connected geolocated lightnings [Briggs et al., 2013; Collier et al., 2011]. Where the geolocated lightning or position of TGF source is available, the distance from the source is usually within 300 km of the satellite nadir, but with some out to a distance of 8-900 km [Briggs et al., 2013; Collier et al., 2011; Fishman et al., 1994; Hazelton et al., 2009; Nisi et al., 2014]. Figure 5.3 show the distance between the RHESSI nadir and the geolocated lightning from WWLLN for the second RHESSI catalog for the years 2002-2011. The set consists of a total of 265 TGFs and the figure is adapted from Nisi et al. [2014]. The figure shows that the density of source lightning is largest close to the satellite nadir. This is as expected, as the TGFs originating from larger distances go through more air and 5.1 Space and time distributions 33 Figure 5.2: The location of the Fermi nadir and the probable source lightning show that most TGFs are originating from coastal regions even if the satellite is inland or above the ocean. The circles marks the location of the source lightning and the start of the line marks the Fermi nadir. The blue circles are TGFs found from the continuous data collection and the red circles are triggered TGFs. The figure is adapted from Briggs et al. [2013]. are hence more attenuated. The intensity of the TGFs are also reduced by the 1/R2 effect, and hence a larger portion of the TGFs from larger distances will fall under the detection threshold of the instrument. The greater loss of intensity for TGFs from large distances is the main reason for doing the distance correction of the fluence when searching for the initial source fluence that is the main purpose of paper 3 of this thesis. Briggs et al. [2013] argue that the density is almost constant out to a distance of 300 km from nadir before falling off. In Figure 5.3 we can not see any such effect. 5.1.3 Annual and diurnal distributions The annual and diurnal TGF distributions also follow the lightning distributions closely. Most TGFs occur in the summer and early fall season and in the afternoon local solar time [Splitt et al., 2010]. It is the available convection energy that are the main driver of these variations. In summer and early fall and in the afternoon, the sun has been heating the surface to a level where the thunderstorms are more likely to occur. Figure 5.4 shows the diurnal pattern of the first RHESSI catalog TGFs and lightning rates from LIS/OTD. The boxes are the lightning measurements, the black columns are the oceanic TGFs, the dark gray columns are the TGFs from inland regions and the light gray columns are for the combination of land and coastal TGFs. It is clear that the diurnal distribution of TGFs follows about the same pattern as the lightning. The oceanic TGFs looks like they might follow a different distribution, but the number of events are small (39 events). The figure is adapted from Splitt et al. [2010]. 5.1.4 Duration of TGFs Table 5.1.4, list the TGF duration as determined from satellite data. The first TGFs from BATSE had a mean duration of around 2 ms [Nemiroff et al., 1997]. It was also noticed that the TGFs from further distances had longer durations. 34 Source properties of TGFs Figure 5.3: The distance between the RHESSI nadir at the time of TGFs and the geolocated lightning from WWLLN for the years 2002-2011. As can be seen the source density is largest close to the satellite nadir. This is as expected as farther distances and more atmosphere between the location of TGF production and the satellite makes more TGFs fall below the detectability threshold of the instrument. Satellite BATSE Fermi trigger Fermi continuous RHESSI Mean duration 2 ms 0.1 ms 0.3 ms 0.3 ms Duration definition Subjectively from light curve t5 0 t9 0 2σ Gaussian Reference Nemiroff et al. [1997] Fishman et al. [2011] Briggs et al. [2013] Table 5.1: The duration of TGFs as measured by different satellites. Note that the definition of duration is different between different papers. The duration is highly dependent on the trigger/selection criteria of the TGFs. This was found to be due to the Compton scattered photons arriving later than the initial photons, prolonging the measurements of the TGF [Celestin and Pasko, 2012; Feng et al., 2002; Grefenstette et al., 2008; Østgaard et al., 2008]. In subsequent satellite experiments, the duration of TGFs are found to be significantly shorter. This is mainly due to the trigger or selection criteria for TGFs at the different instruments. Since BATSE is having a trigger time of 64 ms, only long and powerful TGFs will produce a significant signal relative to the background. For RHESSI and Fermi where all the data are downloaded, using shorter search bin widths makes one able to find shorter events. In the second RHESSI catalog, the mean duration of TGFs (2 σ Gaussian) is around 0.3 ms. The mean duration (t90 value) for Fermi events is also around 0.3 ms [Briggs et al., 2013]. In the search of the RHESSI data set, all events shorter than 0.1 ms is left out due to the high probability of this being a cosmic ray [Gjesteland et al., 2012]. In the Fermi data, Briggs et al. [2013] notes that the shorter events are highly affected by dead time. Both these indicate that the actual mean duration might be shorter. The production process of TGFs is creating a large number of high energy photons in a short period of time, making the number of photons and the duration important in 5.1 Space and time distributions 35 Figure 5.4: The diurnal distribution of TGFs from the first RHESSI catalog and the lightning density from LIS/OTD. The boxes indicate the lightning density, the black is oceanic TGFs, the dark gray is inland TGFs and the light gray is the combined land and coastal TGFs. It is clear that at least the land and coastal TGFs follow the same diurnal distribution as lightning. The figure is adapted from Splitt et al. [2010]. order to establish the production theory. As noted for the BATSE TGFs, the observed duration for TGFs at large distances will be elongated compared to the actual duration. Also the ability of the instrument to detect short events creates an uncertainty about the actual duration of a TGF. 5.1.5 Timing of TGFs The TGF duration is on the order of 0.1 ms, while the duration of lightning is of the order of 100 ms. Thus, determining when during the lightning process a TGF occur will be important in order to develop the production theories further. The RHESSI instrument, that have been most extensively used, have a problem with the timing [Grefenstette et al., 2008]. From a cosmic gamma ray burst, this error was estimated to be around 2 ms [Grefenstette et al., 2008], but whether this error is constant or varying with time is not known. The results from Collier et al. [2011] indicate a systematic error. Nevertheless, Lu et al. [2010] and Cummer et al. [2011] was able to establish that the TGF is produced in the initial phase of the lightning. Østgaard et al. [2013] found one RHESSI TGF over lake Maracaibo with simultaneous optical measurements from LIS and VLF signals from both WWLLN and the network in Duke. They concluded that the TGF were originating from an IC lightning and from the beginning of the lightning flash. As was discussed in section 2.2.3, one should be careful when assigning a VLF signal to the lightning as it might be the TGF electrons that are creating the signal [Connaughton et al., 2013; Østgaard et al., 2013]. In this respect, the result from Østgaard et al. [2013] is a much stronger result. 36 Source properties of TGFs 5.2 Number of TGFs 5.2.1 TGF/lightning It is still not known if all lightning produce TGFs or if only a specific type of lightning create TGFs. Also, if only some lightning produce TGFs what are the special properties these lightnings have in order for those lightnings only to produce TGFs. Cummer [2005] was one of the first to connect TGFs to a specific type of lightning. Using a network of VLF receivers at Duke University they found 26 TGFs that were all connected to positive IC lightning (intra-cloud lightning transporting negative charges upwards). Later, the same has been reported by several studies [Lu et al., 2010; Østgaard et al., 2013; Shao et al., 2010; Stanley et al., 2006]. The reason for the observed TGFs to be connected to +IC lightning might be an effect of the altitude of IC lightning being high compared to CG lightning, making only the TGFs from IC lightning reach space. This in combination with the positive polarity creating TGFs upwards while the negative lighting produce TGFs downwards (in the direction of the transport of negative charges), making only the TGFs from positive IC lightning visible from space. That means that these studies do not exclude the possibility of TGFs being produced in all lightning, as there might exist TGFs that are not possible to observe from space either because they are to weak or because of the TGF developing in the wrong direction. The observed TGF/lightning ratio is seen to change in both space and time. Figure 5.5 show how the TGF/lightning ratio change geographically based on LIS lightning and RHESSI TGFs. 0 is the median ratio, blue colors is a smaller than median ratio, red is higher than median ratio. The figure has taking into account the changes in tropopause altitude (transmission of gamma rays) in time and location. The figure is fully described in Nisi et al. [2014] (Paper 3 of this thesis). It is clear from the figure that the ratio is significantly smaller in Africa than in Asia and America. The same geographical difference is also found in Briggs et al. [2013], using the Fermi TGF measurements. The explanation for the differences is not yet known. Figure 5.5: This map is showing how the TGF/lightning ratio, based on RHESSI TGFs, is changing geographically relative to the median ratio. 0 is median ratio, blue is a lower than median TGF/lightning ratio, red is a higher than median ratio. It can be seen that the ratio is significantly higher in America and Asia than in Africa. The full description of the figure can be found in Nisi et al. [2014](Paper 3 of this thesis) Splitt et al. [2010] show that the TGF/lightning ratio has a diurnal dependence as well. Just after midnight local solar time the ratio can be about 30% higher than average and around mid day the ratio can be as small as 50% less than average. 5.2 Number of TGFs 37 The ratio are probably also having an annual dependence as the tropopause has an annual dependence and thunderstorm tops are mainly following the altitude of the tropopause. In the subtropics and higher latitudes the annual variability is mainly due to the difference in sunlight in summer and winter. The tropopause in the tropics are generally not changing much with latitude or hemisphere, but the tropopause pressure is shown to have an annual pattern with higher pressures in June, July and August (JJA) than in December, January and February (DJF) [Reid and Gage, 1996]. This variation is due to a stronger Brewer-Dobson circulation in the north subtropics winter (DJF) than in the south subtropics winter (JJA), due to more land masses in the north and the topography of these land masses [Fueglistaler et al., 2009]. Since lightning and TGFs mainly occur in local summer, this means that most TGFs in the north will occur in the months when the tropopause pressure is high (JJA), and the TGFs in the south will occur when the tropopause pressure is lower (DJF). The tropopause pressure for the time and place of TGFs is shown in Figure 5.6, which demonstrates that the tropopause pressure for TGFs in JJA is 10-15 hPa higher than in DJF between -20 and 20 degrees latitude. Lower tropopause pressure indicate higher altitudes, with a difference of around 25 hPa being about 1 km altitude difference at these heights. The method used for finding the tropopause altitude is described in Paper 3. These results means that we can expect the measured TGF-to-lightning ratio to be smaller in summer (JJA) than in winter (DJF), due to an easier escape of the gamma rays from the atmosphere during December, January and February. Figure 5.6: Latitudinal difference in tropopause pressure for TGFs occurring in June-JulyAugust and in December-January-February. The lower pressure in DJF is due to a stronger Dobson-Brewer circulation in these months. Figure is from Nisi et al. [2014]. The ratio detected by instruments are of course also depending on properties like energy threshold and efficiency of the instrument. Based on the RHESSI data, Østgaard et al. [2012] found the average ratio of RHESSI TGFs/lightning to be 1 × 10−4 . Briggs et al. [2013] found the average Fermi TGF/lightning ratio to be 3.8 × 10−4 . The 38 Source properties of TGFs differences can be explained by differences in instrumentation and search methods. 5.2.2 Total global number of TGFs The total number of TGFs is also not straight forward as no-one knows how the fluence distribution looks at below the threshold for detection of the instruments. Figure 5.7 is adapted from Gjesteland et al. [2012] and shows how the new search algorithm used in the second RHESSI catalog expanded the fluence distribution to lower numbers. The red curve shows the first catalog TGFs and the black curve shows the second catalog, but what happens at even lower fluences? Figure 5.7: Fluence distribution of the first (red) and second (black) RHESSI catalog TGFs. As the new catalog expands the distribution to lower fluences, it is clear that we might just see the tip of the iceberg and are limited by the detection threshold of the instrument. Figure is adapted from Gjesteland et al. [2012]. If the distribution has a sharp cut off at the low end it means that even with better detectors, we will not detect more TGFs. If there is no such cut of, it means that there are a lot of TGFs below the detection threshold. Somewhere in between would be a roll off. If there is a sharp cut off at low fluences that means that there must be a sharp lower limit to the number of photons/electrons that can exist in a TGF, this will be further discussed in section 5.6 Another question is how quickly the number of events increase with decreasing fluence. If there is a slow increase, we are seeing a larger portion of the TGFs than if there is a large increase. Figure 5.8 shows the fluence distribution as measured by RHESSI in gray and the dead-time corrected fluence distribution in black. If the fitted power laws were expanded to lower fluences, we would expect a lower number of new events with the dead-time corrected distribution than with the measured distribution. On the basis of the instrument detection threshold, several numbers are presented in literature. These are summarized in table 5.2.2. Carlson et al. [2009] and Smith et al. [2010] both used the RHESSI measurements, but different methods to estimate the total number of events. 