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At least 145 records · Page 8

The Intensity Distribution of Faint Gamma-Ray Bursts Detected with BATSE

We have recently completed a search of six years of archival Burst and Transient Source Experiment (BATSE) data for gamma-ray bursts (GRBs) that were too faint to activate the real-time burst detection system running on board the spacecraft. These 'nontriggered' bursts can be combined with the 'triggered' bursts detected on board to produce a GRB intensity distribution that reaches peak fluxes a factor of approximately two lower than could be studied previously. The value of the statistic (in Euclidean space) for the bursts we detect is 0.177 +/- 0.006. This surprisingly low value is obtained because we detected very few bursts on the 4.096 s and 8.192 s timescales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s timescale. If allowance is made for a power-law distribution of intrinsic peak luminosities, the extended peak flux distribution is consistent with models in which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the universe. We argue that this class of models is preferred over those in which the burst rate is independent of redshift. We use the peak flux distribution to derive a limit of 10% (99% confidence) on the fraction of the total burst rate that could be contributed by a spatially homogeneous (in Euclidean space) subpopulation of burst sources, such as type Ib/c supernovae. These results lend support to the conclusions of previous studies predicting that relatively few faint 'classical' GRBs will be found below the BATSE onboard detection threshold.

Kommers, Jefferson M.↗

The Intensity Distribution of Faint Gamma-Ray Bursts Detected with BATSE

We have recently completed a search of 6 years of archival Burst and Transient Source Experiment (BATSE) data for gamma-ray bursts (GRBS) that were too faint to activate the real-time burst detection system running onboard the spacecraft. These "non-triggered" bursts can be combined with the "triggered" bursts detected onboard to produce a GRB intensity distribution that reaches peak fluxes a factor of approximately 2 lower than could be studied previously. The value of the (V/V(max)) statistic (in Euclidean space) for the bursts we detect is 0.177 +/- 0.006. This surprisingly low value is obtained because we detected very few bursts on the 4.096 s and 8.192 s time scales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s time scale. If allowance is made for a power-law distribution of intrinsic peak luminosities, the extended peak flux distribution is consistent with models in which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the Universe. We argue that this class of models is preferred over those in which the burst rate is independent of redshift. These results lend support to the conclusions of previous studies predicting that relatively few faint bursts are waiting to be found below the BATSE onboard detection threshold.

Kommers, Jefferson↗

Time-interval distributions in a digital gamma multi-channel analyzer at extreme input rates

Here, this study explores the relationship between experimentally observed inter-event time-interval distributions (TIDs) and measured dead times for pulses generated by a HPGe gamma detector and processed by a digital spectrometer. The system utilizes a fast and slow channel, pile-up rejector, trapezoid filtering, and flash analog-to-digital converter. The experimentally derived TIDs were compared with theory for validation. The results demonstrate that the theoretical model reliably describes measured TIDs up to 40% dead time. However, significant distortion effects become increasingly pronounced at higher input rates. It appears that the deviation between the measured and calculated time-interval distributions take the shape of higher-order convolutions of the TID, which represent the time difference between counts for more than two successive events. In this work, theoretical functions for the TID are expanded to reproduce measurements up to 90%. This refinement in the interpretation and treatment of the measured TIDs provides improved accuracy and precision in the prediction of the true event rate and measured dead time in the counter. Even though it reflects occasional count loss that is specific to the set-up, it is expected that a similar adjustment may be applicable to other detection systems as well.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Constraints on the gamma-ray burst luminosity function from Pioneer Venus Orbiter and BATSE observations

We examine the width of the gamma ray burst luminosity function through the distribution of Gamma Ray Burst (GRB) peak fluxes as detected by the Pioneer Venus Orbiter (PVO) and the Burst and Transient Source Experiment (BATSE). The strength of the analysis is greatly enhanced by using a merged catalog of peak fluxes from both instruments with good cross-calibration of their sensitivities. The range of peak fluxes is increased by approximately a factor of 20 relative to the BATSE catalog. Thus, more sensitive investigations of the log N - log P distribution are possible. We place constraints on the width of the luminosity function of gamma-ray bursts brighter than the BATSE completeness limit by comparing the intensity distribution in the merged catalog with those produced by a variety of spatial density and luminosity functions. For the models examined, 90% of the detectable bursts have peak luminosities within a range of 10, indicating that the peak luminosities of gamma-ray bursts span a markedly less wide range of values than many other of their measurable properties. We also discuss for which slopes of a power-law luminosity function the observed width is at the upper end of the constrained range. This is essential in determining the power-law slopes for which luminosity-duration correlations could be important.

