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At least 379 records · Page 21

One Galaxy Sample to Rule Them All: Halo Occupation Distribution Modeling of DES Year 3 Source Galaxies

Abstract For the joint analysis of second-order weak-lensing and galaxy clustering statistics, so-called 3 × 2 analyses, the selection and characterization of optimal galaxy samples is a major area of research. One promising choice is to use the same galaxy sample as lenses and sources, which reduces the systematics parameter space that describes the uncertainties related to galaxy samples. Such a “lens-equal-source” analysis significantly improves the self-calibration of photo- z systematics, leading to improved cosmological constraints. With the aim of enabling a lens-equal-source analysis on small scales, we investigate the halo–galaxy connection of DES Year 3 source galaxies. We develop a technique to construct mock source galaxy populations by matching COSMOS/UltraVISTA photometry to U niverse M achine galaxies. These mocks predict a source halo occupation distribution (HOD) that exhibits significant redshift evolution, nontrivial central incompleteness, and galaxy assembly bias. We produce multiple realizations of mock source galaxies drawn from the U niverse M achine posterior, with added uncertainties in the measured Dark Energy Survey photometry and galaxy shapes. We fit a modified HOD formalism to these realizations to produce priors on the galaxy–halo connection for cosmological analyses. We additionally train an emulator that predicts this HOD to ∼2% accuracy from redshift z = 0.1−1.3 that models the dependence of this HOD on (1) observational uncertainties in galaxy size and photometry and (2) uncertainties in the U niverse M achine predictions.

Salcedo, Andrés N. (ORCID:000000031420527X)↗

Dimensional Reduction for Sampled Priors and Application to Photometric Redshift Distributions

A typical Bayesian inference on the values of some parameters of interest q from some data D involves running a Markov Chain (MC) to sample from the posterior $p$($q$,$n$|$D$) $\propto$ $\mathcal{L}$($D$|$q$,$n$)$p$(q)$p$($n$), where n are some nuisance parameters with a separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior p(n) is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of p(n) at arbitrary values of n, i.e., one needs to provide a density estimator over the full n space from the provided samples. But the high dimensionality of n hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the n space into a much lower-dimensional space u, which projects away directions in n space that cannot appreciably alter $\mathcal{L}$. The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on p(n) than other proposed solutions to this issue. We demonstrate this “mode projection” technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the Dark Energy Survey, where n is a binned representation of the redshift distribution n(z) of the galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

CosmoDC2: A Synthetic Sky Catalog for Dark Energy Science with LSST

This paper introduces cosmoDC2, a large synthetic galaxy catalog designed to support precision dark energy science with the Large Synoptic Survey Telescope (LSST). CosmoDC2 is the starting point for the second data challenge (DC2) carried out by the LSST Dark Energy Science Collaboration (LSST DESC). The catalog is based on a trillion-particle, (4.225 Gpc) 3 box cosmological N-body simulation, the Outer Rim run. It covers 440 deg 2 of sky area to a redshift of z = 3 and matches expected number densities from contemporary surveys to a magnitude depth of 28 in the r band. Each galaxy is characterized by a multitude of galaxy properties including stellar mass, morphology, spectral energy distributions, broadband filter magnitudes, host halo information, and weak lensing shear. The size and complexity of cosmoDC2 requires an efficient catalog generation methodology; our approach is based on a new hybrid technique that combines data-based empirical approaches with semianalytic galaxy modeling. A wide range of observation-based validation tests has been implemented to ensure that cosmoDC2 enables the science goals of the planned LSST DESC DC2 analyses. This paper also represents the official release of the cosmoDC2 data set, including an efficient reader that facilitates interaction with the data.

79 ASTRONOMY AND ASTROPHYSICS↗

The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters

Here, we present a catalog of 4195 optically confirmed Sunyaev–Zel’dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg 2 of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 < z < 1.91 (median z = 0.52). The catalog contains 222 z > 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M 500 c > 3.8 × 10 14 M ⊙ , evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 2.'4. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg 2 ), the Hyper Suprime-Cam Subaru Strategic Program (469 deg 2 ), and the Kilo Degree Survey (825 deg 2 ). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr.

