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NASA NTRS2013

Characterization of the Gaseous Companion k Andromedae B* New Keck and LBTI High-contrast Observations

Context. We previously reported the direct detection of a low mass companion at a projected separation of 55+/-2 astronomical units around the B9 type star kappa Andromedae. The properties of the system (mass ratio, separation) make it a benchmark for the understanding of the formation and evolution of gas giant planets and brown dwarfs on wide-orbits. Aims. We present new angular differential imaging (ADI) images of the system at 2.146 (K(sub s)), 3.776 (L'), 4.052 (NB 4.05) and 4.78 micrometers (M') obtained with Keck/NIRC2 and LBTI/LMIRCam, as well as more accurate near-infrared photometry of the star with the MIMIR instrument. We aim to determine the near-infrared spectral energy distribution (SED) of the companion and use it to characterize the object. Methods. We used analysis methods adapted to ADI to extract the companion flux. We compared the photometry of the object to reference young/old objects and to a set of seven PHOENIX-based atmospheric models of cool objects accounting for the formation of dust. We used evolutionary models to derive mass estimates considering a wide range of plausible initial conditions. Finally, we used dedicated formation models to discuss the possible origin of the companion. Results. We derive a more accurate J = 15.86 +/- 0.21, H = 14.95 +/- 0.13, K(sub s) = 14.32 +/- 0.09 mag for kappa And b. We redetect the companion in all our high contrast observations. We confirm previous contrasts obtained at K(sub s) and L' band. We derive NB 4.05 = 13.0 +/- 0.2 and M' = 13.3 +/- 0.3 mag and estimate Log(base 10)(L/solar luminosity) = −3.76 +/- 0.06. Atmospheric models yield T(sub eff) = 1900(+100/−200) K. They do not set constrains on the surface gravity. "Hot-start" evolutionary models predict masses of 14(+25/−2) Jupiter mass based on the luminosity and temperature estimates, and considering a conservative age range for the system (30(+120/−10) million years). "warm-start" evolutionary tracks constrain the mass to M greater than or equal to 11 Jupiter mass. Conclusions. The mass of kappa Andromedae b mostly falls in the brown-dwarf regime, due to remaining uncertainties in age and mass-luminosity models. According to the formation models, disk instability in a primordial disk could account for the position and a wide range of plausible masses of kappa and b.

spectral energy distribution (SED)↗
NASA NTRS2007

SOFIA: Stratospheric Observatory For Infrared Astronomy

This viewgraph presentation reviews the great astronomical observatories both space and land based that are now operational. It shows the history of the development of SOFIA, from its conception in 1986 through the contract awards in 1996 and through the planned first flight in 2007. The major components of the observatory are shown and there is a comparison of the SOFIA with the Kuiper Airborne Observatory (KAO), which is the direct predecessor to SOFIA. The development of the aft ramp of the KAO was developed as a result of the wind tunnel tests performed for SOFIA development. Further slides show the airborne observatory layout and the telescope's optical layout. Included are also vies of the 2.5 Meter effective aperture, and the major telescope's components. The presentations reviews the technical challenges encountered during the development of SOFIA. There are also slides that review the wind tunnel tests, and CFD modeling performed during the development of SOFIA. Closing views show many views of the airplane, and views of SOFIA.

Kunz, Nans↗
NASA NTRS2010

Directivity of a Sparse Array in the Presence of Atmospheric-Induced Phase Fluctuations for Deep Space Communications

Widely distributed (sparse) ground-based arrays have been utilized for decades in the radio science community for imaging celestial objects, but have only recently become an option for deep space communications applications with the advent of the proposed Next Generation Deep Space Network (DSN) array. But whereas in astronomical imaging, observations (receive-mode only) are made on the order of minutes to hours and atmospheric-induced aberrations can be mostly corrected for in post-processing, communications applications require transmit capabilities and real-time corrections over time scales as short as fractions of a second. This presents an unavoidable problem with the use of sparse arrays for deep space communications at Ka-band which has yet to be successfully resolved, particularly for uplink arraying. In this paper, an analysis of the performance of a sparse antenna array, in terms of its directivity, is performed to derive a closed form solution to the expected array loss in the presence of atmospheric-induced phase fluctuations. The theoretical derivation for array directivity degradation is validated with interferometric measurements for a two-element array taken at Goldstone, California. With the validity of the model established, an arbitrary 27-element array geometry is defined at Goldstone, California, to ascertain its performance in the presence of phase fluctuations. It is concluded that a combination of compact array geometry and atmospheric compensation is necessary to ensure high levels of availability.