Ulmer, Andrew↗

Molecular hydrogen in the galaxy and galactic gamma rays

Recent surveys of 2.6 mm CO emission and 100 MeV gamma-radiation in the galactic plane reveal a striking correlation suggesting that both emissions may be primarily proportional to the line-of-sight column density of H2 in the inner galaxy. Both the gamma ray and CO data suggest a prominent ring or arm consisting of cool clouds of H2 at a galactocentric distance of approximately 5 kpc with a mean density of approximately 4 atoms/cu cm. The importance of H2 in understanding galactic gamma ray observations is also reflected in the correlation of galactic latitude distribution of gamma rays and dense dust clouds. A detailed calculation of the gamma ray flux distribution in the 0 deg to 180 deg range using the CO data to obtain the average distribution of molecular clouds in the galaxy shows that most of the enhancement in the inner galaxy is due to pion-decay radiation and the 5 kpc ring plays a major role. Detailed agreement with the gamma ray data is obtained with the additional inclusion of contributions from bremsstrahlung and Compton radiation of secondary electrons and Compton radiation from the intense radiation field near the galactic center.

Stecker, F. W.↗

Gamma-ray evidence for a galactic halo

Gamma-ray evidence for the existence of a cosmic-ray halo around the Galaxy is examined. Gamma-ray data obtained by SAS-2 and COS-B and nonthermal radio continuum data are shown to indicate the nonconfinement of cosmic rays to the spiral arms and thus the existence of a larger propagation disk through which cosmic rays diffuse. The latitudinal distribution of gamma rays observed by SAS-2 is found to be consistent with the existence of a thin disk-shaped electron halo of half-thickness 1.5 kpc. The propagation of nucleons is determined indirectly from their radial distribution in the galactic plane, which is obtained from an analysis of the longitudinal distribution of gamma rays in the plane. The resulting distributions are found to be similar to the distribution of supernovae in the Galaxy, implying a galactic origin for cosmic rays and a half-thickness of less than 3 kpc.

Stecker, F. W.↗

Investigation of the discontinuous precipitation of U-Nb alloys via thermodynamic analysis and phase-field modeling

U-Nb’s discontinuous precipitation, $\gamma^{bcc}_{matrix}$, $\alpha^{orth}_{cellular}$, $\gamma\prime^{bcc}_{cellular}$, is intriguing in the sense that it allows formation and growth of the metastable $\gamma\prime$ phase during the course of its occurrence. Previous attempts to explain the thermodynamic origin of U-Nb’s discontinuous precipitation hypothesized that the energy of $\alpha$ forms an intermediate common tangent with the first potential of the double-well energy of $\gamma$ at the $\gamma\prime$ composition. In this work, we examine different possible mechanisms by which the discontinuous precipitation product in the U-Nb system can be stabilized. We put forward a mechanism by which the bulk free energy of the $\gamma$ can develop a non-monotonic dependency with composition. Additionally we posit that local contributions due to lattice mismatch between the $\alpha$ and $\gamma$ phases may be responsible for the generation of metastable states that may stabilized by thermodynamics as well as by kinetics. Our work suggests that local misfit strain tends to play a crucial role in the growth of the discontinuous precipitation product. Depending on the magnitude of strain developed at the $\alpha$/$\gamma\prime$ interfaces, either an increasing $\gamma\prime$ composition or a random distribution of $\gamma\prime$ compositions around the equiatomic value with respect to increasing temperature could be expected. Moreover, we show how it is possible to stabilize the discontinuous precipitation front through highly anisotropic and fast interface diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Synthesis of observed and simulated rain microphysics to inform a new Bayesian statistical framework for microphysical parameterization in climate models (Final Scientific Report)