79 ASTRONOMY AND ASTROPHYSICS↗

The Impact of Observing Strategy on Cosmological Constraints with LSST

The generation-defining Vera C. Rubin Observatory will make state-of-the-art measurements of both the static and transient universe through its Legacy Survey for Space and Time (LSST). With such capabilities, it is immensely challenging to optimize the LSST observing strategy across the survey's wide range of science drivers. Many aspects of the LSST observing strategy relevant to the LSST Dark Energy Science Collaboration, such as survey footprint definition, single-visit exposure time, and the cadence of repeat visits in different filters, are yet to be finalized. Here, we present metrics used to assess the impact of observing strategy on the cosmological probes considered most sensitive to survey design; these are large-scale structure, weak lensing, type Ia supernovae, kilonovae, and strong lens systems (as well as photometric redshifts, which enable many of these probes). We evaluate these metrics for over 100 different simulated potential survey designs. Our results show that multiple observing strategy decisions can profoundly impact cosmological constraints with LSST; these include adjusting the survey footprint, ensuring repeat nightly visits are taken in different filters, and enforcing regular cadence. We provide public code for our metrics, which makes them readily available for evaluating further modifications to the survey design. We conclude with a set of recommendations and highlight observing strategy factors that require further research.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey: Modeling strategy for multiprobe cluster cosmology and validation for the Full Six-year Dataset

We introduce an updated To&Krause2021 model for joint analyses of cluster abundances and large-scale two-point correlations of weak lensing and galaxy and cluster clustering (termed CL+3x2pt analysis) and validate that this model meets the systematic accuracy requirements of analyses with the statistical precision of the final Dark Energy Survey (DES) Year 6 (Y6) dataset. The validation program consists of two distinct approaches, (1) identification of modeling and parameterization choices and impact studies using simulated analyses with each possible model misspecification (2) end-to-end validation using mock catalogs from customized Cardinal simulations that incorporate realistic galaxy populations and DES-Y6-specific galaxy and cluster selection and photometric redshift modeling, which are the key observational systematics. In combination, these validation tests indicate that the model presented here meets the accuracy requirements of DES-Y6 for CL+3x2pt based on a large list of tests for known systematics. In addition, we also validate that the model is sufficient for several other data combinations: the CL+GC subset of this data vector (excluding galaxy--galaxy lensing and cosmic shear two-point statistics) and the CL+3x2pt+BAO+SN (combination of CL+3x2pt with the previously published Y6 DES baryonic acoustic oscillation and Y5 supernovae data).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Constraints on Nonthermal Pressure at Galaxy Cluster Outskirts from a Joint SPT and XMM-Newton Analysis

We present joint South Pole Telescope and XMM-Newton observations of eight massive galaxy clusters (0.8–2 × 10$^{15}$ M$_{⊙}$) spanning a redshift range of 0.16–0.35. Employing a novel Sunyaev–Zel’dovich + X-ray fitting technique, we effectively constrain the thermodynamic properties of these clusters out to the virial radius. The resulting best-fit electron density, deprojected temperature, and deprojected pressure profiles are in good agreement with previous observations of massive clusters. For the majority of the cluster sample (five out of eight clusters), the entropy profiles exhibit a self-similar behavior near the virial radius. We further derive hydrostatic mass, gas mass, and gas fraction profiles for all clusters up to the virial radius. Comparing the enclosed gas fraction profiles with the universal gas fraction profile, we obtain nonthermal pressure fraction profiles for our cluster sample at >0.5R$_{500}$, demonstrating a steeper increase between R$_{500}$ and R$_{200}$ that is consistent with the hydrodynamical simulations. Our analysis yields nonthermal pressure fraction ranges of 8%–28% (median: 15% ± 11%) at R$_{500}$ and 21%–35% (median: 27% ± 12%) at R$_{200}$. Notably, weak-lensing mass measurements are available for only four clusters in our sample, and our recovered total cluster masses, after accounting for nonthermal pressure, are consistent with these measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

Aubourg, Eric [APC, Paris] (ORCID:000000025592023X↗

SITCOMTN-164: AnaCal Shear Profile of Abell 360 in LSSTComCam Data Preview 1

This technote presents the measurement of the weak-lensing shear profile for the Abell 360 galaxy cluster using LSSTComCam data processed with the AnaCal pipeline. We detail the procedures involved in bright-star masking, source selection, and the estimation of tangential and cross shear around the cluster center. The resulting shear profiles provide key insights into the mass distribution of Abell 360 and demonstrate the capabilities of AnaCal in processing early LSST data, with the tangential shear profile detected at 5σ significance.