5.2 Number of TGFs 39 Figure 5.8: The measured fluence distribution go the second RHESSI catalog (gray) and the dead-time corrected fluence distribution (black). If the power law shown in the figure is expanded to lower fluxes it is clear that a larger number of events would be expected from the soft (gray) distribution than the hard (black) distribution. Figure is from Østgaard et al. [2012](Paper 1 of this thesis). Satellite RHESSI RHESSI AGILE Fermi RHESSI and ADELE RHESSI, Fermi and ADELE Number of TGFs per year 2 × 104 ≥ 5 × 105 8 × 104 -2 × 105 4 × 105 5 × 106 2 × 107 Reference Smith et al. [2010] Carlson et al. [2009] Fuschino et al. [2011] Briggs et al. [2013] Smith et al. [2011b] Østgaard et al. [2012] Table 5.2: Estimated global number of TGFs above the detection threshold and within the orbit of the instruments as presented in the literature. The ADELE airborne instrument has a significantly lower threshold than the other instruments, but with very limited time in the air and only one TGF observation the numbers will have a large uncertainty. Based on the low number of detected TGFs Smith et al. [2011a] concluded that TGFs are a much more rare event than previously thought. The assumptions made to reach this conclusion was partly questioned by Hansen et al. [2013] and Østgaard et al. [2012], and is discussed in Paper 2 of this thesis. Using the one detection and the non-detection of ADELE, Smith et al. [2011b] find a number of 5 × 106 TGFs per year with an error estimate of up to an order of magnitude. Østgaard et al. [2012] (Paper 1 of this thesis) used both RHESSI and Fermi in addition to ADELE. They used the fluence distribution of both RHESSI and Fermi (corrected for orbit and efficiency to be comparable) and the low detection rate of ADELE. They argued that the fluence distributions has a roll off at low fluences and also that it is a reasonable probability of ADELE not detecting more TGFs. Using this they concluded that the global number of TGFs within +/- 38 degrees latitude and above 5/600 of the RHESSI threshold would be at least 2 × 107 , and that the possibility of all lightning producing TGFs could not be ruled out. 40 Source properties of TGFs 5.2.3 x-ray/spark If TGFs are produced by the thermal runaway, x-rays from sparks and lightning might be a low flux and low energy TGF. This has encouraged the search for x-rays in sparks. In different experiments by Dwyer et al. [2005], Dwyer et al. [2008] and Kochkin et al. [2012], up to 70 % of the sparks have been seen to produce x-rays, with no observable difference between x-ray producing sparks and non-producing sparks. The question is if all sparks actually produce x-rays, but that the x-rays are highly directional. If so, the reason for the non-detection will be that the detectors were outside of the region of x-rays. With production through thermal runaway this is not unthinkable. In Eindhoven in January 2013 we set up several detectors in different configurations around a spark generator and produced more than 1000 sparks. The analysis of these sparks is ongoing, and the aim is to look for directionality of the x-rays. Photo...? 5.3 Energy The first observations from BATSE suggested that the phenomenon was energetic, but all photons with energies larger than 300 keV was stored in one energy channel and it was not possible to figure out how high energies that could be present in the TGFs [Fishman et al., 1994]. The data from the RHESSI satellite confirmed the high energies and found photons with energies of at least 20 MeV [Smith et al., 2005]. Recently both AGILE and Fermi has been able to expand this to single photon energies of at least 40 MeV being present in TGFs [Marisaldi et al., 2010b; Tierney et al., 2013]. Both AGILE and RHESSI detect around 10-30 photons in a typical event and to do spectral analysis, the TGFs have to be superposed. The TGFs measured by BATSE and Fermi generally contains enough photons to do spectral analysis on individual TGFs. The spectral analysis provided the first indications on the altitude and emission angle distribution of TGFs. 5.4 Altitude distribution The production altitude of individual TGFs and the altitude distribution of the set of TGFs are important parameters that can develop the production theories further. The first proposed altitude for TGFs was production above 40 km and based on the recognition that low energy photons do not travel far in the Earths atmosphere [Fishman et al., 1994]. As the TGFs contained many photons with energies smaller than 60 keV, Smith et al. [2005] concluded with a production altitude of more than 25 km. This did not take into account that the low energy photons could have been produced at higher altitudes from Compton scattered electrons or that the photons had lost energy through Compton scattering at higher altitudes. When all the important processes for photon interaction in air was included in models, the spectral shape was the main indication of altitude. The spectral analysis of the combined RHESSI spectrum also indicated an initial altitude of less than 20 km [Babich et al., 2008; Carlson et al., 2007; Dwyer and Smith, 2005; Gjesteland et al., 2011; Hazelton et al., 2009]. The first spectral analysis of the BATSE data, showed signs of two altitude regions, one around 40 km and one below 20 km [Østgaard et al., 2008]. After Grefenstette et al. [2008] pointed 5.4 Altitude distribution 41 out significant dead time problems with the BATSE instrument, Gjesteland et al. [2010] revisited the BATSE data and concluded that all TGFs seemed to originate at altitudes consistent with thunderstorm altitudes. One problem with this method of comparing spectra is that the initial direction of the photons also change the spectra. This will be discussed below. Another problem is that the differences between 20 km and lower altitudes are small. Another approach used to derive the initial altitude is to look at the lightning itself with HF and VHF detectors. To do this the TGF producing lightning have to occur within a network of HF receivers. Triangulations of the signals in the receivers can give the position and altitude of the lightning. Stanley et al. [2006] were the first to do so. They analyzed 5 lightnings connected to RHESSI TGFs and found altitudes of 11.5-13.6 km. Later, Lu et al. [2010] and Shao et al. [2010] did analysis for 1 and 9 TGFs and found altitudes of 10-11 km and 10.5-14.1 km respectively. As the TGFs are now determined to originate inside the thunderstorms, the tropopause becomes an important limit. The tropopause is the located between the troposphere and the stratosphere and is the upper boundary for most clouds. Some clouds with exceptionally strong updraft might overshoot the tropopause. Liu and Zipser [2005] investigated cloud tops found from micro wave measurements made with an instrument on-board the TRMM satellite. During 5 years between 1998 and 2003 they found about 9000 clouds that were overshooting the tropopause as defined by NCEP/NCAR. In the same years, LIS (also on-board the TRMM satellite) measured around 1.2 million thunderstorms. This means that around 0.8 % of all thunderstorms within +/35 degrees latitude has overshooting clouds. The tropopause is highest in the tropics, with a maximum of about 16 km, becoming lower at higher latitudes where it can be as low as around 8 km. For a given location, the annual mean usually differs up to 0.5 km between years, while the monthly mean varies around 1 km over a year [Seidel and Randel, 2006]. The day-to-day variability for a given location has a mean of 45 hPa or 1.4 km, but can be as much as 2 km [Das et al., 2008; Seidel and Randel, 2006]. This gives a big variability in the expected maximum altitude of the TGFs. Another important property to consider is how the photons in one TGF is distributed in altitude. Smith et al. [2011a] used the RREA simulations from Dwyer [2007] with a constant sea equivalent electric field of 400 kV/m over an atmospheric depth of 87 g/cm2 of air. To use atmospheric depth as a measure of size of the electric field implies that the avalanche region at low altitudes are more compressed than at high altitudes. At an altitude of 8 km, 87 g/cm2 corresponds to a vertical distance of 1500 m, while at 20 km it corresponds to 5800 m [Hansen et al., 2013]. Figure 5.9 is adapted from Smith et al. [2011a] and shows the photon altitude distribution for a production altitude of 12 km. The figure reveals that most of the photons are produced close to the upper limit of the electric field. Especially for observations at low altitudes with for instance aircrafts or balloons the photons crated at the bottom of the electric field makes a significant difference. This is further discussed in Hansen et al. [2013], which is Paper 2 of this thesis. 42 Source properties of TGFs Figure 5.9: The photon altitude distribution for a TGF for an initial production altitude of 12 km. The electric field is stretching over an atmospheric depth of 87 g/cm2 which corresponds to around 9.7-12 km at this altitudes. The figure is adapted from Smith et al. [2011a] 5.5 Emission angles of TGF photons The spectral shape of the measured TGFs give some clue to the emission angles of the TGF photons. One of the main problems is that the spectral shape change with both emission and observational angle. Figure 5.10, is adapted from Gjesteland et al. [2011] and shows how the fluence change with the two angles, as calculated from the Monte Carlo model of photon transport presented in section 4.1. Figure 5.10 a) show the two angles, the observation angle is α and the emission angle is θ . In b) is shown the simulation results. The solid line is if the photons were emitted in all directions and not attenuated by the air. In this case, the reduced intensity would only be due to the reduction with distance. The dash-dotted line is for an emission angle of 60 degrees, the dashed is 40 degrees emission angle and the dotted is for a 20 degree emission angle. Outside of the emission cone, the only photons measured will be either Compton scattered photons or photons produced by annihilating positrons. As these photons will be reduced in energy from the original energy, the spectrum is expected to be significantly softer for these photons. By comparing modeling results with the measured spectrum from around 100 RHESSI TGFs, Gjesteland et al. [2011] found that the probable emission cone is a broad beam of with at least 40 degrees half angle. This result compared well with previous results from Carlson et al. [2007], Østgaard et al. [2008], Hazelton et al. [2009] and Gjesteland et al. [2010]. 5.6 Number of initial photons a) 43 b) Figure 5.10: Modeling results of how the angle of observation and the half angle of the emission cone affects the fluence observed at a satellite. a) shows an illustration of the setup, α is the observation angle and θ is the half angle of the emission cone. b) shows the number as a function of the observational angle. The source altitude is put at 15 km. The solid curve is showing how the number change if only considering the reduction in fluence with distance. The dashed-dotted curve is for 60 degrees emission angle, the dashed curve for 40 degrees emission half angle and the dotted curve for 20 degrees emission half angle. It is clear that the number of photons drop significantly (but not to 0) outside the emission cone. All the photons outside the cone is either produced by annihilated positrons or they are Compton scattered away from their initial direction. The figure is adapted from Gjesteland et al. [2011] The uncertainty is large in these results. For all the results based on RHESSI measurements, the spectrum used is a cumulative spectrum. This means that the wide beam might be as a result of the tilt of the beam and not only by the width of the emission cone. Another issue is that the altitude of the production is not established. 5.6 Number of initial photons The number of initial photons was first estimated by Dwyer and Smith [2005], who concluded with a number of about 1016 photons above 1 MeV for a source altitude of 21 km and 2 × 1017 for a source altitude of 15 km. The number of 1017 has subsequently been extensively used. The number of photons in a TGF was also estimated and discussed in Hansen et al. [2013] (Paper 2 of this dissertation), by using the RHESSI average. The loss of photons in the atmosphere was estimated using the Monte Carlo model of photon transport described in section 4.1, and the number subsequently estimated from basic geometry. The number of photons reached was on the same order of magnitude as in Dwyer and Smith [2005] for a production altitude of 15 km, and more than an order of magnitude more for production in 10 km altitude. These calculations are average number of photons. As the lightning distribution and the electric fields in the thunderstorms are varying one can expect the number of photons to also follow a distribution. The fluence distribution was discussed in Østgaard et al. [2012] (paper 1 of this thesis) using RHESSI, ADELE and the first 44 Source properties of TGFs results from Fermi. After correcting for dead-time in RHESSI and the orbits of the two satellite the fluence distribution was found to follow a power law with a power law index of −2.3 ± 0.2 down to ∼5/600 of the detection threshold of RHESSI. Tierney et al. [2013] did the same type of analysis for the new Fermi data reported on by Briggs et al. [2013] and found a power law index of 2.20 ± 0.13. These studies did not project the fluence back to the source as was done in Nisi et al. [2014] (Paper 3 of this thesis). As the TGF travels through the atmosphere, photons are attenuated in the air and TGFs from large distances will be detected with a lower fluence due to the reduction in intensity with distance. The question is how this may affect the fluence distribution. In Nisi et al. [2014], we used 10 years of RHESSI data from the second catalog of TGFs. For about 300 TGFs (out of the 2500 total) we had a WWLLN match and was able to estimate the source location. As the tropopause defines approximately the upper limit of the thunderclouds this was used as an upper altitude for TGF production. To find the exact numbers we would need the actual production altitude. By using the tropopause as an upper limit we found that the fluence distribution changed to a slightly softer distribution when the altitude and distance between the satellite and the source was taken into account. Figure 5.11 is adapted from Nisi et al. [2014] (Paper 3 of this thesis) and shows the fluence distribution for the dead time corrected measurements for a selection of the RHESSI TGFs in red and the same sample corrected for the maximum source altitude and distance from the satellite. To the two distributions a power law is fitted. This shows that the projection down to the source region is important to estimate the fluence correctly. Figure 5.11: The fluence distribution of a selection of the second RHESSI catalog TGFs (red) and the fluence distribution of the same selection when corrected for maximum production altitude and distance from the satellite. This shows that the correction change the distribution to a softer distribution, and that it is important to project the fluence back to the source. The figure is adapted from Nisi et al. [2014]. 