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.</p

Euclid:Forecasts for kk-cut 3×23 \times 2 Point Statistics

Modelling uncertainties at small scales, i.e. high $k$ in the power spectrum $P(k)$, due to baryonic feedback, nonlinear structure growth and the fact that galaxies are biased tracers poses a significant obstacle to fully leverage the constraining power of the {\it Euclid} wide-field survey. $k$-cut cosmic shear has recently been proposed as a method to optimally remove sensitivity to these scales while preserving usable information. In this paper we generalise the $k$-cut cosmic shear formalism to $3 \times 2$ point statistics and estimate the loss of information for different $k$-cuts in a $3 \times 2$ point analysis of the {\it Euclid} data. Extending the Fisher matrix analysis of~\citet{blanchard2019euclid}, we assess the degradation in constraining power for different $k$-cuts. We work in the idealised case and assume the galaxy bias is linear, the covariance is Gaussian, while neglecting uncertainties due to photo-z errors and baryonic feedback. We find that taking a $k$-cut at $2.6 \ h \ {\rm Mpc} ^{-1}$ yields a dark energy Figure of Merit (FOM) of 1018. This is comparable to taking a weak lensing cut at $\ell = 5000$ and a galaxy clustering and galaxy-galaxy lensing cut at $\ell = 3000$ in a traditional $3 \times 2$ point analysis. We also find that the fraction of the observed galaxies used in the photometric clustering part of the analysis is one of the main drivers of the FOM. Removing $50 \% \ (90 \%)$ of the clustering galaxies decreases the FOM by $19 \% \ (62 \%)$. Given that the FOM depends so heavily on the fraction of galaxies used in the clustering analysis, extensive efforts should be made to handle the real-world systematics present when extending the analysis beyond the luminous red galaxy (LRG) sample

Euclid preparation: XX. The Complete Calibration of the Color-Redshift Relation survey:LBT observations and data release

The Complete Calibration of the Color-Redshift Relation survey (C3R2) is a spectroscopic programme designed to empirically calibrate the galaxy color-redshift relation to the Euclid depth (I_E=24.5), a key ingredient for the success of Stage IV dark energy projects based on weak lensing cosmology. A spectroscopic calibration sample as representative as possible of the galaxies in the Euclid weak lensing sample is being collected, selecting galaxies from a self-organizing map (SOM) representation of the galaxy color space. Here, we present the results of a near-infrared H- and K-bands spectroscopic campaign carried out using the LUCI instruments at the LBT. For a total of 251 galaxies, we present new highly-reliable redshifts in the 1.

Euclid:Calibrating photometric redshifts with spectroscopic cross-correlations

Cosmological constraints from key probes of the Euclid imaging survey rely critically on the accurate determination of the true redshift distributions, n(z), of tomographic redshift bins. We determine whether the mean redshift, of ten Euclid tomographic redshift bins can be calibrated to the Euclid target uncertainties of 0.002 (1 +z) via cross-correlation, with spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), and Euclid s NISP spectroscopic survey. We construct mock Euclid and spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshift z 1.8 with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to two n(z) models: one is the true n(z) with a free mean; the other a Gaussian process modified to be restricted to non-negative values. We show that is measured in each tomographic redshift bin to an accuracy of order 0.01 or better. By measuring the clustering redshifts on subsets of the full Flagship area, we construct scaling relations that allow us to extrapolate the method performance to larger sky areas than are currently available in the mock. For the full expected Euclid, BOSS, and DESI overlap region of approximately 6000 deg2, the uncertainties attainable by clustering redshifts exceeds the Euclid requirement by at least a factor of three for both n(z) models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration for Euclid if the sources of systematic biases can be determined and removed, or calibrated out with sufficiently realistic simulations. We outline possible future work, in particular an extension to higher redshifts with quasar reference samples.</p

Euclid preparation:XII. Optimizing the photometric sample of the Euclid survey for galaxy clustering and galaxy-galaxy lensing analyses

