Euclid preparation: XVII. Cosmic Dawn Survey: Spitzer Space Telescope observations of the Euclid deep fields and calibration fields

We present a new infrared survey covering the three Euclid deep fields and four other Euclid calibration fields using Spitzer Space Telescope's Infrared Array Camera (IRAC). We combined these new observations with all relevant IRAC archival data of these fields in order to produce the deepest possible mosaics of these regions. In total, these observations represent nearly 11 % of the total Spitzer Space Telescope mission time. The resulting mosaics cover a total of approximately 71.5 deg^{2} in the 3.6 and 4.5 μm bands, and approximately 21.8 deg^{2} in the 5.8 and 8 μm bands. They reach at least 24 AB magnitude (measured to 5σ, in a 2″​​.5 aperture) in the 3.6 μm band and up to ∼5 mag deeper in the deepest regions. The astrometry is tied to the Gaia astrometric reference system, and the typical astrometric uncertainty for sources with 16 "< "[3.6]< 19 is ≲ 0″​​.15. The photometric calibration is in excellent agreement with previous WISE measurements. We extracted source number counts from the 3.6 μm band mosaics, and they are in excellent agreement with previous measurements. Given that the Spitzer Space Telescope has now been decommissioned, these mosaics are likely to be the definitive reduction of these IRAC data. This survey therefore represents an essential first step in assembling multi-wavelength data on the Euclid deep fields, which are set to become some of the premier fields for extragalactic astronomy in the 2020s

Euclid: Covariance of weak lensing pseudo-C_ell estimates. Calculation, comparison to simulations, and dependence on survey geometry

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-C_ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but further away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters describing matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10--20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component

Euclid preparation: VII. Forecast validation for Euclid cosmological probes

Aims: The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. The estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on various individual methodologies and numerical implementations, which were developed for different observational probes and for the combination thereof. In this paper we present validated forecasts, which combine both theoretical and observational ingredients for different cosmological probes. This work is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. / Methods: We describe in detail the methods adopted for Fisher matrix forecasts, which were applied to galaxy clustering, weak lensing, and the combination thereof. We estimated the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations, some of which are made publicly available, in different programming languages, together with a reference training-set of input and output matrices for a set of specific models. These can be used by the reader to validate their own implementations if required. / Results: We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setting, for example flat or non-flat spatial cosmologies, or different cuts at non-linear scales. The numerical implementations are now reliable for these settings. We present the results for an optimistic and a pessimistic choice for these types of settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy figure of merit by at least a factor of three

Euclid preparation: VIII. The Complete Calibration of the Colour–Redshift Relation survey: VLT/KMOS observations and data release

The Complete Calibration of the Colour–Redshift Relation survey (C3R2) is a spectroscopic effort involving ESO and Keck facilities designed specifically to empirically calibrate the galaxy colour–redshift relation – P(z|C) to the Euclid depth (iAB = 24.5) and is intimately linked to the success of upcoming Stage IV dark energy missions based on weak lensing cosmology. The aim is to build a spectroscopic calibration sample that is as representative as possible of the galaxies of the Euclid weak lensing sample. In order to minimise the number of spectroscopic observations necessary to fill the gaps in current knowledge of the P(z|C), self-organising map (SOM) representations of the galaxy colour space have been constructed. Here we present the first results of an ESO@VLT Large Programme approved in the context of C3R2, which makes use of the two VLT optical and near-infrared multi-object spectrographs, FORS2 and KMOS. This data release paper focuses on high-quality spectroscopic redshifts of high-redshift galaxies observed with the KMOS spectrograph in the near-infrared H- and K-bands. A total of 424 highly-reliable redshifts are measured in the 1.3 ≤ z ≤ 2.5 range, with total success rates of 60.7% in the H-band and 32.8% in the K-band. The newly determined redshifts fill 55% of high (mainly regions with no spectroscopic measurements) and 35% of lower (regions with low-resolution/low-quality spectroscopic measurements) priority empty SOM grid cells. We measured Hα fluxes in a 1.″2 radius aperture from the spectra of the spectroscopically confirmed galaxies and converted them into star formation rates. In addition, we performed an SED fitting analysis on the same sample in order to derive stellar masses, E(B − V), total magnitudes, and SFRs. We combine the results obtained from the spectra with those derived via SED fitting, and we show that the spectroscopic failures come from either weakly star-forming galaxies (at z   2 galaxies

Euclid preparation: XXIV. Calibration of the halo mass function in (?)CDM cosmologies

Euclid s photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo finder algorithms, and how the resulting differences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with different spectral indexes, assuming both Einsteinde Sitter and standard CDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 different variants of the CDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future massobservation relations; with the only notable exception of the effect due to the halo finder, that could lead to biased cosmological inference

Euclid preparation: V. Predicted yield of redshift 7<z<9 quasars from the wide survey