79 ASTRONOMY AND ASTROPHYSICS↗

Wide field imaging of solar system objects with an 8192 x 8192 CCD mosaic

As part of this program, we successfully completed the construction of the world's largest CCD camera, an 8192 x 8192 CCD mosaic. The system employs 8 2K x 4K 3-edge buttable CCDs arranged in a 2 x 4 chip mosaic. The focal plane has small gaps (less than 1 mm) between mosaic elements and measures over 120 mm x 120 mm. The initial set of frontside illuminated CCDs were developed with Loral-Fairchild in a custom foundry run. The initial lots yielded of order 20 to 25 functional devices, of which we selected the best eight for inclusion for the camera. We have designed a custom 3-edge-buttable package that ensures the CCD dies are mounted flat to plus or minus 10 microns over the entire area of the mosaic. The mosaic camera system consists of eight separate readout signal chains controlled by two independent DSP microcontrollers. These are in turn interfaced to a Sun Sparc-10 workstation through two high speed fiber optic interfaces. The system saw first-light on the Canada-France-Hawaii Telescope on Mauna Kea in March 1995. First-light on the University of Hawaii 2.2-M Telescope on Mauna Kea was in July 1995. Both runs were quite successful. A sample of some of the early science from the first light run is reported in the publication, 'Observations of Weak Lensing in Clusters with an 8192 x 8192 CCD Mosaic Camera'.

Hall, Donald N. B.↗

A Distant, X-Ray Luminous Cluster of Galaxies at Redshift 0.83

We have observed the most distant (= 0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey (EMSS), with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3(sup 3.1, sub 2.2) keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass approximately 7.4 x 10(exp 14) /h solar mass, if the mean matter density in the universe equals the critical value (OMEGA(sub 0) = 1), or larger if OMEGA(sub 0) < 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an OMEGA(sub 0) = 1 universe. Combining the assumptions that OMEGA(sub 0) = 1 and that the initial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that this probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10(exp -5). Nor is MS1054-0321 the only hot cluster at high redshift; the only two other z > 0.5 EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and OMEGA(sub 0) = 1, we find that each one is improbable at the < 10(exp -2) level. These observations, along with the fact that these luminosities and temperatures of the high-z clusters all agree with the low-z L(sub x) - T(sub x) relation, argue strongly that OMEGA(sub 0) < 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.

Donahue, Megan↗

A Very Hot, High Redshift Cluster of Galaxies: More Trouble for Omega(0) = 1

We have observed the most distant (= 0.829) cluster of galaxies in the Einstein Extended Medium Sensitivity Survey (EMSS), with the ASCA and ROSAT satellites. We find an X-ray temperature of 12.3 (sup +3.1) (sub -2.2)keV for this cluster, and the ROSAT map reveals significant substructure. The high temperature of MS1054-0321 is consistent with both its approximate velocity dispersion, based on the redshifts of 12 cluster members we have obtained at the Keck and the Canada-France-Hawaii telescopes, and with its weak lensing signature. The X-ray temperature of this cluster implies a virial mass approx. 7.4 x 10 (sup 14) h (sup -1) M (circle dot), if the mean matter density in the universe equals the critical value (OMEGA (sub 0) = 1), or larger if OMEGA (sub 0) is less than 1. Finding such a hot, massive cluster in the EMSS is extremely improbable if clusters grew from Gaussian perturbations in an OMEGA (sub 0) = 1 universe. Combining the assumptions that OMEGA (sub 0) = 1 and that the initial perturbations were Gaussian with the observed X-ray temperature function at low redshift, we show that this probability of this cluster occurring in the volume sampled by the EMSS is less than a few times 10 (sup -5). Nor is MS1054-0321 the only hot cluster at high redshift; the only two other z greater than 0.5 EMSS clusters already observed with ASCA also have temperatures exceeding 8 keV. Assuming again that the initial perturbations were Gaussian and OMEGA (sub 0) = 1, we find that each one is improbable at the less than 10 (sup -2) level. These observations, along with the fact that these luminosities and temperatures of the high-z clusters all agree with the low-z L (sub X) - T (sub X) relation, argue strongly that OMEGA (sub 0) less than 1. Otherwise, the initial perturbations must be non-Gaussian, if these clusters' temperatures do indeed reflect their gravitational potentials.

