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L. Moscardini

Publications and source records attributed to L. Moscardini.

At least 19 recordsLinked to original sources

Two-dimensional galaxy cluster shapes using lensing data: a simulated analysis

Context. Cluster morphology reflects assembly history and dynamical state. High-resolution weak lensing can reveal departures from spherical symmetry, but its ability to recover two-dimensional shapes remains less explored. Aims. We assess how reliably weak lensing recovers projected cluster morphology and its dependence on orientation and dynamical state. We also compare large-scale weak-lensing morphology with that traced by strong lensing near the cluster centre. Methods. We study three clusters at $z=0.22$ from The Three Hundred Project, representing relaxed, mildly disturbed and unrelaxed systems. For each, we consider three random projections and three along the principal axes of the mass tensor. For each projection, we generate 128 weak-lensing catalogues with a source density of 30 arcmin$^{-2}$ and intrinsic ellipticity dispersion $σ_ε=0.3$. We constrain mass and concentration from one-dimensional NFW and BMO fits, then recover ellipticity, position angle and centre using a two-dimensional elliptical NFW model. We also measure morphology from true convergence maps, Kaiser \& Squires reconstructions and strong-lensing tangential critical lines. Results. Recovered parameters depend on orientation and dynamical state. The relaxed cluster has similar inner and large-scale shapes, whereas disturbed systems appear more elliptical centrally. Two-dimensional weak-lensing modelling recovers the projected mass orientation despite source sampling and shape noise. Kaiser \& Squires reconstructions recover the position angle well but favour rounder mass distributions. Centroid offsets are larger in unrelaxed systems. Conclusions. Combining weak- and strong-lensing morphology probes cluster structure across physical scales and offers a promising way to investigate morphology and dynamical state.

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Euclid Quick Data Release (Q1). The shape of cluster haloes revealed by intracluster light

Intracluster light (ICL) offers a luminous route for measuring the shapes and orientations of cluster haloes. We used Euclid Quick Data Release (Q1) images to quantify ICL shapes for 205 clusters at $0.1 \leq z \leq 0.8$ selected from the eROSITA All-Sky Survey and the Dark Energy Survey. We measured the ICL properties across five bands ($I_\mathrm{E}$, $Y_\mathrm{E}$, $J_\mathrm{E}$, $H_\mathrm{E}$ and the coadded $YJH_\mathrm{E}$), and find that the shape parameters are consistent across the filters, with the $H_\mathrm{E}$ band probing the profiles to the largest cluster-centric distances ($0.1R_{200\mathrm{c}}\sim100$ kpc). The ICL ellipticity ($e=1-b/a$) distribution peaks at 0.5, consistent with halo ellipticities inferred from strong and weak lensing studies, suggesting that the ICL traces the large-scale structure of the clusters. Cluster cores, dominated by brightest cluster galaxy (BCG) light, are round ($e\sim0.2$), while the ICL becomes progressively more elongated at large radii, reaching an ellipticity of $\sim0.5$ by $0.1R_{200\mathrm{c}}$. We find that the ICL is closely aligned with the BCG (87% lie within 30$^\circ$), but shows a weaker alignment with the satellite galaxy distribution (61% within 30$^\circ$). Robust position angles could be measured using the ICL for 63% of the sample, whereas position angles could be measured for only 30% of the sample using the satellite galaxies. Stacking clusters in redshift bins allows measurements of the ICL surface brightness to $0.6$-$0.8R_{200\mathrm{c}}$ and ellipticity beyond $0.3$-$0.4R_{200\mathrm{c}}$ (300-400 kpc), but we observed a plateau in the ICL ellipticity beyond $0.1R_{200\mathrm{c}}$. These results demonstrate the capability of Euclid to characterise the ICL morphology with high statistical precision, allowing new constraints on cluster halo structure and its evolution with redshift.

