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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

High-resolution Near-infrared Spectroscopic Study of Galactic Supernova Remnants. I. Kinematic Distances

We have carried out high-resolution near-infrared spectroscopic observations toward 16 Galactic supernova remnants (SNRs) showing strong H 2 emission features. A dozen bright H 2 emission lines are clearly detected for individual SNRs, and we have measured their central velocities, line widths, and fluxes. For all SNRs except one (G9.9–0.8), the H 2 line ratios are well consistent with that of thermal excitation at T ~ 2000 K, indicating that the H 2 emission lines are most likely from shock-excited gas and therefore that they are physically associated with the remnants. The kinematic distances to the 15 SNRs are derived from the central velocities of the H 2 lines using a Galactic rotation model. We derive for the first time the kinematic distances to four SNRs: G13.5+0.2, G16.0–0.5, G32.1–0.9, and G33.2–0.6. Among the remaining 11 SNRs, the central velocities of the H 2 emission lines for six SNRs are well consistent (±5 km s -1 ) with those obtained in previous radio observations, while for the other five SNRs (G18.1–0.1, G18.9–1.1, Kes 69, 3C 396, W49B) they are significantly different. We discuss the velocity discrepancies in these five SNRs. In G9.9–0.8, the H 2 emission shows nonthermal line ratios and narrow line width (~4 km s -1 ), and we discuss its origin.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spectroscopic Fourth-order Coronagraph for the Characterization of Terrestrial Planets at Small Angular Separations from Host Stars

We propose a new approach for high-contrast imaging at the diffraction limit using segmented telescopes in a modest observation bandwidth. This concept, named “spectroscopic fourth-order coronagraphy,” is based on a fourth-order coronagraph with a focal-plane mask that modulates the complex amplitude of the Airy disk along one direction. While coronagraphs applying the complex amplitude mask can achieve the theoretical limit performance for any arbitrary pupils, the focal-plane mask severely limits the bandwidth. Here, focusing on the fact that the focal-plane mask modulates the complex amplitude along one direction, we noticed that the mask can be optimized for each spectral element generated by a spectrograph. We combine the fourth-order coronagraph with two spectrographs to produce a stellar spectrum on the focal plane and reconstruct a white pupil on the Lyot stop. Based on the wave-front analysis of an optical design applying an Offner-type imaging spectrograph, we found that the achievable contrast of this concept is 10{sup −10} at 1.2–1.5 times the diffraction limit over the wavelength range of 650–750 nm for the entrance pupil of the LUVOIR telescope. Thus, this coronagraph concept could bring new habitable planet candidates not only around G- and K-type stars beyond 20–30 pc but also around very nearby M-type stars. This approach potentially promotes the characterization of the atmospheres of nearby terrestrial planets with future on- and off-axis segmented large telescopes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682). II. The Spectroscopic Binary Population

We present and analyze 120 spectroscopic binary and triple cluster members of the old (4 Gyr) open cluster M67 (NGC 2682). As a cornerstone of stellar astrophysics, M67 is a key cluster in the WIYN Open Cluster Study (WOCS); radial-velocity (RV) observations of M67 are ongoing and extend back over 45 yr, incorporating data from seven different telescopes, and allowing us to detect binaries with orbital periods ≲10{sup 4} days. Our sample contains 1296 stars (604 cluster members) with magnitudes of 10 ≤ V ≤ 16.5 (about 1.3–0.7 M {sub ⊙}), from the giants down to ∼4 mag below the main-sequence turnoff, and extends in radius to 30′ (7.4 pc at a distance of 850 pc, or ∼7 core radii). This paper focuses primarily on the main-sequence binaries, but orbital solutions are also presented for red giants, yellow giants, and sub-subgiants. Out to our period detection limit and within our magnitude and spatial domain, we find a global main-sequence incompleteness-corrected binary fraction of 34% ± 3%, which rises to 70% ± 17% in the cluster center. We derive a tidal circularization period of P{sub circ}=11.0{sub −1.0}{sup +1.1} days. We also analyze the incompleteness-corrected distributions of binary orbital elements and masses. The period distribution rises toward longer periods. The eccentricity distribution, beyond P {sub circ}, is consistent with a uniform distribution. The mass-ratio distribution is also consistent with a uniform distribution. Overall, these M67 binaries are closely consistent with similar binaries in the galactic field, as well as with the old (7 Gyr) open cluster NGC 188. WOCS. 83.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Spectroscopic and Photometric Monitoring of a Poorly Known Highly Luminous OH/IR Star: IRAS 18278+0931

