We present the Flagship galaxy mock, a simulated catalogue of billions of galaxies designed to support the scientific exploitation of the Euclid mission. Euclid is a medium-class mission of the European Space Agency optimised to determine the properties of dark matter and dark energy on the largest scales of the Universe. It probes structure formation over more than 10 billion years primarily from the combination of weak gravitational lensing and galaxy clustering data. The breath of Euclid's data will also foster a wide variety of scientific analyses. The Flagship simulation was developed to provide a realistic approximation to the galaxies that will be observed by Euclid and used in its scientific analyses. We ran a state-of-the-art N-body simulation with four trillion particles, producing a lightcone on the fly. From the dark matter particles, we produced a catalogue of 16 billion haloes in one octant of the sky in the lightcone up to redshift z=3. We then populated these haloes with mock galaxies using a halo occupation distribution and abundance matching approach, calibrating the free parameters of the galaxy mock against observed correlations and other basic galaxy properties. Modelled galaxy properties include luminosity and flux in several bands, redshifts, positions and velocities, spectral energy distributions, shapes and sizes, stellar masses, star formation rates, metallicities, emission line fluxes, and lensing properties. We selected a final sample of 3.4 billion galaxies with a magnitude cut of H_E<26, where we are complete. We have performed a comprehensive set of validation tests to check the similarity to observational data and theoretical models. In particular, our catalogue is able to closely reproduce the main characteristics of the weak lensing and galaxy clustering samples to be used in the mission's main cosmological analysis. (abridged)

In this paper we present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute the exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ('shot noise') in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.

The Euclid mission, designed to map the geometry of the dark Universe, presents an unprecedented opportunity for advancing our understanding of the cosmos through its photometric galaxy cluster survey. Central to this endeavor is the accurate calibration of the mass- and redshift-dependent halo bias (HB), which is the focus of this paper. Our aim is to enhance the precision of HB predictions, which is crucial for deriving cosmological constraints from the clustering of galaxy clusters. Our study is based on the peak-background split (PBS) model linked to the halo mass function (HMF), and it extends it with a parametric correction to precisely align with results from an extended set of N-body simulations carried out with the OpenGADGET3 code. Employing simulations with fixed and paired initial conditions, we meticulously analyzed the matter-halo cross-spectrum and modeled its covariance using a large number of mock catalogs generated with Lagrangian perturbation theory simulations with the PINOCCHIO code. This ensures a comprehensive understanding of the uncertainties in our HB calibration. Our findings indicate that the calibrated HB model is remarkably resilient against changes in cosmological parameters, including those involving massive neutrinos. The robustness and adaptability of our calibrated HB model provide an important contribution to the cosmological exploitation of the cluster surveys to be provided by the Euclid mission. This study highlights the necessity of continuously refining the calibration of cosmological tools such as the HB to match the advancing quality of observational data. As we project the impact of our calibrated model on cosmological constraints, we find that given the sensitivity of the Euclid survey, a miscalibration of the HB could introduce biases in cluster cosmology analysis. Our work fills this critical gap, ensuring the HB calibration matches the expected precision of the Euclid survey.

To constrain models beyond ΛCDM, the development of the Euclid analysis pipeline requires simulations that capture the nonlinear phenomenology of such models. We present an overview of numerical methods and N-body simulation codes developed to study the nonlinear regime of structure formation in alternative dark energy and modified gravity theories. We review a variety of numerical techniques and approximations employed in cosmological N-body simulations to model the complex phenomenology of scenarios beyond ΛCDM. This includes discussions on solving nonlinear field equations, accounting for fifth forces, and implementing screening mechanisms. Furthermore, we conduct a code comparison exercise to assess the reliability and convergence of different simulation codes across a range of models. Our analysis demonstrates a high degree of agreement among the outputs of different simulation codes, providing confidence in current numerical methods for modelling cosmic structure formation beyond ΛCDM. We highlight recent advances made in simulating the nonlinear scales of structure formation, which are essential for leveraging the full scientific potential of the forthcoming observational data from the Euclid mission.

