<em>Euclid</em> preparation: LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling

\ua9 The Authors 2024. LENSMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies, sampling the posterior distribution of galaxy parameters via Markov chain Monte Carlo, and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. We quantified the scientific performance through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images, realistic clustering with a mean surface number density of 250 arcmin2 (IE &lt; 29.5) for galaxies, and 6 arcmin2 (IE &lt; 26) for stars, and a diffraction-limited chromatic PSF with a full width at half maximum of 02.22 and spatial variation across the field of view. LENSMC measured objects with a density of 90 arcmin2 (IE &lt; 26.5) in 4500 deg2. The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed in future work). We found measurement multiplicative and additive biases of m1 = (3.6 \ub1 0.2) A- 103, m2 = (4.3 \ub1 0.2) A- 103, c1 = (1.78 \ub1 0.03) A- 104, and c2 = (0.09 \ub1 0.03) A- 104; a large detection bias with a multiplicative component of 1.2 A- 102 and an additive component of 3 A- 104; and a measurement PSF leakage of α1 = (9 \ub1 3) A- 104 and α2 = (2 \ub1 3) A- 104. When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies (5 A- 103). Although significant, model bias will be straightforward to calibrate given its weak sensitivity on galaxy morphology parameters. LENSMC is publicly available at gitlab.com/gcongedo/LensMC

<em>Euclid</em> preparation: XLVII. Improving cosmological constraints using a new multi-tracer method with the spectroscopic and photometric samples

\ua9 2024 The Authors. Future data provided by the Euclid mission will allow us to better understand the cosmic history of the Universe. A metric of its performance is the figure-of-merit (FoM) of dark energy, usually estimated with Fisher forecasts. The expected FoM has previously been estimated taking into account the two main probes of Euclid, namely the three-dimensional clustering of the spectroscopic galaxy sample, and the so-called 3 72pt signal from the photometric sample (i.e., the weak lensing signal, the galaxy clustering, and their cross-correlation). So far, these two probes have been treated as independent. In this paper, we introduce a new observable given by the ratio of the (angular) two-point correlation function of galaxies from the two surveys. For identical (normalised) selection functions, this observable is unaffected by sampling noise, and its variance is solely controlled by Poisson noise. We present forecasts for Euclid where this multi-tracer method is applied and is particularly relevant because the two surveys will cover the same area of the sky. This method allows for the exploitation of the combination of the spectroscopic and photometric samples. When the correlation between this new observable and the other probes is not taken into account, a significant gain is obtained in the FoM, as well as in the constraints on other cosmological parameters. The benefit is more pronounced for a commonly investigated modified gravity model, namely the γ parametrisation of the growth factor. However, the correlation between the different probes is found to be significant and hence the actual gain is uncertain. We present various strategies for circumventing this issue and still extract useful information from the new observable

Euclid preparation XLIV. Modelling spectroscopic clustering on mildly nonlinear scales in beyond-ΛCDM models

