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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Is There a Cosmological Constant?

The grant contributed to the publication of 18 refereed papers and 5 conference proceedings. The primary uses of the funding have been for page charges, travel for invited talks related to the grant research, and the support of a graduate student, Charles Keeton. The refereed papers address four of the primary goals of the proposal: (1) the statistics of radio lenses as a probe of the cosmological model (#1), (2) the role of spiral galaxies as lenses (#3), (3) the effects of dust on statistics of lenses (#7, #8), and (4) the role of groups and clusters as lenses (#2, #6, #10, #13, #15, #16). Four papers (#4, #5, #11, #12) address general issues of lens models, calibrations, and the relationship between lens galaxies and nearby galaxies. One considered cosmological effects in lensing X-ray sources (#9), and two addressed issues related to the overall power spectrum and theories of gravity (#17, #18). Our theoretical studies combined with the explosion in the number of lenses and the quality of the data obtained for them is greatly increasing our ability to characterize and understand the lens population. We can now firmly conclude both from our study of the statistics of radio lenses and our survey of extinctions in individual lenses that the statistics of optically selected quasars were significantly affected by extinction. However, the limits on the cosmological constant remain at lambda < 0.65 at a 2-sigma confidence level, which is in mild conflict with the results of the Type la supernova surveys. We continue to find that neither spiral galaxies nor groups and clusters contribute significantly to the production of gravitational lenses. The lack of group and cluster lenses is strong evidence for the role of baryonic cooling in increasing the efficiency of galaxies as lenses compared to groups and clusters of higher mass but lower central density. Unfortunately for the ultimate objective of the proposal, improved constraints on the cosmological constant, the next large survey for gravitational lenses did not release its results during the term of the proposal. The research supported the career development. of six graduate students (polar, Fletcher, Herold, Keeton, Deng and Rusin) and two post-docs (Labor and Munoz).

Kochanek, Christopher↗
DOE OSTI2024

Dark energy survey year 3 results: likelihood-free, simulation-based w CDM inference with neural compression of weak-lensing map statistics

We present simulation-based cosmological wcold dark matter (wCDM) inference using dark energy survey year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky pkdgrav3 dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock dark energy survey lensing data sets. For wCDM inference, for which we allow –1 < w < –$\frac{1}{3}$⁠, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives Ω m = 0.283$^{+0.020}_{–0.027}$⁠, S 8 = 0.804$^{+0.025}_{–0.017⁠}$, and w < –0.80 (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter (Ω⁠ DE , w⁠) precision.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

High dynamic range radio observations of PKS 1413+135: A BL Lacertae object with a parsec-scale counterjet

We report the results of three high dynamic range, high-resolution radio observations with the Very Large Array (VLA), US Very Long Base Interferometry (VLBI) Network, and partially completed Very Long Baseline Array (VLBA) on the peculiar BL Lacertae objects PKS 1413+135. The VLA observations (resolution approximately 1.5 sec) reveal that PKS 1413+135 has no kiloparsec-scale extended structure to a dynamic range limit of 10,000:1. However, its milliarcsecond-scale structure appears to be a triple (i.e., a core, jet plus 'counterjet') at both 3.6 and 18 cm, a unique structure among BL Lac objects but similar to a recently discovered class of VLBI 'mini-triples.' The presence of a counterjet at fluxes comparable to the main jet is incompatible with the standard relativistically beamed jet model for BL Lac objects and with the high value of core dominance exhibited by this source at arcsec resolution. This suggests a nonstandard interpretation in which the radio source lies far in the background of the spiral galaxy it is projected upon so that its VLBI structure may be affected by gravitational lensing. At 18 cm, the core is much weaker than at 3.6 cm suggesting free-free absorption by the high-column-density gas found along this sightline by previous infrared(IR)/optical, X-ray and redshifted H I 21 cm observations. We discuss the roles that free-free absorption and gravitational lensing may have for PKS 1413+135 and other GHz-peaked spectrum radio sources.

