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At least 991 records · Page 55

Space environments and their effects on space automation and robotics

Automated and robotic systems will be exposed to a variety of environmental anomalies as a result of adverse interactions with the space environment. As an example, the coupling of electrical transients into control systems, due to EMI from plasma interactions and solar array arcing, may cause spurious commands that could be difficult to detect and correct in time to prevent damage during critical operations. Spacecraft glow and space debris could introduce false imaging information into optical sensor systems. The presentation provides a brief overview of the primary environments (plasma, neutral atmosphere, magnetic and electric fields, and solid particulates) that cause such adverse interactions. The descriptions, while brief, are intended to provide a basis for the other papers presented at this conference which detail the key interactions with automated and robotic systems. Given the growing complexity and sensitivity of automated and robotic space systems, an understanding of adverse space environments will be crucial to mitigating their effects.

Garrett, Henry B.↗

OSSE observations of GX 339-4

The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory (CGRO) observed the Galactic black hole candidate GX 339-4 as a target of oppurtunity in 1991 September, in response to the outburst reported by Burst and Transient Source Experiment (BATSE). We report here on energy spectra in the 50 keV-10 MeV range obtained by OSSE. The source was detected from 50 to 400 keV at a level relative to the Crab Nebula of approximately 30%. The observed spectrum was prescribed reasonably well by a power law with an exponential cutoff; a least-squares fit yielded a photon index of 0.88 +/- 0.05 and a cutoff energy of 68 +/- 2 keV. The addition of a Compton reflection component did not significantly improve the overall fit. An optically thin thermal bremsstrahlung spectrum also provides a good fit, and the thermal Comptonization model of Sunyaev & Titarchuk, while deficient in describing the data above approximately 200 keV, cannot formally be ruled out. A pure power law with reflection does not fit the observed spectrum. During a follow-up observation made in 1991 November the intensity of the source below 100 keV had dropped by more than a factor of 40, and it was no longer detected above approximately 100 keV. The energy spectrum during the November observation could be characterized by a power law with a photon index of 2.3 +/- 0.3; the spectrum was fitted equally well with the same exponentially cutoff power-law model applied to the September observation, reduced in intensity by a factor of approximately 40. During the 1991 September observation, the luminosity in the 50-400 keV band was approximately 2 x 10(exp 37) ergs/s (assuming a distance of 4 kpc), no more than a factor of 5 below the soft X-ray luminosity of GX 339-4 observed in its X-ray high state. The luminosity during the 1991 November observation was approximately 5 x 10(exp 35) ergs/s. Extrapolations of both the exponentially cutoff power-law and Sunyaev-Titarchuk models to the approximately 5-20 keV X-ray band yield flux levels very close to that observed by Ginga during an overlapping interval in 1991 September, when GX 339-4 was reported to be in its low state. This may be one of the strongest indications to date of a direct correspondence between the low X-ray state and gamma-ray outbursts of GX 339-4.

Grabelsky, D. A.↗

Studying Absorption Line Feature in the Relativistic Jet Source GRS 1915+105

The galactic superluminal source GRS 1915+105 is among the most interesting objects in our Galaxy. It is subject to erratic accretion instabilities with energization of relativistic jets producing X-ray, optical and radio emission. This source was observed by ASCA on Sept. 27, 1994, April 20, 1995, October 23, 1996 and April 25, 1997 as part of a long timescale investigation. We detected strong variability of the source, and in particular the existence of burst/dip structure in October 1996 and April 1997. Clear evidence of transient absorption features at 6.7, 7.0 and 8.0 keV was obtained for the first time in September 1994 and April 1995. Given the phenomenology of plasmoid energization and ejection, these transient spectral features might be produced by material entrained in the radio jets or in other high-velocity outflows. Our contribution to the interpretation is to incorporate these observations into a overall theoretical picture for GRS 1915+105 also taking into account other observations by XTE and BSAX. The emerging picture is complex. The central source is subject to (most likely) super-Eddington instabilities mediated by magnetic field build-up, reconnection and dissipation in the form of blobs that eventually leads to the formation of transient spectral features from the surrounding of the plasmoid emitting region. A comprehensive theoretical investigation is in progress.