5.7 Number of electrons 45 5.7 Number of electrons From models Dwyer and Smith [2005] found that the number of high energy electrons was of the same order as the number of high energy photons and concluded that the number of electrons in a TGF is of the order of 1017 . The bremsstrahlung process was modeled using the Born approximation together with a short wavelength correction. As described in section 4.2, the influence of this assumption on the results are not established. A model avoiding the Born approximation will be able to answer that question. The long spark experiments in Eindhoven described earlier has detectors that are sensitive also to electrons, and only slightly sensitive to x-rays. This was done in order to search for the high energy electrons that produce the x-rays in the spark. Together with models this might make us able to investigate this further. 5.8 How the determination of source properties affects the theories From the knowledge we have to this day, both the feedback theory and the thermal runaway theory is both possible. However, the determination of the initial source properties support different theories. Both the established theories involves electrical fields in the thunderstorm, so the altitude can not be used to differentiate between the two theories. However, establishing the altitude might help determining the beaming of the photons as the angular distribution of the photons are be the main property left that changes the spectrum. In the production region the shape of the electric field will partly determine the beaming, and the direction of the electric field will determine the direction of the TGF. In a uniform vertical field, the RREA will lead to a beam of electrons with a spread that drops to 1/2 at around 20 degrees off the vertical [Grefenstette et al., 2008; Hazelton et al., 2009]. If the field is diverging, the spread in the electrons will be larger. This means that if the beaming of the electrons can be determined, this will give information on the shape of the electric field. What we observe in the TGF is light, so to determine the beaming of the electrons, we will have to determine the beaming of the photons and also get the bremsstrahlung process as accurately as possible. The bremsstrahlung process can be modeled, but to establish if the >40 degree emission angles are a result of a sum of more narrow beams with different directions or if this is the actual beaming more data is required. Another parameter that will be important for establishing the full theory of production is the number of electrons. Here too, the determination of altitude would be helpful as the attenuation of photons is highly dependent on the amount of air the TGF pass through. Both the two theories have been shown to be able to produce 1017 electrons within the duration of a TGF [Dwyer, 2007, 2008, 2012; Liu and Dwyer, 2013; Xu et al., 2012]. However, if the number of electrons is much higher either because of the source altitude being determined lower or the number of high energy photons produced per electron seen to be smaller, one or both theories might fail. A bremsstrahlung model avoiding the Born approximation might result in an improvement of the estimated number of photons/electrons. It would also improve the predicted energy of the electrons producing the TGF. This might support one theory 46 Source properties of TGFs more than the other and will also determine how important the RREA is to the process. This is because the average energy for a RREA that has been going through several avalanche lengths will be 7.3 MeV according to the empirical models [Dwyer et al., 2012a]. The ratio of TGFs/lightning is also very important. The feedback theory will only be creating a reasonable amount of photons if the available potential in the ambient field of the thundercloud is of the order of about 100MV [Dwyer, 2007]. These high potentials are only created in large thunderstorms and the TGF/lightning-ratio would be expected to be small. The thermal runaway are able to create large numbers of high energy photons from electric fields that are common in the tip of the lightning streamers and leaders. Thus the ratio of TGFs/lightning can be expected to be much larger if thermal runaway is what produces TGFs. If we can establish the fluence distribution of TGFs, this might help answer this question. If the power law index of the distribution is soft, we can expect that the observed number will increase much faster than for a harder distribution if the detection threshold is reduced. And if the fluence has a roll off at low fluences this will give a much larger number of TGFs per lightning than if there is a sharp cut off. If there is a sharp cut off this will also imply that there is a lower limit of electrons/photons needed to produce a TGF! If a cutoff is present just below 5/600 of RHESSI threshold, this would imply a lowest number of 1014 photons per TGF, if the sensititvity is increased to 1000 times the RHESSI sensititvity, the lowest number would be 1012 photons [Østgaard et al., 2012]. Lastly, if the x-rays from sparks are just low fluence TGFs, that would suggest that the fluence do not have a sharp cut off. Chapter 6 Introduction to the papers Paper 1: The true fluence distribution of terrestrial gamma flashes at satellite altitude To establish the fluence distribution for TGFs can help researchers to determin how many TGFs occures globally and per lightning. However, the low fluence part of the distribution is heavily affected by the number threshold of the instrument and the high fluence region is affected by dead-time problems in the satellite. This paper used RHESSI, Fermi and ADELE to investigate the fluence distribution. RHESSI was corrected for the known dead-time problems, and the satellites corrected for the differences i n orbit to be comparable. The measurements from these two satellites gave a fluence distribution with a power law of −2.3 ± 0.2. As the threshold of ADELE is much lower than the two satellites, the detection of one TGF out of ∼ 1000 lightnings closer than 10 km from the aircraft and none out of ∼ 130 lightning closer than 4 km from the satellite were used to adress the lower and of the spectrum. The conclution is that this powe law continues down to at least 5/600 of the RHESSI threshold. Unless there is a sharp cut of in the distribution below 5/600 of the RHESSI threshold, we can not rule out that all lightning produce TGFs. Paper 2: How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters In this paper we investigate what we can expect to detect from TGFs using airborne instruments as balloons and aircrafts. The ADELE mission and forthcoming The Coupled Observations from Balloon Related to Asim and Taranis (COBRAT) mission together with other planned projects makes this highly interesting. We assessed this issue by using a Monte Carlo model of photon transport in air. In this model we start with a number of photons with specified initial energy and direction and propagate them through the atmosphere. We then investigated how many photons went through a detector area placed at different altitudes and horizontal distances from the initial position of the starting point of the TGF. In order to find the limits of where the detectors mounted on a balloon or aircraft can be expected to detect TGFs, we also used the model to get the number of initial photons in a TGF. Both the number of initial photons and the limits of detectability is of course highly dependent on the production altitude of the TGFs. The fluence in 14 km altitude is 2-3 orders of magnitude larger for a TGF produced in 10 km than for a TGF produced in 20 km. Other important parameters are altitude dis- 48 Introduction to the papers tribution, initial angular distribution of the photons and the amount of feedback. These are especially important for observational altitudes lower than the production altitude of the TGFs. Paper 3: An altitude and distance correction to the initial fluence distribution of TGFs In this paper we look at how the altitude and distance distribution affects the initial fluence distribution. The study was made possible by the increased number of TGFs in the second RHESSI catalog with connected geolocated lightning. Since TGFs from deep in the atmosphere and/or from far distances will loose more photons between the location of production and the satellite than the ones from high altitudes and close regions, this might make the fluence distribution in the source look different then the fluence distribution at the satellite. We use the tropopause altitude as an approximation of the altitude distribution of the TGFs. With that we assume that the TGF altitude distribution is following the tropopause distribution. We used the The National Centers for Environmental Prediction (NCEP)/NCAR 40 years re-analysis 6 hour values to find the tropopause pressure at the point with the highest tropopause altitude within the satellite field of view. The distance and altitude correction makes the source fluence distribution look slightly softer than the fluence distribution at the satellite showing that these factors are important to take into account. When investigating the tropopause altitudes at the time and location of TGFs, we also noticed that there is an annual variation in the pressure for the tropics. This is explained in literature as being due to a stronger Dobson-Brewer circulation in the north then in the south in the respective winters. 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Splitt (2011b), A terrestrial gamma-ray flash observed from an aircraft, Journal of Geophysical Research, 116(D20124), doi:10.1029/2011JD016252. 2.2.1, 5.2.2, 5.2.2 Splitt, M. E., S. M. Lazarus, D. Barnes, J. R. Dwyer, H. K. Rassoul, D. M. Smith, B. Hazelton, and B. Grefenstette (2010), Thunderstorm characteristics associated with RHESSI identified terrestrial gamma ray flashes, Journal of Geophysical Research, 115(A00E38), doi:10.1029/2009JA014622. 5.1.1, 5.1.3, 5.2.1 Stanley, M. A., X.-M. Shao, D. M. Smith, L. I. Lopez, M. B. Pongratz, J. D. Harlin, M. Stock, and A. Regan (2006), A link between terrestrial gamma-ray flashes and intracloud lightning discharges, Geophysical Research Letters, 33(L06803), doi:10. 1029/2005GL025537. 2.3.2, 5.2.1, 5.4 Stolzenburg, M., and T. C. Marshall (2008), Charge Structure and Dynamics in Thunderstorms, Space Science Reviews, 137, 355–372, doi:10.1007/s11214-008-9338-z. 3.2, 3.2 Stolzenburg, M., W. D. Rust, and T. C. Marshall (1998), Electrical structure in thunderstorm convective regions 3. Synthesis, Journal of Geophysical Research, 103(D12), 14,097–14,108, doi:10.1029/97JD03545. 3.2 Tavani, M., M. Marisaldi, C. Labanti, F. Fuschino, A. Argan, a. Trois, P. Giommi, S. Colafrancesco, C. Pittori, F. Palma, M. Trifoglio, F. Gianotti, A. Bulgarelli, V. Vittorini, F. Verrecchia, L. Salotti, G. Barbiellini, P. Caraveo, P. Cattaneo, A. Chen, T. Contessi, E. Costa, F. D’Ammando, E. Del Monte, G. De Paris, G. Di Cocco, G. Di Persio, I. Donnarumma, Y. Evangelista, M. Feroci, A. Ferrari, M. Galli, A. Giuliani, M. Giusti, I. Lapshov, F. Lazzarotto, P. Lipari, F. Longo, S. Mereghetti, E. Morelli, E. Moretti, A. Morselli, L. Pacciani, A. Pellizzoni, F. Perotti, G. Piano, P. Picozza, M. Pilia, G. Pucella, M. Prest, M. Rapisarda, A. Rappoldi, E. Rossi, A. Rubini, S. Sabatini, E. Scalise, P. Soffitta, E. Striani, E. Vallazza, S. Vercellone, A. Zambra, and D. Zanello (2011), Terrestrial Gamma-Ray Flashes as Powerful Particle Accelerators, Physical Review Letters, 106(018501), doi:10.1103/PhysRevLett.106.018501. 2.1.3 Tierney, D., M. S. Briggs, G. Fitzpatrick, V. L. Chaplin, S. Foley, S. McBreen, V. Connaughton, S. Xiong, D. Byrne, M. Carr, P. N. Bhat, G. J. Fishman, J. Greiner, R. M. Kippen, C. A. Meegan, W. S. Paciesas, R. D. Preece, A. von Kienlin, and C. WilsonHodge (2013), Fluence distribution of terrestrial gamma ray flashes observed by the Fermi Gamma-ray Burst Monitor, Journal of Geophysical Research: Space Physics, 118, 6644–6650, doi:10.1002/jgra.50580. 5.3, 5.6 Williams, E. R. (2006), Problems in lightning physics—the role of polarity asymmetry, Plasma Sources Science and Technology, 15(2), S91–S108, doi:10.1088/0963-0252/ 15/2/S12. 3.2 BIBLIOGRAPHY 59 Wilson, C. T. R. (1924), The electric field of a thundercloud and some of its effects, Proceedings of the Physical Society of London, 37(1), 32D–37D, doi:10.1088/ 1478-7814/37/1/314. 3.1 Xu, W., S. Celestin, and V. P. Pasko (2012), Source altitudes of terrestrial gamma-ray flashes produced by lightning leaders, Geophysical Research Letters, 39(8), L08,801, doi:10.1029/2012GL051351. 5.8 60 BIBLIOGRAPHY Acronyms ADELE The Airborne Detector for Energetic Lightning Emissions. AGILE The Astrorivelatore Gamma a Immagini Leggero. AWESOME The Atmospheric Weather Electromagnetic System for Observation, Modeling, and Education. BATSE The Burst and Transient Source Experiment. BGO Bismuth Germanate. CG Cloud to Ground. CGRO The Compton Gamma-Ray Observatory. COBRAT The Coupled Observations from Balloon Related to Asim and Taranis. DJF December, January and February. ELF Extreme Low Frequency. Fermi The Fermi Gamma-ray Space Telescope. GBM The Gamma-ray Burst Monitor. GRB Gamma-Ray Burst. GV The Gulfstream V jet. HF High Frequency. IC Intra Cloud. JJA June, July and August. LASA The Los Alamos Spheric Array. LIS The Lightning Imaging Sensor. LMA The Lightning Mapping Array. MC Monte Carlo. 