Context. The Euclid space satellite mission will measure the large-scale clustering of galaxies at an unprecedented precision, providing a unique probe of modifications to the ΛCDM model. // Aims. We investigated the approximations needed to efficiently predict the large-scale clustering of matter and dark matter halos in the context of modified gravity and exotic dark energy scenarios. We examined the normal branch of the Dvali–Gabadadze–Porrati model, the Hu–Sawicki f(R) model, a slowly evolving dark energy model, an interacting dark energy model, and massive neutrinos. For each, we tested approximations for the perturbative kernel calculations, including the omission of screening terms and the use of perturbative kernels based on the Einstein–de Sitter universe; we explored different infrared-resummation schemes, tracer bias models and a linear treatment of massive neutrinos; we investigated various approaches for dealing with redshift-space distortions and modelling the mildly nonlinear scales, namely the Taruya–Nishimishi–Saito prescription and the effective field theory of large-scale structure. This work provides a first validation of the various codes being considered by Euclid for the spectroscopic clustering probe in beyond-ΛCDM scenarios. // Methods. We calculated and compared the χ2 statistic to assess the different modelling choices. This was done by fitting the spectroscopic clustering predictions to measurements from numerical simulations and perturbation theory-based mock data. We compared the behaviour of this statistic in the beyond-ΛCDM cases, as a function of the maximum scale included in the fit, to the baseline ΛCDM case. // Results. We find that the Einstein–de Sitter approximation without screening is surprisingly accurate for the modified gravity cases when comparing to the halo clustering monopole and quadrupole obtained from simulations and mock data. Further, we find the same goodness-of-fit for both cases – the one including and the one omitting non-standard physics in the predictions. Our results suggest that the inclusion of multiple redshift bins, higher-order multipoles, higher-order clustering statistics (such as the bispectrum), and photometric probes such as weak lensing, will be essential to extract information on massive neutrinos, modified gravity and dark energy. Additionally, we show that the three codes used in our analysis, namely, PBJ, Pybird and MG-Copter, exhibit sub-percent agreement for k ≤ 0.5 h Mpc−1 across all the models. This consistency underscores their value as reliable tools

Euclid preparation: LVIII. Detecting extragalactic globular clusters in the Euclid survey

\ua9 The Authors 2025.Extragalactic globular clusters (EGCs) are an abundant and powerful tracer of galaxy dynamics and formation, and their own formation and evolution is also a matter of extensive debate. The compact nature of globular clusters means that they are hard to spatially resolve and thus study outside the Local Group. In this work we have examined how well EGCs will be detectable in images from the Euclid telescope, using both simulated pre-launch images and the first early-release observations of the Fornax galaxy cluster. The Euclid Wide Survey will provide high-spatial resolution VIS imaging in the broad IE band as well as near-infrared photometry (YE, JE, and HE). We estimate that the 24 719 known galaxies within 100 Mpc in the footprint of the Euclid survey host around 830 000 EGCs of which about 350 000 are within the survey\u27s detection limits. For about half of these EGCs, three infrared colours will be available as well. For any galaxy within 50 Mpc the brighter half of its GC luminosity function will be detectable by the Euclid Wide Survey. The detectability of EGCs is mainly driven by the residual surface brightness of their host galaxy. We find that an automated machine-learning EGC-classification method based on real Euclid data of the Fornax galaxy cluster provides an efficient method to generate high purity and high completeness GC candidate catalogues. We confirm that EGCs are spatially resolved compared to pure point sources in VIS images of Fornax. Our analysis of both simulated and first on-sky data show that Euclid will increase the number of GCs accessible with high-resolution imaging substantially compared to previous surveys, and will permit the study of GCs in the outskirts of their hosts. Euclid is unique in enabling systematic studies of EGCs in a spatially unbiased and homogeneous manner and is primed to improve our understanding of many understudied aspects of GC astrophysics

Euclid preparation: LXVIII. Extracting physical parameters from galaxies with machine learning

\ua9 The Authors 2025.The Euclid mission is generating a vast amount of imaging data in four broadband filters at a high angular resolution. This data will allow for the detailed study of mass, metallicity, and stellar populations across galaxies that will constrain their formation and evolutionary pathways. Transforming the Euclid imaging for large samples of galaxies into maps of physical parameters in an efficient and reliable manner is an outstanding challenge. Here, we investigate the power and reliability of machine learning techniques to extract the distribution of physical parameters within well-resolved galaxies. We focus on estimating stellar mass surface density, mass-averaged stellar metallicity, and age. We generated noise-free synthetic high-resolution (100 pc 7 100 pc) imaging data in the Euclid photometric bands for a set of 1154 galaxies from the TNG50 cosmological simulation. The images were generated with the SKIRT radiative transfer code, taking into account the complex 3D distribution of stellar populations and interstellar dust attenuation. We used a machine learning framework to map the idealised mock observational data to the physical parameters on a pixel-by-pixel basis. We find that stellar mass surface density can be accurately recovered with a ≤0.130 dex scatter. Conversely, stellar metallicity and age estimates are, as expected, less robust, but they still contain significant information that originates from underlying correlations at a sub-kiloparsec scales between stellar mass surface density and stellar population properties. As a corollary, we show that TNG50 follows a spatially resolved mass-metallicity relation that is consistent with observations. Due to its relatively low computational and time requirements, which has a time-frame of minutes without dedicated high performance computing infrastructure once it has been trained, our method allows for fast and robust estimates of the stellar mass surface density distributions of nearby galaxies from four-filter Euclid imaging data. Equivalent estimates of stellar population properties (stellar metallicity and age) are less robust but still hold value as first-order approximations across large samples