Nessel, James A.↗
NASA NTRS1991

CD-ROM publication of the Mars digital cartographic data base

The recently completed Mars mosaicked digital image model (MDIM) and the soon-to-be-completed Mars digital terrain model (DTM) are being transcribed to optical disks to simplify distribution to planetary investigators. These models, completed in FY 1991, provide a cartographic base to which all existing Mars data can be registered. The digital image map of Mars is a cartographic extension of a set of compact disk read-only memory (CD-ROM) volumes containing individual Viking Orbiter images now being released. The data in these volumes are pristine in the sense that they were processed only to the extent required to view them as images. They contain the artifacts and the radiometric, geometric, and photometric characteristics of the raw data transmitted by the spacecraft. This new set of volumes, on the other hand, contains cartographic compilations made by processing the raw images to reduce radiometric and geometric distortions and to form geodetically controlled MDIM's. It also contains digitized versions of an airbrushed map of Mars as well as a listing of all feature names approved by the International Astronomical Union. In addition, special geodetic and photogrammetric processing has been performed to derive rasters of topographic data, or DTM's. The latter have a format similar to that of MDIM, except that elevation values are used in the array instead of image brightness values. The set consists of seven volumes: (1) Vastitas Borealis Region of Mars; (2) Xanthe Terra of Mars; (3) Amazonis Planitia Region of Mars; (4) Elysium Planitia Region of Mars; (5) Arabia Terra of Mars; (6) Planum Australe Region of Mars; and (7) a digital topographic map of Mars.

Batson, R. M.↗
NASA NTRS1999

Hubble Space Telescope observations of Orion Nebula, Helix Nebula, and NGC 6822

This grant covered the major part of the work of the Principal Investigator and his collaborators as a Guaranteed Time Observer on the Hubble Space Telescope. The work done naturally divided itself into two portions the first being study of nebular objects and the second investigation of the interstellar medium between stars. The latter investigation was pursued through a contract with Princeton University, with Professor Lyman Spitzer as the supervising astronomer, assisted by Dr. Ed Fitzpatrick. Following the abrupt death of Professor Spitzer, his responsibilities were shifted to Dr. Fitzpatrick. When Dr. Fitzpatrick relocated to Villanova University the concluding work on that portion of this grant was concluded under a direct service arrangement. This program has been highly successful and the resulting publications in scientific journals are listed below. To the scientist, this is the bottom line, so that I shall simply try to describe the general nature of what was accomplished. There were three nebular programs conducted, one on the Orion Nebula, the second on the Helix Nebula, and the third on NGC 6822. The largest program was that on the Orion Nebula. This involved both HST observations and supporting groundbased observations obtained with a variety of instruments, including the Coude Feed Telescope at the Kitt Peak National observatory in Arizona, the Cerro Tololo observatory in Chile, and the Keck Observatory on Mauna Kea, Hawaii. Moreover, considerable theoretical modeling was done and all of the data analysis was performed at the Rice University in Houston, except for the PI's period of sabbatical leave (6-96 through 7-97) when he was based at the Max Planck Institute for Astronomy in Heidelberg, Germany. The Orion Nebula program was the most productive part, resulting in numerous papers, but more important in the discovery of a new class of objects, for which we coined the name "proplyds". The proplyds are protoplanetary disks surrounding very young stars still in the process of creation. The Orion Nebula is the residual material from a burst of star formation that occurred about 300,000 years ago. Each of these new stars has a surrounding disk of protoplanetary material. The same physics that renders the Nebula so highly visible means that the proto-planetary disks are also quite visible. With the wisdom of hindsight, we now see that this was to be expected and that we should have been searching specifically for this type of object. The discovery of these objects and their subsequent detailed investigation has lead to an accurate assessment of the frequency of protoplanetary disks in young stars and determination of the likelihood of survival of these disks into an era where planets actually form.

