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J. Rhodes

Publications and source records attributed to J. Rhodes.

At least 19 recordsLinked to original sources

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.

astro-ph.CO↗

Euclid Quick Data Release (Q2) -- The Euclid Galactic Bulge Survey

The Euclid Quick Data Release Q2 provides an unprecedented deep, wide-field, high-angular-resolution view of the inner Galactic bulge through the Euclid Galactic Bulge Survey (EGBS). Nine contiguous fields covering 4.8 deg$^2$ were observed with the VIS instrument over 24 hours in March 2025. Unlike the nominal Euclid survey strategy, the EGBS employed 16 dithered exposures of 400 s each, corresponding to a total integration time of 1.8 hours per field. Dedicated calibration observations were obtained to derive point spread functions (PSFs). The primary objective of the EGBS is gravitational microlensing, with high-angular-resolution imaging enabling lens-mass measurements to better than 10%. The survey provides an optical reference dataset for previously discovered microlensing events and future observations of the Galactic bulge. The Q2 data were processed with the VIS-PF pipeline. The non-standard observing strategy required dedicated calibration products, while the extreme stellar density necessitated modifications to the astrometric calibration and cosmic-ray detection procedures. These improvements have since been incorporated into later pipeline versions. We describe the motivation, observing strategy, data processing, products, and first results of the EGBS. Astrometric residuals with respect to the Gaia DR3 catalogue are 5.5 mas in right ascension and 4.4 mas in declination across the survey area, while the photometric zero points are calibrated to 1.5%. The Q2 release includes calibrated single-dither images, dedicated PSF models, and photometric catalogues containing approximately 45 million detected sources per dither down to AB magnitude 26. Although incomplete because of extreme crowding, these products provide a robust astrometric and photometric foundation for future exploitation of the dataset.

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Star formation quenching precedes morphological transformation in COSMOS-WEB's richest galaxy groups

We analyzed the 25 richest galaxy groups in COSMOS-Web at z = 0.18-3.65, identified via the AMICO algorithm. These groups contain 20-30 galaxies with high (>75%) membership probability. Our study reveals both passive-density and active-density relations: late-type galaxies (LTGs) prefer higher central overdensities than early-type galaxies (ETGs) across all groups, and many massive LTGs exhibit colors typical of quiescent galaxies. We identify red sequences (RS) in 5 groups, prominently established at z < 1, with early emergence in the RS locus up to z ~ 2.2. This suggests group environments represent a transitional phase where star formation quenching precedes morphological transformation, contrasting with the classical morphology-density relation in rich clusters. In the central regions (~33 arcsec / 100 kpc from centers), we identified 86 galaxies: 23 (~27%) ETGs and 63 (~73%) LTGs. High-mass galaxies (M_star > 10^10.5 M_sun) undergo rapid quenching over ~1 Gyr, becoming predominantly spheroidal ETGs. This indicates morphological transformation accelerates in massive systems during peak cosmic star formation. Intermediate-mass galaxies (10^9 < M_star/M_sun < 10^10.5) show mild quenching, while low-mass galaxies (M_star < 10^9 M_sun) remain largely star-forming; here, environmental processes suppress star formation without destroying disks, suggesting group quenching operates on longer timescales than mass quenching. Overall, mass-dependent quenching dominates the high-mass end, while environment shapes lower-mass systems. The HLAGN fraction for both groups and field increases with redshift, peaking at z ~ 2, with groups consistently showing higher fractions. We suggest AGN feedback partially drives rapid quenching in high-mass galaxies, while mergers may trigger AGN activity.

