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At least 163 records · Page 9

Forecast for a growth-rate measurement using peculiar velocities from LSST supernovae

We investigate whether the cosmic growth-rate parameter fσ 8 can be measured using peculiar velocities (PVs) derived from type Ia supernovae (SNe Ia) in the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST). We produced simulations of different SN types using a realistic LSST observing strategy that incorporated noise, a photometric detection from the difference-image analysis (DIA) pipeline, and a PV field modeled from the Uchuu universe machine simulations. We tested three different observational scenarios that ranged from ideal conditions with spectroscopic host galaxy redshifts and spectroscopic SN typing to realistic photometric typing that resulted in a contamination with non-Ia SNe. Using a maximum likelihood technique, we showed that the LSST can measure fσ 8 with a precision of 10% in the redshift range 0.02 < z < 0.14 for our most realistic scenario. In three tomographic bins, the LSST will be able to constrain the growth-rate parameter with errors below 18% up to redshift z = 0.14. We also tested the contamination effect on the maximum likelihood method and found that for a contamination fraction below ∼2%, we recovered unbiased measurements. The results of this analysis highlight that the LSST SN sample is expected to complement traditional redshift-space distortion measurements at high redshift. This will provide a novel avenue for testing general relativity and different dark energy models.

Rosselli, D↗

Preparation of the Multi-Site Data Processing at the Vera C. Rubin Observatory

The Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) Camera is scheduled to start taking data in the summer of 2025. The Data Release Production will run the LSST Science Pipe software at data facilities in the US, France and the UK. The LSST Science Pipeline consists of complex directed acyclic graphs (DAGs) of tasks. Rubin will use the Production and Distributed Analysis (PanDA) workflow and workload management system to orchestrate this complex workflow and the distribution of workloads to the data facilities. When run end-to-end by a team of data production staff, this processing (the Science Pipelines, distributed by the workflow and workload management system) is referred to as a 'campaign'. This paper describes the central services and data facility specific services that support this multi-site data process model, including the service deployment infrastructure, the workload and workflow system, the Campaign Management tools, and connection to Rubin Data Management. This paper will also mention the experience of processing the Rubin Commissioning Camera data. All these are part of the effort to scale up the processing capabilities for the expected very large data volume from the LSST Camera.

Yang, Wei [SLAC]↗

The La Silla Schmidt Southern Survey

We present the La Silla Schmidt Southern Survey (LS4), a new wide-field, time-domain survey to be conducted with the 1 m ESO Schmidt telescope. The 268 megapixel LS4 camera mosaics 32 2k × 4k fully depleted CCDs, providing a ∼20 deg 2 field of view with 1″ pixel −1 resolution. The LS4 camera will have excellent performance at longer wavelengths: in a standard 45 s exposure the expected 5σ limiting magnitudes in g, i, z are ∼21.5, ∼20.9, and ∼20.3 mag (AB), respectively. The telescope design requires a novel filter holder that fixes different bandpasses over each quadrant of the detector. Two quadrants will have i band, while the other two will be g and z band with color information obtained by dithering targets across the different quadrants. The majority (90%) of the observing time will be used to conduct a public survey that monitors the extragalactic sky at both moderate (3 days) and high (1 day) cadence, as well as focused observations within the Galactic plane and bulge. Alerts from the public survey will be broadcast to the community via established alert brokers. LS4 will run concurrently with the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST). The combination of LS4+LSST will enable detailed holistic monitoring of many nearby transients: high-cadence LS4 observations will resolve the initial rise and peak of the light curve while less-frequent but deeper observations by LSST will characterize the years before and after explosion. Here, we summarize the primary science objectives of LS4 including microlensing events in the Galaxy, extragalactic transients powered by massive black holes or stellar explosions, the search for electromagnetic counterparts to multi-messenger events, and supernova cosmology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Stellar splashback: the edge of the intracluster light