Spitzer, Lyman↗
NASA NTRS2002

Holographic Gratings for Optical Processing

Investigation of astronomical objects and tracking of man-made space objects lead to generation of huge amount of information for optical processing. Traditional big-size optical elements (such as optical telescopes) have a tendency for increasing aperture size in order to improve sensitivity. This tendency leads to increasing of weight and costs of optical systems and stimulate search for the new, more adequate technologies. One approach to meet these demands is based on developing of holographic optical elements using new polymeric materials. We have investigated possibility to use new material PQ-PMMA (phenantrenequinone-doped PMMA (Polymethyl Methacrylate)) for fabrication of highly selective optical filters and fast spatial-temporal light modulators. This material was originally developed in Russia and later was tested in CalTech as a candidate material for optical storage. Our theoretical investigation predicts the possibility of realization of fast spatial and temporal light modulation, using volume reflection-type spectral filter. We have developed also model of holographic-grating recording in PQ-PMMA material, based on diffusional amplification. This mechanism of recording allow to receive high diffraction efficiency during recording of reflection-type volume holographic grating (holographic mirror). We also investigated recording of dynamic gratings in the photorefractive crystals LiNbO3 (LN) for space-based spectroscopy and for adaptive correction of aberrations in the telescope's mirrors. We have shown, that specific 'photogalvanic' mechanism of holographic grating recording in LN allow to realize recording of blazed gratings for volume and surface gratings. Possible applications of dynamic gratings in LN for amplification of images, transmitted through an imaging fiber guide was also demonstrated.

Nickolai Kukhtarev↗
NASA NTRS1991

The chemistry of dense interstellar clouds

The basic theme of this program is the study of molecular complexity and evolution in interstellar and circumstellar clouds incorporating the biogenic elements. Recent results include the identification of a new astronomical carbon-chain molecule, C4Si. This species was detected in the envelope expelled from the evolved star IRC+10216 in observations at the Nobeyama Radio Observatory in Japan. C4Si is the carrier of six unidentified lines which had previously been observed. This detection reveals the existence of a new series of carbon-chain molecules, C sub n Si (n equals 1, 2, 4). Such molecules may well be formed from the reaction of Si(+) with acetylene and acetylene derivatives. Other recent research has concentrated on the chemical composition of the cold, dark interstellar clouds, the nearest dense molecular clouds to the solar system. Such regions have very low kinetic temperatures, on the order of 10 K, and are known to be formation sites for solar-type stars. We have recently identified for the first time in such regions the species of H2S, NO, HCOOH (formic acid). The H2S abundance appears to exceed that predicted by gas-phase models of ion-molecule chemistry, perhaps suggesting the importance of synthesis on grain surfaces. Additional observations in dark clouds have studied the ratio of ortho- to para-thioformaldehyde. Since this ratio is expected to be unaffected by both radiative and ordinary collisional processes in the cloud, it may well reflect the formation conditions for this molecule. The ratio is observed to depart from that expected under conditions of chemical equilibrium at formation, perhaps reflecting efficient interchange between cold dust grains in the gas phase.

Irvine, W. M.↗
NASA NTRS1988

Thermal properties of heterogeneous grains

Cometary dust is not spherical nor homogeneous, yet these are the assumptions used to model its thermal, optical, and dynamical properties. To better understand the effects of heterogeneity on the thermal and optical properties of dust grains, the effective dielectric constant for an admixture of magnetite and a silicate were calculated using two different effective medium theories: the Maxwell-Garnett theory and the Bruggeman theory. In concept, the MG theory describes the effective dielectric constant of a matrix material into which is embedded a large number of very small inclusions of a second material. The Bruggeman theory describes the dielectric constant of a well mixed aggregate of two or more types of materials. Both theories assume that the individual particles are much smaller than the wavelength of the incident radiation. The refractivity for a heterogeneous grain using the MG theory is very similar to the refractivity of the matrix material, even for large volume fractions of the inclusion. The equilibrium grain temperature for spherical particles sized from .001 to 100 microns in radius at 1 astronomical unit from the sun was calculated. Further explanation is given.