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Euclid Quick Data Release (Q1). A systematic study of the intracluster light fraction at 0.2 < z < 1.5

We present a homogeneous analysis of the intracluster light (ICL) in approximately 300 galaxy clusters spanning $0.2 10^{10}\,M_\odot$). The inferred ICL fraction also depends systematically on wavelength, while remaining largely insensitive to the adopted outer integration radius of 200-600 kpc. These results highlight the importance of homogeneous ICL analyses and constrain the evolution of diffuse stellar components in clusters.

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Euclid Quick Data Release (Q1). The metallicity of the intracluster light

Colour provides key information to constrain the stellar population of the intracluster light (ICL), the diffuse light within galaxy clusters. We derive radial colour profiles ($Y_\mathrm{E}-H_\mathrm{E}$, $J_\mathrm{E}-H_\mathrm{E}$, $I_\mathrm{E}-H_\mathrm{E}$) of the brightest central galaxy (BCG) and ICL for 168 galaxy clusters from the Dark Energy Survey redMaPPer catalogue within the redshift range $0.1 < z < 0.75$ and halo mass $M_{\rm 200m} > 10^{14.05}M_\odot/h$, within the Euclid Quick Data Release (Q1). By stacking the light profiles measured using elliptical annuli on the BCG and ICL images, we reliably measure the ICL colour out to approximately 300 kpc, over which we find a colour gradient, with the ICL becoming bluer than the BCG out to approximately 150 kpc. Using stellar population synthesis (SPS) models, we find that near-infrared (NIR) colours are sensitive to metallicity, but not age. Thus, we measure a metallicity profile in the BCG and ICL that extends out to 300 kpc for a statistical sample for the first time. While the colours, and the detection of a colour and metallicity gradient, are robust, we note that our metallicity measurement is dependent upon our choice of both SPS model and colour. We find that the metallicity of the BCG is super-solar [$\log_{10} (Z/Z_\odot) > 0.1$], while the ICL is metal-poor [$\log_{10}(Z/Z_\odot)\approx -0.5$], placing the first statistical constraint on the metallicity of the ICL out to large radii. These results support our current understanding of BCG and ICL formation: BCGs form predominantly through mergers with massive galaxies or the cores of satellite galaxies, while the ICL grows via the tidal stripping of lower-metallicity stars from the outskirts of massive satellite galaxies.

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Prevalence of radio Active Galactic Nuclei in galaxy groups since z=3.5 in the COSMOS-Web field

Radio active galactic nuclei (AGN) are key tracers of kinetic feedback from supermassive black holes. Although the dependence of their triggering on host stellar mass is well known, the impact of the large-scale environment across cosmic time is poorly understood. We investigate the role of the environment in triggering radio AGN activity, while also studying the dependence on stellar mass ($10\leq\log M_{\ast}\,{\rm [M_{\odot}]}\leq11.4$), radio luminosity ($22\leq\log L_{1.4}\,{\rm [W\,Hz^{-1}]}\leq26$), and redshift ($0.1\leq z \leq 3.5$). We combine the VLA-COSMOS 3 GHz Large Project with the COSMOS-Web galaxy and group catalogs, selecting radio-excess AGN and building radio luminosity functions (RLF) and radio AGN fractions separately for sources in galaxy groups (124 radio AGN) and in the field (405 radio AGN), out of the total of 20203 galaxies and 1678 galaxy groups. We fit the RLF to derive the cosmic evolution of radio AGN in different environments, and we provide a new parametric description of the radio AGN fractions as a function of environment, $M_{\ast}$, $L_{1.4}$, and z. Besides confirming the known positive correlation of radio AGN fraction with host $M_{\ast}$ in both groups and in the field, more importantly we find that the activation of a radio AGN in groups is enhanced relative to the field by a factor of 3--30 in space density and of 2 in radio AGN fraction at fixed stellar mass; the enhancement is also a function of $M_{\ast}$, $L_{1.4}$, and z. Furthermore, in all z bins, the radio AGN fractions peak within $r \leq 0.2R_{200}$. Overall, dense environments enhance radio AGN triggering out to at least z=3.5. We suggest the existence of a possible transition in the dominant triggering mechanism of radio AGN activity around z~1.5, potentially related to the intragroup medium in the core of groups at lower z and to merger and structure growth at earlier cosmic times.