We examine the outskirts of galaxy clusters in the C-EAGLE simulations to quantify the ‘edges’ of the stellar and dark matter distribution. The radius of the steepest slope in the dark matter, commonly used as a proxy for the splashback radius, is located at $\sim \, r_{200 \rm m}$; the strength and location of this feature depends on the recent mass accretion rate, in good agreement with previous work. Interestingly, the stellar distribution (or intracluster light, ICL) also has a well-defined edge, which is directly related to the splashback radius of the halo. Thus, detecting the edge of the ICL can provide an independent measure of the physical boundary of the halo, and the recent mass accretion rate. We show that these caustics can also be seen in the projected density profiles, but care must be taken to account for the influence of substructures and other non-diffuse material, which can bias and/or weaken the signal of the steepest slope. This is particularly important for the stellar material, which has a higher fraction bound in subhaloes than the dark matter. Finally, we show that the ‘stellar splashback’ feature is located beyond current observational constraints on the ICL, but these large projected distances (>> 1 Mpc) and low surface brightnesses (μ>>32 mag arcsec -2 ) can be reached with upcoming observational facilities such as the Vera C. Rubin Observatory, the Nancy Grace Roman Space Telescope, and Euclid.

79 ASTRONOMY AND ASTROPHYSICS↗

Photometric calibration in u -band using blue halo stars

ABSTRACT We develop a method to calibrate u-band photometry based on the observed colour of blue Galactic halo stars. The Galactic halo stars belong to an old stellar population of the Milky Way and have relatively low metallicity. The ‘blue tip’ of the halo population – the main sequence turn-off (MSTO) stars – is known to have a relatively uniform intrinsic edge u-g colour with only slow spatial variation. In SDSS data, the observed variation is correlated with Galactic Latitude, which we attribute to contamination by higher metallicity disc stars and fit with an empirical curve. This curve can then be used to calibrate u-band imaging if g-band imaging of matching depth is available. Our approach can be applied to single-field observations at |b| > 30°, and removes the need for standard star observations or overlap with calibrated u-band imaging. We include in our method the calibration of g-band data with ATLAS-Refcat2. We test our approach on stars in KiDS DR 4, ATLAS DR 4, and DECam imaging from the NOIRLab Source Catalog (NSC DR2), and compare our calibration with SDSS. For this process, we use synthetic magnitudes to derive the colour equations between these data sets, in order to improve zero-point accuracy. We find an improvement for all data sets, reaching a zero-point precision of 0.016 mag for KiDS (compared to the original 0.033 mag), 0.020 mag for ATLAS (originally 0.027 mag), and 0.016 mag for DECam (originally 0.041 mag). Thus, this method alone reaches the goal of 0.02 mag photometric precision in u-band for the Rubin Observatory’s Legacy Survey of Space and Time (LSST).

79 ASTRONOMY AND ASTROPHYSICS↗

Deep learning methods for obtaining photometric redshift estimations from images

ABSTRACT Knowing the redshift of galaxies is one of the first requirements of many cosmological experiments, and as it is impossible to perform spectroscopy for every galaxy being observed, photometric redshift (photo-z) estimations are still of particular interest. Here, we investigate different deep learning methods for obtaining photo-z estimates directly from images, comparing these with ‘traditional’ machine learning algorithms which make use of magnitudes retrieved through photometry. As well as testing a convolutional neural network (CNN) and inception-module CNN, we introduce a novel mixed-input model that allows for both images and magnitude data to be used in the same model as a way of further improving the estimated redshifts. We also perform benchmarking as a way of demonstrating the performance and scalability of the different algorithms. The data used in the study comes entirely from the Sloan Digital Sky Survey (SDSS) from which 1 million galaxies were used, each having 5-filtre (ugriz) images with complete photometry and a spectroscopic redshift which was taken as the ground truth. The mixed-input inception CNN achieved a mean squared error (MSE) =0.009, which was a significant improvement ($30{{\ \rm per\ cent}}$) over the traditional random forest (RF), and the model performed even better at lower redshifts achieving a MSE = 0.0007 (a $50{{\ \rm per\ cent}}$ improvement over the RF) in the range of z < 0.3. This method could be hugely beneficial to upcoming surveys, such as Euclid and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), which will require vast numbers of photo-z estimates produced as quickly and accurately as possible.