We present the time-dependent properties of a poorly known OH/IR star, IRAS 18278+0931 (hereafter IRAS 18+09), toward the Ophiuchus constellation. We have carried out long-term optical/near-infrared photometric and spectroscopic observations to study the object. From optical R- and I-band light curves, the period of IRAS 18+09 is estimated to be 575 ± 30 days and the variability amplitudes range from ΔR ∼ 4.0 mag to ΔI ∼ 3.5 mag. From the standard period–luminosity relations, the distance (D) to the object, 4.0 ± 1.3 kpc, is estimated. Applying this distance in the radiative transfer model, the spectral energy distribution is constructed from multiwavelength photometric and IRAS-LRS spectral data, which provide the luminosity, optical depth, and gas mass-loss rate of the object to be 9600 ± 500 L {sub ⊙}, 9.1 ± 0.6 at 0.55 μm, and 1.0 × 10{sup −6} M {sub ⊙} yr{sup −1}, respectively. The current mass of the object is inferred to be in the range 1.0−1.5 M {sub ⊙} assuming solar metallicity. Notably, the temporal variation of atomic and molecular features (e.g., TiO, Na i, Ca i, CO, H{sub 2}O) over the pulsation cycle of the OH/IR star illustrates the sensitivity of the spectral features to the dynamical atmosphere as observed in pulsating AGB stars.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Photometric and Spectroscopic Analysis of Four Contact Binaries

We present the photometric and spectroscopic analysis of four W UMa binaries J015829.5+260333 (hereinafter as J0158), J030505.1+293443 (hereinafter as J0305), J102211.7+310022 (hereinafter as J1022), and KW Psc. The VR {sub c} I {sub c} band photometric observations are carried out with the 1.3 m Devasthal Fast Optical Telescope (DFOT). For low-resolution spectroscopy, we used the 2 m Himalayan Chandra Telescope (HCT) as well as the archival data from the 4 m LAMOST survey. The systems J0158 and J0305 show a period increase rate of 5.26( ± 1.72) × 10{sup −7} days yr{sup −1} and 1.78( ± 1.52) × 10{sup −6} days yr{sup −1}, respectively. The period of J1022 is found to be decreasing with a rate of 4.22 ( ± 1.67) × 10{sup −6} days yr{sup −1}. The period analysis of KW Psc displays no change in its period. The PHOEBE package is used for the light-curve modeling and basic parameters are evaluated with the help of the GAIA parallax. The asymmetry of light curves is explained with the assumption of cool spots at specific positions on one of the components of the system. On the basis of temperatures, mass ratios, fill-out factors, and periods, the system J1022 is identified as a W-subtype system while the others show some mixed properties. To probe the chromospheric activities in these W UMa binaries, their spectra are compared with the known inactive stars’ spectra. The comparison shows emission in H {sub α}, H {sub β}, and Ca II. To understand the evolutionary status of these systems, the components are plotted in mass–radius and mass–luminosity planes with other well characterized binary systems. The secondary components of all the systems are away from ZAMS, which indicates that the secondary is more evolved than the primary component.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

The Robotic Multiobject Focal Plane System of the Dark Energy Spectroscopic Instrument (DESI)