62 Acronyms MCAL The Mini-Calorimeter. NaI Sodium Iodide. NCAR The National Center for Atmospheric Research. NCEP The National Centers for Environmental Prediction. NLDN The National Lightning Detection Network. OTD The Optical Transient Detector. RHESSI The Reuven Ramaty High Energy Solar Spectroscopic Imager. RREA Relativistic Runaway Electron Avalanche. TRMM The Tropical Rainfall Measuring Mission. VHF Very High Frequency. VLF Very Low Frequency. WWLLN The World Wide Lightning Location Network. Nomenclature α The fine structure constant, α = 1/137. β1 The energy of the incoming electron in the bremsstrahlung process in units of the light velocity. β2 The energy of the outgoing electron in the bremsstrahlung process in units of the light velocity. E Electric field strength. ε The energy of an electron. εth The minimum energy for an electron to be a seed electron for an electric field of strength E. ε1 The energy of the incomming electron in Bremsstrahlung calculations. ε2 The energy of the outgoing electron in Bremsstrahlung calculations. Eb The smallest electrical field that can give runaway electrons, Eb ≈ 200 kV/m. Ec The critical electric field to accelerate low energy electrons to relativistic energies, Ec ≈32 MV/m. Ek The conventional breakdown electric field, Ek ≈3.2 MV/m. Est− The electric field required for a negative streamer to form, Est− ≈1200 kV/m. Est+ The electric field required for a positive streamer to form, Est+ ≈440 kV/m. Et h The threshold electric field for the Relativistic Runaway Electron Avalanche. Eb ≈ 2.8 × 105 V/m. F0 The number of initial seed electrons in a Relativistic Runaway Electron Avalanche. 64 Nomenclature Fd The average energy loss rate for the electrons in the direction of the avalanche in a Relativistic Runaway Electron Avalanche, Fd ≈0.275 MeV/m. FE The Elwert factor, a correction factor to get a finite cross section at the short wave limit in the Born approximation, used in bremsstrahlung calculations.. Ff b The number of electrons produced in the feedback process. fre Runaway electrons per unit energy after a Relativistic Runaway Electron Avalanche. FRREA The number of electrons created in a Relativistic Runaway Electron Avalanche. γ The feedback factor, defined as the number of new avalanches created by each Relativistic Runaway Electron Avalanche. k The energy of the photon produced in the Bremsstrahlung process. L The total length of the avalanche region in a Relativistic Runaway Electron Avalanche. λ The avalanche length of a Relativistic Runaway Electron Avalanche defined as the length the avalanche needs for the number of photons to increase by e. |M| The matrix element for the electron transition 1→2 of the Hamiltonian of the electron in the interaction of a radiation field, used in the bremsstrahlung calculations. Ω Denotes solid angle in Bremsstrahlung calculations. p1 The momentum of the incoming electron in Bremsstrahlung calculations. p2 The momentum of the outgoing electron in Bremsstrahlung calculations. R The radial distance from the source of a TGF to the point of measurement. σ The standard deviation of a distribution. τ The time of one feedback cycle. t90 The length of the interval in which 90% of the counts are accumulated, with 5% of the counts occurring before and 5% after this interval. Nomenclature z The distance from the start of the avalanche in Relativistic Runaway Electron Avalanche. 65 66 Nomenclature Scientific results 68 Scientific results Paper 1 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude Østgaard, N., Gjesteland, T., Hansen, R. S., Collier, A. B., and Carlson, B. Journal of Geophysical Research Space Physics, 117(A03327), doi:10.1029/2011JA017365, 2012 70 Scientific results 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude 71 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, A03327, doi:10.1029/2011JA017365, 2012 The true fluence distribution of terrestrial gamma flashes at satellite altitude N. Østgaard,1 T. Gjesteland,1 R. S. Hansen,1 A. B. Collier,2,3 and B. Carlson1 Received 11 November 2011; revised 20 January 2012; accepted 1 February 2012; published 24 March 2012. [1] In this paper we use the fluence distributions observed by two different instruments, RHESSI and Fermi GBM, corrected for the effects of their different orbits, combined with their different daily TGF detection rates and their relative sensitivities to make an estimate of the true fluence distribution of TGFs as measured at satellite altitudes. The estimate is then used to calculate the dead-time loss for an average TGF measured by RHESSI. An independent estimate of RHESSI dead-time loss and true fluence distribution is obtained from a Monte Carlo (MC) simulation in order to evaluate the consistency of our results. The two methods give RHESSI dead-time losses of 24–26% for average fluence of 33–35 counts. Assuming a sharp cut-off the true TGF fluence distribution is found to follow a power law with l = 2.3 0.2 down to 5/600 of the detection threshold of RHESSI. This corresponds to a lowest number of electrons produced in a TGF of 1014 and a global production rate within 38 latitude of 50000 TGFs/day or about 35 TGFs every minute, which is 2% of all IC lightning. If a more realistic distribution with a roll-off below 1/3 (or higher) of the RHESSI lower detection threshold with a true distribution with l ≤ 1.7 that corresponds to a source distribution with l ≤ 1.3 is considered, we can not rule out that all discharges produce TGFs. In that case the lowest number of total electrons produced in a TGF is 1012. Citation: Østgaard, N., T. Gjesteland, R. S. Hansen, A. B. Collier, and B. Carlson (2012), The true fluence distribution of terrestrial gamma flashes at satellite altitude, J. Geophys. Res., 117, A03327, doi:10.1029/2011JA017365. 1. Introduction [2] With the discovery of terrestrial gamma flashes (TGFs) above thunderstorms [Fishman et al., 1994] by the Burst and Transient Source Experiment (BATSE) a new mechanism of the coupling between the lower atmosphere and space was found. The phenomenon involves both gamma photons, relativistic electrons and positrons. Charged particles are accelerated in extremely strong electric fields (>300 kV/m sea level equivalent) associated with lightning discharges and initiate a relativistic runaway process [Gurevich et al., 1992]. Through interaction with the neutral atmosphere bremsstrahlung is produced, resulting in the escape of electrons [Dwyer et al., 2008], positrons [Briggs et al., 2011] and gamma photons into space. There are still many open questions related to TGFs, and one of them will be addressed in this paper: How common are TGFs? Or more specifically: What is the true fluence distribution of TGFs as measured from satellite altitude? [3] From the first observations it was believed that the TGFs are produced above 40 km and that they were related 1 Department of Physics and Technology, University of Bergen, Bergen, Norway. 2 SANSA Space Science, Hermanus, South Africa. 3 University of KwaZulu-Natal, Durban, South Africa. Copyright 2012 by the American Geophysical Union. 0148-0227/12/2011JA017365 to transient luminous events [Fishman et al., 1994; Nemiroff et al., 1997], a reasonable suggestion given the relatively few observations of about 10 TGF/year by BATSE (78 TGFs in 9 years according to http://www.batse.msfc.nasa.gov/batse/ misc/triggers.html). However, results from Reuvan Ramaty High Energy Solar Spectroscopic Imager (RHESSI) ten years later indicated that their production altitude is most likely around 15–21 km [Dwyer and Smith, 2005]. While BATSE had an on-board trigger algorithm with a 64 ms search window, the data from RHESSI were downloaded and a more sophisticated, but still rather conservative, search algorithm with a search window of 1 ms was applied. For more details about the search algorithm we refer to Grefenstette et al. [2009]. Having a trigger window significantly longer than the typical duration of a TGF(<1 ms), like BATSE had, only events with high count rates that exceed the statistical fluctuations of background counts will be classified as TGFs. However, RHESSI had a search window comparable to the duration of a TGF and could identify much weaker TGFs. Thus, RHESSI was able to report more than 100 TGFs/year (975 TGFs in 8.5 years according to http://scipp.ucsc.edu/ dsmith/tgflib_public/). Reanalyses of the BATSE data have also confirmed a production altitude of TGFs below 20 km [Carlson et al., 2007; Østgaard et al., 2008; Gjesteland et al., 2010]. Consistent with this production altitude and general lightning physics, Williams [2006] speculated that TGFs are related to positive intracloud lightning, a suggestion that has been supported by a few studies comparing TGFs with A03327 1 of 8 72 A03327 Scientific results ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE A03327 ADELE’s sensitivity and the non-detection of TGFs by this aircraft. 2. The Measured TGF Fluence Distributions and Average Duration Figure 1. The fluence distributions of TGFs measured by RHESSI (grey histogram) and Fermi (black histogram). Power functions are fitted to both distributions. The average values for Fermi are for TGF pulses, defined as counts in the central 50% of duration. electromagnetic characteristics of lightning [Cummer et al., 2005; Shao et al., 2010; Cummer et al., 2011]. As intracloud lightning accounts for about 75% of all the lightning [Boccippio et al., 2001] and most of these are positive intracloud lightning bringing negative charges upward, this may imply that TGFs are a rather common phenomenon. X-ray bursts have been observed from negative leader steps in cloud-to-ground (CG–) lightning [Dwyer et al., 2005] and from dart leaders in rocket triggered lightning [Dwyer et al., 2004] before the return strokes of the CG– lightning. Discharge experiments in the laboratory [Nguyen et al., 2008] have also shown that bursts of X-rays are observed slightly before (1 ms) the discharge return stroke. All these studies give some hints that TGFs might be more common than observations from space have indicated so far. On the other hand, Smith et al. [2011] suggested that the non-detection of TGFs by the Airborne Detector for Energetic Lightning Emissions (ADELE) may indicate the opposite, that there are very few TGFs with intensities two-three orders of magnitude weaker than those observed by RHESSI. [4] Measurements from space have been hampered by the loss of counts due to dead-time in the electronics, limited instrument sensitivity and limitations due to the on-board trigger window. In this paper we will use the fluence distributions observed by two different instruments, RHESSI and Fermi GBM, corrected for the effects of their different orbits, combined with their different daily TGF detection rates and their relative sensitivities to make an estimate of the true fluence distribution of TGFs at satellite altitudes. This estimate is then used to calculate the dead-time loss for an average TGF fluence measured by RHESSI. Independent estimates of RHESSI dead-time loss and true fluence distribution are obtained from a Monte Carlo (MC) simulation in order to evaluate the consistency of our results. Finally, we discuss our results in the context of [5] The fluence distribution of the 591 TGFs measured by RHESSI (March 4, 2002–December 31, 2005) and the first 53 TGFs measured by Fermi (Aug 7, 2008–March 10, 2010) are shown in Figure 1. The RHESSI TGFs were downloaded from http://scipp.ucsc.edu/dsmith/tgflib_public/ and are the same as used in the quantitatively analysis by Grefenstette et al. [2009] obtained before the degradation of the instrument’s sensitivity when the effective detector area was still 256 cm2. The Fermi TGFs are taken from Fishman et al. [2011, Table 2]. The three double peaks in that table are treated as separate TGFs giving a total of 53 TGF pulses. All these TGFs were detected when an on-board 16 ms trigger window was used. A power function with the form dN ¼ A0 n dn l ð1Þ (dN is the number of TGFs with fluence within dn and A0 is a scaling factor) has been fitted to each of the distribution, giving l of 3.5 and 1.4, for RHESSI and Fermi, respectively. The fit is based on 14 (4) bins from the peak using bin size of 2 (50) counts for the RHESSI (Fermi) distribution. A power function was chosen because the measured RHESSI fluence distribution could be fairly well fitted with such a function. The accuracy of the fit will be discussed in section 5. We interpret the very soft fluence distribution (meaning relatively many low fluence TGFs) from RHESSI to be caused by dead-time losses that are most significant for high photon fluxes. Although Fermi also has dead-time losses, the very hard fluence distribution (meaning relatively many high fluence TGFs) from Fermi can probably be explained by the long trigger window of 16 ms, which favors high fluence TGFs. For these reasons we believe that the true fluence distribution is somewhere in between these two distributions. [6] The durations of the 591 RHESSI TGFs have a mean of 374 ms and a median of 299 ms. The duration of a TGF is defined as the 2s of a Gaussian function fitted to the light curve of total counts. The majority of the first 53 TGF pulses measured by Fermi have durations between 100 ms and 400 ms [Fishman et al., 2011]. For comparison Gjesteland et al. [2010] reported 5 TGFs measured by BATSE to have a production duration of 200–250 ms. 3. Differences in Sensitivity and Total Number of Observed TGFs [7] For the 591 RHESSI TGFs observed before January 1, 2006 the average time between TGFs was 2.35 day or 0.42 TGFs/day using a lower threshold cut-off of 17 counts [Grefenstette et al., 2009]. For the first 53 TGFs measured by Fermi they observed 0.03 TGFs/day when a 16 ms onboard trigger window was applied to the NaI scintillators, which increased to 0.3 TGFs/day when the same window was applied to the BGO detectors [Fishman et al., 2011]. However, after the Fermi team started downloading most of the data obtained over regions where TGFs are produced, Fishman [2011] reported that more than 1 TGF/day has been 2 of 8 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude A03327 ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE Figure 2. The average lower threshold of RHESSI (grey) and FERMI (black) given on the RHESSI scale of counts/ TGF. The distribution of TGFs with an exponent of 2.3 is shown as a grey curve. observed. According to Briggs [2011; M. Briggs, personal communication, 2011] their ground search found 234 TGFs in 591.8 hours of data over regions which are expected to have a high TGF rate. Over the same hours and from the same regions, they found 23 triggered TGFs, a 10.2 times increase in detection rate. According to Fishman et al. [2011] 35 