79 ASTRONOMY AND ASTROPHYSICS↗

Detecting strongly lensed type Ia supernovae with LSST

ABSTRACT Strongly lensed supernovae are rare and valuable probes of cosmology and astrophysics. Upcoming wide-field time-domain surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), are expected to discover an order-of-magnitude more lensed supernovae than have previously been observed. In this work, we investigate the cosmological prospects of lensed type Ia supernovae (SNIa) in LSST by quantifying the expected annual number of detections, the impact of stellar microlensing, follow-up feasibility, and how to best separate lensed and unlensed SNIa. We simulate SNIa lensed by galaxies, using the current LSST baseline v3.0 cadence, and find an expected number of 44 lensed SNIa detections per year. Microlensing effects by stars in the lensing galaxy are predicted to lower the lensed SNIa detections by ∼8 per cent. The lensed events can be separated from the unlensed ones by jointly considering their colours and peak magnitudes. We define a ‘gold sample’ of ∼10 lensed SNIa per year with time delay >10 d, >5 detections before light curve peak, and sufficiently bright (mi < 22.5 mag) for follow-up observations. In 3 yr of LSST operations, such a sample is expected to yield a 1.5 per cent measurement of the Hubble constant.

Astronomy & Astrophysics↗

A Bayesian approach to strong lens finding in the era of wide-area surveys

ABSTRACT The arrival of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), Euclid-Wide and Roman wide-area sensitive surveys will herald a new era in strong lens science in which the number of strong lenses known is expected to rise from $\mathcal {O}(10^3)$ to $\mathcal {O}(10^5)$. However, current lens-finding methods still require time-consuming follow-up visual inspection by strong lens experts to remove false positives which is only set to increase with these surveys. In this work, we demonstrate a range of methods to produce calibrated probabilities to help determine the veracity of any given lens candidate. To do this we use the classifications from citizen science and multiple neural networks for galaxies selected from the Hyper Suprime-Cam survey. Our methodology is not restricted to particular classifier types and could be applied to any strong lens classifier which produces quantitative scores. Using these calibrated probabilities, we generate an ensemble classifier, combining citizen science, and neural network lens finders. We find such an ensemble can provide improved classification over the individual classifiers. We find a false-positive rate of 10−3 can be achieved with a completeness of 46 per cent, compared to 34 per cent for the best individual classifier. Given the large number of galaxy–galaxy strong lenses anticipated in LSST, such improvement would still produce significant numbers of false positives, in which case using calibrated probabilities will be essential for population analysis of large populations of lenses and to help prioritize candidates for follow-up.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards quantifying the impact of triaxiality on optical signatures of galaxy clusters: weak lensing and galaxy distributions

ABSTRACT We present observational evidence of the impact of triaxiality on radial profiles that extend to 40 Mpc from galaxy cluster centres in optical measurements. We perform a stacked profile analysis from a sample of thousands of nearly relaxed galaxy clusters from public data releases of the Dark Energy Survey and the Dark Energy Camera Legacy Survey. Using the central galaxy elliptical orientation angle as a proxy for galaxy cluster orientation, we measure cluster weak lensing and excess galaxy density axis-aligned profiles, extracted along the central galaxy’s major or minor axes on the plane of the sky. Our measurements show a ≳ 2σ–3σ difference per radial bin between the normalized axis-aligned profiles. The profile difference between each axis-aligned profile and the azimuthally averaged profile ($\sim \pm 10\,\rm per\ cent-20~{{\ \rm per\ cent}}$ along major/minor axis) appears inside the clusters (∼0.4 Mpc) and extends to the large-scale structure regime (∼10–20 Mpc). The magnitude of the difference appears to be relatively insensitive to cluster richness and redshift, and extends further out in the weak lensing surface mass density than in the galaxy overdensity. Looking forward, this measurement can easily be applied to other observational or simulation data sets and can inform the systematics in cluster mass modelling related to triaxiality. We expect imminent upcoming wide-area deep surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, to improve our quantification of optical signatures of cluster triaxiality.

