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Francisco J. Castander

Publications and source records attributed to Francisco J. Castander.

At least 19 recordsLinked to original sources

The Power of DESI for Photometric Redshift Calibration: A Case Study with KiDS-1000

Accurate redshift estimates are a critical requirement for weak lensing surveys and one of the main uncertainties in constraints on dark energy and large-scale cosmic structure. In this paper, we study the potential to calibrate photometric redshift (photo-z) distributions for gravitational lensing using the Dark Energy Spectroscopic Instrument (DESI). Since beginning its science operations in 2021, DESI has collected more than 50 million redshifts, adding about one million monthly. In addition to its large-scale structure samples, DESI has also acquired over 256k high-quality spectroscopic redshifts (spec-zs) in the COSMOS and XMM and VVDS fields. This is already a factor of 3 larger than previous spec-z calibration compilations in these two regions. Here, we explore calibrating photo-zs for the subset of KiDS-1000 galaxies that fall into joint self-organizing map (SOM) cells overlapping the DESI COSMOS footprint using the DESI COSMOS observations. Estimating the redshift distribution in KiDS-1000 with the new DESI data, we find broad consistency with previously published results while also detecting differences in the mean redshift in some tomographic bins with an average shifts of Delta Mean(z) = -0.028 in the mean and Delta Median(z) = +0.011 in the median across tomographic bins. However, we also find that incompleteness per SOM cell, i.e., groups of galaxies with similar colors and magnitudes, can modify n(z) distributions. Finally, we comment on the fact that larger photometric catalogs, aligned with the DESI COSMOS and DESI XMM and VVDS footprints, would be needed to fully exploit the DESI dataset and would extend the coverage to nearly eight times the area of existing 9-band photometry.

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Halo Lightcones with Optimised Orientation and Interpolation in Cosmological Simulations -- an application to mock H$α$ selected galaxies

A critical step to create realistic mock catalogs that support large-scale photometric and spectroscopic sky surveys is the production of cosmological simulations that accurately model the survey observables taking into account the redshift-dependent galaxy formation and evolution processes. Here we develop an efficient framework, HOLCon (Halo Optimised Lightcone Constructor), for post-facto construction of dark matter halo lightcones from simulations and use them to generate a mock galaxy catalogue. HOLCon includes a module to optimise the lightcone's orientation within the simulation box, minimising repeated structures when the survey volume exceeds a single box -- a common challenge in modern surveys. A linear interpolation scheme tracks the evolution of halo properties across snapshots. Applied to the publicly available Uchuu simulation, we construct a lightcone of 50 ${\rm deg}^2$ and extending up to $z = 10$, providing representative coverage of deep fields of Stage IV surveys. We validate the lightcone for cosmological applications by comparing the dark matter halo clustering in the lightcone with those from the original simulation snapshots. Subsequently, we make the galaxy-halo connection on the lightcone with a redshift extended version of the SciPIC algorithm producing a comprehensive set of descriptive galaxy attributes. HOLCon leverages Dask, a scalable parallel computing pythonic framework for fast construction of dark matter halo lightcones enabling rapid creation of multiple statistical realizations essential for robust cosmological inference. The produced galaxy mock makes predictions for clustering of H$α$ emitters, making it a useful cosmology resource.

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The ANDICAM-SOFI Near-infrared and Optical type Ia Supernova (ASNOS) sample: Description and data release

Type Ia supernovae (SNe Ia) provide the most robust means of measuring extragalactic distances. While most of the effort has focused on increasing the number of SNe Ia observed in the optical, near-infrared (NIR) observations remain scarce despite their advantages, that is, reduced dust extinction and a more intrinsic standard candle behavior, requiring little to no empirical corrections. Here, we present ASNOS (ANDICAM-SOFI Near-infrared and Optical type Ia Supernova), a dataset with sample size of 1,482 epochs in the $BVRIYJH$ filters from the ANDICAM instrument on the 1.3-meter SMARTS telescope at Cerro Tololo Inter-American Observatory, along with 125 $JHK$ epochs from the SOFI instrument on the 3.58-meter New Technology Telescope on the La Silla Observatory. Additionally, we incorporate optical forced photometry from the Zwicky Transient Facility and the Asteroid Terrestrial-impact Last Alert System. The sample comprises 41 SNe Ia in total, including 29 normal events, eight 1991T-like objects, and four peculiar subtypes, all located at redshifts $z < 0.085$. This paper provides a detailed overview of the ASNOS sample selection, data reduction, SN photometry, host-galaxy spectral energy distribution construction, both global and local, and SN light-curve fitting using three methods: SALT3-NIR, SNooPy, and BayeSN. A companion paper will present the cosmological analysis.