Lien, David J.↗
NASA NTRS1977

The molecular composition of dense interstellar clouds

Presented in this paper is an ab initio chemical model for dense interstellar clouds that incorporates 598 grain surface reactions, with small grains providing the reaction area. Gas-phase molecules are depleted through collisions with grains. The abundances of 372 chemical species are calculated as a function of time and are found to be of sufficient magnitude to explain most observations. Peak abundances are achieved on time scales of the order of 100,000 to 1 million years, depending on cloud density and kinetic temperature. The reaction rates for ion-molecule chemistry are approximately the same, indicating that surface and gas-phase chemistry may be coupled in certain regions. The composition of grain mantles is shown to be a function of grain radius. In certain grain-size ranges, large molecules containing two or more heavy atoms are more predominant than lighter 'ices' - H2O, NH3, and CH4. It is possible that absorption due to these large molecules in the mantle may contribute to the observed 3-micron band in astronomical spectra.

Allen, M.↗
NASA NTRS2018

Image Guider Subsystem Analysis for the GHAPS Project

The Gondola for High-Altitude Planetary Science (GHAPS) project is a balloon-borne astronomical observatory designed operate in the UV, Visible, and near-mid IR spectral region. The GHAPS Optical Telescope Assembly (OTA) is designed around a one meter aperture narrow field-of-view telescope with near diffraction limited performance. GHAPS will utilize Wallops Arc-Second Pointing System (WASP) for pointing the OTA with an accuracy of 1 arc second or better. WASP relies heavily on a self-contained star tracker assembly to determine the OTA line of sight. Preliminary structural analysis indicated that potential misalignments could be present between the OTA line of sight and the star tracker FOV center during the expected flight conditions that could compromise GHAPS pointing accuracy. An analysis is presented that estimates the worst case long-term (or bias) pointing misalignments for the GHAPS opto-mechanical configuration, examines the need for additional hardware to correct pointing errors, and determines the best hardware and software implementation to do so. The analysis includes the development of a photometric model to predict the limiting magnitude of a GHAPS Facility Guide System (FGS) for a variety of image sensor technologies from visible to mid IR. FGS system performance is estimated using star magnitude and spectral data from actual star catalogs for more realistic predictions. Based on expected performance and other factors, such as size, weight, power, and cost, a final recommendation is made for the GHAPS configuration.

Telescope Guider↗
NASA NTRS1993

Diurnal tides in the Arctic Ocean

A 2D numerical model with a space grid of about 14 km is applied to calculate diurnal tidal constituents K(1) and O(1) in the Arctic Ocean. Calculated corange and cotidal charts show that along the continental slope, local regions of increased sea level amplitude, highly variable phase and enhanced currents occur. It is shown that in these local regions, shelf waves (topographic waves) of tidal origin are generated. In the Arctic Ocean and Northern Atlantic Ocean more than 30 regions of enhanced currents are identified. To prove the near-resonant interaction of the diurnal tides with the local bottom topography, the natural periods of oscillations for all regions have been calculated. The flux of energy averaged over the tidal period depicts the gyres of semitrapped energy, suggesting that the shelf waves are partially trapped over the irregularities of the bottom topography. It is shown that the occurrence of near-resonance phenomenon changes the energy flow in the tidal waves. First, the flux of energy from the astronomical sources is amplified in the shelf wave regions, and afterwards the tidal energy is strongly dissipated in the same regions.

Kowalik, Z.↗
NASA NTRS1988

Planetary astronomy: Rings, satellites, and asteroids

Studies of planetary rings focus on the dynamical processes that govern astronomically observable ring properties and structure. These investigations thus help reveal properties of the rings as well as probe the gravity fields of the planets. Satellite studies involve interpretation of orbital motion to extract information regarding the gravity fields of the outer planets and the physical properties of the satellites themselves. Asteroid lightcurve work is designed to investigate the large-scale shapes of the asteroids, as well as to reveal anomalous features such as major topography, possible satellites, or albedo variations. Work on the nature of viscous transport in planetary rings, emphasizing the role of individual particles' physical properties, has yielded a method for estimating both angular momentum and mass transport given an optical-thickness gradient. This result offers the prospect of ringlet instability, which may explain the square-profile ringlets in Saturn's C Ring. Thermal and reflected lightcurves of 532 Herculina have been interpreted to show that albedo variations cannot be the primary cause of variations. A lightcurve simulation has been developed to model complex asteroidal figures. Bamberga was observed during the December occultation as part of the joint LPL-Lowell program.