Tavani, Marco↗

Bright microwave pulses from PSR B0531+21 observed with a prototype transient survey receiver

Recent discoveries of transient radio events have renewed interest in time-variable astrophysical phenomena. Many radio transient events are rare, requiring long observing times for reliable statistical study. The National Aeronautics and Space Administration/Jet Propulsion Laboratory's Deep Space Network (DSN) tracks spacecraft nearly continuously with 13 large-aperture, low system temperature radio antennas. During normal spacecraft operations, the DSN processes only a small fraction of the pre-detection bandwidth available from these antennas; any information in the remaining bandwidth, e.g., from an astronomical source in the same antenna beam as the spacecraft, is currently ignored. As a firmware modification to the standard DSN tracking receiver, we built a prototype receiver that could be used for astronomical transient surveys. Here, we demonstrate the receiver's utility through observations of bright pulses from the Crab pulsar and describe attributes of potential transient survey observations piggybacking on operational DSN tracks.

79 ASTRONOMY AND ASTROPHYSICS↗

The soft gamma-ray spectrum of A0535+26: Detection of an absorption feature at 110 keV by OSSE

We present soft gamma-ray observations by the Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray Observatory (GRO) of the transient X-ray binary pulsar A0535+26. The observations were made 1994 February 8-17, immediately prior to the peak of a giant outburst. The phase averaged spectrum is complex and cannot be described by a single-component model. We find that structure in the spectrum above 100 keV can best be modeled by an absorption feature near 110 keV, which we interepret as the signature of cyclotron resonant scattering. Because of OSSE's 45 keV threshold, we are unable to make a definitive statement on the presence of a 55 keV absorption line; however, we can conclude that if this line does exist, it must have a smaller optical depth than the line at 110 keV. A first harmonic (=fundamental) cyclotron resonance at 110 keV corresponds to a magnetic field strength at the surface of the neutron star of approximately 1 x 10(exp 13) G (approximately 5 x 10(exp 12) G if the first harmonic is at 55 keV).

Grove, J. E.↗

Transient Infall Events in the Disk of AB Aurigae: The Beta Pictoris Phenomenon at 2-4 Mega Years

Surveys of Herbig Ae/Be stars have indicated that infalling circumstellar gas similar to that routinely detected toward beta Pic is preferentially observed close to the disk midplane. Recent millimeter interferometry of the historically prototypical Herbig Ae star, AB Aur, indicates that this star is viewed slightly above the disk midplane (i = 76 deg). The wealth of archival spectroscopic data for this star makes it an ideal test of the geometry for infalling or accreting gas in these stars. We present a review of the extant IUE and Hubble Space Telescope GHRS spectral data for AB Aur and find, in contrast to previous studies of this star, which focused on Mg II, that infalling gas is detected at all epochs with covering factors similar to those reported for HD 100546 and that an episode of enhanced infall was serendipitously detected during the 1990 monitoring run.

Grady, C. A.↗

Machine Learning-based Cyber-Physical Anomaly Detection in Wide Area Voltage Control Systems

Wide-area voltage control systems (WAVCS) are widely deployed in power grid to improve the voltage stability in transmission system using Flexible AC Transmission System (FACTS) devices. The WAVCS relies on wide-area measurement and control signals for closed-loop control of FACTS devices to improve the transient voltage stability in power grid in real-time. Since the WAVCS utilizes a cyber-layer communication during its normal operation, they are susceptible to cyber attacks from adversaries which can lead to a voltage collapse if the attacks go undetected and unmitigated. This paper proposes a supervised machine learning (ML)-based anomaly detection algorithm for detecting various stealthy cyber attacks in the context of WAVCS cybersecurity. In particular, a fuzzy logic-based wide-area controller, as proposed by the Bonneville Power Administration (BPA), is implemented on the Kundur’s four machine two-area system that is integrated with a static var compensator (SVC) to improve voltage profile on sensitive buses. Later, different types of data integrity attacks, including pulse and ramp attacks, are considered on the wide-area measurement and control signals to analyze the performance of the proposed anomaly detector. Our experimental evaluation shows a promising performance with a high true-positive rate (more than 99%) and low false-negative rate (less than 1%) while exhibiting a small prediction time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