TGFs were observed after the trigger algorithm change (from NaI to BGO) in at least 141 days of data. Of the 35 triggered TGFs 21 were inside the regions where all the data have been downloaded [Briggs, 2011] and the scaling factor of 10.2 should apply. We do not know if this ratio is also valid for the areas outside the boxes which are mostly over ocean. Although there are fewer thunderstorms over ocean the ratio of IC/CG and the fluence distribution of TGFs might be the same. As we are not aware of any studies that give any information whether the TGF distribution over ocean is softer or harder than over land, we will apply an uncertainty of 50% for the triggered-to-search ratio for the regions outside the boxes. This uncertainty also accounts for any seasonal biases in the downloaded data. This gives us a daily detection rate of 2.5 0.5 TGFs/day (35/141 10.2 and 21/141 10.2 + 14/141 (15.3 or 5.1)). [8] From the RHESSI data we know that TGFs have a strong latitudinal dependence with fewer TGFs produced at higher latitudes. As Fermi, due to its inclination of 25.6 spends more time over regions with more TGFs than RHESSI (38 inclination), Fermi should see more TGFs than RHESSI. As we want to derive a relative daily detection rate that only depends on sensitivity differences we need to correct for this effect. This correction is performed as follows: First, we consider the RHESSI TGF fluence distribution (NR) versus latitude (q), dNR/dq, corrected for the latitudinal cosine effect on area. Then we calculate the fraction of the orbit RHESSI (OR) spends at various latitudes, dOR/dq, when the orbit is given as a sine function with amplitude of 38 + 3 latitude. A similar calculation is performed for Fermi, dOF/dq, but with an amplitude of 25.6 +3 latitude. The extra 3 is to account for a field of view of about 400 km. The expected Fermi TGF distribution is then given as dNF dNR dOF =dq ¼ dq dq dOR =dq ð2Þ 73 A03327 By integrating dNR/dq and dNF/dq over latitudes we estimate that Fermi, just due to orbital differences between the two spacecraft, is expected to see 65% more TGFs than RHESSI. This means that the relative detection rate between Fermi and RHESSI due to sensitivity differences only, Y, is given by (2.5 0.5)/1.65/0.42 = 3.6 0.7. It should be noted that this is what Fermi would have seen if they downloaded data similar to RHESSI and is what we will use as the relative detection rate between the two instruments. However, the real detection rate for Fermi is 1.6 TGFs/day (21 10.2/141 + 14/141). [9] Even if the photon flux of a TGF has a rapid rise, the decay, due to Compton scattering, is usually slow [Østgaard et al., 2008] and there is no reason to believe that RHESSI, due to dead-time losses, should miss TGFs with high fluence. Dead-time losses would only lead to underestimating the fluence of strong TGFs. When Fermi sees more TGFs than RHESSI it implies that its sensitivity is better. Although Fermi BGO detectors have a slightly larger effective detector area than RHESSI, that is 320 cm2 [Meegan et al., 2009; Briggs et al., 2010] compared to 256 cm2 [Grefenstette et al., 2009] flying at practically the same altitude, the most important reason for the higher sensitivity is that a more efficient trigger algorithm for the on-ground analysis has been developed for Fermi. According to Briggs [2011] the on-ground trigger algorithm requires ≥4 counts in each of the two BGO detector, ≥4 in all the 12 NaI detectors and with a probability less than 10 11 giving a lower threshold of 19 counts in all detectors. For the comparison with the 591 RHESSI TGFs for which a lower cut-off threshold of 17 counts (before background subtraction) have been used we use the ≥8 counts (also before background subtraction) in the two BGO detectors with an energy averaged effective detector area of 160 cm2 2 = 320 cm2 to obtain the relative sensitivity, X, between Fermi and RHESSI as X ¼ 17 320 ¼ 2:7 8 256 ð3Þ This is equivalent to Fermi having a lower threshold of 6.3 on the RHESSI scale as visualized in Figure 2. Although there are uncertainties related to this estimate we will show that it provides results that converge with the rest of the information we have and are consistent with an independent MC simulation of RHESSI dead-time. Uncertainties related to the relative sensitivity will be discussed. 4. The True Fluence Distribution and RHESSI Dead-Time Losses [10] In the search algorithm to find the 591 RHESSI TGFs with the daily detection rate of 0.42 TGFs/day a lower threshold cut-off of 17 counts was used. However, our MC simulations of dead-time loss indicates that RHESSI only has a one-to-one response up to 10 counts (see Figure 4a). However, between 10 and 20 counts the errors of the estimated true counts are still overlapping the one-to-one response. We will therefore use a fluence of 15 counts as the threshold where the RHESSI results start to be affected by dead-time losses, but also show the effect of using 10 and 20 counts. 3 of 8 74 Scientific results ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE A03327 A03327 With relative sensitivity, X = 2.7, and relative daily detection rate, Y = 3.6 0.7, this can be solved to get an exponent l ¼ 2:3 0:2 ð6Þ Knowing the distribution of TGFs measured by RHESSI, with l = 3.5 and the estimated true TGF distributions, with l = 2.3 we can calculate RHESSI dead-time losses as a function of incoming photons. For a specific number of TGFs within a fluence interval, dN/dn, in Figure 3a the dead-time loss is the difference between the true fluence, nT, and the measured fluence nM divided by nT. This is shown in Figure 3b where we have used a fluence of 15 (solid line), with 10 and 20 as uncertainties (dotted lines), Figure 3. (a) The distribution measured by RHESSI (thick grey) and the estimated true TGF distribution at RHESSI altitude based on the two instrument’s different photon detection sensitivities and their relative daily TGF detection rate. (b) The loss due to dead-time in the RHESSI electronics as a function of true counts (incoming photon fluence). Solid line is for 15 counts used as the threshold where RHESSI experiences dead-time losses. Dotted lines are for lower threshold of 10 counts (upper) and 20 counts (lower). The grey cross is the average dead-time loss determined by the MC simulations described in section 5. [11] Given that both RHESSI and Fermi are measuring from a true fluence distribution that follows a power law with an unknown exponent, l, but with different lower detection thresholds, we have the following expression for the total number of TGFs detected by Fermi: NF ¼ Z ∞ A0 n l dn ¼ n0F A0 l 1 n10F l ð4Þ where n is fluence and n0F is the lower threshold of detection. The total number of TGFs detected by RHESSI, NR can be expressed similarly, but with a different lower threshold, n0R. We can then express the relative total number of detected TGFs which is equivalent to the relative daily detection rate, Y, as a function of the two lower thresholds Y ¼ NF n0F ¼ ð Þ1 NR n0R l 1 ¼ ð Þ1 X l ð5Þ Figure 4. (a) Monte Carlo simulation of the TGF observed May 2, 2005, with a duration of 361 ms, with increasing true fluence from 0 to 100. Vertical line denotes the measured counts and the true counts can be read out from the intersection between MC values and horizontal line, here 45 7. The diagonal line indicates that RHESSI has no dead-time losses up to about 15 counts. (b) Grey histogram is the measured fluence distribution of the 591 RHESSI TGFS, while black histogram is the true fluence distribution running the MC model on each of the 591 TGFs. Due to background subtraction there are TGFs with less than 17 counts. The black, grey and red lines show the fitted power distributions for the measured (l = 3.5) true (l = 2.6) and the lower bins of the true (l = 1.7). 4 of 8 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude A03327 ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE 75 A03327 of photons within the duration, which is shown as vertical lines in Figure 4a. The black horizontal line at 34 counts is what RHESSI measured for this specific TGF and the true counts can be read out from the intersection between the MC values and the horizontal line, here 45 7. This curve would have been identical to the one shown in Figure 3b if both the measured counts and duration were equal to the averages, 34 counts and 374 ms. When this MC scheme is applied to all the 591 RHESSI TGFs a true fluence distribution of TGFs can be obtained, as shown by the black histogram in Figure 4b. Using the average fluence of the true distribution and the measured distribution we get the dead-time losses for an average RHESSI TGF of 26%, as shown as a grey cross in Figure 3b. Power functions can be fitted to the distributions. Depending on how many bins from the peak value that are used for the fit we find that the measured distribution before dead time correction (grey histogram) can be fitted with power exponents ranging from 3.2 (11 bins) to 3.7 (17 bins). A c2-test (reduced) of these fits is equally good (c2R ≤ 0.15). Similarly, for the dead time corrected distribution (black histogram) we find power exponents ranging from 2.3 (10 bins) to 3.0 (19 bins), which are equally good with c2R ≤ 0.2. In Figure 4b we have chosen to show exponents in the middle of the intervals, l of 3.5 for the non-corrected distribution, that was used for estimating the RHESSI dead time losses in section 4. For the corrected distribution we show a l of 2.6 for the entire distribution and a l of 1.7 for the lower part, indicating a roll-off, as will be discussed in section 6. Figure 5. How the exponent, l, depends on (a) the relative sensitivity of the two instruments and (b) the relative daily detection rate. In Figure 5a the vertical line is the relative sensitivity we have based our calculation on. The dashed lines show the same dependence when the upper and lower limits of Y are used. In Figure 5b the solid vertical line is the relative daily detection rate with lower and upper limits as dashed lines with the corresponding upper and lower limits for l (horizontal dashed lines). In both panels the dotted lines are the l for the measured distributions by RHESSI (grey) and Fermi (black). as the level where dead-time losses start to affect the RHESSI counts. The loss for an average TGF (33 counts) is 24% which is fairly close to what was obtained from the MC simulations (grey cross), 26% for an average of 35 counts (Figure 4b). 5. Monte Carlo Simulation of RHESSI Dead-Time Losses [12] To obtain an independent estimate of RHESSI deadtime losses a MC simulation was performed. For this MC simulation we used the characteristic times of the RHESSI electronics [Grefenstette et al., 2009] to determine the deadtime in each of the 8 detectors. Then, for each TGF the following two steps are performed: 1) The duration of the TGF is calculated as within 2 standard deviations of a Gaussian fit to the TGF light-curve. 2) By increasing the number of photons distributed randomly within the duration of each TGF a detection efficiency curve is obtained. As this was performed hundred times for each number of photons we obtain the statistical error due to the random distribution 6. Discussion [13] Fermi also has a dead-time loss up to 50% for intense TGFs [Briggs et al., 2010]. Because Fermi is seeing 3.6 0.7 times more TGFs than RHESSI, we believe that Fermi due to its more sophisticated search algorithm, is seeing the weaker part of the TGF fluence distribution. We can not rule out that Fermi may lose some counts due to dead-time even for these weak TGFs, but we will argue that the lower threshold of TGF detection for Fermi is most likely determined by the signal-to-noise ratio rather than dead-time losses. [14] There are two important values that our estimated true fluence distribution depends on: 1) the relative sensitivity (X) of the two instruments and 2) the relative daily detection rate (Y), where we have used X = 2.7 and Y = 3.6 0.7. To examine how uncertainties in these two estimates may influence our result we can rewrite equation (5) to obtain l¼1þ lnðY Þ lnðX Þ ð7Þ [15] In Figure 5a we keep the relative daily TGF detection rate fixed at Y = 3.6 and let the relative sensitivity (X) vary from 1 to 5. One can see that if Fermi is more sensitive relative to RHESSI than we have estimated (moving to higher values) the true distribution will be slightly harder. On the other hand, if the two instruments have almost similar sensitivities the true fluence distribution quickly becomes very soft. The dashed lines show the same dependence when the upper and lower limits of Y are used. We have based our estimate of relative sensitivity on information presented by 5 of 8 76 A03327 Scientific results ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE Grefenstette et al. [2009], Meegan et al. [2009], Briggs et al. [2010], and Briggs [2011, also personal communication, 2011]. For the RHESSI data we have only used the 591 TGFs before the degradation of the instrument occurred. The average effective detection area is adopted from Briggs et al. [2010], but looking at Figure 11 of Meegan et al. [2009] one could argue that the average is closer to 170 cm2. This would have given us a l of 2.2, but introduces an uncertainty too small to affect the 0.2 used in equation (6). [16] In Figure 5b we keep the relative sensitivity fixed at X = 2.7 and let the daily TGF detection rate (Y) vary from 1 to 6. The daily TGF detection rate for RHESSI is fairly well established by Grefenstette et al. [2009], while Fermi’s daily detection rate is given as approximately 1 [Fishman, 2011]. As described above, based on the information given by Briggs [2011, also personal communication, 2011] we found that the equivalent (to RHESSI) daily detection rate for Fermi after downloading data, due to sensitivity differences only, is 1.5 0.3 TGFs/day, with 1.2 (1.8) TGFs/day corresponding to TGFs with higher (lower) fluence over ocean than land. The grey shaded box in Figure 5b shows the range spanned by the two extreme values and indicates that the true fluence distribution of TGFs as measured from satellite altitude follows a power law with l = 2.3 0.2. This is in good agreement with the estimated power distributions with l ranging from 1.9 to 2.5 reported by Gjesteland et al. [2011], using geolocation and energy spectra of RHESSI TGFs. [17] The two methods we have used give converging l-values. Furthermore, if 10 to 12 bins were used for the fit to dead-time corrected distribution in Figure 4b we would get l = 2.3. As we in our first approach focus