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ANNZ+: an enhanced photometric redshift estimation algorithm with applications on the PAU Survey

ANNZ is a fast and simple algorithm which utilises artificial neural networks (ANNs), it was known as one of the pioneers of machine learning approaches to photometric redshift estimation decades ago. We enhanced the algorithm by introducing new activation functions like tanh, softplus, SiLU, Mish and ReLU variants; its new performance is then vigorously tested on legacy samples like the Luminous Red Galaxy (LRG) and Stripe-82 samples from SDSS, as well as modern galaxy samples like the Physics of the Accelerating Universe Survey (PAUS). This work focuses on testing the robustness of activation functions with respect to the choice of ANN architectures, particularly on its depth and width, in the context of galaxy photometric redshift estimation. Our upgraded algorithm, which we named ANNZ+, shows that the tanh and Leaky ReLU activation functions provide more consistent and stable results across deeper and wider architectures with > 1 per cent improvement in root-mean-square error ($σ_{\textrm{RMS}}$) and 68th percentile error ($σ_{68}$) when tested on SDSS data sets. While assessing its capabilities in handling high dimensional inputs, we achieved an improvement of 11 per cent in $σ_{\textrm{RMS}}$ and 6 per cent in $σ_{68}$ with the tanh activation function when tested on the 40-narrowband PAUS dataset; it even outperformed ANNZ2, its supposed successor, by 44 per cent in $σ_{\textrm{RMS}}$. This justifies the effort to upgrade the 20-year-old ANNZ, allowing it to remain viable and competitive within the photo-z community today. The updated algorithm ANNZ+ is publicly available at https://github.com/imdadmpt/ANNzPlus.

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The PAU Survey: galaxy stellar population properties estimates with narrowband data

Narrowband galaxy surveys have recently gained interest as a promising method to achieve the necessary accuracy on the photometric redshift estimate of individual galaxies for stage-IV cosmological surveys. One key advantage is the ability to provide higher spectral resolution information about galaxies that should allow a more accurate and precise estimation of galaxy stellar population properties. However, the impact of adding narrow-band photometry on the stellar population properties estimate is largely unexplored. The scope of this work is two-fold: on one side, leveraging the predictive power of broad-band and narrow-band data to infer galaxy physical properties such as stellar masses, ages, star formation rates and metallicities. On the other hand, evaluating the improvement of performance in estimating galaxy properties when we use narrow-band data instead of broad-band. In this work we measure the stellar population properties of a sample of galaxies in the COSMOS field for which both narrowband and broadband data are available. In particular, we employ narrowband data from PAUS and broad-band data from CFHTLS. We use two different spectral energy distribution fitting codes to measure galaxy properties, namely CIGALE and Prospector. We find that the increased spectral resolution of narrow-band photometry does not yield a substantial improvement on constraining galaxy properties using spectral energy distribution fitting. Still we find that we obtain a more diverse distribution of metallicities and dust optical depths with cigale when employing the narrowband data. The effect is not as prominent as expected, which we relate this to the low narrowband SNR of a majority of the galaxies, the respective drawbacks of both codes as well as the coverage only in the optical regime. The measured properties are afterwards compared to the COSMOS2020 catalogue, showing good agreement.