Abstract A system of 5020 robotic fiber positioners was installed in 2019 on the Mayall Telescope, at Kitt Peak National Observatory. The robots automatically retarget their optical fibers every 10–20 minutes, each to a precision of several microns, with a reconfiguration time of fewer than 2 minutes. Over the next 5 yr, they will enable the newly constructed Dark Energy Spectroscopic Instrument (DESI) to measure the spectra of 35 million galaxies and quasars. DESI will produce the largest 3D map of the universe to date and measure the expansion history of the cosmos. In addition to the 5020 robotic positioners and optical fibers, DESI’s Focal Plane System includes six guide cameras, four wave front cameras, 123 fiducial point sources, and a metrology camera mounted at the primary mirror. The system also includes associated structural, thermal, and electrical systems. In all, it contains over 675,000 individual parts. We discuss the design, construction, quality control, and integration of all these components. We include a summary of the key requirements, the review and acceptance process, on-sky validations of requirements, and lessons learned for future multiobject, fiber-fed spectrographs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

The Target-selection Pipeline for the Dark Energy Spectroscopic Instrument

Abstract In 2021 May, the Dark Energy Spectroscopic Instrument (DESI) began a 5 yr survey of approximately 50 million total extragalactic and Galactic targets. The primary DESI dark-time targets are emission line galaxies, luminous red galaxies, and quasars. In bright time, DESI will focus on two surveys known as the Bright Galaxy Survey and the Milky Way Survey. DESI also observes a selection of “secondary” targets for bespoke science goals. This paper gives an overview of the publicly available pipeline ( desitarget ) used to process targets for DESI observations. Highlights include details of the different DESI survey targeting phases, the targeting ID ( TARGETID ) used to define unique targets, the bitmasks used to indicate a particular type of target, the data model and structure of DESI targeting files, and examples of how to access and use the desitarget code base. This paper will also describe “supporting” DESI target classes, such as standard stars, sky locations, and random catalogs that mimic the angular selection function of DESI targets. The DESI target-selection pipeline is complex and sizable; this paper attempts to summarize the most salient information required to understand and work with DESI targeting data.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Performance of the Quasar Spectral Templates for the Dark Energy Spectroscopic Instrument

Abstract Millions of quasar spectra will be collected by the Dark Energy Spectroscopic Instrument (DESI), leading to a fourfold increase in the number of known quasars. High-accuracy quasar classification is essential to tighten constraints on cosmological parameters measured at the highest redshifts DESI observes ( z > 2.0). We present spectral templates for identification and redshift estimation of quasars in the DESI Year 1 data release. The quasar templates are comprised of two quasar eigenspectra sets, trained on spectra from the Sloan Digital Sky Survey. The sets are specialized to reconstruct quasar spectral variation observed over separate yet overlapping redshift ranges and, together, are capable of identifying DESI quasars from 0.05 < z < 7.0. The new quasar templates show significant improvement over the previous DESI quasar templates regarding catastrophic failure rates, redshift precision and accuracy, quasar completeness, and the contamination fraction in the final quasar sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Astrometric Calibration and Performance of the Dark Energy Spectroscopic Instrument Focal Plane

Abstract The Dark Energy Spectroscopic Instrument, consisting of 5020 robotic fiber positioners and associated systems on the Mayall telescope at Kitt Peak, Arizona, is carrying out a survey to measure the spectra of 40 million galaxies and quasars and produce the largest 3D map of the universe to date. The primary science goal is to use baryon acoustic oscillations to measure the expansion history of the universe and the time evolution of dark energy. A key function of the online control system is to position each fiber on a particular target in the focal plane with an accuracy of 11 μ m rms 2D. This paper describes the set of software programs used to perform this function along with the methods used to validate their performance.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

