arXiv subjects

David M. Goldberg

Publications and source records attributed to David M. Goldberg.

At least 19 recordsLinked to original sources

arXiv2026

Adaptive Reconstruction of Cluster Halos (ARCH): Integrating Shear and Flexion for Substructure Detection

We present ARCH (Adaptive Reconstruction of Cluster Halos), a new gravitational lensing pipeline for cluster mass reconstruction that applies a joint shear-flexion analysis to JWST imaging. Previous approaches have explored joint shear+flexion reconstructions through forward modeling and Bayesian inference frameworks; in contrast, ARCH adopts a staged optimization strategy that incrementally filters and selects candidate halos rather than requiring a global likelihood model or strong priors. This design makes reconstruction computationally tractable and flexible, enabling systematic tests of multiple signal combinations within a unified framework. ARCH employs staged candidate generation, local optimization, filtering, forward selection, and global strength refinement, with a combined fit metric weighted by per-signal uncertainties. Applies to Abell 2744 and El Gordo, the pipeline recovers convergence maps and subcluster masses consistent with published weak+strong lensing results. In Abell 2744 the central core mass within 300$h^{-1}$ kpc is $2.1\times 10^{14} M_\odot h^{-1}$, while in El Gordo the northwestern and southeastern clumps are recovered at $2.6\times 10^{14} M_\odot h^{-1}$ and $2.3\times 10^{14} M_\odot h^{-1}$. Jackknife resampling indicates typical 1$σ$ uncertainties of $10^{12}-10^{13} M_\odot h^{-1}$, with the all signal and shear+$\mathcal{F}$ reconstructions providing the most stable results. These results demonstrate that flexion, when anchored by shear, enhances sensitivity to cluster substructure while maintaining stable cluster-scale mass recovery.

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arXiv2022

Cosmic flexion

Cosmic flexion, like cosmic shear, is a correlation function whose signal originates from the large-scale structure of the universe. Building on the observational success of cosmic shear, along with the unprecedented quality of large-scale cosmological datasets, the time is ripe to explore the practical constraints from cosmic flexion. Unlike cosmic shear, which has a broad window function for power, cosmic flexion is only measurable on small scales and therefore can uniquely place constraints on the small-scale matter power spectrum. Here, we present a full theoretical formalism for cosmic flexion, including both flexion-flexion and shear-flexion two-point correlations. We present forecasts for measuring cosmic flexion in the Dark Energy Survey (DES), a Stage III cosmological survey, and comment on the future prospects of measuring these cosmological flexion signals in the upcoming era of Stage IV experiments.

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arXiv2022

Bayes' Theorem, Inflation, and the Ekpyrotic Universe

We calculate the Bayesian evidences for a class of Ekpyrotic universe models, and compare with a model of single field inflation with a Higgs-type potential. Combining parsimony and observational constraints, this gives us a systematic way to evaluate the degree to which Ekpyrotic models are constrained by CMB data from Planck. We integrate the equations of motion numerically to define a likelihood using Planck 2018 data and sample this likelihood to obtain Bayesian evidences. Priors are justified and used to put Ekpyrotic models and inflation on equal footing. We find reasonable preference for one of the considered Ekpyrotic models over the others, but that even this one is disfavored compared with Higgs inflation.

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arXiv2021

Flat Maps that improve on the Winkel Tripel

Goldberg & Gott (2008) developed six error measures to rate flat map projections on their verisimilitude to the sphere: Isotropy, Area, Flexion, Skewness, Distances, and Boundary Cuts. The first two depend on the metric of the projection, the next two on its first derivatives. By these criteria, the Winkel Tripel (used by National Geographic for world maps) was the best scoring of all the known projections with a sum of squares of the six errors of 4.563, normalized relative to the Equirectangular in each error term. We present here a useful Gott-Wagner variant with a slightly better error score of only 4.497. We also present a radically new class of flat double-sided maps (like phonograph records) which have correct topology and vastly improved error scores: 0.881 for the azimuthal equidistant version. We believe it is the most accurate flat map of Earth yet. We also show maps of other solar system objects and sky maps.