on extending the distribution down to fluences below the RHESSI lower threshold, we conclude that both methods support a distribution with l = 2.3 0.2. [18] What we have estimated is the true TGF distribution as measured from satellite altitude, which is not necessarily the same as the true TGF source distribution. Flying much closer to the source, an experiment like ADELE is probably exposed to a distribution more similar to the latter. In a recent paper Carlson et al. [2012] have calculated the relationship between the two and for hard distributions the differences are significant. For a distribution with l = 2.3 0.2 the true source distribution would have l = 2.0 0.2. As reported by Smith et al. [2011] ADELE, flying at 14 km altitude, saw only one TGF when passing 1213 lightning discharges less than 10 km away. However, ADELE was closer than 4 km to 133 discharges and according to the model results presented in that paper the sensitivity of ADELE is increased about two-to-three orders of magnitude from 10 km to 4 km. [19] It has been suggested that TGFs are associated with IC lightning bringing negative charges upward [Cummer et al., 2005; Williams, 2006; Shao et al., 2010; Cummer et al., 2011]. As this type of lightning accounts for about 75% of all lightning [Boccippio et al., 2001] this would imply that almost all lightning discharges have an associated TGF. We will now discuss this hypothesis in the context of the power distributions we have found and the non-detection of TGFs by ADELE as well as the sensitivity of ADELE versus RHESSI. A03327 [20] First, we estimate the relative sensitivity between ADELE at 10 km and RHESSI. We use 400 km as the radius of the effective detection area below RHESSI [see Collier et al., 2011, Figure 6] and notice that RHESSI detects TGFs produced within 38 latitude. Then, the global production rate of TGFs within this latitude range and with strength larger than the RHESSI threshold of 17 counts is about 260 TGFs/day. The global lightning rate is 3.8 106/ day [Christian et al., 2003], but within 38 latitude it is 3.5 106/day. If we only consider the IC lightning (75% of total) we get a RHESSI-TGF/lightning ratio of 9.8 10 5. Of 1213 lightning RHESSI would have seen 0.1 TGF, while ADELE saw 1. Solving equations (5) or (7) with Y = 10 and l = 2.3 gives X = 6 indicating that ADELE’s sensitivity at 10 km is about 6 times better than RHESSI and 2 times better than Fermi. If the source distribution with l = 2.0 were used these number would be larger. [21] In Figure 6a we show the integrated distribution of TGFs, N, as a function of lower detection threshold, n0, (equation (4)) from 1213 and 133 lightning discharges assuming that they all make TGFs with a fluence distribution following a power law with l = 2.0 (solid lines). The two values of n0 denote the lower threshold (relative scale) for detecting 1 TGF (N = 1). For l = 2.0 the sensitivity has to increase by a factor of 10 (1/0.1) to see 1 TGF from a distribution of 133 given that 1 TGF was detected from a distribution of 1213. ADELE’s sensitivity is modeled to be 100–1000 times better at 4 km compared to 10 km [Smith et al., 2011] and corresponds to having a lower threshold of n0 = 1/100 to 1/1000 (Figure 6a). This would imply that ADELE should have seen about 10 (at n0 = 1/100) TGFs from the 133 lightning discharges if they all produce TGFs, and the probability of non-detection is very low. [22] It should be noticed that the modeling of ADELE’s sensitivity is based on certain assumptions. The model is only valid for IC+ discharges, while at least 50% of the subset shown in Figure 2 (top and middle) of Smith et al. [2011] are CG– discharges. A fixed 87 g/cm2 is used for the avalanche region, which might be reasonable for charge top below 16 km (3 km charge separation), but is very large (5 km) for the higher charge tops. [23] Assuming that ADELE’s sensitivity is indeed 1000 times better at 4 km compared to 10 km our results indicate that there is a cut-off (or roll-off) in the TGF distribution. Such a cut-off is implicit in the analysis of a fixed number of lightning discharges: the lower limit must be chosen such that the integral of the distribution matches the number of events. ADELE’s single observation at a relative intensity of n0 = 1 out of 1213 lightning discharges implies a minimum intensity threshold of n0 1/1000, the minimum value on the x axis in Figure 6a. We can estimate at which fluence value relative to the lower threshold of RHESSI detection this cut-off might be, assuming that the TGFs follow Poisson statistics. The probability, p, of non-detection when predicted number of detection is NP, is given by pN0 ¼ e NP ð8Þ [24] In Figure 6b we show the probability of non-detection given that one TGF was observed at 10 km as a function of the relative sensitivity of ADELE between 10 km and 4 km, 6 of 8 6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude A03327 ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE Figure 6. (a) The distribution of TGFs if all the 1213 and 133 lightning discharges can produce TGFs with a power law distribution with l = 2.0 (solid). The values, n0, indicate the relative lower threshold for detecting one TGF for l = 2.0 (solid). The vertical dotted line is the highest number of observed TGFs given a sharp cut-off in the distribution. The dashed lines are for a power distribution with l = 1.3. (b) The probability of non-detection as a function of relative sensitivity for ADELE at 10 km and 4 km given that one TGF was detected at 10 km. Probabilities are shown for distributions with l = 2.0 (solid) and l = 1.8 and 2.2 (dotted) and l = 1.3 (dashed). The horizontal dotted line indicates a probability of 1 out of 10. given by the relative lower thresholds of detection, n4/n10. Given that 0.1 (NP = 2.6) from the 133 distribution is a reasonable probability of non-detection (marked with a dotted horizontal line in Figure 6b) this cut-off is at a sensitivity level of 5/100 of ADELE at 10 km, which is 5/600 of the weakest TGF observed by RHESSI (RHESSI has 1/6 of ADELE sensitivity at 10 km), or 3/600 if one compares with the average RHESSI TGF, which is a factor of 2 larger than the RHESSI lower threshold. If the increase of ADELE’s sensitivity is less than three orders of magnitude (from 10 km to 4 km) this cut-off would move to lower values. If all the lightning discharges produces TGFs, the modeling results of Smith et al. [2011] would have to be off by a little less than one order of magnitude. 77 A03327 [25] We can relate this cut-off in the TGF distribution to the lowest number of electrons that can be produced in a TGF and what the global TGF production rate would be. Our modeling results, using the model described by Østgaard et al. [2008], indicate that the total number of photons produced in an average RHESSI TGF ranges from 1016 (21 km production altitude) to 1018 (15 km production altitude) in agreement with others [e.g., Smith et al., 2011]. The probability of bremsstrahlung production increases non-linearly with energies and is about 10% for 2 MeV electrons [Berger and Seltzer, 1972] and approaches 100% at higher electron energies. Measured photon energies >20 MeV indicate that we are in this energy range, which implies that the number of electrons is also ranging from 1016 to 1018. With a cut-off in the TGF distribution at 5/600 of the RHESSI threshold the lowest possible number of electrons produced in a TGF would be 1014. [26] From Figure 6a one can see that a cut-off at n0 = 5/100 which corresponds to 5/100 of ADELE at 10 km and 5/600 of the RHESSI lower threshold would give 20 TGFs from the 1213 lightnings from which RHESSI would have seen 0.1 TGF. This implies that the global production rate of TGFs within 38 latitude is about 200 (20/0.1) times what we estimated from RHESSI TGF detection. This gives 50000 TGFs/day or about 35 TGFs every minute and compared to the IC lightning occurrence frequency within the same latitude range of 2.7 106/day, the ratio of TGF/ lightning is about 2%. These numbers are slightly larger than estimated by Smith et al. [2011]. [27] We should emphasize that these estimates are based on only one single TGF observation from 10 km. Furthermore, they are based on the assumption of having a sharp cut-off in the TGF distribution. In reality there is probably a roll-off which would decrease the lowest number of electrons and increase the global TGF production rate. Our estimates are consistent with the non-detection by ADELE and depend strongly on these results. If future aircraft or balloon missions find slightly different results our estimates need to be recalculated. [28] Finally, we will discuss the implication of a roll-off instead of a sharp cut-off in the TGF distribution which is a more realistic distribution. Our results indicate that the power law with l = 2.3 is valid at least down to the Fermi threshold, which is 1/3 of RHESSI. Looking at the black histogram in Figure 4b one can argue that there is indeed a roll-off in the lower 8 bins from the peak value, which can be fitted with a l of 1.7. According to Carlson et al. [2012], this corresponds to a source distribution with l < 1.3. As long as the roll-off threshold is at 1/3 of RHESSI lower threshold or higher, ADELE is observing from the part of the distribution with l = 1.3. Such a distribution is shown as dashed lines in Figure 6a, and one can see that the ADELE’s sensitivity would have to increase 3 orders of magnitude (n0 decreases from 107 to 104 on the relative scale) to see 1 TGF from a distribution of 133 TGFs. As can be seen from Figure 6b the probability of non-detecting at 4 km (n4/n10 = 1/10000) is only 0.1. In this case we can not rule out that all IC lightning discharges produce TGFs. Using the true distribution as seen from space (l = 1.3) an ideal instrument with sensitivity 10000 times better than RHESSI would have seen about N = 4000 TGFs/day within 7 of 8 78 A03327 Scientific results ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE a radius of 400 km. The lowest number of total electrons produced in a TGF would then be 1012. 7. Summary [29] To summarize, we have used two independent methods to find the RHESSI dead-time losses and an estimate of the true fluence distribution of TGFs as measured from satellite altitude. The two methods give dead-time losses of 24% and 26% for an average RHESSI TGF 33–35 counts. Assuming a sharp cut-off the true TGF fluence distribution is found to follow a power law with l = 2.3 0.2 down to 5/600 of the detection threshold of RHESSI. This corresponds to a lowest number of electron produced in a TGF to be 1014 and a global production rate within 38 latitude of 50000 TGFs/day or about 35 TGFs every minute, which is 2% of all IC lightning. If a more realistic distribution with a roll-off below 1/3 (or higher) of the RHESSI lower detection threshold with a true distribution with l ≤ 1.7 that corresponds to a source distribution with l ≤ 1.3 is considered, we can not rule out that all discharges produce TGFs. In that case the lowest number of total electrons produced in a TGF is 1012. [30] Acknowledgments. We are indebted to the RHESSI and Fermi GBM teams for the design and successful operations of the two missions. We thank D. A. Smith for the use of RHESSI data and M. Briggs for the use of Fermi GBM data. This study was supported by the Norwegian Research Council, under the two contracts 197638/V30 and 208028/F50. [31] Robert Lysak thanks the reviewers for their assistance in evaluating this paper. References Berger, M. J., and S. M. Seltzer (1972), Bremsstrahlung in the atmosphere, J. Atmos. Terr. Phys., 34, 85–108. Boccippio, D. J., K. L. Cummings, H. J. Christian, and S. J. 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Smith (2010), A closer examination of terrestrial gamma-ray flash-related lightning processes, J. Geophys. Res., 115, A00E30, doi:10.1029/2009JA014835. Smith, D. M., et al. (2011), The rarity of terrestrial gamma-ray flashes, Geophys. Res. Lett., 38, L08807, doi:10.1029/2011GL046875. Williams, E. R. (2006), Problems in lightning physics—the role of polarity asymmetry, Plasma Sources Sci. Technol., 15(2), 91–108, doi:10.1088/ 0963-0252/15/2/S12. B. Carlson, T. Gjesteland, R. S. Hansen, and N. Østgaard, Department of Physics and Technology, University of Bergen, Allegt. 55, N-5007 Bergen, Norway. ([email protected]) A. B. Collier, SANSA Space Science, Hospital Street, Hermanus, 7200 South Africa. 8 of 8 Paper 2 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters R. S. Hansen, N. Østgaard, T. Gjesteland, and B. Carlson Journal of Geophysical Research Space Physics, 118, doi:10.1002/jgra.50143, 2013 80 Scientific results 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters 81 JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 1–7, doi:10.1002/jgra.50143, 2013 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters R. S. Hansen,1,2 N. Østgaard,1,2 T. Gjesteland,1,2 and B. Carlson1,2 Received 8 August 2012; revised 21 November 2012; accepted 24 January 2013. [1] Up to a few years ago, terrestrial gamma ray flashes (TGFs) were only observed by spaceborne instruments. The aircraft campaign ADELE was able to observe one TGF, and more attempts on aircraft observations are planned. There is also a planned campaign with stratospheric balloons, COBRAT. In this context an important question that arises is what count rates we can expect and how these estimates are affected by the initial properties of the TGFs. Based on simulations of photon propagation in air we find the photon fluence at different observation points at aircraft and balloon altitudes. The observed fluence is highly affected by the initial parameters of the simulated TGFs. One of the most important parameters is the number of initial photons in a TGF. In this paper, we give a semi-analytical approach to find the initial number of photons with an order of magnitude accuracy. The resulting number varies over several orders of magnitude, depending mostly on the production altitude of the TGF. The initial production altitude is also one of the main parameters in the simulations. Given the same number of initial photons, the fluence at aircraft and balloon altitude from a TGF produced at 10 km altitude is 2–3 orders of magnitude smaller then a TGF originating from 20 km altitude. Other important parameters are altitude distribution, angular distribution and amount of feedback. The differences in altitude, altitude distribution and amount of feedback are especially important for the fluence of photons observed at altitudes less than 20 km, and for instruments with a low-energy threshold larger than 100 keV. We find that the maximum radius of observation in 14 km for a TGF with the intensity of an average RHESSI TGF is smaller than the results reported by Smith et al. (2011), and our results support the conclusion in Gjesteland et al. (2012) and Østgaard et al. (2012) that TGFs probably are a more common phenomenon than previously reported. Citation: Hansen, R. S., N. Østgaard, T. Gjesteland, and B. Carlson (2013), How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters, J. Geophys. Res. Space Physics, 118, doi:10.1002/jgra.50143. 