This project aimed to investigate a new approach to bulk microphysics schemes. We identified the need to move beyond the fixed structural assumptions and approximation of existing schemes. For example, most schemes assume some functional form for the rain drop size distribution (e.g. a gamma or exponential distribution). Most schemes then evolve some number of statistical moments of that distribution via various processes, such as evaporation, sedimentation, collision-coalescence, and collisional breakup. These microphysical processes, in turn, are typically some fixed functional form derived from either some other (more detailed) model, or using some single-particle rates that are then integrated over the size distribution. While these process rate functions may have some free parameters to adjust, in other cases doing so is impossible (e.g. when the process rates are analytical or piecewise solutions to some target function). Our goal was to build and test a scheme that assumed no size distribution form, and used a series of power laws as the basis for the process rates. Moments of the size distribution would be predicted, but no underlying size distribution would be specified. Any number or choice of size distribution moments could be used, and any number of power laws could be employed to model the process rates. Thus, our approach is flexible, and can seamlessly scale across levels of complexity, as demanded by the data. Bayesian inference then would provide the formalism to estimate the model parameters and structure, allowing for robust uncertainty quantification. We proposed testing this framework in idealized simulations using bin microphysical schemes as a data source. We also proposed using real data to inform our microphysics scheme, and also that we would integrate our scheme into WRF.

58 GEOSCIENCES↗

Software Validation Work With The ZPPR-15 Data

The analysis activities for fast reactors involve using many different pieces of software that are relied upon for their predictive capabilities. For this software to be considered reliable, documented proof that the predictions of the software are accurate is required. In this manuscript, the validation work that covers some of the Argonne software used in fast reactor design activities is discussed and displayed. This validation work includes neutron and gamma flux distributions, reaction rate distributions, and reactivity worth. In an ideal world, a reactor development program would have access to a comprehensive set of experimental facilities to help inform the design aspects of the reactor itself. While thermal-hydraulics experiments, and to a limited degree mechanical experiments, can be carried out today for validation needs, neutronics related experimental facilities are rather impractical because of the lack of experimental facilities. Given the desired time table for construction of new reactors, the reconstitution or creation of new neutronic experimental facilities is untenable and thus those reactor development programs must rely upon any available experimental measurements that are qualitatively similar to the design. While a methodology has been proposed to assess the similarity between the past experimental measurements and the reactor itself, that aspect is beyond the scope of this manuscript. In this manuscript, the focus is entirely placed on the analysis results for a series of experiments carried out at the ZPPR facility in Idaho in the mid-1980s. In this regard, this manuscript only shows the validation of the stated neutronics software for specific loadings of the ZPPR reactor. Because of the fuel form, its proposed enrichment, and the material content of the reactor core, the ZPPR-15 experiments were identified as potential validation data for the reactor. The ZPPR-15 experiments were intended as mockups of a 330 MWe Integral Fast Reactor program which was a follow on program to the Clinch River Breeder Reactor. In the ZPPR-15 series of experiments, measurements of the neutron spectrum, control rod worth, sodium void worth, foil reaction rate distributions, Doppler worth of heated samples, gamma dose, and axial expansion worth were all carried out and published. In many cases, these reactivity coefficients are good candidates to validate the reactivity coefficient calculation scheme used by the analysis software and included in the safety analysis activities of fast reactor development projects today. This manuscript discusses the modeling methodology and accuracy of the calculated experimental results using the LANL software MCNP and the ANL software package ARC (Argonne Reactor Codes). As will be shown, for many of the experimental measurements, the two software packages are found to be good predictive analysis tools for those experiments. In other cases, problems with the analysis methodology or underlying cross section data are exposed which indicates where predictive analysis is not as reliable. Finally, in some of the measurements the conclusion is reached that the experimental measurement cannot be reproduced with the analysis software as it is simply too difficult.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Software Validation Work With The ZPPR-15 Data