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Modeling Intrinsic Galaxy Alignment in the MICE Simulation

The intrinsic alignment (IA) of galaxies is potentially a major limitation in deriving cosmological constraints from weak lensing surveys. In order to investigate this effect we assign intrinsic shapes and orientations to galaxies in the light-cone output of the MICE simulation, spanning $\sim5000\,{\rm deg}^2$ and reaching redshift $z=1.4$. This assignment is based on a 'semi-analytic' IA model that uses photometric properties of galaxies as well as the spin and shape of their host halos. Advancing on previous work, we include more realistic distributions of galaxy shapes and a luminosity dependent galaxy-halo alignment. The IA model parameters are calibrated against COSMOS and BOSS LOWZ observations. The null detection of IA in observations of blue galaxies is accounted for by setting random orientations for these objects. We compare the two-point alignment statistics measured in the simulation against predictions from the analytical IA models NLA and TATT over a wide range of scales, redshifts and luminosities for red and blue galaxies separately. We find that both models fit the measurements well at scales above $8\,h^{-1}{\rm Mpc}$, while TATT outperforms NLA at smaller scales. The IA parameters derived from our fits are in broad agreement with various observational constraints from red galaxies. Lastly, we build a realistic source sample, mimicking DES Year 3 observations and use it to predict the IA contamination to the observed shear statistics. We find this prediction to be within the measurement uncertainty, which might be a consequence of the random alignment of blue galaxies in the simulation.

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Accurate dark matter halo elongation from weak-lensing stacking analysis

Shape estimates that quantify the halo anisotropic mass distribution are valuable parameters that provide information on their assembly process and evolution. Measurements of the mean shapes for a sample of cluster-sized halos can be used to test halo formation scenarios, as well as improving the modelling of potential biases in constraining cosmological parameters using these systems. In this work, we test the recovery of halo cluster shapes and masses applying weak-lensing stacking techniques. To this end, we use lensing $shear$ and a new dark matter halo catalogue, derived from the light-cone output of the cosmological simulation MICE-GC. We perform this study by combining the lensing signals obtained for several samples of halos, selected according to their mass and redshift, taking into account the main directions of the dark-matter distributions. In the analysis we test the impact of several potential systematics, such as the adopted modelling, the contribution of the neighbouring mass distributions, miscentering and misalignment effects. Our results show that, when some considerations regarding the halo relaxation state are taken into account, the lensing semi-axis ratio estimates are in agreement within $5\%$ with the mean shapes of the projected dark-matter particle distribution of the stacked halos. The methodology presented provides a useful tool to derive reliable shapes of galaxy clusters and to contrast them with those expected from numerical simulations. Furthermore, our proposed modelling, which takes into account the contribution of neighbouring halos, allows one to constrain the elongation of the surrounding mass distribution.

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The PAU Survey: Measurements of the 4000 Å spectral break with narrow-band photometry

The D4000 spectral break index is one of the most important features in the visible spectrum, as it is a proxy for stellar ages and is also used in galaxy classification. However, its direct measurement has always been reserved to spectroscopy. Here, we present a general method to directly measure the D4000 with narrow-band (NB) photometry; it has been validated using realistic simulations, and then evaluated with PAUS NBs, cross-matched with VIPERS spectra ($i_{\rm AB} < 22.5$, $0.562 < z < 0.967$). We also reconstruct the D4000 with the SED-fitting code CIGALE; the use of PAUS NBs instead of broad bands significantly improves the SED fitting results. For D4000$_{\rm n}$, the direct measurement has $\rm \langle SNR \rangle \sim 4$, but we find that for $i_{\rm AB}<21$ all direct D4000 measurements have $\rm SNR>3$. The CIGALE D4000$_{\rm n}$ has $\rm \langle SNR \rangle \sim 20$, but underestimates the error by $>$50\%. Furthermore, the direct method recreates well the D4000-SFR relation, as well as the D4000-mass relation for blue galaxies (for red galaxies, selection effects impact the results). On the other hand, CIGALE accurately classifies galaxies into red and blue populations. We conclude that the direct measurement of D4000 with narrow-band photometry is a promising tool to determine average properties of galaxy samples, with results compatible with spectroscopy.

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New catalogue of dark-matter halo properties identified in MICE-GC -- I. Analysis of density profile distributions