We provide predictions of the yield of 7 < z < 9 quasars from the Euclid wide survey, updating the calculation presented in the Euclid Red Book in several ways. We account for revisions to the Euclid near-infrared filter wavelengths; we adopt steeper rates of decline of the quasar luminosity function (QLF; Φ) with redshift, Φ ∝ 10k(z−6) , k = −0.72, and a further steeper rate of decline, k = −0.92; we use better models of the contaminating populations (MLT dwarfs and compact early-type galaxies); and we make use of an improved Bayesian selection method, compared to the colour cuts used for the Red Book calculation, allowing the identification of fainter quasars, down to JAB ∼ 23. Quasars at z > 8 may be selected from Euclid OY JH photometry alone, but selection over the redshift interval 7 < z < 8 is greatly improved by the addition of z-band data from, e.g., Pan-STARRS and LSST. We calculate predicted quasar yields for the assumed values of the rate of decline of the QLF beyond z = 6. If the decline of the QLF accelerates beyond z = 6, with k = −0.92, Euclid should nevertheless find over 100 quasars with 7.0 < z < 7.5, and ∼ 25 quasars beyond the current record of z = 7.5, including ∼ 8 beyond z = 8.0. The first Euclid quasars at z > 7.5 should be found in the DR1 data release, expected in 2024. It will be possible to determine the bright-end slope of the QLF, 7 < z < 8, M1450 < −25, using 8 m class telescopes to confirm candidates, but follow-up with JWST or E-ELT will be required to measure the faint-end slope. Contamination of the candidate lists is predicted to be modest even at JAB ∼ 23. The precision with which k can be determined over 7 < z < 8 depends on the value of k, but assuming k = −0.72 it can be measured to a 1σ uncertainty of 0.07

Euclid preparation: V. Predicted yield of redshift 7 < z < 9 quasars from the wide survey

We provide predictions of the yield of 7 8 may be selected from Euclid OY JH photometry alone, but selection over the redshift interval 7 7.5 should be found in the DR1 data release, expected in 2024. It will be possible to determine the bright-end slope of the QLF, 7 < z < 8, M1450 < −25, using 8 m class telescopes to confirm candidates, but follow-up with JWST or E-ELT will be required to measure the faint-end slope. Contamination of the candidate lists is predicted to be modest even at JAB ∼ 23. The precision with which k can be determined over 7 < z < 8 depends on the value of k, but assuming k = −0.72 it can be measured to a 1σ uncertainty of 0.07

Euclid preparation: X. The Euclid photometric-redshift challenge

Forthcoming large photometric surveys for cosmology require precise and accurate photometric redshift (photo-z) measurements for the success of their main science objectives. However, to date, no method has been able to produce photo-zs at the required accuracy using only the broad-band photometry that those surveys will provide. An assessment of the strengths and weaknesses of current methods is a crucial step in the eventual development of an approach to meet this challenge. We report on the performance of 13 photometric redshift code single value redshift estimates and redshift probability distributions (PDZs) on a common set of data, focusing particularly on the 0.2−2.6 redshift range that the Euclid mission will probe. We designed a challenge using emulated Euclid data drawn from three photometric surveys of the COSMOS field. The data was divided into two samples: one calibration sample for which photometry and redshifts were provided to the participants; and the validation sample, containing only the photometry to ensure a blinded test of the methods. Participants were invited to provide a redshift single value estimate and a PDZ for each source in the validation sample, along with a rejection flag that indicates the sources they consider unfit for use in cosmological analyses. The performance of each method was assessed through a set of informative metrics, using cross-matched spectroscopic and highlyaccurate photometric redshifts as the ground truth. We show that the rejection criteria set by participants are efficient in removing strong outliers, that is to say sources for which the photo-z deviates by more than 0.15(1 + z) from the spectroscopic-redshift (spec-z). We also show that, while all methods are able to provide reliable single value estimates, several machine-learning methods do not manage to produce useful PDZs. We find that no machine-learning method provides good results in the regions of galaxy color-space that are sparsely populated by spectroscopic-redshifts, for example z > 1. However they generally perform better than template-fitting methods at low redshift (z < 0.7), indicating that template-fitting methods do not use all of the information contained in the photometry. We introduce metrics that quantify both photo-z precision and completeness of the samples (post-rejection), since both contribute to the final figure of merit of the science goals of the survey (e.g., cosmic shear from Euclid). Template-fitting methods provide the best results in these metrics, but we show that a combination of template-fitting results and machine-learning results with rejection criteria can outperform any individual method. On this basis, we argue that further work in identifying how to best select between machine-learning and template-fitting approaches for each individual galaxy should be pursued as a priority

Euclid preparation XIII. Forecasts for galaxy morphology with the Euclid Survey using deep generative models

We present a machine learning framework to simulate realistic galaxies for the Euclid Survey, producing more complex and realistic galaxies than the analytical simulations currently used in Euclid. The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real Hubble Space Telescope observations by deep generative models. We simulate a galaxy field of 0.4 deg2 as it will be seen by the Euclid visible imager VIS, and we show that galaxy structural parameters are recovered to an accuracy similar to that for pure analytic Sérsic profiles. Based on these simulations, we estimate that the Euclid Wide Survey (EWS) will be able to resolve the internal morphological structure of galaxies down to a surface brightness of 22.5 mag arcsec−2, and the Euclid Deep Survey (EDS) down to 24.9 mag arcsec−2. This corresponds to approximately 250 million galaxies at the end of the mission and a 50% complete sample for stellar masses above 1010.6 M⊙ (resp. 109.6 M⊙) at a redshift z ∼ 0.5 for the EWS (resp. EDS). The approach presented in this work can contribute to improving the preparation of future high-precision cosmological imaging surveys by allowing simulations to incorporate more realistic galaxies