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The ALPINE-CRISTAL-JWST Survey: JWST/IFU Optical Observations for 18 Main-Sequence Galaxies at z=4-6

To fully characterize the formation and evolution of galaxies, we need to observe their stars, gas, and dust on resolved spatial scales. We present the ALPINE-CRISTAL-JWST survey, which combines kpc-resolved imaging and spectroscopy from HST, JWST, and ALMA for 18 representative main-sequence galaxies at z=4-6 and log(M/$M_\odot$) > 9.5 to study their star formation, chemical properties, and extended gas reservoirs. The co-spatial measurements resolving the ionized gas, molecular gas, stars, and dust on 1-2 kpc scales make this a unique benchmark sample for the study of galaxy formation and evolution at $z\sim5$, connecting the Epoch of Reionization with the cosmic noon. In this paper, we outline the survey goals and sample selection, and present a summary of the available data for the 18 galaxies. In addition, we measure spatially integrated quantities (such as global gas metallicity), test different star formation rate indicators, and quantify the presence of H$α$ halos. Our targeted galaxies are relatively metal rich (10-70% solar), complementary to JWST samples at lower stellar mass, and there is broad agreement between different star formation indicators. One galaxy has the signature of an active galactic nuclei (AGN) based on its emission line ratios. Six show broad H$α$~emission suggesting type 1 AGN candidates. We conclude with an outlook on the exciting science that will be pursued with this unique sample in forthcoming papers.

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Euclid: Methodology for derivation of IPC-corrected conversion gain of nonlinear CMOS APS

We introduce a fast method to measure the conversion gain in Complementary Metal-Oxide-Semiconductors (CMOS) Active Pixel Sensors (APS), which accounts for nonlinearity and interpixel capacitance (IPC). The standard 'mean-variance' method is biased because it assumes pixel values depend linearly on signal, and existing methods to correct for nonlinearity are still introducing significant biases. While current IPC correction methods are prohibitively slow for a per-pixel application, our new method uses separate measurements of the IPC kernel to make an almost instantaneous calculation of gain. Validated using test data from a flight detector from the ESA Euclid mission, the IPC correction recovers the results of slower methods within 0.1% accuracy. Meanwhile the nonlinearity correction ensures an estimation of the gain that is independent of signal, correcting a bias of more than 2.5% on gain estimation.

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Euclid: Relativistic effects in the dipole of the 2-point correlation function

Gravitational redshift and Doppler effects give rise to an antisymmetric component of the galaxy correlation function when cross-correlating two galaxy populations or two different tracers. In this paper, we assess the detectability of these effects in the Euclid spectroscopic galaxy survey. We model the impact of gravitational redshift on the observed redshift of galaxies in the Flagship mock catalogue using a Navarro-Frenk-White profile for the host haloes. We isolate these relativistic effects, largely subdominant in the standard analysis, by splitting the galaxy catalogue into two populations of faint and bright objects and estimating the dipole of their cross-correlation in four redshift bins. In the simulated catalogue, we detect the dipole signal on scales below $30\,h^{-1}{\rm Mpc}$, with detection significances of $4\,σ$ and $3\,σ$ in the two lowest redshift bins, respectively. At higher redshifts, the detection significance drops below $2\,σ$. Overall, we estimate the total detection significance in the Euclid spectroscopic sample to be approximately $6\,σ$. We find that on small scales, the major contribution to the signal comes from the nonlinear gravitational potential. Our study on the Flagship mock catalogue shows that this observable can be detected in Euclid Data Release 2 and beyond.

astro-ph.CO↗

Tracing High-z Galaxies in X-rays with JWST and Chandra

We leverage JWST data from the COSMOS-Web Survey in order to provide updated measurements on the auto-power spectrum of the now resolved Cosmic Infrared Background (CIB) and its coherence with the unresolved soft Cosmic X-ray Background (CXB) observed by Chandra at z > 6. Maps of the CIB in the F277W and F444W NIRCam filters are constructed with sources fainter than AB mag = 25 and cross-correlated with the CXB in the [0.5-2] keV band. We find that on scales between 1 and 1000'' the CIB-CXB cross-power in both NIRCam filters is statistically significant with signal-to-noise ratios (S/N) of 4.80 and 6.20 respectively from redshifts 0 < z < 13. In our high-z (6 < z < 13) interval we find coherence in both filters with a S/N of 7.32 and 5.39 respectively. These results suggest that there are X-ray emitting galaxies resolved by JWST, including star-forming galaxies (SFGs) and active galactic nuclei (AGNs). We fit the large-scale biasing of the IR sources producing the CIB as a function of z with results consistent with prior measurements and place constraints on the CXB flux and biasing at low- and high-z. The CXB flux measurements presented in this study suggest that approximately 94% of the [0.5-2] keV CXB is resolved, and this value is consistent within 2$σ$ with the complete resolution of the [0.5-2] keV CXB.