Constraints on dark matter halo masses from weak gravitational lensing can be improved significantly by using additional information about the morphology of their density distribution, leading to tighter cosmological constraints derived from the halo mass function. This work is the first of two in which we investigate the accuracy of halo morphology and mass measurements in 2D and 3D. To this end, we determine several halo physical properties in the MICE-Grand Challenge dark matter only simulation. We present a public catalogue of these properties that includes density profiles and shape parameters measured in 2D and 3D, the halo centre at the peak of the 3D density distribution as well as the gravitational and kinetic energies and angular momentum vectors. The density profiles are computed using spherical and ellipsoidal radial bins, taking into account the halo shapes. We also provide halo concentrations and masses derived from fits to 2D and 3D density profiles using NFW and Einasto models for halos with more than $1000$ particles ($\gtrsim 3 \times 10^{13} h^{-1} M_{\odot}$). We find that the Einasto model provides better fits compared to NFW, regardless of the halo relaxation state and shape. The mass and concentration parameters of the 3D density profiles derived from fits to the 2D profiles are in general biased. Similar biases are obtained when constraining mass and concentrations using a weak-lensing stacking analysis. We show that these biases depend on the radial range and density profile model adopted in the fitting procedure, but not on the halo shape.

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The PAU Survey: Measurement of Narrow-band galaxy properties with Approximate Bayesian Computation

Narrow-band imaging surveys allow the study of the spectral characteristics of galaxies without the need of performing their spectroscopic follow-up. In this work, we forward-model the Physics of the Accelerating Universe Survey (PAUS) narrow-band data. The aim is to improve the constraints on the spectral coefficients used to create the galaxy spectral energy distributions (SED) of the galaxy population model in Tortorelli et al. 2020. In that work, the model parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) data using Approximate Bayesian Computation (ABC). This led to stringent constraints on the B-band galaxy luminosity function parameters, but left the spectral coefficients only broadly constrained. To address that, we perform an ABC inference using CFHTLS and PAUS data. This is the first time our approach combining forward-modelling and ABC is applied simultaneously to multiple datasets. We test the results of the ABC inference by comparing the narrow-band magnitudes of the observed and simulated galaxies using Principal Component Analysis, finding a very good agreement. Furthermore, we prove the scientific potential of the constrained galaxy population model to provide realistic stellar population properties by measuring them with the SED fitting code \textsc{CIGALE}. We use CFHTLS broad-band and PAUS narrow-band photometry for a flux-limited ($\mathrm{i}<22.5$) sample of galaxies up to redshift $\mathrm{z \sim 0.8}$. We find that properties like stellar masses, star-formation rates, mass-weighted stellar ages and metallicities are in agreement within errors between observations and simulations. Overall, this work shows the ability of our galaxy population model to correctly forward-model a complex dataset such as PAUS and the ability to reproduce the diversity of galaxy properties at the redshift range spanned by CFHTLS and PAUS.

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The PAU Survey: narrowband photometric redshifts using Gaussian processes

We study the performance of the hybrid template-machine-learning photometric redshift (photo-$z$) algorithm Delight, which uses Gaussian processes, on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the $40$ PAUS narrow bands with $6$ broadband fluxes ($uBVriz$) in the COSMOS field using three different methods, including a new method which utilises the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms. Delight achieves a photo-$z$ $68$th percentile error of $σ_{68}=0.0081(1+z)$ without any quality cut for galaxies with $i_\mathrm{auto}<22.5$ as compared to $0.0089(1+z)$ and $0.0202(1+z)$ for the BPz and ANNz2 codes, respectively. Delight is also shown to produce more accurate probability distribution functions for individual redshift estimates than BPz and ANNz2. Common photo-$z$ outliers of Delight and BCNz2 (previously applied to PAUS) are found to be primarily caused by outliers in the narrowband fluxes, with a small number of cases potentially indicating spectroscopic redshift failures in the reference sample. In the process, we introduce performance metrics derived from the results of BCNz2 and Delight, allowing us to achieve a photo-$z$ quality of $σ_{68}<0.0035(1+z)$ at a magnitude of $i_\mathrm{auto}<22.5$ while keeping $50$ per cent objects of the galaxy sample.