Photometric redshifts (photo-zs) are one of the main ingredients in the analysis of cosmological probes. Their accuracy particularly affects the results of the analyses of galaxy clustering with photometrically selected galaxies (GCph) and weak lensing. In the next decade, space missions such as Euclid will collect precise and accurate photometric measurements for millions of galaxies. These data should be complemented with upcoming ground-based observations to derive precise and accurate photo-zs. In this article we explore how the tomographic redshift binning and depth of ground-based observations will affect the cosmological constraints expected from the Euclid mission. We focus on GCph and extend the study to include galaxy-galaxy lensing (GGL). We add a layer of complexity to the analysis by simulating several realistic photo-z distributions based on the Euclid Consortium Flagship simulation and using a machine learning photo-z algorithm. We then use the Fisher matrix formalism together with these galaxy samples to study the cosmological constraining power as a function of redshift binning, survey depth, and photo-z accuracy. We find that bins with an equal width in redshift provide a higher figure of merit (FoM) than equipopulated bins and that increasing the number of redshift bins from ten to 13 improves the FoM by 35% and 15% for GCph and its combination with GGL, respectively. For GCph, an increase in the survey depth provides a higher FoM. However, when we include faint galaxies beyond the limit of the spectroscopic training data, the resulting FoM decreases because of the spurious photo-zs. When combining GCph and GGL, the number density of the sample, which is set by the survey depth, is the main factor driving the variations in the FoM. Adding galaxies at faint magnitudes and high redshift increases the FoM, even when they are beyond the spectroscopic limit, since the number density increase compensates for the photo-z degradation in this case. We conclude that there is more information that can be extracted beyond the nominal ten tomographic redshift bins of Euclid and that we should be cautious when adding faint galaxies into our sample since they can degrade the cosmological constraints

Euclid preparation:XI. Mean redshift determination from galaxy redshift probabilities for cosmic shear tomography

The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on the accurate knowledge of the galaxy mean redshift $\langle z \rangle$. We investigate the possibility of measuring $\langle z \rangle$ with an accuracy better than $0.002\,(1+z)$, in ten tomographic bins spanning the redshift interval $0.299.8\%$. The zPDF approach could also be successful if we debias the zPDF using a spectroscopic training sample. This approach requires deep imaging data, but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the debiasing method and confirm our finding by applying it to real-world weak-lensing data sets (COSMOS and KiDS+VIKING-450)

Euclid preparation:XVI. Exploring the ultra low-surface brightness Universe with Euclid/VIS

Context. While Euclid is an ESA mission specifically designed to investigate the nature of dark energy and dark matter, the planned unprecedented combination of survey area (∼15â 000 deg2), spatial resolution, low sky-background, and depth also make Euclid an excellent space observatory for the study of the low surface brightness Universe. Scientific exploitation of the extended low surface brightness structures requires dedicated calibration procedures that are yet to be tested. Aims. We investigate the capabilities of Euclid to detect extended low surface brightness structure by identifying and quantifying sky-background sources and stray-light contamination. We test the feasibility of generating sky flat-fields to reduce large-scale residual gradients in order to reveal the extended emission of galaxies observed in the Euclid survey. Methods. We simulated a realistic set of Euclid/VIS observations, taking into account both instrumental and astronomical sources of contamination, including cosmic rays, stray-light, zodiacal light, interstellar medium, and the cosmic infrared background, while simulating the effects of background sources in the field of view. Results. We demonstrate that a combination of calibration lamps, sky flats, and self-calibration would enable recovery of emission at a limiting surface brightness magnitude of μlim = 29.5-0.27+0.08 mag arcsec-2 (3σ, 10â ×â 10 arcsec2) in the Wide Survey, and it would reach regions deeper by 2 mag in the Deep Surveys. Conclusions.Euclid/VIS has the potential to be an excellent low surface brightness observatory. Covering the gap between pixel-To-pixel calibration lamp flats and self-calibration observations for large scales, the application of sky flat-fielding will enhance the sensitivity of the VIS detector at scales larger than 1″, up to the size of the field of view, enabling Euclid to detect extended surface brightness structures below μlimâ =â 31 mag arcsec-2 and beyond.</p

Euclid:Effects of sample covariance on the number counts of galaxy clusters

Aims: We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods: By analysing 1000 Euclid-like light cones, produced with the PINOCCHIO approximate method, we validated the analytical model of Hu &amp; Kravtsov (2003, ApJ, 584, 702) for the covariance matrix, which takes into account both sources of statistical error. Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints. Results: The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with full covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors, and that the cosmology-dependence of the covariance must be taken into account. This paper is published on behalf of the Euclid Consortium