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COSMOS-Web: A history of galaxy migrations over the stellar mass-star formation rate plane

The stellar mass-star formation rate ($\mathrm{M_*}$-$\mathrm{SFR}$) plane is a fundamental diagnostic for distinguishing galaxy populations. However, the evolutionary pathways of galaxies within this plane across cosmic time remain poorly understood. This study aims to observationally characterize galaxy migration in the $\mathrm{M_*}$-$\mathrm{SFR}$ plane using reconstructed star formation histories (SFHs) of galaxies at $z < 4$. Our goal is to provide insights into the physical processes governing star formation and quenching. We analyze a sample of 299,131 galaxies at $z < 4$ from the COSMOS-Web NIRCam survey ($m_{\mathrm{F444W}} < 27$, 0.54 deg$^2$). Using non-parametric SFH modeling with CIGALE, we derive physical properties and reconstruct SFHs. To trace galaxy evolution, we define migration vectors, quantifying their direction ($Φ_{\mathrm{dt}}$ [deg]) and velocity norm ($r_{\mathrm{dt}}$ [dex/Gyr]) on the $\mathrm{M_*}$-$\mathrm{SFR}$ plane. The reliability of these vectors is assessed using the Horizon-AGN simulation. We find that main-sequence galaxies exhibit low-amplitude migration with scattered directions, suggesting oscillations within the main sequence. Their progenitors predominantly lie on the main sequence 1 Gyr earlier. Starburst galaxies show rapid mass assembly ($50\%$ within 350 Myr) and originate from the main sequence, while passive galaxies display uniformly declining SFHs. Massive passive galaxies emerge as early as $3.5 < z < 4$, increasing in number density over time. Only $<20\%$ of passive galaxies were starbursts 1 Gyr prior, indicating diverse quenching pathways. By reconstructing SFHs to $z < 4$, we present a coherent picture of galaxy migration in the $\mathrm{M_*}$-$\mathrm{SFR}$ plane, linking evolutionary phases to their star formation signatures.

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Testing for Intrinsic Type Ia Supernova Luminosity Evolution at z>2 with JWST

The James Webb Space Telescope} (JWST) is opening new frontiers of transient discovery and follow-up at high-redshift. Here we present the discovery of a spectroscopically confirmed Type Ia supernova (SN Ia; SN $2023$aeax) at $z=2.15$ with JWST, including a NIRCam multi-band light curve. SN $2023$aeax lands at the edge of traditional low-$z$ cosmology cuts because of its blue color (peak rest-frame $B-V\sim-0.3$) but with a normal decline rate ($Δm_{15}(B)\sim1.25$), and applying a fiducial standardization with the BayeSN model we find the SN $2023$aeax luminosity distance is in $\sim0.1σ$ agreement with $Λ$CDM. SN $2023$aeax is only the second spectroscopically confirmed SN Ia in the dark matter-dominated Universe at $z>2$ (the other is SN $2023$adsy), giving it rare leverage to constrain any potential evolution in SN Ia standardized luminosities. Similar to SN $2023$adsy ($B-V\sim0.8)$, SN $2023$aeax has a fairly extreme (but opposite) color, which may be due to the small sample size or a secondary factor, such as host galaxy properties. Nevertheless, the SN $2023$aeax spectrum is well-represented by normal low-$z$ SN Ia spectra and we find no definitive evolution in SN Ia standardization with redshift. Still, the first two spectroscopically confirmed $z>2$ SNe Ia have peculiar colors and combine for a $\sim1σ$ distance slope relative to $Λ$CDM, though in agreement with recent SN Ia cosmological measurements.