First Annual Report on Pulsed Thermal Tomography Nondestructive Evaluation of Additively Manufactured Reactor Materials and Components: Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components

Additive manufacturing (AM, or 3D printing) for commercial nuclear energy applications is an emerging method for cost-efficient manufacturing aimed at replacing aging nuclear reactor parts and reducing costs for new construction. Because of the geometry of metallic structures of interest for nuclear applications, which consist of planar primitives with no symmetry of revolution, limited options are available for nondestructive evaluation (NDE), either during or post manufacturing. Known material flaws in AM include low-density regions consisting of non-sintered powder, which have to be detected to ensure the safety of long-term performance nuclear reactor components. As a solution to NDE of AM, we are developing pulsed thermal tomography (PTT) models and depth inversion algorithms for 3D imaging. PTT has many advantages because the method is non-contact and allows for in-service, NDE of AM nuclear reactor parts. By analyzing transients of surface temperature response due to internal thermal resistances, one can obtain 3D reconstructions of material effusivity using a unique inversion algorithm developed at Argonne. This report provides results of preliminary performance evaluation of PTT capability in detection of flaws in metallic structures, as well imaging complex geometry AM structures. Performance of PTT was investigated through modeling and experiments, Computer models of PTT were developed using COMSOL Heat Transfer module. Defects were modeled as cylindrical flat bottom holes (FBH), which is a common model of calibrated material flaws in thermal tomography experiments. Materials considered in this study include stainless steel 316 (SS316), stainless steel 304 (SS304), and Inconel 718. Theoretical analyses were conducted to validate inversion of simulated PTT data with COMSOL for a plate. Subsequently, 3D reconstructions were performed on COMSOL simulations for FBH, revealing a decrease in spatial resolution over depth due to thermal diffusion. The results of this study show that the performance of the inversion algorithm for detecting smaller defects depends strongly on the depth of the defect as well as the incident heat flux. The size of detectable defect was estimated by fitting a Gaussian function to surface temperature profile. The criteria for detectability was taken as 20mK noise equivalent temperature difference (NETD), which is currently the sensitivity limit of high-performance infrared cameras. It was determined through computer simulations that the smallest detectable FBH in SS316 has a 50µm diameter and is located 0.5mm below the plate surface. Preliminary experimental studies were performed to evaluate PTT performance in detecting calibrated flaws using metallic specimens with AM defects simulated as drilled-in FBH’s. High strength Stainless Steel 316 and Inconel 718 alloys were considered, as well as lower grade Stainless Steel 304, Nickel 200, and Hastelloy C276. Specimens investigated in this report consisted of approximately 1/4in-thick plates made out of these alloys using conventional manufacturing methods. The diameters of FBH’s varied from 1mm to 8mm, and their depths below the plate flat surface varied between 1mm and 6mm. The size of the smallest FBH was limited to 1mm because conventional mechanical drills were used for creating the holes. PTT imaging results have shown that 1mm-diameter FBH located 1mm and 2mm below the surface were detectable. Larger size FBH were detectable at greater depth. For example, 6mm-diameter FBH could be detected at 8mm depth. Image contrast varied slightly between the specimens, with the best reconstructions obtained in SS316 and C276 plates. Finally, PTT capability in imaging several AM structures fabricated from Inconel 718 (IN718) powder feedstock was investigated. The AM structures have complex geometry, but do not have calibrated internal defects. The objective is to determine PTT settings, such as the total integration time, for imaging of representative AM structures. A new FLIR X8500sc IR camera with higher spatial resolution (1280x1024 at 181Hz frame rate) was integrated into the PTT laboratory setup. Software tools were developed to ensure compatibility of new camera files with legacy effusivity reconstruction codes. The new camera was used to obtain 3-D reconstructions of AM IN718 nozzle plate and a particle filter plate. It was shown that PTT can scan through 2/3in-thick Inconel 718 plates in approximately 15s. Several modes of 3-D data visualization were explored, including using ImageJ and MATLAB software packages. The results demonstrate the capability of PTT in 3-D imaging of complex geometry AM structures. Intermediate results demonstrated in this report will be developed further to investigate detection of flaws in AM specimens.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Pre-Launch GOES-R Risk Reduction Activities for the Geostationary Lightning Mapper