Perlman, Eric S.↗
DOE OSTI2023

DeepZipper. II. Searching for Lensed Supernovae in Dark Energy Survey Data with Deep Learning

Gravitationally lensed supernovae (LSNe) are important probes of cosmic expansion, but they remain rare and difficult to find. Current cosmic surveys likely contain 5–10 LSNe in total while next-generation experiments are expected to contain several hundred to a few thousand of these systems. We search for these systems in observed Dark Energy Survey (DES) five year SN fields—10 3 sq. deg. regions of sky imaged in the griz bands approximately every six nights over five years. To perform the search, we utilize the DeepZipper approach: a multi-branch deep learning architecture trained on image-level simulations of LSNe that simultaneously learns spatial and temporal relationships from time series of images. We find that our method obtains an LSN recall of 61.13% and a false-positive rate of 0.02% on the DES SN field data. DeepZipper selected 2245 candidates from a magnitude-limited (m i < 22.5) catalog of 3,459,186 systems. We employ human visual inspection to review systems selected by the network and find three candidate LSNe in the DES SN fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Lensinglike tensions in the Planck legacy release

We analyze the final release of the Planck satellite data to constrain the gravitational lensing potential in a model-independent manner. The amount of lensing determined from the smoothing of the acoustic peaks in the temperature and polarization power spectra is 2σ too high when compared with the measurements using the lensing reconstruction and 2.8σ too high when compared with Λ CDM expectation based on the "unlensed" portion of the temperature and polarization power spectra. The largest change from the previous data release is the Λ CDM expectation, driven by improved constraints to the optical depth to reionization. Here, the anomaly still is inconsistent with actual gravitational lensing, given that the lensing reconstruction constraints are discrepant independent of the model. Within the context of Λ CDM, improvements in its parameter constraints from lensing reconstruction bring this tension to 2.1σ and from further adding baryon acoustic oscillation and Pantheon supernova data to a marginally higher 2.2σ. Once these other measurements are included, marginalizing this lensing-like anomaly cannot substantially resolve tensions with low-redshift measurements of H 0 and S 8 in Λ CDM, Λ CDM + N eff or ΛCDM + Σm ν ; furthermore the artificial strengthening of constraints on Σm ν is less than 20%.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Constraints on cold dark matter theories from observations of massive x-ray-luminous clusters of galaxies at high redshift

During the course of a gravitational lensing survey of distant, X-ray selected Einstein Observatory Extended Medium Sensitivity Survey (EMSS) clusters of galaxies, we have studied six X-ray-luminous (L(sub x) greater than 5 x 10(exp 44)(h(sub 50)(exp -2))ergs/sec) clusters at redshifts exceeding z = 0.5. All of these clusters are apparently massive. In addition to their high X-ray luminosity, two of the clusters at z approximately 0.6 exhibit gravitationally lensed arcs. Furthermore, the highest redshift cluster in our sample, MS 1054-0321 at z = 0.826, is both extremely X-ray luminous (L(sub 0.3-3.5keV)=9.3 x 10(exp 44)(h(sub 50)(exp -2))ergs/sec) and exceedingly rich with an optical richness comparable to an Abell Richness Class 4 cluster. In this Letter, we discuss the cosmological implications of the very existence of these clusters for hierarchical structure formation theories such as standard Omega = 1 CDM (cold dark matter), hybrid Omega = 1 C + HDM (hot dark matter), and flat, low-density Lambda + CDM models.

Luppino, G. A.↗
DOE OSTI2023

TDCOSMO. X. Automated modeling of nine strongly lensed quasars and comparison between lens-modeling software

When strong gravitational lenses are to be used as an astrophysical or cosmological probe, models of their mass distributions are often needed. We present a new, time-efficient automation code for the uniform modeling of strongly lensed quasars with GLEE, a lens-modeling software for multiband data. By using the observed positions of the lensed quasars and the spatially extended surface brightness distribution of the host galaxy of the lensed quasar, we obtain a model of the mass distribution of the lens galaxy. We applied this uniform modeling pipeline to a sample of nine strongly lensed quasars for which images were obtained with the Wide Field Camera 3 of the Hubble Space Telescope. The models show well-reconstructed light components and a good alignment between mass and light centroids in most cases. We find that the automated modeling code significantly reduces the input time during the modeling process for the user. The time for preparing the required input files is reduced by a factor of 3 from ~3 h to about one hour. The active input time during the modeling process for the user is reduced by a factor of 10 from ~ 10 h to about one hour per lens system. This automated uniform modeling pipeline can efficiently produce uniform models of extensive lens-system samples that can be used for further cosmological analysis. A blind test that compared our results with those of an independent automated modeling pipeline based on the modeling software Lenstronomy revealed important lessons. Quantities such as Einstein radius, astrometry, mass flattening, and position angle are generally robustly determined. Other quantities, such as the radial slope of the mass density profile and predicted time delays, depend crucially on the quality of the data and on the accuracy with which the point spread function is reconstructed. Better data and/or a more detailed analysis are necessary to elevate our automated models to cosmography grade. Nevertheless, our pipeline enables the quick selection of lenses for follow-up and further modeling, which significantly speeds up the construction of cosmography-grade models. This important step forward will help us to take advantage of the increase in the number of lenses that is expected in the coming decade, which is an increase of several orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dark matter substructure or source model systematics? A case study of cluster lens Abell S1063