The analysis activities for fast reactors involve using many different pieces of software that are relied upon for their predictive capabilities. For this software to be considered reliable, documented proof that the predictions of the software are accurate is required. In this manuscript, the validation work that covers some of the Argonne software used in fast reactor design activities is discussed and displayed. This validation work includes neutron and gamma flux distributions, reaction rate distributions, and reactivity worth. In an ideal world, a reactor development program would have access to a comprehensive set of experimental facilities to help inform the design aspects of the reactor itself. While thermal-hydraulics experiments, and to a limited degree mechanical experiments, can be carried out today for validation needs, neutronics related experimental facilities are rather impractical because of the lack of experimental facilities. Given the desired time table for construction of new reactors, the reconstitution or creation of new neutronic experimental facilities is untenable and thus those reactor development programs must rely upon any available experimental measurements that are qualitatively similar to the design. While a methodology has been proposed to assess the similarity between the past experimental measurements and the reactor itself, that aspect is beyond the scope of this manuscript. In this manuscript, the focus is entirely placed on the analysis results for a series of experiments carried out at the ZPPR facility in Idaho in the mid-1980s. In this regard, this manuscript only shows the validation of the stated neutronics software for specific loadings of the ZPPR reactor. Because of the fuel form, its proposed enrichment, and the material content of the reactor core, the ZPPR-15 experiments were identified as potential validation data for the reactor. The ZPPR-15 experiments were intended as mockups of a 330 MWe Integral Fast Reactor program which was a follow on program to the Clinch River Breeder Reactor. In the ZPPR-15 series of experiments, measurements of the neutron spectrum, control rod worth, sodium void worth, foil reaction rate distributions, Doppler worth of heated samples, gamma dose, and axial expansion worth were all carried out and published. In many cases, these reactivity coefficients are good candidates to validate the reactivity coefficient calculation scheme used by the analysis software and included in the safety analysis activities of fast reactor development projects today. This manuscript discusses the modeling methodology and accuracy of the calculated experimental results using the LANL software MCNP and the ANL software package ARC (Argonne Reactor Codes). As will be shown, for many of the experimental measurements, the two software packages are found to be good predictive analysis tools for those experiments. In other cases, problems with the analysis methodology or underlying cross section data are exposed which indicates where predictive analysis is not as reliable. Finally, in some of the measurements the conclusion is reached that the experimental measurement cannot be reproduced with the analysis software as it is simply too difficult.

Aliberti, Gerardo↗

Comparison of gamma-gamma Phase Coarsening Responses of Three Powder Metal Disk Superalloys

The phase microstructures of several powder metal (PM) disk superalloys were quantitatively evaluated. Contents, chemistries, and lattice parameters of gamma and gamma strengthening phase were determined for conventionally heat treated Alloy 10, LSHR, and ME3 superalloys, after electrolytic phase extractions. Several of long term heat treatments were then performed, to allow quantification of the precipitation, content, and size distribution of gamma at a long time interval to approximate equilibrium conditions. Additional coarsening heat treatments were performed at multiple temperatures and shorter time intervals, to allow quantification of the precipitation, contents and size distributions of gamma at conditions diverging from equilibrium. Modest differences in gamma and gamma lattice parameters and their mismatch were observed among the alloys, which varied with heat treatment. Yet, gamma coarsening rates were very similar for all three alloys in the heat treatment conditions examined. Alloy 10 had higher gamma dissolution and formation temperatures than LSHR and ME3, but a lower lattice mismatch, which was slightly positive for all three alloys at room temperature. The gamma precipitates of Alloy 10 appeared to remain coherent at higher temperatures than for LSHR and ME3. Higher coarsening rates were observed for gamma precipitates residing along grain boundaries than for those within grains in all three alloys, during slow-moderate quenching from supersolvus solution heat treatments, and during aging at temperatures of 843 C and higher.

Superalloys↗

Extracting the gamma-ray source-count distribution below the Fermi-LAT detection limit with deep learning

We reconstruct the extra-galactic gamma-ray source-count distribution, or dN/dS, of resolved and unresolved sources by adopting machine learning techniques. Specifically, we train a convolutional neural network on synthetic 2-dimensional sky-maps, which are built by varying parameters of underlying source-counts models and incorporate the Fermi-LAT instrumental response functions. The trained neural network is then applied to the Fermi-LAT data, from which we estimate the source count distribution down to flux levels a factor of 50 below the Fermi-LAT threshold. We perform our analysis using 14 years of data collected in the (1,10) GeV energy range. The results we obtain show a source count distribution which, in the resolved regime, is in excellent agreement with the one derived from cataloged sources, and then extends as dN/dS ~ S -2 in the unresolved regime, down to fluxes of 5 · 10 -12 cm -2 s -1 . The neural network architecture and the devised methodology have the flexibility to enable future analyses to study the energy dependence of the source-count distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