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arXiv2021

Shape, Color and Distance in Weak Gravitational Flexion

Canonically, elliptical galaxies might be expected to have a perfect rotational symmetry, making them ideal targets for flexion studies - however, this assumption hasn't been tested. We have undertaken an analysis of low and high redshift galaxy catalogs of known morphological type with a new gravitational lensing code, Lenser. Using color measurements in the u-r band and fit Sersic index values, objects with characteristics consistent with early-type galaxies are found to have a lower intrinsic scatter in flexion signal than late-type galaxies. We find this measured flexion noise can be reduced by more than a factor of two at both low and high redshift.

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arXiv2016

Flexion in Abell 2744

We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing "cosmic telescope" galaxy clusters, observed as part of the Hubble Frontier Fields initiative. Using HST observations of Abell 2744 (z = 0.308), we apply a modified Analytic Image Model (AIM) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin$^{-2}$. By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43' from the cluster core. We generate two types of nonparametric reconstructions: a flexion aperture mass map, which identifies the central potential and substructure peak with mass signal-to-noise of 3.5$σ$ and 2.3$σ$ respectively; and a convergence map derived directly from the smoothed flexion field. For the primary peak we find a mass of $1.93\times10^{14}\,h^{-1}\,M_{\odot}$ within a 45" (145h$^{-1}$ kpc) aperture, and for the western substructure we find a mass of $7.12\times10^{13}\,h^{-1}\,M_{\odot}$ within a 25" (80h$^{-1}$ kpc) aperture. The associated peak velocity dispersions were determined to be $σ_v$ = 1630 km/s and $σ_v$ = 766 km/s, respectively, by fitting nonsingular isothermal sphere profiles to the flexion data. Additionally, we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure, and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions. Finally, we perform the same analysis on the Abell 2744 parallel sky field, and find no strong phantom signals in the noise reconstructions.

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arXiv2015

The Galaxy Cluster Concentration-Mass Scaling Relation

Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration ($\mathrm{c_{vir}}$) and mass ($\mathrm{M_{vir}}$). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the reconstruction technique used. We also find concentrations derived from dark matter only simulations (at approximately $\mathrm{M_{vir} \sim 10^{14} M_{\odot}}$) to be inconsistent with the WL and WL+SL relations at the $\mathrm{1σ}$ level, even after the projection of triaxial halos is taken into account. However, to fully determine consistency between simulations and observations, a volume-limited sample of clusters is required, as selection effects become increasingly more important in answering this. Interestingly, we also find evidence for a steeper WL+SL relation as compared to WL alone, a result which could perhaps be caused by the varying shape of cluster isodensities, though most likely reflects differences in selection effects caused by these two techniques. Lastly, we compare concentration and mass measurements of individual clusters made using more than one technique, highlighting the magnitude of the potential bias which could exist in such observational samples.

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arXiv2012

Mass Reconstruction using Particle Based Lensing II: Quantifying substructure with Strong+Weak lensing and X-rays

We report a mass reconstruction of A1689 using Particle Based Lensing (PBL), a new technique for Strong+Weak lensing that allows a variable resolution depending on the data density and the signal-to-noise. Using PBL we also calculate the covariance matrix for the resulting mass map. The reconstruction of A1689 shows a secondary mass peak in the north-east direction confirming previous optical observations. This indicates that the central region of the cluster is still undergoing a weak merger. We have used this mass map to measure power ratios of the dark matter distribution and compared it to the X-ray distribution. We find that the power in the X-ray distribution is lower suggesting a smoother and rounder gas distribution compared to the dark matter distribution. We fitted an NFW profile to the profile derived from the mass map and we find that the lensing mass within 1 Mpc is $1.5\pm0.33\times 10^{15}M_\odot$. This is higher than the X-ray mass.