Euclid preparation: LXIV. The Cosmic Dawn Survey (DAWN) of the Euclid Deep and Auxiliary Fields

\ua9 2025 The Authors.Euclid will provide deep near-infrared (NIR) imaging to ∼26.5 AB magnitude over ∼59 deg2 in its deep and auxiliary fields. The Cosmic DAWN survey combines dedicated and archival UV- NIR observations to provide matched depth multiwavelength imaging of the Euclid deep and auxiliary fields. The DAWN survey will provide consistently measured Euclid NIR-selected photometric catalogues, accurate photometric redshifts, and measurements of galaxy properties to a redshift of z ∼ 10. The DAWN catalogues include Spitzer IRAC data that are critical for stellar mass measurements at z ≳ 2.5 and high-z science. These catalogues complement the standard Euclid catalogues, which will not include Spitzer IRAC data. In this paper, we present an overview of the survey, including the footprints of the survey fields, the existing and planned observations, and the primary science goals for the combined data set

Euclid preparation: XXXIX. The effect of baryons on the halo mass function

The Euclid photometric survey of galaxy clusters stands as a powerful cosmological tool, with the capacity to significantly propel our understanding of the Universe. Despite being subdominant to dark matter and dark energy, the baryonic component of our Universe holds substantial influence over the structure and mass of galaxy clusters. This paper presents a novel model that can be used to precisely quantify the impact of baryons on the virial halo masses of galaxy clusters using the baryon fraction within a cluster as a proxy for their effect. Constructed on the premise of quasi-adiabaticity, the model includes two parameters, which are calibrated using non-radiative cosmological hydrodynamical simulations, and a single large-scale simulation from the Magneticum set, which includes the physical processes driving galaxy formation. As a main result of our analysis, we demonstrate that this model delivers a remarkable 1% relative accuracy in determining the virial dark matter-only equivalent mass of galaxy clusters starting from the corresponding total cluster mass and baryon fraction measured in hydrodynamical simulations. Furthermore, we demonstrate that this result is robust against changes in cosmological parameters and against variation of the numerical implementation of the subresolution physical processes included in the simulations. Our work substantiates previous claims regarding the impact of baryons on cluster cosmology studies. In particular, we show how neglecting these effects would lead to biased cosmological constraints for a Euclid-like cluster abundance analysis. Importantly, we demonstrate that uncertainties associated with our model arising from baryonic corrections to cluster masses are subdominant when compared to the precision with which mass–observable (i.e. richness) relations will be calibrated using Euclid and to our current understanding of the baryon fraction within galaxy clusters

Euclid preparation: XXXVII. Galaxy colour selections with Euclid and ground photometry for cluster weak-lensing analyses