Greenberg, Richard↗
NASA NTRS1995

The unusual helium variable AM Canum Venaticorum

The unusual variable star AM CVn has puzzled astronomers for over 40 years. This object, both a photometric and spectroscopic variable, is believed to contain a pair of hydrogen-deficient white dwarfs of extreme mass ratio, transferring material via an accretion disk. We examine the photometric properties of AM CVn, analyzing 289 hours of high-speed photometric data spanning 1976 to 1992. The power spectrum displays significant peaks at 988.7, 1248.8, 1902.5, 2853.8, 3805.2, 4756.5, and 5707.8 microHz (1011.4, 800.8, 525.6, 350.4, 262.8, 210.2, and 175.2 s). We find no detectable power at 951.3 microHz (1051 s), the previously reported main frequency. The 1902.5, 2853.9, and 3805.2 microHz peaks are multiplets, with frequency splitting in each case of 20.77 +/- 0.05 microHz. The 1902.5 microHz seasonal pulse shapes are identical, within measurement noise, and maintain the same amplitude and phase as a function of color. We have determined the dominant frequency to be 1902.50902 +/- 0.00001 microHz with dot P = +1.71 (+/- 0.04) x 10(exp -11) s/s. We discuss the implications of these findings on a model for AM CVn.

Provencal, J. L.↗
NASA NTRS1994

Stellar density enhancements associated with IRAS sources in L1641

We obtained H and K' images of 59 Infrared Astronomical Satellite (IRAS) sources associated with dense molecular gas in L1641. Some of the sources were also imaged in narrow-band L and M. Using these near-IR images and photometry, we are able to identify the near-IR counterparts for most of the IRAS sources. The spectral energy distributions of the sources suggest that all of them are young stellar objects (class I and II sources). Most importantly, we find in this study that 14 IRAS sources are associated with small (but statistically significant) groupings of bright near-IR sources defined as stellar density enhancements (SDEs). The spatial distribution of young stars in the Orion A molecular cloud can be characterized by a range of stellar densities, from the Trapezium Cluster, to the SDEs, to individual stars. We conjecture that the SDEs are regions of continuous star formation within or around dense molecular cores and that they may represent an important mode of star formation in L1641. If true, adjustments to the standard star formation model may be required.

Chen, Hua↗
NASA NTRS2004

Recent Progress in Understanding the Sun's Magnetic Dynamo

100 years ago we thought that the Sun and stars shone as a result of slow gravitational contraction over a few tens of millions of years - putting astronomers at odds with geologists who claimed that the Earth was much, much older. That mystery was solved in the 1920s and 30s with the discovery of nuclear energy (proving that the geologists had it right all along). Other scientific mysteries concerning the Sun have come and gone but three major mysteries remain: 1) How does the Sun produce sunspots with an 11-year cycle? 2) What produces the huge explosions that result in solar flares, prominence eruptions, and coronal mass ejections? and 3) Why is the Sun's outer atmosphere, the corona, so darned hot? Recent progress in solar astronomy reveals a single key to understanding all three of these mysteries.The 11-year time scale for the sunspot cycle indicates the presence of a magnetic dynamo within the Sun. For decades this dynamo was though to operate within the Sun's convection zone - the outmost 30% of the Sun where convective currents transport heat and advect magnetic lines of force. The two leading theories for the dynamo had very different models for the dynamics of the convection zone. Actual measurements of the dynamics using the techniques of helioseismology showed that both of these models had to be wrong some 20 years ago. A thin layer of strongly sheared flow at the base of the convection zone (now called the tachocline) was then taken to be the seat of the dynamo. Over the last 10 years it has become apparent that a weak meridional circulation within the convection zone also plays a key role in the dynamo. This meridional circulation has plasma rising up from the tachocline in the equatorial regions, spreading out toward the poles at a top speed of about 10-20 m/s at the surface, sinking back down to the tachocline in the polar regions, and then flowing back toward the equator at a top speed of about 1-2 m/s in the tachocline itself. Recent dynamo models that include this meridional flow now appear to have some power for predicting the size of future sunspot cycles.