79 ASTRONOMY AND ASTROPHYSICS↗

Joint modelling of astrophysical systematics for cosmology with LSST cosmic shear

ABSTRACT We present a novel framework for jointly modelling the weak lensing source galaxy redshift distribution and the intrinsic alignment (IA) of galaxies through a shared luminosity function (LF). In the context of a Rubin Observatory’s Legacy Survey of Space and Time (LSST) Year 1 and Year 10 cosmic shear analysis, we show that our novel approach produces cosmological parameter constraints which are comparable to standard methods, while offering more physical insight into IA and selection effects. We clarify the relationship between individual parameters of a Schechter LF and the redshift distribution of a magnitude-limited sample, showing the consequences of marginalizing over these parameters when modelling IAs in standard cosmic shear analyses. We explore the impact of the shape of the LF on the cosmic shear data vector, and we outline the potential of this method to naturally model selection functions in redshift distribution estimation. Although this work focuses on LSST cosmic shear, the proposed joint modelling framework is broadly applicable to weak lensing surveys.

Šarčević, Nikolina (ORCID:0000000173016415)↗

Reducing model error using optimized galaxy selection: weak lensing cluster mass estimation

Galaxy clusters are one of the most powerful probes to study extensions of General Relativity and the Standard Cosmological Model. Upcoming surveys like the Vera Rubin Observatory’s Legacy Survey of Space and Time are expected to revolutionise the field, by enabling the analysis of cluster samples of unprecedented size and quality. To reach this era of high-precision cluster cosmology, the mitigation of sources of systematic error is crucial. A particularly important challenge is bias in cluster mass measurements induced by the mismodelling of photometric redshift estimates of source galaxies. This work proposes a method to optimise the source sample selection in cluster weak lensing analyses drawn from wide-field survey lensing catalogs to reduce the bias on reconstructed cluster masses. We use a combinatorial optimisation scheme and methods from variational inference to select galaxies in latent space to produce a probabilistic galaxy source sample catalog for highly accurate cluster mass estimation. We show that our method reduces the critical surface mass density Σ crit relative modelling bias on the 60-70% level, while maintaining up to 90% of galaxies. We highlight that our methodology has applications beyond cluster mass estimation as an approach to jointly combine galaxy selection and model inference under sources of systematics.

79 ASTRONOMY AND ASTROPHYSICS↗

Soft X-ray quantum efficiency of a commercial CMOS imaging sensor

The demonstrated performance and cost-effectiveness of complementary metal-oxide-semiconductor (CMOS) sensors make them a potentially attractive option for low-cost space-based X-ray observatories. We have previously reported on the performance of a commercially available backside-illuminated Sony IMX290LLR-C CMOS sensor and found it to offer X-ray spectral resolutions comparable to the charged coupled devices (CCDs) aboard Suzaku and Chandra and to have a sufficient radiation hardness for use in low Earth orbit. Here, in this work, we report on the quantum efficiency (QE) of this sensor, an essential metric for modeling the sensitivity of an instrument as an X-ray detector. Using the Advanced Photon Source at Argonne National Laboratory, we measure the soft X-ray QE of this CMOS sensor to be 0.28 ± 0.02 at a photon energy of 490.5 eV. This energy was chosen for its proximity to the astrophysically important O VII triplet emission lines (~574 eV) studied by the HaloSat mission. Although not surpassing that of the back-illuminated CCDs aboard Suzaku and Chandra, this QE compares favorably to that of the front-illuminated CCDs aboard the same observatories and is competitive with that of the silicon drift detectors used aboard HaloSat, making it a strong candidate for use on future X-ray small satellite (SmallSat) missions.