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COSMOS-Web: The Role of Galaxy Interactions and Disk Instabilities in Producing Starbursts at z<4

We study of the role of galaxy-galaxy interactions and disk instabilities in producing starburst activity in galaxies out to z = 4. For this, we use a sample of 387 galaxies with robust total star formation rate measurements from Herschel, gas masses from ALMA, stellar masses and redshifts from multi-band photometry, and JWST/NIRCam rest-frame optical imaging. Using mass-controlled samples, we find an increased fraction of interacting galaxies in the starburst regime at all redshifts out to z = 4. This increase correlates with star formation efficiency (SFE), but not with gas fraction. However, the correlation is weak (and only significant out to z = 2), which could be explained by the short duration of SFE increase during interaction. In addition, we find that isolated disk galaxies make up a significant fraction of the starburst population. The fraction of such galaxies with star-forming clumps ("clumpy disks") is significantly increased compared to the main-sequence disk population. Furthermore, this fraction directly correlates with SFE. This is direct observational evidence for a long-term increase of SFE maintained due to disk instabilities, contributing to the majority of starburst galaxies in our sample and hence to substantial mass growth in these systems. This result could also be of importance for explaining the growth of the most massive galaxies at z > 6.

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Euclid. II. The VIS Instrument

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information.

astro-ph.IM↗

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

Euclid will provide deep NIR imaging to $\sim$26.5 AB magnitude over $\sim$59 deg$^2$ in its deep and auxiliary fields. The Cosmic DAWN survey complements the deep Euclid data with matched depth multiwavelength imaging and spectroscopy in the UV--IR to provide consistently processed Euclid selected photometric catalogs, accurate photometric redshifts, and measurements of galaxy properties to a redshift of $z\sim 10$. 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.

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Euclid preparation XLVI. The Near-IR Background Dipole Experiment with Euclid

Verifying the fully kinematic nature of the cosmic microwave background (CMB) dipole is of fundamental importance in cosmology. In the standard cosmological model with the Friedman-Lemaitre-Robertson-Walker (FLRW) metric from the inflationary expansion the CMB dipole should be entirely kinematic. Any non-kinematic CMB dipole component would thus reflect the preinflationary structure of spacetime probing the extent of the FLRW applicability. Cosmic backgrounds from galaxies after the matter-radiation decoupling, should have kinematic dipole component identical in velocity with the CMB kinematic dipole. Comparing the two can lead to isolating the CMB non-kinematic dipole. It was recently proposed that such measurement can be done using the near-IR cosmic infrared background (CIB) measured with the currently operating Euclid telescope, and later with Roman. The proposed method reconstructs the resolved CIB, the Integrated Galaxy Light (IGL), from Euclid's Wide Survey and probes its dipole, with a kinematic component amplified over that of the CMB by the Compton-Getting effect. The amplification coupled with the extensive galaxy samples forming the IGL would determine the CIB dipole with an overwhelming signal/noise, isolating its direction to sub-degree accuracy. We develop details of the method for Euclid's Wide Survey in 4 bands spanning 0.6 to 2 mic. We isolate the systematic and other uncertainties and present methodologies to minimize them, after confining the sample to the magnitude range with negligible IGL/CIB dipole from galaxy clustering. These include the required star-galaxy separation, accounting for the extinction correction dipole using the method newly developed here achieving total separation, accounting for the Earth's orbital motion and other systematic effects. (Abridged)

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Euclid: Early Release Observations -- Programme overview and pipeline for compact- and diffuse-emission photometry

The Euclid ERO showcase Euclid's capabilities in advance of its main mission, targeting 17 astronomical objects, from galaxy clusters, nearby galaxies, globular clusters, to star-forming regions. A total of 24 hours observing time was allocated in the early months of operation, engaging the scientific community through an early public data release. We describe the development of the ERO pipeline to create visually compelling images while simultaneously meeting the scientific demands within months of launch, leveraging a pragmatic, data-driven development strategy. The pipeline's key requirements are to preserve the image quality and to provide flux calibration and photometry for compact and extended sources. The pipeline's five pillars are: removal of instrumental signatures; astrometric calibration; photometric calibration; image stacking; and the production of science-ready catalogues for both the VIS and NISP instruments. We report a PSF with a full width at half maximum of 0.16" in the optical and 0.49" in the three NIR bands. Our VIS mean absolute flux calibration is accurate to about 1%, and 10% for NISP due to a limited calibration set; both instruments have considerable colour terms. The median depth is 25.3 and 23.2 AB mag with a SNR of 10 for galaxies, and 27.1 and 24.5 AB mag at an SNR of 5 for point sources for VIS and NISP, respectively. Euclid's ability to observe diffuse emission is exceptional due to its extended PSF nearly matching a pure diffraction halo, the best ever achieved by a wide-field, high-resolution imaging telescope. Euclid offers unparalleled capabilities for exploring the LSB Universe across all scales, also opening a new observational window in the NIR. Median surface-brightness levels of 29.9 and 28.3 AB mag per square arcsec are achieved for VIS and NISP, respectively, for detecting a 10 arcsec x 10 arcsec extended feature at the 1 sigma level.