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The PAU Survey: An improved photo-$z$ sample in the COSMOS field

We present -- and make publicly available -- accurate and precise photometric redshifts in the ACS footprint from the COSMOS field for objects with $i_{\mathrm{AB}}\leq 23$. The redshifts are computed using a combination of narrow band photometry from PAUS, a survey with 40 narrow bands spaced at $100Å$ intervals covering the range from $4500Å$ to $8500Å$, and 26 broad, intermediate, and narrow bands covering the UV, visible and near infrared spectrum from the COSMOS2015 catalogue. We introduce a new method that models the spectral energy distributions (SEDs) as a linear combination of continuum and emission line templates and computes its Bayes evidence, integrating over the linear combinations. The correlation between the UV luminosity and the OII line is measured using the 66 available bands with the zCOSMOS spectroscopic sample, and used as a prior which constrains the relative flux between continuum and emission line templates. The flux ratios between the OII line and $\mathrm{H}_α$, $\mathrm{H}_β$ and $\mathrm{OIII}$ are similarly measured and used to generate the emission line templates. Comparing to public spectroscopic surveys via the quantity $Δ_z\equiv(z_{\mathrm{photo}}-z_{\mathrm{spec}})/(1+z_{\mathrm{spec}})$, we find the photometric redshifts to be more precise than previous estimates, with $σ_{68}(Δ_z) \approx (0.003, 0.009)$ for galaxies at magnitude $i_{\mathrm{AB}}\sim18$ and $i_{\mathrm{AB}}\sim23$, respectively, which is $3\times$ and $1.66\times$ tighter than COSMOS2015. Additionally, we find the redshifts to be very accurate on average, yielding a median of the $Δ_z$ distribution compatible with $|\mathrm{median}(Δ_z)|\leq0.001$ at all redshifts and magnitudes considered. Both the added PAUS data and new methodology contribute significantly to the improved results.

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CosmoHub: Interactive exploration and distribution of astronomical data on Hadoop

We present CosmoHub (https://cosmohub.pic.es), a web application based on Hadoop to perform interactive exploration and distribution of massive cosmological datasets. Recent Cosmology seeks to unveil the nature of both dark matter and dark energy mapping the large-scale structure of the Universe, through the analysis of massive amounts of astronomical data, progressively increasing during the last (and future) decades with the digitization and automation of the experimental techniques. CosmoHub, hosted and developed at the Port d'Informació Científica (PIC), provides support to a worldwide community of scientists, without requiring the end user to know any Structured Query Language (SQL). It is serving data of several large international collaborations such as the Euclid space mission, the Dark Energy Survey (DES), the Physics of the Accelerating Universe Survey (PAUS) and the Marenostrum Institut de Ciències de l'Espai (MICE) numerical simulations. While originally developed as a PostgreSQL relational database web frontend, this work describes the current version of CosmoHub, built on top of Apache Hive, which facilitates scalable reading, writing and managing huge datasets. As CosmoHub's datasets are seldomly modified, Hive it is a better fit. Over 60 TiB of catalogued information and $50 \times 10^9$ astronomical objects can be interactively explored using an integrated visualization tool which includes 1D histogram and 2D heatmap plots. In our current implementation, online exploration of datasets of $10^9$ objects can be done in a timescale of tens of seconds. Users can also download customized subsets of data in standard formats generated in few minutes.

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The Dark Energy Spectroscopic Instrument (DESI)

We present the status of the Dark Energy Spectroscopic Instrument (DESI) and its plans and opportunities for the coming decade. DESI construction and its initial five years of operations are an approved experiment of the US Department of Energy and is summarized here as context for the Astro2020 panel. Beyond 2025, DESI will require new funding to continue operations. We expect that DESI will remain one of the world's best facilities for wide-field spectroscopy throughout the decade. More about the DESI instrument and survey can be found at https://www.desi.lbl.gov.

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The Physics of the Accelerating Universe Camera

The PAU (Physics of the Accelerating Universe) Survey goal is to obtain photometric redshifts (photo-z) and Spectral Energy Distribution (SED) of astronomical objects with a resolution roughly one order of magnitude better than current broad band photometric surveys. To accomplish this, a new large field of view camera (PAUCam) has been designed, built, commissioned and is now operated at the William Herschel Telescope (WHT). With the current WHT Prime Focus corrector, the camera covers ~1-degree diameter Field of View (FoV), of which, only the inner ~40 arcmin diameter are unvignetted. The focal plane consists of a mosaic of 18 2k$x4k Hamamatsu fully depleted CCDs, with high quantum efficiency up to 1 micrometers in wavelength. To maximize the detector coverage within the FoV, filters are placed in front of the CCDs inside the camera cryostat (made out of carbon fiber) using a challenging movable tray system. The camera uses a set of 40 narrow band filters ranging from ~4500 to ~8500 Angstroms complemented with six standard broad-band filters, ugrizY. The PAU Survey aims to cover roughly 100 square degrees over fields with existing deep photometry and galaxy shapes to obtain accurate photometric redshifts for galaxies down to i_AB~22.5, detecting also galaxies down to i_AB~24 with less precision in redshift. With this data set we will be able to measure intrinsic alignments, galaxy clustering and perform galaxy evolution studies in a new range of densities and redshifts. Here, we describe the PAU camera, its first commissioning results and performance.