Aims. We derived galaxy colour selections from Euclid and ground-based photometry, aiming to accurately define background galaxy samples in cluster weak-lensing analyses. These selections have been implemented in the Euclid data analysis pipelines for galaxy clusters. / Methods. Given any set of photometric bands, we developed a method for the calibration of optimal galaxy colour selections that maximises the selection completeness, given a threshold on purity. Such colour selections are expressed as a function of the lens redshift. / Results. We calibrated galaxy selections using simulated ground-based griz and EuclidYEJEHE photometry. Both selections produce a purity higher than 97%. The griz selection completeness ranges from 30% to 84% in the lens redshift range zl ∈ [0.2, 0.8]. With the full grizYEJEHE selection, the completeness improves by up to 25 percentage points, and the zl range extends up to zl = 1.5. The calibrated colour selections are stable to changes in the sample limiting magnitudes and redshift, and the selection based on griz bands provides excellent results on real external datasets. Furthermore, the calibrated selections provide stable results using alternative photometric aperture definitions obtained from different ground-based telescopes. The griz selection is also purer at high redshift and more complete at low redshift compared to colour selections found in the literature. We find excellent agreement in terms of purity and completeness between the analysis of an independent, simulated Euclid galaxy catalogue and our calibration sample, except for galaxies at high redshifts, for which we obtain up to 50 percentage points higher completeness. The combination of colour and photo-z selections applied to simulated Euclid data yields up to 95% completeness, while the purity decreases down to 92% at high zl. We show that the calibrated colour selections provide robust results even when observations from a single band are missing from the ground-based data. Finally, we show that colour selections do not disrupt the shear calibration for stage III surveys. The first Euclid data releases will provide further insights into the impact of background selections on the shear calibration

<em>Euclid</em> preparation: LVI. Sensitivity to non-standard particle dark matter models

\ua9 The Authors 2025. The Euclid mission of the European Space Agency will provide weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and its extensions, with an opportunity to test the properties of dark matter beyond the minimal cold dark matter paradigm. We present forecasts from the combination of the Euclid weak lensing and photometric galaxy clustering data on the parameters describing four interesting and representative non-minimal dark matter models: a mixture of cold and warm dark matter relics; unstable dark matter decaying either into massless or massive relics; and dark matter undergoing feeble interactions with relativistic relics. We modelled these scenarios at the level of the non-linear matter power spectrum using emulators trained on dedicated N-body simulations. We used a mock Euclid likelihood and Monte Carlo Markov chains to fit mock data and infer error bars on dark matter parameters marginalised over other parameters. We find that the Euclid photometric probe (alone or in combination with cosmic microwave background data from the Planck satellite) will be sensitive to the effect of each of the four dark matter models considered here. The improvement will be particularly spectacular for decaying and interacting dark matter models. With Euclid, the bounds on some dark matter parameters can improve by up to two orders of magnitude compared to current limits. We discuss the dependence of predicted uncertainties on different assumptions: the inclusion of photometric galaxy clustering data, the minimum angular scale taken into account, and modelling of baryonic feedback effects. We conclude that the Euclid mission will be able to measure quantities related to the dark sector of particle physics with unprecedented sensitivity. This will provide important information for model building in high-energy physics. Any hint of a deviation from the minimal cold dark matter paradigm would have profound implications for cosmology and particle physics

Euclid preparation XLI. Galaxy power spectrum modelling in real space

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of a Eulerian galaxy bias expansion using state-of-the-art prescriptions from the effective field theory of large-scale structure (EFTofLSS) with a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the flagship I N-body simulation at z = (0.9, 1.2, 1.5, 1.8), which have been populated with Hα galaxies leading to catalogues of millions of objects within a volume of about 58 h−3 Gpc3. Our analysis suggests that both models can be used to provide a robust inference of the parameters (h, ωc) in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion – which includes local and non-local bias parameters, a matter counter term, and a correction to the shot-noise contribution – can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber of kmax = 0.45 h Mpc−1, and with a measurement precision of well below the percentage level. Fixing either of the tidal bias parameters to physically motivated relations still leads to unbiased cosmological constraints, and helps in reducing the severity of projection effects due to the large dimensionality of the model. We finally show how we repeated our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, such as purity and completeness, showing that we can get constraints on the combination (h, ωc) that are consistent with the fiducial values to better than the 68% confidence interval over this range of scales and redshifts