The GOES-R Geostationary Lightning Mapper (GLM) is a new instrument planned for GOES-R that will greatly improve storm hazard nowcasting and increase warning lead time day and night. Daytime detection of lightning is a particularly significant technological advance given the fact that the solar illuminated cloud-top signal can exceed the intensity of the lightning signal by a factor of one hundred. Our approach is detailed across three broad themes which include: Data Processing Algorithm Readiness, Forecast Applications, and Radiance Data Mining. These themes address how the data will be processed and distributed, and the algorithms and models for developing, producing, and using the data products. These pre-launch risk reduction activities will accelerate the operational and research use of the GLM data once GOES-R begins on-orbit operations. The GLM will provide unprecedented capabilities for tracking thunderstorms and earlier warning of impending severe and hazardous weather threats. By providing direct information on lightning initiation, propagation, extent, and rate, the GLM will also capture the updraft dynamics and life cycle of convective storms, as well as internal ice precipitation processes. The GLM provides information directly from the heart of the thunderstorm as opposed to cloud-top only. Nowcasting applications enabled by the GLM data will expedite the warning and response time of emergency management systems, improve the dispatch of electric power utility repair crews, and improve airline routing around thunderstorms thereby improving safety and efficiency, saving fuel and reducing delays. The use of GLM data will assist the Bureau of Land Management (BLM) and the Forest Service in quickly detecting lightning ground strikes that have a high probability of causing fires. Finally, GLM data will help assess the role of thunderstorms and deep convection in global climate, and will improve regional air quality and global chemistry/climate modeling. The GLM has a robust design that benefits and improves upon its strong heritage of NASA-developed LEO predecessors, the Optical Transient Detector (OTD) and the Lightning Imaging Sensor (LIS). GLM will have a substantially larger number of pixels within the focal plane, two lens systems, and multiple Real-Time Event Processors REPS for on-board event detection and data compression to provide continuous observations of the Americas and adjacent oceans.

Goodman, S. J.↗

A highly specific test for periodicity

We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely, that the time series can be interpolated by a periodic function whose local extrema are also present in the time series. Our method is intended for the analysis of time series generated by deterministic time-continuous dynamical systems, where it can help telling periodic dynamics from chaotic or transient ones. We empirically investigate our method's performance and compare it to an approach based on marker events (or Poincaré sections). We demonstrate that our method is capable of detecting small deviations from periodicity and outperforms the marker-event-based approach in typical situations. Our method requires no adjustment of parameters to the individual time series, yields the period length with a precision that exceeds the sampling rate, and its runtime grows asymptotically linear with the length of the time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A multimodal flow reactor for photocatalysis under atmospheric conditions

Photocatalysis is a promising concept for the direct conversion of solar energy into fuels and chemicals. The design, experimental protocol, and performance of a multimodal and versatile flow reactor for the characterization of powdered and immobilized photocatalysts are presented in this report. Ultimately, this instrument enables rigorous evaluation of photocatalysis performance metrics. The apparatus quantifies transient gas-phase reaction products via online real-time gas analyzer mass spectrometry (RTGA-MS). For H 2 , the most challenging gas, the photocatalytic system’s RTGA-MS gas detection sensitivity spans over three orders of magnitude and can detect down to tens of parts per million under atmospheric conditions. Using Pt nanoparticles supported on anatase TiO 2 photocatalyst via wet impregnation, the instrument’s capability for the characterization of photocatalytic H 2 evolution is demonstrated, resulting in an apparent quantum yield (AQY) of 48.1% ± 0.9% at 320 nm, 45.7% ± 0.3% at 340 nm and 31% ± 1% at 360 nm. The photodeposition of Pt on anatase TiO 2 was employed to demonstrate the instrument’s capability to track the transient behavior of photocatalysts, resulting in an improved 55% ± 2% AQY for H 2 evolution at 340 nm from aqueous methanol. This photocatalytic instrument enables systematic study of a wide variety of photocatalytic reactions such as water splitting and CO 2 reduction to valuable C2+ fuels and chemicals.