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Euclid: Impact of halo mass-conversion model assumptions on galaxy cluster number-count analyses

The large catalogues of galaxy clusters expected from the Euclid survey will enable cosmological analyses of cluster number counts that require accurate cosmological model predictions. One possibility is to use parametric fits calibrated against $N$-body simulations, that capture the cosmological parameter dependence of the halo mass function. Several studies have shown that this can be obtained through a calibration against haloes with spherical masses defined at the virial overdensity. In contrast, if different mass definitions are used for the HMF and the scaling relation, a mapping between them is required. Here, we investigate the impact of such a mapping on the cosmological parameter constraints inferred from galaxy cluster number counts. Using synthetic data from $N$-body simulations, we show that the standard approach, which relies on assuming a concentration-mass relation, can introduce significant systematic bias. In particular, depending on the mass definition and the relation assumed, this can lead to biased constraints at more than 2$σ$ level. In contrast, we find that in all the cases we have considered, the mass conversion based on the halo sparsity statistics result in a systematic bias smaller than the statistical error.

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COSMOS-Web: From early star-formation enhancement to late suppression in galaxy groups

Galaxy groups trace dense environments where interactions, gas removal, and reduced accretion may drive quenching. Common diagnostics trace star formation over short timescales ($\lesssim100$ Myr); time-resolved star formation histories (SFHs) separate recent changes from longer-term evolution at fixed mass and redshift. Using COSMOS-Web data, we test how group environment correlates with star-formation activity and its evolution with cosmic time and group-centric distance, contrasting high-richness groups with excluded field galaxies. We combine COSMOS2025/COSMOS-Web stellar masses and non-parametric SFHs with group detections and memberships from AMICO (Adaptive Matched Identifier of Clustered Objects), comparing stacked SFHs of matched group and field galaxies and measuring how the SFH offset evolves with group-centric distance for the richest groups. Massive galaxies ($\log(M_\star/M_\odot)>10.5$) show the largest offsets but are already quenched in both environments. For lower masses ($8.1<\log(M_\star/M_\odot)<10.5$), suppression is clearest at $z<1.5$ (deficit up to 0.8 dex), while at $z>1.5$ SFHs show weak suppression or occasional enhancement. The radial signal evolves similarly: quenching is broad at low $z$, the inner-outer contrast sharpens at $z\gtrsim1$, and any ordering at $z\gtrsim2$ is tentative given growing uncertainties in the AMICO centroids. These results suggest an evolving picture: groups are more mixed at early epochs, with both suppressed and occasionally elevated SFHs, partly reflecting high-$z$ uncertainties, while suppression dominates from $z\lesssim1.5$, most clearly for low-to-intermediate-mass galaxies. Inner-region galaxies likely spend more time in the group potential, undergo more passages through dense intra-group gas, and accrete less pristine cold gas, making quenching progressively clearer with cosmic time.

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Euclid: Quick Data Release (Q1) -- Optical hotspots in powerful radio galaxies

The hotspots of powerful radio galaxies are the sites of high-energy particle acceleration, but radio observations give us limited information on the electron energy distributions that they generate, which affects our overall understanding of their physics and energetics. Optical synchrotron counterparts to radio galaxy hotspots, which probe high electron energies, have been known for many years, but have only been studied in a small number of objects selected as being very bright in the radio. By combining Low-Frequency Array (LOFAR) observations with the Euclid Q1 data release in the Euclid Deep Field North, we identify 77 powerful radio galaxies with hotspots and show that a small but significant fraction of them, 7--15\%, may have detected infrared and optical counterparts to their hotspots. The hotspot spectral energy distributions in our clearest cases are consistent with particle acceleration up to (but not beyond) 1\,TeV in energy on the assumption of field strengths close to equipartition, whereas non-detected hotspots either do not reach such high electron energies or would have to have very different electron energy spectra or significantly sub-equipartition magnetic field strengths. Two new candidate optical hotspots are clearly detected matching high-resolution LOFAR data; one is remarkable as both the highest-redshift optical hotspot known to date ($z \approx 1.6$) and also the first optical detection of the hotspot of the inner lobe of a restarting source. We discuss approaches to performing a large-scale study of hotspots with the full wide-area Euclid surveys, particularly when combined with the international baselines of LOFAR, enabling for the first time a statistical analysis of high-energy particle acceleration in hotspots.