The Early Data Release of the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) completed its 5 month Survey Validation in 2021 May. Spectra of stellar and extragalactic targets from Survey Validation constitute the first major data sample from the DESI survey. This paper describes the public release of those spectra, the catalogs of derived properties, and the intermediate data products. In total, the public release includes good-quality spectral information from 466,447 objects targeted as part of the Milky Way Survey, 428,758 as part of the Bright Galaxy Survey, 227,318 as part of the Luminous Red Galaxy sample, 437,664 as part of the Emission Line Galaxy sample, and 76,079 as part of the Quasar sample. In addition, the release includes spectral information from 137,148 objects that expand the scope beyond the primary samples as part of a series of secondary programs. Here, we describe the spectral data, data quality, data products, Large-Scale Structure science catalogs, access to the data, and references that provide relevant background to using these spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The Optical Corrector for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is currently measuring the spectra of 40 million galaxies and quasars, the largest such survey ever made to probe the nature of cosmological dark energy. The 4 m Mayall telescope at Kitt Peak National Observatory has been adapted for DESI, including the construction of a 3$_{.}^{°}$2 diameter prime focus corrector that focuses astronomical light onto a 0.8 m diameter focal surface with excellent image quality over the DESI bandpass of 360–980 nm. The wide-field corrector includes six lenses, as large as 1.1 m in diameter and as heavy as 237 kilograms, including two counterrotating wedged lenses that correct for atmospheric dispersion over zenith angles from 0° to 60°. The lenses, cells, and barrel assembly all meet precise alignment tolerances on the order of tens of microns. The barrel alignment is maintained throughout a range of observing angles and temperature excursions in the Mayall dome by use of a hexapod, which is itself supported by a new cage, ring, and truss structure. In this paper we describe the design, fabrication, and performance of the new corrector and associated structure, focusing on how they meet DESI requirements. In particular, we describe the prescription and specifications of the lenses, design choices and error budgeting of the barrel assembly, stray light mitigations, and integration and test at the Mayall telescope. We conclude with some validation highlights that demonstrate the successful corrector on-sky performance, and we list some lessons learned during the multiyear fabrication phase.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Archetype-based Redshift Estimation for the Dark Energy Spectroscopic Instrument Survey

We present a computationally efficient galaxy archetype-based redshift estimation and spectral classification method for the Dark Energy Survey Instrument (DESI) survey. The DESI survey currently relies on a redshift fitter and spectral classifier using a linear combination of principal component analysis–derived templates, which is very efficient in processing large volumes of DESI spectra within a short time frame. However, this method occasionally yields unphysical model fits for galaxies and fails to adequately absorb calibration errors that may still be occasionally visible in the reduced spectra. Our proposed approach improves upon this existing method by refitting the spectra with carefully generated physical galaxy archetypes combined with additional terms designed to absorb data reduction defects and provide more physical models to the DESI spectra. We test our method on an extensive data set derived from the survey validation (SV) and Year 1 (Y1) data of DESI. Our findings indicate that the new method delivers marginally better redshift success for SV tiles while reducing catastrophic redshift failure by 10%–30%. At the same time, results from millions of targets from the main survey show that our model has relatively higher redshift success and purity rates (0.5%–0.8% higher) for galaxy targets while having similar success for QSOs. These improvements also demonstrate that the main DESI redshift pipeline is generally robust. Additionally, it reduces the false-positive redshift estimation by 5%–40% for sky fibers. We also discuss the generic nature of our method and how it can be extended to other large spectroscopic surveys, along with possible future improvements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Overview of the Fiber System for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is a revolutionary instrument designed for precise measurements of cosmic distances and the investigation of dark energy. DESI utilizes 5000 optical fibers to simultaneously measure the spectra of distant objects and aims to measure 40 million galaxies and quasars in a 5 yr survey. One of the critical challenges to DESI's success was ensuring that the fiber system was not only highly efficient but also delivered a highly stable beam enabling more reliable sky subtraction for measurements of faint objects. We achieved this stability by minimizing the stress on the fiber system during the manufacture and operation of the telescope and fiber positioning robots. We installed the DESI fiber system on the 4 m Mayall telescope with ≥99% of fibers intact, and the instrument has delivered superb optical performance throughout the initial years of the DESI survey, including ≥90% average throughput when injected with a focal ratio of ~f/3.9 as delivered by the primary focus corrector, excluding fiber absorption losses. The design of DESI required multiple innovations to achieve these requirements, such as cleaved fibers bonded with a UV-curing epoxy to glass ferrules in the focal plane and fusion splicing instead of physical connectors. In this paper, we describe the development, delivery, and installation of the fiber system, the innovations that made the state-of-the-art performance possible, and the key lessons learned that could benefit future projects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