Hathaway, David. H.↗
NASA NTRS2011

COMPASS Final Report: Enceladus Solar Electric Propulsion Stage

The results of the NASA Glenn Research Center (GRC) COllaborative Modeling and Parametric Assessment of Space Systems (COMPASS) internal Solar Electric Propulsion (SEP) stage design are documented in this report (Figure 1.1). The SEP Stage was designed to deliver a science probe to Saturn (the probe design was performed separately by the NASA Goddard Space Flight Center s (GSFC) Integrated Mission Design Center (IMDC)). The SEP Stage delivers the 2444 kg probe on a Saturn trajectory with a hyperbolic arrival velocity of 5.4 km/s. The design carried 30 percent mass, 10 percent power, and 6 percent propellant margins. The SEP Stage relies on the probe for substantial guidance, navigation and control (GN&C), command and data handling (C&DH), and Communications functions. The stage is configured to carry the probe and to minimize the packaging interference between the probe and the stage. The propulsion system consisted of a 1+1 (one active, one spare) configuration of gimbaled 7 kW NASA Evolutionary Xenon Thruster (NEXT) ion propulsion thrusters with a throughput of 309 kg Xe propellant. Two 9350 W GaAs triple junction (at 1 Astronomical Unit (AU), includes 10 percent margin) ultra-flex solar arrays provided power to the stage, with Li-ion batteries for launch and contingency operations power. The base structure was an Al-Li hexagonal skin-stringer frame built to withstand launch loads. A passive thermal control system consisted of heat pipes to north and south radiator panels, multilayer insulation (MLI) and heaters for the Xe tank. All systems except tanks and solar arrays were designed to be single fault tolerant.

Oleson, Steven R.↗
NASA NTRS1995

Nucleosynthesis in AGB stars: Observation of Mg-25 and Mg-26 in IRC+10216 and possible detection of Al-26

We report the detection in the circumstellar envelope IRC+10216 of millimeter lines of the rare isotopomers (25)MgNC and (26)MgNC, as well as of a line at 234433 MHz, which could be the J= 7-6 transition of (26)AlF (an alternate, although less likely identified would be the J= 9-8 transition of NaF). The derived Mg-24:Mg-25:Mg-26 isotopic abundance ratios (78 : 11+/- 1 : 11 +/-1) are consistent with the solar system values (79.0:10.0:11.0), following Anders & Grevesse 1989). According to new calculations of evolutionary models of 3 solar mass and 5 solar mass asymptotic giant branch (AGB) stars, these ratios and the previously measured N, O and Si isotopic ratios imply that the central star had an initial mass 3 solar mass (less than or equal to M(sub *, ini) less than 5 solar mass and has already experienced many 3rd dredge-up events. From this, it can be predicted that the Al-26/Al-27 isotopics ratio lies between 0.01 and 0.08; in fact, the value derived in the case that U234433 arises from (26)AlF is Al-26/Al-27 = 0.04. The identification of the (25)MgNC and (26)MgNC lines was made possible by ab-initio quantum mechanical calculations of the molecule geometrical structure. It was confirmed through millimeter-wave laboratory measurements. The quantum mechanical calculations are briefly described and the laboratory results presented in some detail. The rotation constants B, D, H and the spin-rotation constant gamma of (25)MgNC and (26)MgNC are determined from a fit of laboratory and astronomical data.

Guelin, M.↗
NASA NTRS2003

Low-Energy Study of Gamma-Ray Bursts Having Spectral Line Features

Gamma-ray bursts (GRBs) are energetic, short-duration emissions of gamma-rays. The Burst and Transient Source Experiment (BATSE) that was onboard NASA s Compton Gamma-Ray Observatory has done much to advance our understanding of GRBs. Perhaps foremost is to establish that GRBs originate from astronomical sources that exist well beyond our galaxy. Another area in which BATSE has been instrumental is to provide high-resolution data that can be used in spectral studies. Before BATSE, there were many reports of GRB spectra containing what appeared to be spectral absorption lines, whereas Briggs, after an extensive computer search of 117 bright BATSE GRBs, reported finding only one case that might be an absorption line and ten cases that might be emission lines. None of the eleven BATSE cases were definitively identified as spectral lines, and Briggs indicated reasons as to why the pre-BATSE reports should not be taken as conclusive. It remains an open question as to what these spectral-like features are, or if they are even real. The purpose of this work is, for the subset of the eleven BATSE GRBs for which low-energy data are available from two BATSE's Spectroscopy Detectors (SDs), to include these data in the spectral analysis. Such a study will provide additional constraints on the model spectral functions to better ascertain the reality of the line features. The spectral analysis program used was RMFIT. Of the six GRBs that met the selection criteria, the analysis was performed on only three of them due to a lack of time.

Pangia, Michael J.↗