Gamma Source Verification for GAMSRC and GAMSOR

Nuclear reactors that rely upon the fission reaction have two modes of thermal energy deposition in the reactor system: neutron absorption and gamma absorption. The gamma rays are typically generated by neutron capture reactions or during the fission process which means the primary driver of energy production is of course the neutron interactions. The GAMSOR program was first built in the mid 1980s to properly account for the gamma heating in an operating reactor core on core internals. The GAMSOR code is sequence of DIF3D calculations to compute the neutron and gamma flux and combine them to define both the neutron and gamma heating throughout the modeled domain. The goal of this manuscript is to present the software verification of GAMSOR. The first step of the GAMSOR sequence of calculations involves of a modified version of DIF3D (called DIF3D-GAMSOR) which generates a gamma source distribution for the follow-on DIF3D gamma transport calculation (step 2). This modified version of DIF3D increases the burden of maintenance and verification work on GAMSOR as one must reverify the DIF3D capabilities which is undesirable. Because the calculation of the gamma source is the only unique aspect of GAMSOR beyond the regular DIF3D capabilities, that part was put in a standalone code called GAMSRC such that one can use the verified DIF3D code in step 1 followed by GAMSRC to carry out the same GAMSOR calculation step. As a consequence, this manuscript is focused on verification of the gamma source files generated by GAMSRC. The verification of the modified version of DIF3D (DIF3D-GAMSOR) will be done less rigorously in that it will be verified that it produces the same output that GAMSRC does and thus GAMSRC is equivalent to GAMSOR on the problems studied here. Hand calculations and independent numerical calculations of the gamma source generation are used for the verification work. This work follows the same methodology of GAMSRC. As expected, the results agree well with those calculated by GAMSRC as will be shown.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Gamma Source Verification for GAMSRC and GAMSOR

Nuclear reactors that rely upon the fission reaction have two modes of thermal energy deposition in the reactor system: neutron absorption and gamma absorption. The gamma rays are typically generated by neutron capture reactions or during the fission process which means the primary driver of energy production is of course the neutron interactions. The GAMSOR program was first built in the mid 1980s to properly account for the gamma heating in an operating reactor core on core internals. The GAMSOR code is sequence of DIF3D calculations to compute the neutron and gamma flux and combine them to define both the neutron and gamma heating throughout the modeled domain. The goal of this manuscript is to present the software verification of GAMSOR. The first step of the GAMSOR sequence of calculations involves of a modified version of DIF3D (called DIF3D-GAMSOR) which generates a gamma source distribution for the follow-on DIF3D gamma transport calculation (step 2). This modified version of DIF3D increases the burden of maintenance and verification work on GAMSOR as one must reverify the DIF3D capabilities which is undesirable. Because the calculation of the gamma source is the only unique aspect of GAMSOR beyond the regular DIF3D capabilities, that part was put in a standalone code called GAMSRC such that one can use the verified DIF3D code in step 1 followed by GAMSRC to carry out the same GAMSOR calculation step. As a consequence, this manuscript is focused on verification of the gamma source files generated by GAMSRC. The verification of the modified version of DIF3D (DIF3D-GAMSOR) will be done less rigorously in that it will be verified that it produces the same output that GAMSRC does and thus GAMSRC is equivalent to GAMSOR on the problems studied here. Hand calculations and independent numerical calculations of the gamma source generation are used for the verification work. This work follows the same methodology of GAMSRC. As expected, the results agree well with those calculated by GAMSRC as will be shown.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Testing of an Optical Fiber--Based Gamma Thermometer in the High Flux Isotope Reactor Gamma Irradiation Facility