14 SOLAR ENERGY↗

Adaptive Narrowband Damping for Improving Harmonic Stability of Modular Multilevel Converter

Harmonic instability events between modular multilevel converter (MMC) and ac systems have been widely reported in recent years. To damp harmonic resonance, this paper proposes an adaptive narrowband damping control that automatically programs, adds, and adjusts the damping around the oscillation frequency when an oscillation is detected. First, the paper presents a low-pass filter design for MMC control loops that pushes all negative damping of the MMC impedance down to the medium-frequency range (< ~ 1000 Hz). Then, an adaptive damping control that uses online oscillation detection is proposed, which can automatically configure the narrowband damper to provide positive damping to the MMC around the detected oscillation frequency. In contrast to existing narrowband damping methods, the proposed adaptive narrowband damper dynamically adjusts the damping gain and the width of the damping range based on continuous monitoring of system resonance conditions (e.g., adjust damping gain to zero when the system resonance disappears). Electromagnetic transient simulation results validate the efficacy of the proposed method in two typical MMC-based power systems.

active damping↗

Deep drilling in the time domain with DECam – II: characterizing the light curves of candidates in the extragalactic fields

ABSTRACT In this second paper on the DECam deep-drilling field (DDF) program, we release 2020 optical $gri$-band light curves for transients and variables in the extragalactic COSMOS and ELAIS fields based on time series observations with a 3-d cadence from semester 2021A through 2023A. In order to demonstrate the wide variety of time domain events detected by the program and encourage others to use the data set, we characterize the sample by presenting a brief analysis of the light-curve parameters such as time span, amplitude, and peak brightness. We also present preliminary light-curve categorizations, and identify potential stellar variables, active galactic nuclei, tidal disruption events, supernovae (SNe) (such as Type Ia, Type IIP, superluminous, and gravitationally lensed SNe), and fast transients. Where relevant, the number of identified transients is compared to the predictions of the original proposal. We also discuss the challenges of analyzing DDF data in the context of the upcoming Vera C. Rubin Observatory and its Legacy Survey of Space and Time, which will include DDFs. Images from the Dark Energy Camera DDF program are available without proprietary period and the light curves presented in this work are publicly available for analysis.

Graham, Melissa L. (ORCID:0000000291543136)↗

Preferential Charge Generation at Aggregate Sites in Narrow Band Gap Infrared Photoresponsive Polymer Semiconductors

Infrared organic photodetector materials are investigated using transient absorption spectroscopy, demonstrating that ultrafast charge generation assisted by polymer aggregation is essential to compensate for the energy gap law, which dictates that excited state lifetimes decrease as the band gap narrows. Short sub–picosecond singlet exciton lifetimes are measured in a structurally related series of infrared–absorbing copolymers that consist of alternating cyclopentadithiophene electron–rich “push” units and strong electron–deficient “pull” units, including benzothiadiazole, benzoselenadiazole, pyridalselenadiazole, or thiadiazoloquinoxaline. While the ultrafast lifetimes of excitons localized on individual polymer chains suggest that charge carrier generation will be inefficient, high detectivity for polymer:PC 71 BM infrared photodetectors is measured in the 0.6 < λ < 1.5 µm range. The photophysical processes leading to charge generation are investigated by performing a global analysis on transient absorption data of blended polymer:PC 71 BM films. In these blends, charge carriers form primarily at polymer aggregate sites on the ultrafast time scale (within our instrument response), leaving quickly decaying single–chain excitons unquenched. Lastly, the results have important implications for the further development of organic infrared optoelectronic devices, where targeting processes such as excited state delocalization over aggregates may be necessary to mitigate losses to ultrafast exciton decay as materials with even lower band gaps are developed.