The Backup Program of the Dark Energy Spectroscopic Instrument’s Milky Way Survey

The Milky Way Backup Program (MWBP), a survey currently underway with the Dark Energy Spectroscopic Instrument (DESI) on the Nicholas U. Mayall 4 m Telescope, works at the margins of the DESI Main surveys to obtain spectra of millions of additional stars from the Gaia catalog. Efficiently utilizing times between ∼12° and 18° twilight and poor weather conditions, the MWBP extends the range of stellar sources studied to both brighter magnitudes and lower Galactic latitude and declination than the stars studied in DESI’s Main Milky Way Survey. While the MWBP prioritizes candidate giant stars selected from the Gaia catalog (using color and parallax criteria), it also includes an unbiased sample of bright stars (i.e., 11.2 ≲ G < 16 mag) as well as fainter sources (to G ≲ 19 mag). As of 2025 March 1, the survey had obtained spectra of ∼7 million stars, approximately 1.2 million of which are included in the DESI Data Release 1. The DESI spectra cover the wavelength range from 3600 to 9800 Å at a resolution λ/Δλ varying from 2000 to 5000. The full survey, when completed, will cover an area of more than 21,000 deg 2 and include approximately 10 million Gaia sources, roughly equal to the number of stellar spectra obtained through the DESI Main Survey, while only utilizing ≈9% of all DESI observing time. This paper provides an overview of the MWBP, describing the target selection, observing strategy, and an introduction to the resulting data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The HectoMAP Cluster Survey: Spectroscopically Identified Clusters and their Brightest Cluster Galaxies (BCGs)

We apply a friends-of-friends (FoF) algorithm to identify galaxy clusters and we use the catalog to explore the evolutionary synergy between brightest cluster galaxies (BCGs) and their host clusters. We base the cluster catalog on the dense HectoMAP redshift survey (2000 redshifts deg -2 ). The HectoMAP FoF catalog includes 346 clusters with 10 or more spectroscopic members within the range 0.05 < z < 0.55 and with a median z = 0.29. We list these clusters and their members. We also include central velocity dispersions (σ*, BCG ) for the FoF cluster BCGs, a distinctive feature of the HectoMAP FoF catalog. HectoMAP clusters with higher galaxy number density (80 systems) are all genuine clusters with a strong concentration and a prominent BCG in Subaru/Hyper Suprime-Cam images. The phase-space diagrams show the expected elongation along the line of sight. Lower-density systems include some low reliability systems. We establish a connection between BCGs and their host clusters by demonstrating that σ*, BCG /σ cl decreases as a function of cluster velocity dispersion (σ cl ), in contrast, numerical simulations predict a constant σ*, BCG /σ cl . Sets of clusters at two different redshifts show that BCG evolution in massive systems is slow over the redshift range z < 0.4. The data strongly suggest that minor mergers may play an important role in BCG evolution in clusters with σ cl ≳ 300 km s -1 . For lower mass systems (σ cl < 300 km s -1 ), major mergers may play a significant role. The coordinated evolution of BCGs and their host clusters provides an interesting test of simulations in high-density regions of the universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Contribution of Gaia Sausage to the Galactic Stellar Halo Revealed by K Giants and Blue Horizontal Branch Stars from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, Sloan Digital Sky Survey, and Gaia