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Euclid: Galaxy cluster detection through the weak lensing effect - algorithm assessment and selection

Weak gravitational lensing offers a powerful way to detect galaxy clusters by directly tracing their total matter content. Its effectiveness increases with the density of background galaxies, a requirement that is now being met by the high sensitivity and wide coverage of current large-area surveys. A prime example is the Euclid telescope, which will map approximately 14 000 deg2 of the sky, measuring the shapes of billions of galaxies and opening a meaningful window for detecting galaxy clusters uniquely through their weak lensing signal. We present the results of nine galaxy cluster detection algorithms in a blind challenge, using 1200 deg2 of Euclid-like weak lensing observations from the DEMNUni-Cov simulations. The performance of these methods was assessed by matching their detections to known synthetic clusters with signal-to-noise ratios greater than 2, satisfying the z-M selection cut, and adopting two different matching procedures. The purpose of the challenge was to identify and improve strategies for galaxy cluster detection via weak lensing for the upcoming Euclid data releases. We pre-selected four methods based on their individual performance and complementarity. Each pre-selected method adopts a distinct approach: AMICO-WL uses an optimal filtering technique, DoG employs Gaussian filtering, O21 relies on aperture-mass filtering, and W234 applies multi-scale wavelet filtering. Together, the results of these methods can be merged to enhance the processing of Euclid data. Individually, these algorithms reach approximately 10% completeness for a mean purity of 90%, while their combination leads to roughly a two-fold improvement in overall performance, exceeding 70% completeness for low-redshift, high-mass clusters. When extrapolating the results of this work to Euclid Data Release 1, we expect to detect approximately 2500 galaxy clusters via weak gravitational lensing.

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Observation-driven simulations of strong lensing galaxy clusters

Galaxy clusters are the most powerful strong lenses: they greatly magnify the flux of distant and faint sources. Strong lensing also allows for the reconstruction of their mass distribution with-1% level accuracy and enables investigating cosmological parameters. The number of known systems of this type is bound to increase in the next years thanks to wide imaging surveys. Using simulations in this context is crucial to validate the analysis methods before they are applied to real data, and to train machine learning algorithms that can handle large volumes of images. In this work, we present a simulated set of one hundred images of galaxy clusters that we have produced with a novel code for simulating cluster-scale strong lenses. One of the main novelties of our approach, distinguishing it from other existing codes, is the use of empirical relations, derived from state-of-the-art observations, for modelling the characteristics, such as morphology, color, and spatial distribution of the cluster member population. This allows us to reliably reproduce the complexity of real observations. The simulations are partly carried out with the latest version of SkyLens, a code that creates mock observations of strong lensing events in different systems and observational setups. The main improvements we introduce are the use of the message passage interface (MPI) paradigm, a standard for parallel programming that leverages the use of several processors to perform some given task, and the implementation of score-based diffusion models to augment the images of the background sources. Together, they lead to more efficient and realistic image simulations. We also present the validation of the code and simulations by comparing the properties of the mock clusters to those of real ones. [Abridged]

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Euclid. A two-point correlation approach to diagnosing star-related systematics in the Euclid spectroscopic survey