We investigate the level of accuracy and precision of cluster weak-lensing (WL) masses measured with the data processing pipeline. We use the DEMNUni-Cov N-body simulations to assess how well the WL mass probes the true halo mass, and, then, how well WL masses can be recovered in the presence of measurement uncertainties. We consider different halo mass density models, priors, and mass point estimates. WL mass differs from true mass due to, e.g., the intrinsic ellipticity of sources, correlated or uncorrelated matter and large-scale structure, halo triaxiality and orientation, and merging or irregular morphology. In an ideal scenario without observational or measurement errors, the maximum likelihood estimator is the most accurate, with WL masses biased low by ⟨ b_M ⟩ = -14.6 ± 1.7 % on average over the full range M_200c > 5 × 10^13 M_⊙ and z < 1. Due to the stabilising effect of the prior, the biweight, mean, and median estimates are more precise. The scatter decreases with increasing mass and informative priors significantly reduce the scatter. Halo mass density profiles with a truncation provide better fits to the lensing signal, while the accuracy and precision are not significantly affected. We further investigate the impact of additional sources of systematic uncertainty on the WL mass, namely the impact of photometric redshift uncertainties and source selection, the expected performance of cluster detection algorithms, and the presence of masks. Taken in isolation, we find that the largest effect is induced by non-conservative source selection. This effect can be mostly removed with a robust selection. As a final -like test, we combine systematic effects in a realistic observational setting and find results similar to the ideal case, ⟨ b_M ⟩ = - 15.5 ± 2.4 %, under a robust selection.

We present a detailed kinematical and dynamical study of the galaxy cluster RXCJ1111.6+4050 (RXCJ1111), at z = 0.0756 using 104 new spectroscopic redshifts of galaxies observed at the Telescopio Nazionale Galileo and SDSS DR16 public archive. Our analysis is performed in a multiwavelength context in order to study and compare mainly optical and X-ray properties using XMM-Newton data. We find that RXCJ1111 is a galaxy cluster showing a velocity distribution with clear deviations from Gaussianity, that we are able to explain by the presence of a substructure within the cluster. The two cluster components show velocity dispersions of 644 ± 56 km s−1 and 410 ± 123 km s−1, which yield dynamical masses of M200 = 1.9 ± 0.4 × 1014 M⊙ and 0.6 ± 0.4 × 1014 M⊙ for the main system and substructure, respectively. The 2D spatial distribution of galaxies and X-ray surface brightness of RXCJ1111 presents an elongation in the North–South direction. These observational facts, together with a gradient of 250−350 km s−1 Mpc−1 in the velocity field, following the NNE–SSE direction, suggest that the merger axis between the main system and substructure is slightly tilted with respect to the line-of-sight. The substructure is characterized by a magnitude gap Δm12 ≥ 1.8, so it fits the “fossil-like” definition of a galaxy group. From the X-ray observations, we estimate a M500, X = 1.68 ± 0.25 × 1014 M⊙, which is in good agreement with the dynamical masses when two galaxy components are considered separately. This suggests that the mass estimates obtained from X-ray and velocity dispersion are compatible even for non-relaxed clusters, at least when we are able to identify and separate galaxy clumps and derive masses by considering the virialized regions. We propose a 3D merging model and find that the fossil group is in an early phase of collision with the RXCJ1111 main cluster and placed at ∼8° ( ± 3° ) from line-of-sight. This merging model would explain the slight increase found in the TX with respect to what we would expect for relaxed clusters. Due to the presence of several brightest galaxies, after this collision, the substructure would presumably lose its fossil condition. Therefore, RXCJ1111 represents the observational evidence that the fossil stage of a system can be temporary and transitional.

We report on the discovery of the X-ray luminous cluster XMMU J100750.5+125818 at redshift 1.082 based on 19 spectroscopic members, which displays several strong lensing features. S ED modeling of the lensed arc features from multicolor imagi ng with the VLT and the LBT reveals likely redshifts ∼2.7 for the most prominent of the lensed background galaxies . Ma s estimates are derived for different radii from the velocity dispersion of the cluster memb rs,M200 ≃ 1.8 × 1014 M⊙, from the X-ray spectral parameters, M500 ≃ 1.0× 1014 M⊙, and the largest lensing arc, MSL ≃ 2.3× 1013 M⊙. The projected spatial distribution of cluster galaxies ap pears to be elongated, and the brightest galaxy lies o ff center with respect to the X-ray emission indicating a not ye t relaxed structure. XMMU J100750.5+125818 offers excellent diagnostics of the inner mass distribution of a distant cluster with a combination of strong and weak lensing, optical and X-ray spectroscopy.