1. Introduction [3] From spectral analyses of the TGFs seen from space, TGFs have been found to have production altitudes between 15 and 20 km [Dwyer and Smith, 2005; Gjesteland et al., 2010]. There might be TGFs produced at lower altitudes, but due to atmospheric attenuation they will not be detectable from space. Dwyer and Smith [2005] showed that an average RHESSI TGF could be fairly accurately modeled by assuming 1017 initial photons produced at 15 km altitude. Østgaard et al. [2012] have suggested that there might exist TGFs with intensities down to 1012 initial photons. [4] Several studies have also aimed at finding the initial angular distribution of the photons in a TGF. Gjesteland et al. [2011] used TGF and lightning observations together with simulations and found the observations to be consistent with an isotropic angular distribution inside a cone with half angle between 30° and 40°. Hazelton et al. [2009] used an anisotropic angular distribution out to 90 degrees and found the best fit to be for a beam with a half maximum at 35° (read out from Figure 2b of Hazelton et al. [2009]). [2] Terrestrial gamma ray flashes (TGFs) are short bursts of high energy radiation originating from the Earth’s atmosphere and observed from space. The radiation is produced, through the bremsstrahlung process, by energetic electrons that are accelerated by relativistic runaway electrons in strong electric fields. The TGFs are found to be closely connected to thunderstorms and lightning discharges [Inan et al., 1996; Cohen et al., 2010; Shao et al., 2010], so the electric fields are expected to be located in or around thunderstorms. 1 Department of Physics and Technology, University of Bergen, Bergen, Norway. 2 Birkeland Centre for Space Science, N-5020 Bergen, Norway Corresponding author: R. S. Hansen, Department of Physics and Technology, Allegt. 55, N-5007, Bergen, Norway. ([email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9380/13/10.1002/jgra.50143 1 82 Scientific results HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES 13 [5] So far, most observations of TGFs have been obtained by spaceborne instruments. The first observations were made by the Burst and Transient Source experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) [Fishman, 1994]. During the last 10 years, observations have also been made by Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) [Smith et al., 2005], FERMI [Briggs, 2010], and AGILE [Marisaldi, 2010]. [6] In 2009, an effort to observe TGFs using aircraftborne instruments was carried out [Smith, 2011a]. During 37 hrs of observations the ADELE instrument detected only one event [Smith, 2011b]. During the flight time, there were more than 1000 lightning discharges closer than 10 km from the aircraft. Smith [2011a] also made a simulation and calculation of the expected number of TGFs. Due to the very few detected events, they concluded that only 0.1–1% of all flashes produce TGFs and that the TGF intensities cannot follow a power law distribution below 1/100 of the average RHESSI TGFs. However, a recent study by Østgaard et al. [2012] based on Fermi and RHESSI TGFs as well as the non-detection by ADELE argued that one cannot rule out that all lightning produce TGFs. This is also supported by the findings of more TGFs in the RHESSI data [Gjesteland et al., 2012] and in the GBM Fermi data [Østgaard et al., 2012]. [7] In this paper, we show the results of a simulation of photon fluence at aircraft altitudes as well as at balloon altitudes. As should be clear from this introduction, the constraints obtained from observations still open up for a broad variation of initial conditions, and we show that the resulting fluence is highly dependent on these initial conditions. We also show that the number of initial photons in a TGF seen from space is dependent on the initial conditions used in the simulation. Altitude [km] 12 11 10 9 0.0 0.2 0.4 0.6 0.8 1.0 Relative number of photons/km Figure 1. The altitude distribution from Smith [2011a] shown for an initial production altitude of 12 km. The photons are distributed over an atmospheric depth of 87 g/cm2 . spectrum one can get from bremsstrahlung and the cutoff corresponds to the largest single photon energy observed by AGILE [Marisaldi, 2010]. Tavani [2011] claim to have observed photons with energies up to 100 MeV, but the number of photons with these energies is very small. As the expected production altitude of TGFs is below 20 km, we have used initial production altitudes between 8 and 20 km. To be able to compare with earlier modeling results, we have also used both discrete and distributed photon production altitude distributions. For the distributed altitudes, we have used the distribution described in Smith [2011a] where the avalanche region extends over 87 g/cm2 of air. Figure 1 shows the altitude distribution for a production altitude of 12 km and is taken directly from Smith [2011a]. For other altitudes, this distribution is scaled to stretch over 87 g/cm2 at that specific altitude with the maximum of the distribution at the altitude in question. This means that the vertical length of the distribution is large for large initial altitudes and smaller for low initial altitudes. The distributed altitudes will be discussed below and our results will be compared with the results of Smith [2011a]. [10] We use three different angular distributions: (1) all photons distributed isotropically within a cone of ˙30° half angle, (2) distributed isotropically within ˙40° half angle, and (3) angular distributions out to 90° as shown in Figure 2a of Hazelton et al. [2009], all centered around the vertical direction. The angular distribution of Hazelton et al. [2009] was obtained from a model of the RREA with a vertical electric field and gave an energy-dependent angular distribution. For photons with energy less than 1 MeV, we have used the red distribution shown in Figure 2a of Hazelton et al. [2009]; for photons with energy more than 1 MeV, we have used the blue distribution in the same figure. Gjesteland et al. [2011] found all of these angular 2. Monte Carlo Simulations [8] The simulation used to find the expected detection rates is based on the Monte Carlo model developed by Østgaard et al. [2008]. This model is a more simple model than for instance GEANT or the model of Dwyer [2012], but Østgaard et al. [2008] found good correspondence between this model and GEANT. The model propagates photons through the atmosphere in length steps. The density of the atmosphere is approximated by an exponential fit to MSIS data. The initial photons are given an initial energy (E), altitude, and direction and are propagated through the atmosphere. The model takes Compton scattering, photoelectric absorption, and pair production into account. The Compton electrons are not taken into account, the photons produced by bremsstrahlung from the electron and positron after pair production is not taken into account, and the positron is assumed to annihilate at the same position as the production of the positron. Østgaard et al. [2008] showed that this simplification gives about 7% less photons, in the energy range below 80 keV. As the lower energy threshold for instruments is typically in the range from 200 to 400 keV, the simplification will not affect our results significantly. [9] We have used 100 million initial photons with an initial energy spectrum as a 1/E spectrum with a cutoff at 40 MeV for all simulations. This is the hardest energy 2 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters 83 HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES NI = R m I( )dA( ) R m 0 dA( ) 0 (1) where I is the fluence at a given angle , dA is a small annular area at the angle , and m is the maximum angle of observation. If we assume an isotropic initial angular distribution, the fluence is given as I( ) = kI0 d2 (2) where I0 is the initial number of photons per steradian, d = h/ cos as shown in Figure 3, and k is a factor to account for the loss of photons in the atmosphere. From the geometry of the calculation shown in Figure 3, we get dA = 2ada = 2h2 tan d cos2 (3) Solving these equations for I0 , we get Figure 2. The geometry for the simulations. Horizontal radius is the distance from the initial photon production. I0 = R sin NIh2 0m cos 3 d R m k tan d (4) 0 distributions to be consistent with observations. The photons going downward due to the feedback process described in Dwyer [2007, 2012] have been approximated by sending 0% (no feedback), 0.1% (weak feedback), or 1% (strong feedback) of the initial photons downward with the same initial angular distribution as the photons going upward. The fraction of photons initially traveling downward is determined by using the average number of downward traveling positrons produced per runaway electrons found by Dwyer [2012]. The number is found to be 3 10–4 rn positrons per runaway electron per meter, where rn is the number density of air relative to the ground. With electric field strengths just above the runaway threshold, around 30% of these positrons will turn around and be accelerated downward in the electric field [Dwyer, 2012, Figure B3]. The vertical field size needed to get an average RHESSI TGF is found by Dwyer and Smith [2005] to be of the order of 100 m/rn . These numbers give about 1% photons initially traveling downward. The fraction of about 1% is also consistent with strong feedback in Figure 1 in Babich [2005]. [11] We have sampled all photons passing through detection altitudes of 14, 20 (aircraft altitudes), and 35 km (balloon altitude) and sorted them in intervals of 1 km horizontal radius from the initial position. The geometry is shown in Figure 2. The number of photons are then scaled according to the number of initial photons assumed. The total initial number of photons is then found by multiplying this with the solid angle: N0 = I0 2(1 – cos m ) (5) [13] The factor k is calculated from the Monte Carlo results as the relative number between the number of photons escaping the atmosphere to the number of initial photons. For each choice of initial parameters, we get a different k. The initial altitude distribution and the initial photon angular distribution give some contribution, but the main parameter is the production altitude. As we are only trying to determine the order of magnitude of k, we neglect other contributions than the initial production altitude. The values of k are in the range between 10–2 and 10–4 for altitudes from 20 km to 10 km. By using a discrete initial altitude distribution and the initial photon angular distribution of Hazelton et al. [2009, Figure 2a], we get a number of photons as given in Table 1. 3. Number of Initial Photons [12] The number of initial photons in an average RHESSI TGF can be calculated semi-analytically. The average TGF detected by RHESSI has a fluence of NI = 0.1 photons/cm2 and RHESSI has been shown to see TGFs at least out to 600 km away from nadir [Cohen et al., 2010; Gjesteland et al., 2011; Collier et al., 2011]. The average fluence of photons in a circular area can be expressed as Figure 3. The geometry used for the calculation of number of initial photons. d is the distance between the initial photon production and the satellite, h is the difference in altitude between the initial photon production and the satellite, and is the angle between h and d. 3 84 Scientific results HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES Table 1. Number of Initial Photons for Different Initial Production Altitudes Initial Photon Altitude Number of Initial Photons 10 km 15 km 20 km 1018 1017 1016 [14] As seen in Table 1, the initial production altitude gives a large variation in the number of initial photons needed to match the average intensities observed by RHESSI. These numbers are calculated with m = 45°, and the result is sensitive to the choice of this parameter. TGFs have been observed out to m = 60° [Cohen et al., 2010] but the small number of TGFs at these large angles may suggest that these TGFs are especially strong. If we use m = 60°, the number of initial photons increase with a factor of 2–3. When using a distributed initial production altitude distribution, the number of initial photons increases by approximately 10%. A change in the initial photon angular distribution gives an increase of up to 20%, while varying the production altitude gives variations of a factor of 10 and 100. Figure 5. Fluence of photons at 20 km altitude. The detection threshold is set to 300 keV, the initial number of photons is 1017 , and the initial photon altitude distribution is discrete. some will be at the same altitude or above. The fluence of photons is then highly dependent on the other initial conditions. Figure 4 also shows how the fluence varies with initial angular distribution. As long as the observation altitude is higher than the initial production altitude, the main difference between the initial angular distributions is that the two isotropic distributions give a clear drop in fluence around the maximum angle of 30° or 40°. This is an effect of observing inside or outside the initial cone of the photon angular distribution. When the photons are distributed smoothly out to 90°, there is no such cutoff. For horizontal distances larger than where we see the drop off distance, the fluence for all angular distributions is similar. [17] As long as the TGFs are observed above the initial production altitude, the fluence does not depend significantly on the initial production altitude distribution (not shown). For isotropic initial angular photon distribution, the drop at 30° or 40° half angle is sharper for a discrete initial production altitude than for a distributed initial production altitude. The effect of feedback is also small for observational altitudes higher than the initial production altitude. [18] Figure 5 is fluence for observation at 20 km altitude and shows the same features as commented in connection to observations at 35 km