The Euclid spectroscopic survey will measure galaxy clustering with unprecedented precision, requiring stringent control of observational and instrumental systematics. Star-related effects may contaminate spectroscopic images through photometric persistence and imperfect masking of stars. We characterized their impact on galaxy clustering analyses, focusing on angular features identifiable in the data. We used angular and spatial auto- and cross-correlation statistics. For galaxies, we used mock spectroscopic catalogues from the EuclidLargeMocks in a 330 deg2 region of the Euclid Wide Survey (EWS). For stars, we used Gaia and 2MASS catalogues in the same area. To simulate photometric persistence, we implemented a simplified detector-level model calibrated on spectroscopic measurements and varied its strength to introduce different interloper fractions. For stellar masking, we modelled inconsistencies between the mask applied to the data and to the random catalogue. We measured star-star, galaxy-galaxy, and star-galaxy angular correlation functions using the Landy--Szalay estimator, and quantified deviations from the expected null star-galaxy correlation. We also evaluated the large-scale impact of such systematics through the three-dimensional two-point correlation function (2PCF). Photometric persistence produces a characteristic feature in the star-galaxy angular cross-correlation at scales of order 100", corresponding to the Euclid dithering pattern and grism dispersion geometry, and a spurious positive signal approximately constant up to 1°. Star-galaxy cross-correlation can detect residual persistence at contamination levels as low as 10% in a Data Release 1 spectroscopic catalogue. In contrast, stellar-mask mismatches produce strong small-scale angular signatures but have negligible impact on the large-scale 2PCF under realistic EWS conditions.

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Euclid preparation. XCI. Validation method for the detections in the Euclid Catalogue of Galaxy Clusters using external data

We present our methodology for identifying known clusters as counterparts to objects in the Euclid Catalogue of Galaxy Clusters (ECGC). Euclid is expected to detect a large number of optically-selected galaxy clusters over the approximately 14000 square degrees of its extragalactic sky survey. Extending out well beyond redshift unity, the catalogue will contain many new high-redshift clusters, while at lower redshifts a fraction of the clusters will have been observed in other surveys. Identifying these known clusters as counterparts to the Euclid-detected clusters is an important step in the validation and construction of the ECGC to augment information with external observables. We present a set of catalogues and meta-catalogues of known clusters that we have assembled for this step, and we illustrate their application and our methodology using the Dark Energy Survey Year 1 RedMaPPer cluster catalogue in lieu of the future ECGC. In the process of this work, we have constructed and delivered an updated EC-RedMaPPer catalogue with multi-wavelength counterparts.

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Euclid preparation. Testing template-fitting models for the multipoles of the two-point clustering of galaxy clusters

The Euclid satellite will deliver a catalogue of optically selected galaxy clusters spanning from around 2000 deg$^2$ in Data Release (DR) 1 to around $14\,000$ deg$^2$ in DR3. In this work, we assess the validity of cluster clustering (CC) models for template-fitting, which complements the full-shape methodology by providing cosmological information from the anisotropy of the redshift-space two-point correlation function (2PCF). Both methods will be used to analyse the cluster 2PCF multipoles with Euclid. We examined the multipoles of the two-point redshift-space clustering of galaxy clusters simulated with the semi-analytic PINOCCHIO code using third-order Lagrangian perturbation theory, assuming a Euclid DR1-like footprint of 500 deg$^2$ in the northern hemisphere and 1400 deg$^2$ in the southern hemisphere. We estimated the first three even multipoles of the 2PCF and associated covariance matrix from 1000 DR1-like synthetic catalogues. We studied the impact of modelling the relevant non-linearities, halo bias, and photometric redshift uncertainties on the 2PCF. We applied three clustering models to the mock catalogues at 0 10^{14}\;h^{-1}\,M_\odot$ under realistic and optimistic photometric redshift uncertainty scenarios. We formulated a set of permissive and conservative criteria that ought to be fulfilled by the multipole cut-off scales and validated them against 100 mock catalogues via an inference of the growth rate multiplied by the matter power spectrum normalisation parameter, $fσ_8$. We tested the dispersion, Scoccimarro, and Taruya-Nishimichi-Saito models. We find that the dispersion model yields unbiased inferences on $fσ_8$ from CC down to 10 $h^{-1}$ Mpc in a DR1-like setting. All clustering models provide similar goodness-of-fit metrics in the presence of DR1-like cluster redshift uncertainties.