Donahue, Megan↗

The Clustering of Galaxies and Dark Matter at Intermediate Redshifts

Theoretical work in the study of weak lensing was begun while the Scientific PI (Jain) was at the Johns Hopkins University. A new postdoctoral fellow, Rita Kim, was hired to work for 0.5 years on the proposed research. She was unable to join JHU until March 2001 owing to delays in her PhD work. Meanwhile PI Jain moved to the University of Pennsylvania in January 2001. Owing to the above circumstances, the work for the proposed research was delayed and was expected to be carried out in the remainder of 2001. New measures of lensing based on the magnification effect were to be investigated by Drs. Jain and Kim. The simulations needed to test the analytical computations were already in place; hence the work was expected to proceed fairly rapidly. Owing to the close proximity of JHU and UPenn, the collaborative work was expected to proceed smoothly. It was requested therefore that the funds for the first grant year (2000-2001) be transferred to the second year. Part of the funding was spent at JHU on the salary for the Postdoctoral Fellow, Rita Kim, and the remainder at the University of Pennsylvania. The work from this grant is incomplete and will be continued under another grant.

Jain, Bhuvnesh↗

Theoretical Astrophysics at Fermilab

The Theoretical Astrophysics Group works on a broad range of topics ranging from string theory to data analysis in the Sloan Digital Sky Survey. The group is motivated by the belief that a deep understanding of fundamental physics is necessary to explain a wide variety of phenomena in the universe. During the three years 2001-2003 of our previous NASA grant, over 120 papers were written; ten of our postdocs went on to faculty positions; and we hosted or organized many workshops and conferences. Kolb and collaborators focused on the early universe, in particular and models and ramifications of the theory of inflation. They also studied models with extra dimensions, new types of dark matter, and the second order effects of super-horizon perturbations. S tebbins, Frieman, Hui, and Dodelson worked on phenomenological cosmology, extracting cosmological constraints from surveys such as the Sloan Digital Sky Survey. They also worked on theoretical topics such as weak lensing, reionization, and dark energy. This work has proved important to a number of experimental groups [including those at Fermilab] planning future observations. In general, the work of the Theoretical Astrophysics Group has served as a catalyst for experimental projects at Fennilab. An example of this is the Joint Dark Energy Mission. Fennilab is now a member of SNAP, and much of the work done here is by people formerly working on the accelerator. We have created an environment where many of these people made transition from physics to astronomy. We also worked on many other topics related to NASA s focus: cosmic rays, dark matter, the Sunyaev-Zel dovich effect, the galaxy distribution in the universe, and the Lyman alpha forest. The group organized and hosted a number of conferences and workshop over the years covered by the grant. Among them were:

Source record↗

Modeling and Correcting the Time-Dependent ACS PSF

The ability to accurately measure the shapes of faint objects in images taken with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST) depends upon detailed knowledge of the Point Spread Function (PSF). We show that thermal fluctuations cause the PSF of the ACS Wide Field Camera (WFC) to vary over time. We describe a modified version of the TinyTim PSF modeling software to create artificial grids of stars across the ACS field of view at a range of telescope focus values. These models closely resemble the stars in real ACS images. Using 10 bright stars in a real image, we have been able to measure HST s apparent focus at the time of the exposure. TinyTim can then be used to model the PSF at any position on the ACS field of view. This obviates the need for images of dense stellar fields at different focus values, or interpolation between the few observed stars. We show that residual differences between our TinyTim models and real data are likely due to the effects of Charge Transfer Efficiency (CTE) degradation. Furthermore, we discuss stochastic noise that is added to the shape of point sources when distortion is removed, and we present MultiDrizzle parameters that are optimal for weak lensing science. Specifically, we find that reducing the MultiDrizzle output pixel scale and choosing a Gaussian kernel significantly stabilizes the resulting PSF after image combination, while still eliminating cosmic rays/bad pixels, and correcting the large geometric distortion in the ACS. We discuss future plans, which include more detailed study of the effects of CTE degradation on object shapes and releasing our TinyTim models to the astronomical community.