Mapping the small-scale structure of the universe through gravitational lensing is a promising tool for probing the particle nature of dark matter. Curved Arc Basis (CAB) has been proposed as a local lensing formalism in galaxy clusters, with the potential to detect low-mass dark matter substructure. In this work, we analyse the cluster lens Abell S1063 in search of dark matter substructure with the CAB formalism, using multiband imaging data from James Webb Space Telescope ( JWST ). We use two different source modelling methods: shapelets and pixel-based source reconstruction based on Delaunay triangulation. We find that source modelling systematics from shapelets result in a disagreement between CAB parameters measured from different filters. Source modelling with Delaunay significantly alleviates this systematic, as seen in the improvement in agreement across filters. We also find that inadequate complexity in source modelling can result in convincing spurious detections of dark matter substructure from strong gravitational lenses, as seen by our $\Delta \text{BIC} > 20$ measurement of a $M \sim 10^{10}$ ${\rm M}_{\odot }$ subhalo with shapelets, a spurious detection that is not reproduced with Delaunay source modelling. We demonstrate that multiband analysis with different JWST filters is key for disentangling source and lens model systematics from dark matter substructure detections.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1998

Galaxy Cluster Masses at Moderate Redshifts

The masses of galaxy clusters are dominated by dark matter, and a robust determination of their masses has the potential of indicating how much dark matter exists on large scales in the universe, and the cosmological parameter Omega. X-ray observations of galaxy clusters provide a direct measure of both the gas mass in the intra-cluster medium, and also the total gravitating mass of the cluster. We used new and archival ROSAT observations to measure these quantities for a sample of intermediate redshift clusters which have also been subject to intensive dynamical studies, in order to compare the mass estimates from different methods. We used data from 14 of the CNOC cluster sample at 0.18 less than z less than 0.55 for this study. A direct comparison of dynamical mass estimates from Carlberg, Yee & Ellingson (1997) yielded surprisingly good results. The X-ray/dynamical mass ratios have a mean of 0.96+/- 0.10, indicating that for this sample, both methods are probably yielding very robust mass estimates. Comparison with mass estimates from gravitational lensing studies from the literature showed a small systematic with weak lensing estimates, and large discrepancies with strong lensing estimates. This latter is not surprising, given that these measurement are made close to the central core, where optical and X-ray estimates are less certain, and where substructure and the effects of individual galaxies will be more pronounced. These results are presented in Lewis, Ellingson, Morris/Carlberg, 1998, submitted to the Astrophysical Journal. (Note that Lewis is Ellingson's Ph.D. thesis, who received direct support from this grant and is using this investigation as part of his thesis.) Three additional papers are in preparation. The first provides a comparison of the mass profiles as measured in X- rays and in galaxy dynamics. These profiles are difficult to determine for individual clusters, and are subject to asphericity and other individual quirks of each cluster. However, a composite profile for each method will allow us to test our assumptions of hydrostatic/dynamical equilibrium in the sample as a whole. A second paper provides a more detailed look at the cluster MS0906+11, which is a merging system. A third paper authord with J. Mohr at U. Chicago will invetigate the size-temoerature relationship for intermediate redshift clusters and its impications on cluster formation and cosmology. Future work on these data will include comparisons of the cluster galaxy populations and the extent of the intra-cluster medium, and a more homogeneous analysis of gravitational lensing.