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Euclid preparation. CosmoPostProcess: A simulation calibrated framework for weak lensing selection bias in richness-selected galaxy clusters

We present \texttt{CosmoPostProcess}, a simulation-based forward-modelling algorithm calibrated to reproduce Euclid optical cluster observables. Its main deliverable is a correction for stacked surface-density profiles, binned in richness and redshift, accounting for selection systematics in richness-selected samples relative to unbiased references. We focus on the Euclid richness definition foreseen for cosmological analyses, which does not apply a colour selection; red-sequence richness is not considered. The algorithm processes $N$-body simulations by painting galaxies with a halo-occupation model and emulating survey detection and richness assignment. We also implement a novel estimate of optical cluster centres from projected galaxy densities, validated against Euclid pipelines. Baryonic effects are included through a correction calibrated on hydrodynamical simulations; the baryon-corrected excess surface density agrees within \(2\,\%\) over \(r\in[0.1,\,5]\,h^{-1}\,\mathrm{Mpc}\). Selection-bias contributions are assessed by varying cosmology and the mass--richness relation. Projection-induced selection bias follows a robust pattern: correlated large-scale structure projected along the line of sight enhances the stacked profile near the one-halo to two-halo transition, peaking at about \(1\,h^{-1}\,\mathrm{Mpc}\) with an amplitude of \(20\!-\!40\,\%\), depending on richness and redshift. The effect is mild at low and intermediate redshift ($z\lesssim0.7$), at the few-percent level, but becomes more relevant at higher redshift ($z\gtrsim0.7$). Baryonic modifications remain sub-dominant outside the core, at about \(2\,\%\) beyond \(r\gtrsim0.3\,h^{-1}\,\mathrm{Mpc}\). The framework delivers radial profile corrections with uncertainties, combining projection-induced selection bias, baryonic physics, and miscentring, to control systematics in Euclid DR1 cluster cosmology. (abridged)

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Euclid: Optimising tomographic redshift binning for 3$\times$2pt power spectrum constraints on dark energy

We present a simulation-based method to explore the optimum tomographic redshift binning strategy for 3x2pt analyses with Euclid, focusing on the expected configuration of its first major data release (DR1). To do this, we 1) simulate a Euclid-like observation and generate mock shear catalogues from multiple realisations of the 3x2pt fields on the sky, and 2) measure the 3x2pt Pseudo-Cl power spectra for a given tomographic configuration and derive the constraints that they place on the standard dark energy equation of state parameters (w0, wa). For a simulation including Gaussian-distributed photometric redshift uncertainty and shape noise under a LambdaCDM cosmology, we find that bins equipopulated with galaxies yield the best constraints on (w0, wa) for an analysis of the full 3x2pt signal, or the angular clustering component only. For the cosmic shear component, the optimum (w0, wa) constraints are achieved by bins equally spaced in fiducial comoving distance. However, the advantage with respect to alternative binning choices is only a few percent in the size of the $1\,σ\,$(w0, wa) contour, and we conclude that the cosmic shear is relatively insensitive to the binning methodology. We find that the information gain extracted on (w0, wa) for any 3x2pt component starts to saturate at $\gtrsim$ 7-8 bins. Any marginal gains resulting from a greater number of bins is likely to be limited by additional uncertainties present in a real measurement, and the increasing demand for accuracy of the covariance matrix. Finally, we consider a 5% contamination from catastrophic photometric redshift outliers and find that, if these errors are not mitigated in the analysis, the bias induced in the 3x2pt signal for 10 equipopulated bins results in dark energy constraints that are inconsistent with the fiducial LambdaCDM cosmology at $>5\,σ$.