We explore the contribution of the Gaia Sausage to the stellar halo of the Milky Way by making use of a Gaussian mixture model (GMM) and applying it to halo star samples of Large Sky Area Multi-Object Fiber Spectroscopic Telescope K giants, Sloan Extension for Galactic Understanding and Exploration K giants, and Sloan Digital Sky Survey blue horizontal branch stars. The GMM divides the stellar halo into two parts, of which one represents a more metal-rich and highly radially biased component associated with an ancient, head-on collision referred to as the Gaia Sausage, and the other one is a more metal-poor and isotropic halo. A symmetric bimodal Gaussian is used to describe the distribution of spherical velocity of the Gaia Sausage, and we find that the mean absolute radial velocity of the two lobes decreases with the Galactocentric radius. We find that the Gaia Sausage contributes about 41%–74% of the inner (Galactocentric radius r gc < 30 kpc) stellar halo. The fraction of stars of the Gaia Sausage starts to decline beyond r gc ~ 25–30 kpc, and the outer halo is found to be significantly less influenced by the Gaia Sausage than the inner halo. After the removal of halo substructures found by integrals of motion, the contribution of the Gaia Sausage falls slightly within r gc ~ 25 kpc but is still as high as 30%–63%. Finally, we select several possible Sausage-related substructures consisting of stars on highly eccentric orbits. The GMM/Sausage component agrees well with the selected substructure stars in their chemodynamical properties, which increases our confidence in the reliability of the GMM fits.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space Telescope

The Nancy Grace Roman Space Telescope will conduct a High Latitude Spectroscopic Survey (HLSS) over a large volume at high redshift, using the near-IR grism (1.0–1.93 μm, R = 435–865) and the 0.28 deg 2 wide-field camera. We present a reference HLSS that maps 2000 deg 2 and achieves an emission-line flux limit of 10 -16 erg s -1 cm -2 at 6.5σ, requiring ~0.6 yr of observing time. We summarize the flowdown of the Roman science objectives to the science and technical requirements of the HLSS. We construct a mock redshift survey over the full HLSS volume by applying a semianalytic galaxy formation model to a cosmological N-body simulation and use this mock survey to create pixel-level simulations of 4 deg 2 of HLSS grism spectroscopy. We find that the reference HLSS would measure ~10 million H α galaxy redshifts that densely map large-scale structure at z = 1–2 and 2 million [O III] galaxy redshifts that sparsely map structures at z = 2–3. We forecast the performance of this survey for measurements of the cosmic expansion history with baryon acoustic oscillations and the growth of large-scale structure with redshift-space distortions. We also study possible deviations from the reference design and find that a deep HLSS at f line > 7 × 10 -17 erg s -1 cm -2 over 4000 deg 2 (requiring ~1.5 yr of observing time) provides the most compelling stand-alone constraints on dark energy from Roman alone. This provides a useful reference for future optimizations. The reference survey, simulated data sets, and forecasts presented here will inform community decisions on the final scope and design of the Roman HLSS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Spectroscopic View of the JWST/GTO Strong Lensing Cluster A1489

We discuss a spectroscopic survey of the strong lensing cluster A1489 that includes redshifts for 195 cluster members along with central velocity dispersions for 188 cluster members. The caustic technique applied to the redshift survey gives the dynamical parameters M 200 = (1.25 ± 0.09) × 10 15 M ⊙ , R 200 = 1.97 ± 0.05 Mpc, and a cluster line-of-sight velocity dispersion of 1150 ± 72 km s -1 within R 200 . These parameters are very similar to those of other strong lensing systems with comparably large Einstein radii. We use the spectroscopy and deep photometry to demonstrate that A1489 is probably dynamically active; its four brightest cluster galaxies have remarkably different rest-frame radial velocities. Like other massive strong lensing clusters, the velocity dispersion function for members of A1489 shows an excess for dispersions ≳250 km s -1 . The central dispersions also provide enhanced constraints on future lensing models.

79 ASTRONOMY AND ASTROPHYSICS↗