47 OTHER INSTRUMENTATION↗

Improving Dark Energy Constraints Using Low-Redshift Large-Scale Structures

The primary goal of this project was to improve constraints on dark energy measurements by improving our ability to extract cosmological information from low redshift large-scale structures. PI Clowe's project's primary aim was to reduce the bias in measurements of the masses of clusters of galaxies to a level where the evolution of the cluster mass function can be used in the Vera Rubin Observatory's Legacy Survey of Space and Time Dark Energy Science Collaboration survey to improve the accuracy of the measurement of dark energy and other cosmological parameters. Co-PI Seo's project studied observational systematics affecting large-scale clustering of galaxies, which will be used to improve dark energy constraints from the Dark Energy Spectroscopic Instrument (DESI). The cluster lensing project employed a series of simulations and observations of clusters of galaxies to test numerous potential systematic errors in cluster mass measurements using weak gravitational lensing as the accuracy of current weak lensing measurements are more than order of magnitude worse than what is required to use clusters of galaxies for accurate determination of dark energy parameters. PI Clowe and group developed and analyzed simulations to test for, and correct biases introduced in, the weak lensing measurement process. Finally, PI Clowe and group developed a method of detecting clusters using galaxy overdensities and applied the method to the BLISS and DES surveys. The success of spectroscopic dark energy mission such as the extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic Instrument (DESI) will depend on a thorough understanding of various observational systematics in the target density fluctuations that would give rise to spurious, non-cosmological signals. PI Seo and group developed a deep learning, artificial neural network (ANN) technique that modeled and mitigated such effects, aimed at deriving more robust galaxy clustering signals not only for the baryon acoustic oscillation feature and redshift-space distortions but also for primordial non-Gaussianity constraint.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 6 Results: Point-Spread Function Modeling

We present the point-spread function (PSF) modeling for weak lensing shear measurement using the full six years of the Dark Energy Survey (DES Y6) data. We review the PSF estimation procedure using the PIFF (PSFs In the Full FOV) software package and describe the key improvements made to PIFF and modeling diagnostics since the DES year three (Y3) analysis: (i) use of external Gaia and infrared photometry catalogs to ensure higher purity of the stellar sample used for model fitting, (ii) addition of color-dependent PSF modeling, the first for any weak lensing analysis, and (iii) inclusion of model diagnostics inspecting fourth-order moments, which can bias weak lensing measurements to a similar degree as second-order modeling errors. Through a comprehensive set of diagnostic tests, we demonstrate the improved accuracy of the Y6 models evident in significantly smaller systematic errors than those of the Y3 analysis, in which all g band data were excluded due to insufficiently accurate PSF models. For the Y6 weak lensing analysis, we include g band photometry data in addition to the riz bands, providing a fourth band for photometric redshift estimation. Looking forward to the next generation of wide-field surveys, we describe several ongoing improvements to PIFF, which will be the default PSF modeling software for weak lensing analyses for the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

What’s the Difference? The Potential for Convolutional Neural Networks for Transient Detection without Template Subtraction

Abstract We present a study of the potential for convolutional neural networks (CNNs) to enable separation of astrophysical transients from image artifacts, a task known as “real–bogus” classification, without requiring a template-subtracted (or difference) image, which requires a computationally expensive process to generate, involving image matching on small spatial scales in large volumes of data. Using data from the Dark Energy Survey, we explore the use of CNNs to (1) automate the real–bogus classification and (2) reduce the computational costs of transient discovery. We compare the efficiency of two CNNs with similar architectures, one that uses “image triplets” (templates, search, and difference image) and one that takes as input the template and search only. We measure the decrease in efficiency associated with the loss of information in input, finding that the testing accuracy is reduced from ∼96% to ∼91.1%. We further investigate how the latter model learns the required information from the template and search by exploring the saliency maps. Our work (1) confirms that CNNs are excellent models for real–bogus classification that rely exclusively on the imaging data and require no feature engineering task and (2) demonstrates that high-accuracy (>90%) models can be built without the need to construct difference images, but some accuracy is lost. Because, once trained, neural networks can generate predictions at minimal computational costs, we argue that future implementations of this methodology could dramatically reduce the computational costs in the detection of transients in synoptic surveys like Rubin Observatory's Legacy Survey of Space and Time by bypassing the difference image analysis entirely.