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Euclid: Inferring star-formation history via cross-correlations of photometric clustering and shear with the cosmic infrared background

The cosmic infrared background, sourced by dust heated by star-forming activity, encodes the integrated history of the star-formation distribution over a large swathe of cosmic time. Decomposing the contribution from galaxies at different redshifts to the observed CIB maps provides a powerful tool for probing the large-scale star-formation history across cosmic times. To this end, we perform a forecast tomographic cross-correlation analysis using simulated photometric galaxy clustering and weak lensing data based on the Euclid mission survey specifications, combined with Planck CIB observations. The analysis adopts templates constructed from the halo occupation distribution model to measure the bias-weighted star-formation-rate density, $\langle b ρ_{\rm SFRD}\rangle$, as a function of redshift. We present forecasts for the $\langle b ρ_{\rm SFRD}\rangle$ constraints based on these simulations and quantify the expected constraining power using Fisher information matrix methods. Compared with results obtained using the same dataset as in previous works, we find that Euclid will tighten the constraints on $\langle b ρ_{\rm SFRD}\rangle$ across all redshift bins by a factor of about $2$ and provide more measurements over a deeper redshift range. This leads to improved constraints on all HOD parameters, typically reducing the marginalized uncertainties by a factor of about $2.5$, while also breaking parameter degeneracies.

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Euclid: Measuring the intrinsic alignment of galaxies around cosmic voids in the \Euclid Flagship simulation\

We present a methodology to measure the intrinsic alignment (IA) signal of galaxies in the vicinity of cosmic voids using the \Euclid-like Flagship cosmological simulation from the Euclid Consortium. The IA signal is quantified and compared with the predictions of the linear alignment (LA) model, providing one of the first detailed investigations of this effect in underdense large-scale environments. While the IA signal around cosmic voids has received little attention to date, it may constitute a non-negligible systematic in forthcoming cosmological analyses that exploit void-lensing measurements. Our analysis examines red and blue galaxy populations separately, enabling a comparison of their alignment behaviour in void environments with the corresponding trends measured in galaxy-galaxy correlations. We find that the redshift evolution of the IA amplitude in cosmic voids is broadly consistent with that measured in the general galaxy population for both colour-selected samples. Additionally, our modelling allows us to estimate the linear bias of voids, $b_{\rm V}(z)$ which characterises how cosmic voids trace the underlying dark-matter density field, for voids with radii in the range $10 < R_{\rm V}/(h^{-1} {\rm Mpc}) < 15$. The measured bias exhibits a positive trend with redshift, consistent with theoretical predictions for the clustering of underdense regions. These results highlight the importance of accurately modelling IA in void studies, both to mitigate systematic effects in void-lensing cosmology and to further improve our understanding of galaxy-environment interactions in low-density regions of the Universe.

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Euclid: Precise inference of defocus wavefront error from image diffraction spike measurements

The success of the Euclid cosmological weak lensing measurements requires unprecedented knowledge of the point spread function (PSF) shape. Defocus wavefront errors induce variations in PSF size that directly bias inferred galaxy shapes. We present a rapid, model-independent estimator of the Euclid visible instrument defocus based on measuring subpixel shifts in diffraction spikes from bright stars, arising from the non-mirror-symmetric placement of the telescope spiders. This estimate requires no a-priori PSF model and can be directly inferred from individual survey exposures within seconds. We express defocus as the secondary mirror displacement along the optical axis, $Δz$, achieving a per-exposure precision of $σ(Δz) = 0.022\,μ\text{m}$ in standard Euclid wide-survey images, corresponding to a peak-to-valley optical-path difference of $0.75\,\text{nm}$. This sensitivity resolves thermally induced shifts, typically 0.1-0.3$\,μ\text{m}$, and enables tracking of temporal evolution and field-of-view variations when combining exposures within periods of stability. Since July 2024, the Euclid telescope has been exceptionally stable, while changes to defocus are effectively homogeneous across the field of view. By correlating defocus with PSF size, we find that the Euclid DR3 requirement of a fractional PSF size bias of $\left|ΔR_\mathrm{PSF}^2/R_\mathrm{PSF}^2\right|<10^{-3}$ corresponds to field-averaged secondary mirror displacements exceeding $\langle Δz_\mathrm{thr}\rangle = (0.0683 \pm 0.0024)\,μ\text{m}$. Our estimator provides a robust real-time monitoring tool, supplies a stringent prior for computationally intensive PSF model fitting, and is applicable not only to the Euclid telescope, but to other telescopes whose spider vanes are not mirror-symmetrically arranged.

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