This report describes the design, thermal modeling, and gamma irradiation testing of an optical fiber–based gamma thermometer (OFBGT), which was irradiated in the High Flux Isotope Reactor (HFIR) Gamma Irradiation Facility (GIF). OFBGTs are a promising technology for application in nuclear reactors because they can provide a distributed measurement of gamma ray heating rate, unlike thermocouple-based gamma thermometers, which are fixed in-core sensors that can be used in boiling water reactors to calibrate local power range monitors. OFBGTs measure gamma ray heating rate by measuring the temperature difference between a pair of optical fibers; one fiber is in thermal contact with a heat sink (usually the reactor coolant), and the other is in thermal contact with a thermally isolated mass. The device can be calibrated with a heating wire within the thermal mass. The OFBGT that was designed and fabricated at Oak Ridge National Laboratory can measure distributed gamma ray heating rate over an effective measurement length of 61 cm, and the outer diameter of the sensor is 12.7 mm, giving the prototypical sensor design a relatively small footprint. The sensor housing is backfilled with Ar to ensure a well-predicted thermal response that is not affected by humidity or chemical interactions during operation. For calibration, the sensor design uses a Ni–Cr wire, which can be supplied with currents from 0 to 1 A to capture the wide range of potential gamma ray heating rates expected in HFIR’s spent fuel elements. The OFBGT was thermally modeled analytically and numerically; both models account for temperature-dependent thermal conductivities of the materials and show good agreement. The thermal response of the sensor inside spent HFIR fuel elements was simulated for times up to 1 year after discharge of the fuel element. Out-of-pile open-air tests indicated that the steady-state response of the sensor matches modeled results within experimental uncertainty. Calibration tests were performed using electrical heating in the HFIR spent fuel pool, above the fuel elements, to establish a relationship between the difference in spectral shift measured by optical fibers located inside and outside the OFBGT and the applied electrical heating. Subsequently, the OFBGT was placed within the the spent fuel element from HFIR cycle 501 to measure the spatial profile of the gamma heating rates. Results showed good agreement between the theoretical and measured gamma dose rate profiles, with maximum deviations of ~10% or less.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Code Coverage Status of the ARC code GAMSRC

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. GAMSOR serves as procedure to obtain the neutron and gamma power distribution information in the ARC code system. GAMSOR is a specially modified version of DIF3D (dif3d.x becomes dif3d_gamsor.x). After some work, it was determined that carrying out software on GAMSOR was impractical and would not fit well with commercial grade dedication. GAMSRC was written in the last decade to replace GAMSOR such that the user can rely soley upon the verified DIF3D (dif3d.x) code and GAMSRC to obtain the neutron and gamma power distribution information. GAMSRC is also fully verified and ready for commercial grade dedication. In the coming years, GAMSOR will be deprecated and GAMSRC will fully take over in the ARC code system. This document identifies the set of test problems used to assess the code coverage for GAMSRC. The goal is to document what parts of the existing GAMSRC code are touched by the set of test problems and which are not. The code coverage analysis of GAMSRC was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of GAMSRC. The code coverage tables are given for each submodule of GAMSRC. Because GAMSRC links to modules in DIF3D, some details on coverage changes to the DIF3D lined files is provided. As will be seen, most of the uncovered parts/files can be ignored because they are either for error message and debugging output or obviously not needed by GAMSRC today.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Error Distribution of BATSE Gamma-Ray Burst Locations

Empirical probability models for BATSE gamma-ray burst (GRB) location errors are developed via a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the Interplanetary Network (IPN). Models are compared and their parameters estimated using 392 GRBs with single IPN annuli and 19 GRBs with intersecting IPN annuli. Most of the analysis is for the 4Br BATSE catalog; earlier catalogs are also analyzed. The simplest model that provides a good representation of the error distribution has 78% of the probability in a "core" term with a systematic error of 1.85 deg and the remainder in an extended tail with a systematic error of 5.1 deg, which implies a 68% confidence radius for bursts with negligible statistical uncertainties of 2.2 deg. There is evidence for a more complicated model in which the error distribution depends on the BATSE data type that was used to obtain the location. Bright bursts are typically located using the CONT data type, and according to the more complicated model, the 68% confidence radius for CONT-located bursts with negligible statistical uncertainties is 2.0 deg.

Briggs, Michael S.↗

On the Galactic disk and halo models of gamma-ray bursts

Statistical properties of the distribution of gamma-ray bursts are calculated for a large range of different luminosity functions assumed for the sources. Surprisingly, the observable parameters are almost the same as in the 'standard-candle' scenario. In particular, no way is found to reconcile the observed distribution of gamma-ray bursts with any Galactic disk model. A Galactic halo distribution must have a core radius greater than 18 kpc to have no measurable dipole anisotropy. A cosmological distribution of the bursters is a more reasonable alternative.

Mao, Shude↗