79 ASTRONOMY AND ASTROPHYSICS↗

Lens Modeling of STRIDES Strongly Lensed Quasars Using Neural Posterior Estimation

Strongly lensed quasars can be used to constrain cosmological parameters through time-delay cosmography. Models of the lens masses are a necessary component of this analysis. To enable time-delay cosmography from a sample of $\mathcal{O}(10^3)$ lenses, which will soon become available from surveys like the Rubin Observatory’s Legacy Survey of Space and Time and the Euclid Wide Survey, we require fast and standardizable modeling techniques. To address this need, we apply neural posterior estimation (NPE) for modeling galaxy-scale strongly lensed quasars from the Strong Lensing Insights into the Dark Energy Survey (STRIDES) sample. NPE brings two advantages: speed and the ability to implicitly marginalize over nuisance parameters. We extend this method by employing sequential NPE to increase precision of mass model posteriors. We then fold individual lens models into a hierarchical Bayesian inference to recover the population distribution of lens mass parameters, accounting for out-of-distribution shift. After verifying our method using simulated analogs of the STRIDES lens sample, we apply our method to 14 Hubble Space Telescope single-filter observations. We find the population mean of the power-law elliptical mass distribution slope, γ lens , to be $\mathcal{M}_γ$ lens = 2.13 ± 0.06. Our result represents the first population-level constraint for these systems. This population-level inference from fully automated modeling is an important stepping stone toward cosmological inference with large samples of strongly lensed quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

DeepZipper: A Novel Deep-learning Architecture for Lensed Supernovae Identification

Large-scale astronomical surveys have the potential to capture data on large numbers of strongly gravitationally lensed supernovae (LSNe). To facilitate timely analysis and spectroscopic follow-up before the supernova fades, an LSN needs to be identified soon after it begins. To quickly identify LSNe in optical survey data sets, we designed ZipperNet, a multibranch deep neural network that combines convolutional layers (traditionally used for images) with long short-term memory layers (traditionally used for time series). We tested ZipperNet on the task of classifying objects from four categories—no lens, galaxy-galaxy lens, lensed Type-Ia supernova, lensed core-collapse supernova—within high-fidelity simulations of three cosmic survey data sets: the Dark Energy Survey, Rubin Observatory’s Legacy Survey of Space and Time (LSST), and a Dark Energy Spectroscopic Instrument (DESI) imaging survey. Among our results, we find that for the LSST-like data set, ZipperNet classifies LSNe with a receiver operating characteristic area under the curve of 0.97, predicts the spectroscopic type of the lensed supernovae with 79% accuracy, and demonstrates similarly high performance for LSNe 1–2 epochs after first detection. We anticipate that a model like ZipperNet, which simultaneously incorporates spatial and temporal information, can play a significant role in the rapid identification of lensed transient systems in cosmic survey experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

ADDGALS: Simulated Sky Catalogs for Wide Field Galaxy Surveys

Abstract We present a method for creating simulated galaxy catalogs with realistic galaxy luminosities, broadband colors, and projected clustering over large cosmic volumes. The technique, denoted Addgals (Adding Density Dependent GAlaxies to Lightcone Simulations), uses an empirical approach to place galaxies within lightcone outputs of cosmological simulations. It can be applied to significantly lower-resolution simulations than those required for commonly used methods such as halo occupation distributions, subhalo abundance matching, and semi-analytic models, while still accurately reproducing projected galaxy clustering statistics down to scales of r ∼ 100 h −1 kpc . We show that Addgals catalogs reproduce several statistical properties of the galaxy distribution as measured by the Sloan Digital Sky Survey (SDSS) main galaxy sample, including galaxy number densities, observed magnitude and color distributions, as well as luminosity- and color-dependent clustering. We also compare to cluster–galaxy cross correlations, where we find significant discrepancies with measurements from SDSS that are likely linked to artificial subhalo disruption in the simulations. Applications of this model to simulations of deep wide-area photometric surveys, including modeling weak-lensing statistics, photometric redshifts, and galaxy cluster finding, are presented in DeRose et al., and an application to a full cosmology analysis of Dark Energy Survey (DES) Year 3 like data is presented in DeRose et al. We plan to publicly release a 10,313 square degree catalog constructed using Addgals with magnitudes appropriate for several existing and planned surveys, including SDSS, DES, VISTA, Wide-field Infrared Survey Explorer, and Rubin Observatory’s Legacy Survey of Space and Time.

79 ASTRONOMY AND ASTROPHYSICS↗