Ellingson, E.↗
DOE OSTI2020

Millimeter-wave Point Sources from the 2500 Square Degree SPT-SZ Survey: Catalog and Population Statistics

In this work, we present a catalog of emissive point sources detected in the SPT-SZ survey, a contiguous 2530- square-degree area surveyed with the South Pole Telescope (SPT) from 2008 - 2011 in three bands centered at 95, 150, and 220GHz. The catalog contains 4845 sources measured at a significance of 4.5σ or greater in at least one band, corresponding to detections above approximately 9.8, 5.8, and 20.4 mJy in 95, 150, and 220 GHz, respectively. Spectral behavior in the SPT bands is used for source classification into two populations based on the underlying physical mechanisms of compact, emissive sources that are bright at millimeter wavelengths: synchrotron radiation from active galactic nuclei and thermal emission from dust. The latter population includes a component of high-redshift sources often referred to as submillimeter galaxies (SMGs). In the relatively bright flux ranges probed by the survey, these sources are expected to be magnified by strong gravitational lensing. The survey also contains sources consistent with protoclusters, groups of dusty galaxies at high redshift undergoing collapse. We cross-match the SPT-SZ catalog with external catalogs at radio, infrared, and X-ray wavelengths and identify available redshift information. The catalog splits into 3980 synchrotron-dominated and 865 dust-dominated sources and we determine a list of 506 SMGs. Ten sources in the catalog are identified as stars. We calculate number counts for the full catalog, and synchrotron and dusty components, using a bootstrap method and compare our measured counts with models. This paper represents the third and final catalog of point sources in the SPT-SZ survey.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Measurements of the E-mode polarization and temperature-E-mode correlation of the CMB from SPT-3G 2018 data

We present measurements of the E -mode ( E E ) polarization power spectrum and temperature- E -mode ( T E ) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg 2 region at 95, 150, and 220 GHz taken over a four-month period in 2018. We report binned values of the E E and T E power spectra over the angular multipole range 300 ≤ ℓ < 3000 , using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges 300 ≤ ℓ ≤ 1400 for E E and 300 ≤ ℓ ≤ 1700 for T E , resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G data set is well fit by a Λ CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find H 0 = 68.8 ± 1.5 km s - 1 Mpc - 1 and σ 8 = 0.789 ± 0.016 , with a gravitational lensing amplitude consistent with the Λ CDM prediction ( A L = 0.98 ± 0.12 ). We combine the SPT-3G and the Planck data sets and obtain joint constraints on the Λ CDM model. The volume of the 68% confidence region in six-dimensional Λ CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with no significant shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

TDCOSMO. VII. Boxyness/discyness in lensing galaxies: Detectability and impact on H 0

In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios of point-like sources (i.e. flux ratio anomalies). Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterised, nor has its impact on the H 0 inference. We address this task by creating mock images of a point source embedded in an extended source and lensed by an elliptical galaxy on which multipolar components are added to emulate boxy or discy isodensity contours. Modelling such images with a density profile free of angular structure allows us to explore the detectability of image deformation induced by the multipoles in the residual frame. Multipole deformations are almost always detectable for our highest signal-to-noise ratio (S/N) mock data. However, the detectability depends on the lens ellipticity and Einstein radius, on the S/N of the data, and on the specific lens modelling strategy. Multipoles also introduce small changes to the time-delays. We therefore quantify how undetected multipoles would impact H 0 inference. When no multipoles are detected in the residuals, the impact on H 0 for a given lens is in general less than a few k ms -1 Mpc -1 , but in the worst-case scenario, combining low S/N in the ring and large intrinsic boxyness or discyness, the bias on H0 can reach 10-12 km s -1 Mpc -1 . If we now look at the inference on H 0 from a population of lensing galaxies with a distribution of multipoles representative of what is found in the light profile of elliptical galaxies, we find a systematic bias on H 0 of less than 1%. A comparison of our mock systems to the state-of-the-art time-delay lens sample studied by the H0LiCOW and TDCOSMO collaborations indicates that multipoles are currently unlikely to be a source of substantial systematic bias on the inferred value of H 0 from time-delay lenses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Large-misalignment mechanism for the formation of compact axion structures: Signatures from the QCD axion to fuzzy dark matter