altitudes. For production at 20 km altitude (black curve), we see that the differences between the initial photon angular distributions are small. Hence, the number of backscattered photons is quite similar for the three different cases. [19] Figure 6 shows the fluence of photons at 14 km. Observations at this altitude show a large difference between observations above or below the initial production altitude of the TGF. The photons below the initial production altitudes consist of photons being Compton scattered down and photons produced by positrons moving down. In the process of Compton scattering, the photons will in general lose much of their energy. As seen in the figure, the fluence from a TGF produced at 20 km is much smaller than for production closer to the observational altitude. Here, the solid lines are for production at discrete altitude and the dashed lines are for distributed initial altitudes. A distributed initial production altitude gives a slightly larger fluence when the observations are made below the initial production altitude. This will be discussed below. The difference between 4. Dependence on Initial Conditions [15] For the simulations presented in the beginning of this section, we have used an initial number of photons of 1017 , of which 108 are simulated and then scaled with 109 . This corresponds to a production altitude of 15 km for an average RHESSI TGF and is the most used number of initial photons in other models [Dwyer, 2012]. The results when using different number of initial photons for the different initial altitudes are shown at the end of the section. [16] The initial production altitude of the photons is very important due to the attenuation in the dense lower atmosphere. As shown in Figure 4, the difference in fluence when observed at 35 km varies 2–3 orders of magnitude when assuming production altitudes from 10 km to 20 km. For observations at 14 km and 20 km, some of the initial production altitudes will be below the observation altitude and Figure 4. Fluence of photons at 35 km altitude. The detection threshold is set to 300 keV, the initial number of photons is 1017 , and the initial photon altitude distribution is discrete. The drop in the two isotropic angular distributions is due to the effect of being inside or outside of the initial cone. 4 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters 85 HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES Table 2. Maximum Radius of Detection of All the Various TGFs Modeled in This Worka Detection Altitude 14 km 20 km 35 km Unscaled 300 keV 100 keV 6 km 14 km 27 km 8 km 19 km 32 km Scaled 300 keV 100 keV 3 km 18 km 39 km 6 km 23 km 51 km a Unscaled is maximum radius for a TGF with 1017 initial photons at all altitudes, scaled is for TGFs initial number of photons scaled according to Table 1. The maximum radius is given for instruments with a low energy threshold of 100 keV and 300 keV. main part of the observed photons is backscattered photons originally directed upward. This makes the intensity difference between TGFs with and without feedback very small at radial distances larger than about 1 km. [22] What mostly affects the ability to detect TGFs at different observational altitudes is the maximum horizontal distance of detection. Table 2 shows the maximum horizontal distance from the source at which the instrument can still detect all the various TGFs, independent of initial conditions, within the constraints of this paper. In other words, we have used the initial conditions that give the smallest fluence at the observational altitude in consideration. The instrument is assumed to have a detection limit of 0.1 photon/cm2 . With an energy threshold of 300 keV, the instrument can detect all the various TGFs within a radial distance of 27 km when observed at 35 km altitude. At 20 km altitude, the maximum radial distance is 14 km, and at 14 km altitude maximum distance is 6 km. [23] Another major difference is the change between observing the TGF from a position above or below the altitude where the TGF originates. When observed at 14 km altitude, the probability of detection is highly affected by the amount of feedback and the altitude distribution of the initial photons. The fluence of photons is much smaller with no or weak feedback (0.1%), than with an average feedback (1%) or more, which also makes the maximum radius of detection much smaller. This is further discussed below. [24] With a decreasing lower energy threshold from E > 300 keV to E > 100 keV, the fluence and the maximum radial distance of detection increase. This is shown in Table 2. The increased number of photons is most important at large radial distances where the relative number of low energy photons to high energy photons is largest. When the photons are distributed out to 30° or 40°, all photons detected at large angles/large horizontal distance have experienced Compton scattering and lost energy [Østgaard et al., 2008; Hazelton et al., 2009]. Thus, we see a larger number of high energy photons at large distances when the photons are distributed out to 90° 4.1. Differentiated Number of Initial Photons [25] Table 2 and Figure 8 show the maximum radius of observation and fluence at 35 km altitude when we use 1016 initial photons for a TGF originating at 20 km altitude, 1017 initial photons for a TGF produced at 15 km altitude, and 1018 initial photons for a TGF produced at 10 km altitude. Figure 8 shows that the fluence of photons is about similar when using differentiated number of initial photons. This is because the number of photons is calculated to match the average RHESSI TGF, and the fluence of photons at a given Figure 6. Fluence of photons at 14 km altitude. The detection threshold is 300 keV, the initial number of photons is 1017 , and the photons have an initial angular distribution out to 90°. The TGFs with distributed altitudes are distributed according to Figure 1. distributed and discreet altitudes for TGFs produced at 10 km and 15 km is small. This is because the distributed altitudes have a very narrow peak which means that the main part of the photons are originating close to the maximum altitude of the distribution. [20] Figure 7 shows the effect of feedback when the observations are made below the initial production altitude. At these observational altitudes, even a small feedback will give a larger fluence than with no feedback, and an increased feedback will increase the fluence significantly. The fluence falls off somewhat faster with radial distance when feedback is included. All the profiles are for discrete production altitudes, and the differences are larger for discrete altitudes than for distributed altitudes. [21] When observing from below the production altitude, the drop at 30° or 40° half angles is only seen when feedback is included. This is an effect of using the same initial photon angular distributions for photons going downward and upward. For the TGF originating at 15 km altitude, the Figure 7. Fluence of photons at 14 km altitude. The detection threshold is 300 keV, the initial number of photons is 1017 , the photons have an initial angular distribution out to 90°, and the initial photon altitude distribution is discrete. Feedback is approximated by giving 1% of the photons an initial downward direction, see section 5 for discussion. 5 86 Scientific results HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES et al. [2005] show the existence of electric fields larger than the limit for relativistic breakdown only extend over 1 km at 6 km altitude. This corresponds to an atmospheric depth of 70 g/cm, which is comparable to a 5 km vertical extension of the electric field at 20 km altitude. In balloon observations reported by Stolzenburg et al. [2007], from several observations at higher altitudes, the electric field seems to extend over even smaller vertical distances. [27] Having electric fields at the threshold for RREA over an atmospheric depth of 87g/cm2 implies a potential difference of 200 MV for any altitude. This is the lower limit for the production of high energy photons across the whole vertical distance used as the distributed altitudes in our modeling. From balloon soundings, the potential between the nearest relative maximum and minimum potential in thunderclouds was reported by Marshall and Stolzenburg [2001] to be up to 132 ˙ 2 MV. Most thunderclouds are therefore not expected to have potentials of more than 200 MV which is required for RREA over 87 g/cm2 . As the altitude distribution in Smith [2011a] is derived from the assumption of a very powerful thunderstorm, they probably overestimate the feedback factor as well as the prediction of seeing TGFs by letting the photons being produced over a too large altitude range. [28] A consequence of having electric fields over large vertical distances is that at least 10% of the photons will have initial production altitudes lower than 15 km for all the different initial altitudes. This also explains the difference between discrete and distributed initial production altitudes for observations in 14 km altitude in our results. [29] Figure 9 shows a comparison between our results and Figure 1 in Smith [2011a]. The figure of Smith [2011a] gives the contours for 20, 200, 2000, and 20,000 counts in the detector used by ADELE. We have not been able to propagate out photons through the aircraft body, which means that we overestimate the number of photons. We have used an effective area of the detector of 65 cm2 [Smith, 2011a]. Figure 8. Fluence of photons at 35 km altitude. The detection threshold is set to 300 keV and the initial photon altitude distribution is discrete. The number of initial photons is scaled according to Table 1. altitude should then be the same for all initial production altitudes. If we had used the exact number from the calculation, instead of order of magnitude, all three curves should be equal. This also underlines that the number of initial photons is an important parameter for simulations of TGFs and that the production altitude is the main parameter determining the final flux. 5. Discussion [26] To compare our results with the results of Smith [2011a], we have distributed the initial photons over 87 g/cm2 of atmosphere. At 8 km altitude, this corresponds to a vertical distance of 1500 m. Due to the exponential decrease in density of the atmosphere with altitude, this vertical distance will increase for higher altitudes. At 20 km altitude, the photons are distributed over 5800 m vertical distance with the top of the distribution at 20 km. Using balloon measurements of electric fields in thunderstorms, Marshall Figure 9. Contours of counts in the detector used by ADELE [Smith, 2011a]. The black curves are results from Smith [2011a], and the gray curves are our results including error bars. The left figure shows our results without feedback and the right figure is with 1% feedback. The curves are for an observational altitude of 14 km, with initial production altitudes distributed over 87 g/cm2 and initial production angles out to 90°. 6 6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters 87 HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES References In Figure 9, the results of Smith [2011a] are shown in black and our results are shown in gray with error bars. As we calculate the flux of photons at every kilometer radius, we will have an error of ˙1 km. The figure on the left shows our results without feedback and the figure to the right shows the results with 1% feedback. Without feedback, our contours drop faster to 0 radius at high production altitudes compared to Smith [2011a]. With 1% feedback, the curves are more similar, but we have to include 5% feedback to be able to replicate the shape of the contours from Smith [2011a]. However, we are not able to replicate the distances that are shown by Smith [2011a]. The main difference in our simulations and the simulations of Smith [2011a] is the energy-angle distribution. We assumed the same energy distribution for the downward running photons produced by feedback as the upward moving photons. Then we have implemented the energy-dependent angular distribution of Hazelton et al. [2009] by distributing all energies >1 MeV according to Figure 2a in Hazelton et al. [2009], but have neglected that the high energy part of the photon spectrum has a narrower angular distribution. Hence, the high energy photons in our model is distributed more widely than is the case in Hazelton et al. [2009] and Smith [2011a]. This results in a small bias toward larger observational distances in our results. [30] The results in this paper are based on the intensities of an average TGF. However, according to Østgaard et al. [2012], one can expect a large number of TGFs with lower initial intensity. For these TGFs, the maximum radius of detection will be even smaller. ADELE had 133 discharges closer than 4 km to the aircraft. The results of our simulations show that if the assumptions made by Smith [2011a] are valid then the non-detection of ADELE means that TGFs are rare events. However, if the TGFs are produced in a shorter altitude interval and with less feedback, or with lower intensities than an average RHESSI TGF, then the TGFs might not be detectable to ADELE even at small radial distances. The results presented here combined with the fluence distribution found by Østgaard et al. 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Lett., 106 (1), 1–5, doi:10.1103/ PhysRevLett.106.018501. 6. Conclusion [31] In this paper we have shown how simulations of photon fluence at aircraft and balloon altitudes depend on the initial conditions. For all observational altitudes the number of photons and the initial production altitude are the two main parameters. When observations are made below the initial production altitude of the TGF, other parameters such as initial production altitude distribution, initial photon angular distribution and amount of feedback also give large differences. This means that one have to be careful when making conclusions based on these type of simulations. The comparisons to the non detection of ADELE together with the results of Østgaard et al. [2012] support the possibility that all discharges may produce TGFs. [32] Acknowledgment. This study was supported by the Norwegian Research Council under contract 208028/F50. 7 88 Scientific results Paper 3 6.3 An altitude and distance correction to the initial fluence distribution of TGFs R. S. Nisi, N. Østgaard, T. Gjesteland, and A. Collier Journal of Geophysical Research Space Physics, 2014 90 Scientific results