Rhodes, Jason↗

DESTINY, The Dark Energy Space Telescope

We have proposed the development of a low-cost space telescope, Destiny, as a concept for the NASA/DOE Joint Dark Energy Mission. Destiny is a 1.65m space telescope, featuring a near-infrared (0.85-1.7m) survey camera/spectrometer with a moderate flat-field field of view (FOV). Destiny will probe the properties of dark energy by obtaining a Hubble diagram based on Type Ia supernovae and a large-scale mass power spectrum derived from weak lensing distortions of field galaxies as a function of redshift.

Pasquale, Bert A.↗

The Atacama Cosmology Telescope: A Measurement of the Primordial Power Spectrum

We present constraints on the primordial power spectrum of adiabatic fluctuations using data from the 2008 Southern Survey of the Atacama Cosmology Telescope (ACT). The angular resolution of ACT provides sensitivity to scales beyond l = 1000 for resolution of multiple peaks in the primordial temperature power spectrum, which enables us to probe the primordial power spectrum of adiabatic scalar perturbations with wavenumbers up to k approx. = 0.2 Mp/c. We find no evidence for deviation from power-law fluctuations over two decades in scale. Matter fluctuations inferred from the primordial temperature power spectrum evolve over cosmic time and can be used to predict the matter power spectrum at late times; we illustrate the overlap of the matter power inferred from CMB measurements (which probe the power spectrum in thc linear regime) with existing probes of galaxy clustering, cluster abundances and weak lensing constraints on the primordial power. This highlights the range of scales probed by current measurement.s of the matter power spectrum.

Hlozek, Renee↗

Wide-Field Infrared Survey Telescope (WFIRST) Interim Report

The New Worlds, New Horizons (NWNH) in Astronomy and Astrophysics 2010 Decadal Survey prioritized the community consensus for ground-based and space-based observatories. Recognizing that many of the community s key questions could be answered with a wide-field infrared survey telescope in space, and that the decade would be one of budget austerity, WFIRST was top ranked in the large space mission category. In addition to the powerful new science that could be accomplished with a wide-field infrared telescope, the WFIRST mission was determined to be both technologically ready and only a small fraction of the cost of previous flagship missions, such as HST or JWST. In response to the top ranking by the community, NASA formed the WFIRST Science Definition Team (SDT) and Project Office. The SDT was charged with fleshing out the NWNH scientific requirements to a greater level of detail. NWNH evaluated the risk and cost of the JDEM-Omega mission design, as submitted by NASA, and stated that it should serve as the basis for the WFIRST mission. The SDT and Project Office were charged with developing a mission optimized for achieving the science goals laid out by the NWNH re-port. The SDT and Project Office opted to use the JDEM-Omega hardware configuration as an initial start-ing point for the hardware implementation. JDEM-Omega and WFIRST both have an infrared imager with a filter wheel, as well as counter-dispersed moderate resolution spectrometers. The primary advantage of space observations is being above the Earth's atmosphere, which absorbs, scatters, warps and emits light. Observing from above the atmosphere enables WFIRST to obtain precision infrared measurements of the shapes of galaxies for weak lensing, infrared light-curves of supernovae and exoplanet microlensing events with low systematic errors, and infrared measurements of the H hydrogen line to be cleanly detected in the 1<z<2 redshift range important for baryon acoustic oscillation (BAO) dark energy measurements. The Infrared Astronomical Satellite (IRAS), the Cosmic Background Explorer (COBE), Herschel, Spitzer, and Wide-field Infrared Sur-vey Explorer (WISE) are all space missions that have produced stunning new scientific advances by going to space to observe in the infrared. This interim report describes progress as of June 2011 on developing a requirements flowdown and an evaluation of scientific performance. An Interim Design Reference Mission (IDRM) configuration is presented that is based on the specifications of NWNH with some refinements to optimize the design in accordance with the new scientific requirements. Analysis of this WFIRST IDRM concept is in progress to ensure the capability of the observatory is compatible with the science requirements. The SDT and Project will continue to refine the mission concept over the coming year as design, analysis and simulation work are completed, resulting in the SDT s WFIRST Design Reference Mission (DRM) by the end of 2012.

Green, J.↗