Axions are some of the best motivated particles beyond the Standard Model. We show how the attractive self-interactions of dark matter (DM) axions over a broad range of masses, from 10 –22 eV to 10 7 GeV, can lead to nongravitational growth of density fluctuations and the formation of bound objects. This structure formation enhancement is driven by parametric resonance when the initial field misalignment is large, and it affects axion density perturbations on length scales of order the Hubble horizon when the axion field starts oscillating, deep inside the radiation-dominated era. This effect can turn an otherwise nearly scale-invariant spectrum of adiabatic perturbations into one that has a spike at the aforementioned scales, producing objects ranging from dense DM halos to scalar-field configurations such as solitons and oscillons. We call this class of cosmological scenarios for axion DM production “the large-misalignment mechanism.” In this work, we explore observational consequences of this mechanism for axions with masses up to 10 eV. For axions heavier than 10 –5 eV, the compact axion halos are numerous enough to significantly impact Earth-bound direct detection experiments, yielding intermittent but coherent signals with repetition rates exceeding one per decade and crossing times less than a day. These episodic increases in the axion density and kinematic coherence suggest new approaches for axion DM searches, including for the QCD axion. Dense structures made up of axions from 10 –22 eV to 10 –5 eV are detectable through gravitational lensing searches, and their gravitational interactions can also perturb baryonic structures and alter star formation. At very high misalignment amplitudes, the axion field can undergo self-interaction-induced implosions long before matter-radiation equality, producing potentially-detectable low-frequency stochastic gravitational waves.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

When Spectral Modeling Meets Convolutional Networks: A Method for Discovering Reionization-era Lensed Quasars in Multiband Imaging Data

Over the last two decades, around 300 quasars have been discovered at z ≳ 6, yet only one has been identified as being strongly gravitationally lensed. We explore a new approach—enlarging the permitted spectral parameter space, while introducing a new spatial geometry veto criterion—which is implemented via image-based deep learning. We first apply this approach to a systematic search for reionization-era lensed quasars, using data from the Dark Energy Survey, the Visible and Infrared Survey Telescope for Astronomy Hemisphere Survey, and the Wide-field Infrared Survey Explorer. Our search method consists of two main parts: (i) the preselection of the candidates, based on their spectral energy distributions (SEDs), using catalog-level photometry; and (ii) relative probability calculations of the candidates being a lens or some contaminant, utilizing a convolutional neural network (CNN) classification. The training data sets are constructed by painting deflected point-source lights over actual galaxy images, to generate realistic galaxy–quasar lens models, optimized to find systems with small image separations, i.e., Einstein radii of θ E ≤ 1''. Visual inspection is then performed for sources with CNN scores of P lens > 0.1, which leads us to obtain 36 newly selected lens candidates, which are awaiting spectroscopic confirmation. These findings show that automated SED modeling and deep learning pipelines, supported by modest human input, are a promising route for detecting strong lenses from large catalogs, which can overcome the veto limitations of primarily dropout-based SED selection approaches.

High-redshift galaxies↗
DOE OSTI2023

Strong lensing of high-energy neutrinos

Here, we consider the effects of strong gravitational lensing by galaxy-scale deflectors on the observations of high-energy ( E $\gg$ GeV ) neutrinos (HENs). For HENs at cosmological distances, the optical depth for multiple imaging is ~10 –3 , implying that while we do not expect any multiply imaged HENs with present samples, next-generation experiments should be able to detect the first such event. We then present the distribution of expected time delays to aid in the identification of such events, in combination with directional and energy information. In order to assist in the evaluation of HEN production mechanisms, we illustrate how lensing affects the observed number counts for a variety of intrinsic luminosity functions of the source population. Finally, we see that the lensing effects on the cosmic neutrino background flux calculation would be negligible by taking kiloparsec-scale jets as an example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1994

Can we identify lensed gamma-ray bursts?

A gravitationally lensed gamma-ray burst (GRB) would appear as multiple bursts with identical light curves, separated in time and differing only by the scaling of their amplitudes. In reality, the detected bursts will be noisy, and therefore they may be difficult to identify as lensed images. Furthermore, faint, intrinsically similar, yet distinct light curves may be falsely identified as lensing events. In this paper we develop two statistical tests to distinguish noisy burst light curves. We use Fourier analysis techniques to analyze the signals for both intrinsic variability and variability due to noise. We are able to determine the noise level, and we compare the bursts only at frequency channels that are signal dominated. Utilizing these methods, we are able to make quantitative statements about whether two bursts are distinct. We apply these statistics to scaled versions of two subbursts of GRB 910503 -- subbursts previously investigated by Wambsganss using a different statistical test. We find that our methods are able to distinguish these bursts at slightly smaller amplitudes than those at which Wambsganss's method succeeds. We then apply our techniques to 'candidate' lensing events taken from the Burst and Transient Source Experiment (BATSE) catalog, and we find that nearly all of them, except for the very shortest ones (durations approx. less than 3 sec), are distinguishable. We therefore expect that a majority of bursts will be distinguishable from one another.

Nowak, Michael A.↗