3 - prodotto gia presente in altro archivio Open Access, es. VizieR (allegare file read.me al passo 5-Carica)

3 - prodotto gia presente in altro archivio Open Access, es. VizieR (allegare file read.me al passo 5-Carica)

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky survey of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing >103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y5R500 are robust to pressureprofile variation and beam systematics, but accurate conversion to Y500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.

We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with telescopes at the Canary Islands observatories as part of the general optical follow-up programme undertaken by the Planck Collaboration. In total, 78 SZ sources are discussed. Deep-imaging observations were obtained for most of these sources; spectroscopic observations in either in long-slit or multi-object modes were obtained for many. We effectively used 37.5 clear nights. We found optical counterparts for 73 of the 78 candidates. This sample includes 53 spectroscopic redshift determinations, 20 of them obtained with a multi-object spectroscopic mode. The sample contains new redshifts for 27 Planck clusters that were not included in the first Planck SZ source catalogue (PSZ1).

Observations and cosmological simulations show galaxy clusters as a family of nearly self-similar objects with properties that can be described by scaling relations as a function of e.g. mass and time. Here we study the scaling relations between the galaxy velocity dispersion and X-ray quantities like X-ray bolometric luminosity and temperature in galaxy clusters at high redshifts (0.64 $\leq$ z $\leq$ 1.46). We also compare our results with the similar study of the local HIFLUGCS sample. For the analysis, we use a set of 15 distant galaxy clusters extracted from the literature plus a sample of 10 newly discovered clusters selected in X-rays by the \XMM Distant Cluster Project (XDCP) with more than 10 confirmed spectroscopic members per cluster. We also study the evolution of this scaling relation by comparing the high redshift results with the data from the local HIFLUGCS sample. We also investigated the $L_X - T_X$ and the $\sigma_v - T_X$ relations for the 15 clusters in the literature sample. We report the results of the X-ray and kinematic analysis of 10 newly detected high redshift clusters and provide their spectroscopic and kinematic details. For the entire, distant sample we find a slope fully consistent with the one typical of local clusters, albeit with a large associated uncertainty. The study on the evolution of the amplitude reveals a positive offset if the self-similar evolution is neglected, hence possibly indicating the need for including evolutionary effects. However, the $L_X - T_X$ relation is found to be in good agreement with the local relation without any significant redshift evolution. Finally, the $\sigma_v - T_X$ relation appears to slightly deviate from the theoretical expectation that galaxies and gas particles have a similar specific kinetic energy. However, the associated uncertainty is currently too large for making any conclusive statement in this regard.

The survey of galaxy clusters performed by Planck through the Sunyaev-Zeldovich effect has already discovered many interesting objects, thanks to its full sky coverage. One of the SZ candidates detected in the early months of the mission near to the signal-to-noise threshold, PLCKG214.6+37.0, was later revealed by XMM-Newton to be a triple system of galaxy clusters. We present the results from a deep XMM-Newton re-observation of PLCKG214.6+37.0, part of a multi-wavelength programme to investigate Planck discovered superclusters. The characterisation of the physical properties of the three components has allowed us to build a template model to extract the total SZ signal of this system with Planck data. We have partly reconciled the discrepancy between the expected SZ signal derived from X-rays and the observed one, which are now consistent within 1.2σ. We measured the redshift of the three components with the iron lines in the X-ray spectrum, and confirm that the three clumps are likely part of the same supercluster structure. The analysis of the dynamical state of the three components, as well as the absence of detectable excess X-ray emission, suggests that we are witnessing the formation of a massive cluster at an early phase of interaction.

We have developed an approximate technique, based on the principles of multi-mode Gaussian optics, for studying the behaviour of shaped off-axis mirrors. We describe a mirror as an inclined phase-transforming plane, where the phase transformation across the plane is determined by the depth of the mirror as a function of position. The scattering matrix is calculated in the usual way by evaluating the overlap integrals over some surface for which the amplitudes and phases of the incoming and outgoing fields are known; because, however, the modes are not orthogonal over the surface of interest, a system of linear equations has to be solved. We demonstrate the “thin-mirror” technique by studying the behaviour of paraboloidal and ellipsoidal mirros, and we show how the performance of measured and approximate surfaces can be assessed.