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Euclid preparation. XXXIV. The effect of linear redshift-space distortions in photometric galaxy clustering and its cross-correlation with cosmic shear

The cosmological surveys that are planned for the current decade will provide us with unparalleled observations of the distribution of galaxies on cosmic scales, by means of which we can probe the underlying large-scale structure (LSS) of the Universe. This will allow us to test the concordance cosmological model and its extensions. However, precision pushes us to high levels of accuracy in the theoretical modelling of the LSS observables, so that no biases are introduced into the estimation of the cosmological parameters. In particular, effects such as redshift-space distortions (RSD) can become relevant in the computation of harmonic-space power spectra even for the clustering of the photometrically selected galaxies, as has previously been shown in literature. In this work, we investigate the contribution of linear RSD, as formulated in the Limber approximation by a previous work, in forecast cosmological analyses with the photometric galaxy sample of the Euclid survey. We aim to assess their impact and to quantify the bias on the measurement of cosmological parameters that would be caused if this effect were neglected. We performed this task by producing mock power spectra for photometric galaxy clustering and weak lensing, as is expected to be obtained from the Euclid survey. We then used a Markov chain Monte Carlo approach to obtain the posterior distributions of cosmological parameters from these simulated observations. When the linear RSD is neglected, significant biases are caused when galaxy correlations are used alone and when they are combined with cosmic shear in the so-called 3$\times$2pt approach. These biases can be equivalent to as much as $5\,σ$ when an underlying $Λ$CDM cosmology is assumed. When the cosmological model is extended to include the equation-of-state parameters of dark energy, the extension parameters can be shifted by more than $1\,σ$.

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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 sub-dominant to dark matter and dark energy, the baryonic component in our Universe holds substantial influence over the structure and mass of galaxy clusters. This paper presents a novel model to precisely quantify the impact of baryons on galaxy cluster virial halo masses, using the baryon fraction within a cluster as proxy for their effect. Constructed on the premise of quasi-adiabaticity, the model includes two parameters 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 one percent 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 varying the numerical implementation of the sub-resolution physical processes included in the simulations. Our work substantiates previous claims about 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 sub-dominant when compared to the precision with which mass-observable relations will be calibrated using Euclid, as well as our current understanding of the baryon fraction within galaxy clusters.

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Euclid: The search for primordial features

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the $Euclid$ space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum, one linearly spaced in $k$-space the other logarithmically spaced in $k$-space. We forecast uncertainties applying a Fisher matrix method to spectroscopic galaxy clustering, weak lensing, photometric galaxy clustering, cross correlation between photometric probes, spectroscopic galaxy clustering bispectrum, CMB temperature and $E$-mode polarization, temperature-polarization cross correlation, and CMB weak lensing. We also study a nonlinear density reconstruction method to retrieve the oscillatory signals in the primordial power spectrum. We find the following percentage relative errors in the feature amplitude with $Euclid$ primary probes for the linear (logarithmic) feature model: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at 68.3% confidence level (CL) using GC$_{\rm sp}$+WL+GC$_{\rm ph}$+XC. Combining all the sources of information explored expected from $Euclid$ in combination with future SO-like CMB experiment, we forecast ${\cal A}_{\rm lin} \simeq 0.010 \pm 0.001$ at 68.3% CL and ${\cal A}_{\rm log} \simeq 0.010 \pm 0.001$ for GC$_{\rm sp}$(PS rec + BS)+WL+GC$_{\rm ph}$+XC+SO-like both for the optimistic and pessimistic settings over the frequency range $(1,\,10^{2.1})$.

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