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arXiv2011

Analyzing the Flux Anomalies of the Large-Separation Lensed Quasar SDSS J1029+2623

Using a high resolution radio image, we successfully resolve the two fold image components B and C of the quasar lens system SDSS J1029+2623. The flux anomalies associated with these two components in the optical regime persist, albeit less strongly, in our radio observations, suggesting that the cluster must be modeled by something more than a single central potential. We argue that placing substructure close to one of the components can account for a flux anomaly with negligible changes in the component positions. Our best fit model has a substructure mass of ~10^8 solar masses up to the mass-sheet degeneracy, located roughly 0.1 arcsecs West and 0.1 arcsecs North of component B. We demonstrate that a positional offset between the centers of the source components can explain the differences between the optical and radio flux ratios.

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arXiv2010

New Constraints on the Complex Mass Substructure in Abell 1689 from Gravitational Flexion

In a recent publication, the flexion aperture mass statistic was found to provide a robust and effective method by which substructure in galaxy clusters might be mapped. Moreover, we suggested that the masses and mass profile of structures might be constrained using this method. In this paper, we apply the flexion aperture mass technique to HST ACS images of Abell 1689. We demonstrate that the flexion aperture mass statistic is sensitive to small-scale structures in the central region of the cluster. While the central potential is not constrained by our method, due largely to missing data in the central 0.5$^\prime$ of the cluster, we are able to place constraints on the masses and mass profiles of prominent substructures. We identify 4 separate mass peaks, and use the peak aperture mass signal and zero signal radius in each case to constrain the masses and mass profiles of these substructures. The three most massive peaks exhibit complex small-scale structure, and the masses indicated by the flexion aperture mass statistic suggest that these three peaks represent the dominant substructure component of the cluster ($\sim 7\times 10^{14}h^{-1}M_\odot$). Their complex structure indicates that the cluster -- far from being relaxed -- may have recently undergone a merger. The smaller, subsidiary peak is located coincident with a group of galaxies within the cluster, with mass $\sim 1\times10^{14}h^{-1}M_\odot$. These results are in excellent agreement with previous substructure studies of this cluster.

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arXiv2010

Fold Lens Flux Anomalies: A Geometric Approach

We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared, and compare our estimates to the Monte Carlo based results of Keeton, Gaudi, and Petters. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from from this ratio almost certainly contain significant substructure.

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arXiv2009

Measuring dark matter ellipticity of Abell 901/902 using Particle Based Lensing

We present a non-parametric measure of the ellipticity and the alignment of the dark matter halos in Abell 901/902 supercluster. This super-cluster is a system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of view. We map the mass distribution of each individual peak using an improved version of Particle Based Lensing (PBL) and measure the ellipticity of the dark matter halos associated with two of the peaks directly from the mass map and by fitting them to a singular isothermal ellipse. The parametric and non-parametric measurements are consistent for A901b while the position angle for the Southwest Group is different for the two techniques. We account for this discrepancy to substructure present in the Southwest Peak. We estimate an axis ratio of $0.37\pm 0.1$ for A901b and $0.54^{+0.08}_{-0.09}$ for the Southwest Group.

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arXiv2009

Weak lensing ellipticities in a strong lensing regime

It is now routine to measure the weak gravitational lensing shear signal from the mean ellipticity of distant galaxies. However, conversion between ellipticity and shear assumes local linearity of the lensing potential (ie that the spatial derivatives of the shear are small), and this condition is not satisfied in some of the most interesting regions of the sky. We extend a derivation of lensing equations to include higher order terms, and assess the level of biases introduced by assuming that first-order weak lensing theory holds in a relatively strong shear regime. We find that, even in a worst-case scenario, a fully linear analysis is accurate to within 1% outside ~1.07 times the Einstein radius of a lens, by deriving an analytic function that can be used to estimate the applicability of any first-order analysis. The effect is too small to explain the discrepancy between weak- and strong-lensing estimates of the mass of the bullet cluster, and should not impact cluster surveys for the forseeable future. In fact, it means that arclets can be used to measure shears closer to a cluster core than has been generally appreciated. However, at the level of accuracy demanded by future lensing surveys, this bias ought to be considered in measurements of the inner slope of cluster mass distributions and the small-scale end of the mass power spectrum. Both of these are central in determining the relationship between baryonic and dark matter.