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Overview of the DESI Legacy Imaging Surveys

The DESI Legacy Imaging Surveys are a combination of three public projects (the Dark Energy Camera Legacy Survey, the Beijing-Arizona Sky Survey, and the Mayall z-band Legacy Survey) that will jointly image approximately 14,000 deg^2 of the extragalactic sky visible from the northern hemisphere in three optical bands (g, r, and z) using telescopes at the Kitt Peak National Observatory and the Cerro Tololo Inter-American Observatory. The combined survey footprint is split into two contiguous areas by the Galactic plane. The optical imaging is conducted using a unique strategy of dynamically adjusting the exposure times and pointing selection during observing that results in a survey of nearly uniform depth. In addition to calibrated images, the project is delivering a catalog, constructed by using a probabilistic inference-based approach to estimate source shapes and brightnesses. The catalog includes photometry from the grz optical bands and from four mid-infrared bands (at 3.4, 4.6, 12 and 22 micorons) observed by the Wide-field Infrared Survey Explorer (WISE) satellite during its full operational lifetime. The project plans two public data releases each year. All the software used to generate the catalogs is also released with the data. This paper provides an overview of the Legacy Surveys project.

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The Buzzard Flock: Dark Energy Survey Synthetic Sky Catalogs

We present a suite of 18 synthetic sky catalogs designed to support science analysis of galaxies in the Dark Energy Survey Year 1 (DES Y1) data. For each catalog, we use a computationally efficient empirical approach, ADDGALS, to embed galaxies within light-cone outputs of three dark matter simulations that resolve halos with masses above ~5x10^12 h^-1 m_sun at z <= 0.32 and 10^13 h^-1 m_sun at z~2. The embedding method is tuned to match the observed evolution of galaxy counts at different luminosities as well as the spatial clustering of the galaxy population. Galaxies are lensed by matter along the line of sight --- including magnification, shear, and multiple images --- using CALCLENS, an algorithm that calculates shear with 0.42 arcmin resolution at galaxy positions in the full catalog. The catalogs presented here, each with the same LCDM cosmology (denoted Buzzard), contain on average 820 million galaxies over an area of 1120 square degrees with positions, magnitudes, shapes, photometric errors, and photometric redshift estimates. We show that the weak-lensing shear catalog, redMaGiC galaxy catalogs and redMaPPer cluster catalogs provide plausible realizations of the same catalogs in the DES Y1 data by comparing their magnitude, color and redshift distributions, angular clustering, and mass-observable relations, making them useful for testing analyses that use these samples. We make public the galaxy samples appropriate for the DES Y1 data, as well as the data vectors used for cosmology analyses on these simulations.

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The PAU Survey: Operation and orchestration of multi-band survey data

The Physics of the Accelerating Universe (PAU) Survey is an international project for the study of cosmological parameters associated with Dark Energy. PAU's 18-CCD camera (PAUCam), installed at the prime focus of the William Herschel Telescope at the Roque de los Muchachos Observatory (La Palma, Canary Islands), scans part of the northern sky, to collect low resolution spectral information of millions of galaxies with its unique set of 40 narrow-band filters in the optical range from 450 nm to 850 nm, and a set of 6 standard broad band filters. The PAU data management (PAUdm) team is in charge of treating the data, including data transfer from the observatory to the PAU Survey data center, hosted at Port d'Informació Científica (PIC). PAUdm is also in charge of the storage, data reduction and, finally, of making the results available to the scientific community. We describe the technical solutions adopted to cover different aspects of the PAU Survey data management, from the computing infrastructure to support the operations, to the software tools and web services for the data process orchestration and exploration. In particular we will focus on the PAU database, developed for the coordination of the different PAUdm tasks, and to preserve and guarantee the consistency of data and metadata.

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