36 MATERIALS SCIENCE↗

MULTI-MESSENGER ASTRONOMY OF GRAVITATIONAL-WAVE SOURCES WITH FLEXIBLE WIDE-AREA RADIO TRANSIENT SURVEYS

We explore opportunities for multi-messenger astronomy using gravitational waves (GWs) and prompt, transient low-frequency radio emission to study highly energetic astrophysical events. We review the literature on possible sources of correlated emission of GWs and radio transients, highlighting proposed mechanisms that lead to a short-duration, high-flux radio pulse originating from the merger of two neutron stars or from a superconducting cosmic string cusp. We discuss the detection prospects for each of these mechanisms by low-frequency dipole array instruments such as LWA1, the Low Frequency Array and the Murchison Widefield Array. We find that a broad range of models may be tested by searching for radio pulses that, when de-dispersed, are temporally and spatially coincident with a LIGO/Virgo GW trigger within a ∼30 s time window and ∼200–500 deg{sup 2} sky region. We consider various possible observing strategies and discuss their advantages and disadvantages. Uniquely, for low-frequency radio arrays, dispersion can delay the radio pulse until after low-latency GW data analysis has identified and reported an event candidate, enabling a prompt radio signal to be captured by a deliberately targeted beam. If neutron star mergers do have detectable prompt radio emissions, a coincident search with the GW detector network and low-frequency radio arrays could increase the LIGO/Virgo effective search volume by up to a factor of ∼2. For some models, we also map the parameter space that may be constrained by non-detections.

79 ASTRONOMY AND ASTROPHYSICS↗

Utilization of the LS-APGD microplasma/orbitrap-FTMS booster system for detection and isotopic analysis of neodymium nanoparticles

Detection and isotopic analysis of particle populations has seen rapid growth across several application areas, including environmental analysis, nuclear forensics, and food safety. The ability to characterize the particles' unique elemental and isotopic fingerprints could provide information related to formation, processing history, and transport. Regarding nuclear forensics, isotopic analysis of particles derived from diverse materials is often used as a tool to trace the origin and processing history. Mass spectrometric-based techniques currently used for particle population analysis often suffer from limited mass resolution, particularly when dealing with real-world samples that are affected by isobaric and polyatomic interferences from the matrix. To address these analytical challenges, we propose a novel method utilizing the liquid sampling-atmospheric pressure glow discharge (LS-APGD) microplasma ionization source coupled to an ultrahigh resolution Orbitrap mass spectrometer, further enhanced with the FTMS X2T Booster data acquisition and processing unit. The FTMS Booster enables acquisition of extended transient times of up to 3 s, significantly improving mass resolution, thereby reducing or even eliminating the need for prior separation of isobaric or polyatomic interferences. Additionally, the detection of low-abundance isotopes was improved by increasing the signal-to-noise (S/N) ratio. As proof of concept, this study demonstrates the feasibility of the LS-APGD/Orbitrap-FTMS X2T Booster platform for direct analysis using a suspension of well-characterized ∼120 nm neodymium particles. The quality of the isotope ratios values obtained from a few hundred particles were in good agreement with those obtained from homogeneous ionic solutions. These results highlight the potential of the LS-APGD/Orbitrap platform for rapid, accurate, and interference-resilient isotope ratio analysis of particle populations without the need for dissolution and subsequent chemical separations, offering significant advantages for nuclear forensics, safeguards, and environmental applications. The effort here also points to further paths forward, hopefully towards single particle (SP) analysis using microplasma ionization and the ultrahigh resolving power of the Orbitrap mass analyzer.

FTMS X2T booster↗

Spitzer point-source catalogs of ∼ 300,000 stars in seven nearby galaxies

We present Spitzer IRAC 3.6–8 μm and Multiband Imaging Photometer 24 μm point-source catalogs for seven galaxies: NGC 6822, M33, NGC 300, NGC 2403, M81, NGC 0247, and NGC 7793. The catalogs contain a total of ∼300,000 sources and were created by dual-band selection of sources with >3σ detections at both 3.6 and 4.5 μm. The source lists become significantly incomplete near m{sub 3.6}=m{sub 4.5}≃18. We complement the 3.6 and 4.5 μm fluxes with 5.8, 8.0, and 24 μm fluxes or 3σ upper limits using a combination of PSF and aperture photometry. This catalog is a resource as an archive for studying mid-infrared transients and for planning observations with the James Webb Space Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on the luminosity function of gamma-ray bursts detected by BATSE

We have utilized the integral moment analysis technique of Horack & Emslie to extract information on the allowable form of the luminosity function for gamma-ray bursts observed by Burst and Transient Source Experiment (BATSE). Using the general properties of moments, we are able to derive constraints on the range of luminosity from which the gamma-ray bursts must be sampled. These constraints are independent of the form of the radial distribution of the gamma-ray bursts, and depend only on the assumptions that space is Euclidean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(sub 0)L(exp -alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed approximately 6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.

Horack, J. M.↗