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arXiv2008

Reconstruction of Cluster Masses using Particle Based Lensing I: Application to Weak Lensing

We present Particle-Based Lensing (PBL), a new technique for gravitational lensing mass reconstructions of galaxy clusters. Traditionally, most methods have employed either a finite inversion or gridding to turn observational lensed galaxy ellipticities into an estimate of the surface mass density of a galaxy cluster. We approach the problem from a different perspective, motivated by the success of multi-scale analysis in smoothed particle hydrodynamics. In PBL, we treat each of the lensed galaxies as a particle and then reconstruct the potential by smoothing over a local kernel with variable smoothing scale. In this way, we can tune a reconstruction to produce constant signal-noise throughout, and maximally exploit regions of high information density. PBL is designed to include all lensing observables, including multiple image positions and fluxes from strong lensing, as well as weak lensing signals including shear and flexion. In this paper, however, we describe a shear-only reconstruction, and apply the method to several test cases, including simulated lensing clusters, as well as the well-studied ``Bullet Cluster'' (1E0657-56). In the former cases, we show that PBL is better able to identify cusps and substructures than are grid-based reconstructions, and in the latter case, we show that PBL is able to identify substructure in the Bullet Cluster without even exploiting strong lensing measurements. We also make our codes publicly available.

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arXiv2008

Beowulf Analysis Symbolic INterface BASIN: Interactive Parallel Data Analysis for Everyone

The advent of affordable parallel computers such as Beowulf PC clusters and, more recently, of multi-core PCs has been highly beneficial for a large number of scientists and smaller institutions that might not otherwise have access to substantial computing facilities. However, there has not been an analogous progress in the development and dissemination of parallel software: scientists need the expertise to develop parallel codes and have to invest a significant amount of time in the development of tools even for the most common data analysis tasks. We describe the Beowulf Analysis Symbolic INterface (BASIN) a multi-user parallel data analysis and visualization framework. BASIN is aimed at providing scientists with a suite of parallel libraries for astrophysical data analysis along with general tools for data distribution and parallel operations on distributed data to allow them to easily develop new parallel libraries for their specific tasks.

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arXiv2007

Gravitational Shear, Flexion and Strong Lensing in Abell 1689

We present a gravitational lensing analysis of the galaxy cluster Abell 1689, incorporating measurements of the weak shear, flexion, and strong lensing induced in background galaxies. This is the first time that a shapelet technique has been used to reconstruct the distribution of mass in this cluster, and the first time that a flexion signal has been measured using cluster members as lenses. From weak shear measurements alone, we generate a non-parametric mass reconstruction, which shows significant substructure corresponding to groups of galaxies within the cluster. Additionally, our galaxy-galaxy flexion signal demonstrates that the cluster galaxies can be well-fit by a singular isothermal sphere model with a characteristic velocity dispersion of $σ_v = 295\pm 40 km/s $. We identify a major, distinct dark matter clump, offset by 40$h^{-1}$kpc from the central cluster members, which was not apparent from shear measurements alone. This secondary clump is present in a parametric mass reconstruction using flexion data alone, and its existence is suggested in a non-parametric reconstruction of the cluster using a combination of strong and weak lensing. As found in previous studies, the mass profile obtained by combining weak and strong lensing data shows a much steeper profile than that obtained from only weak lensing data.

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arXiv2007

Measuring Flexion

We describe practical approaches to measuring flexion in observed galaxies. In particular, we look at the issues involved in using the Shapelets and HOLICs techniques as means of extracting 2nd order lensing information. We also develop an extension of HOLICs to estimate flexion in the presence of noise, and with a nearly isotropic PSF. We test both approaches in simple simulated lenses as well as a sample of possible background sources from ACS observations of A1689. We find that because noise is weighted differently in shapelets and HOLICs approaches, that the correlation between measurements of the same object is somewhat diminished, but produce similar scatter due to measurement noise.

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arXiv2007

Flexion and Skewness in Map Projections of the Earth

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall.

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