arXiv subjects

F. Marulli

Publications and source records attributed to F. Marulli.

At least 163 records · Page 9Linked to original sources

arXiv2021

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

The accuracy of photometric redshifts (photo-zs) particularly affects the results of the analyses of galaxy clustering with photometrically-selected galaxies (GCph) and weak lensing. In the next decade, space missions like Euclid will collect photometric measurements for millions of galaxies. These data should be complemented with upcoming ground-based observations to derive precise and accurate photo-zs. In this paper, we explore how the tomographic redshift binning and depth of ground-based observations will affect the cosmological constraints expected from Euclid. We focus on GCph and extend the study to include galaxy-galaxy lensing (GGL). We add a layer of complexity to the analysis by simulating several realistic photo-z distributions based on the Euclid Consortium Flagship simulation and using a machine learning photo-z algorithm. We use the Fisher matrix formalism and these galaxy samples to study the cosmological constraining power as a function of redshift binning, survey depth, and photo-z accuracy. We find that bins with equal width in redshift provide a higher Figure of Merit (FoM) than equipopulated bins and that increasing the number of redshift bins from 10 to 13 improves the FoM by 35% and 15% for GCph and its combination with GGL, respectively. For GCph, an increase of the survey depth provides a higher FoM. But the addition of faint galaxies beyond the limit of the spectroscopic training data decreases the FoM due to the spurious photo-zs. When combining both probes, the number density of the sample, which is set by the survey depth, is the main factor driving the variations in the FoM. We conclude that there is more information that can be extracted beyond the nominal 10 tomographic redshift bins of Euclid and that we should be cautious when adding faint galaxies into our sample, since they can degrade the cosmological constraints.

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arXiv2021

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

The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on the accurate knowledge of the galaxy mean redshift $\langle z \rangle$. We investigate the possibility of measuring $\langle z \rangle$ with an accuracy better than $0.002\,(1+z)$, in ten tomographic bins spanning the redshift interval $0.2 99.8\%$. The zPDF approach could also be successful if we debias the zPDF using a spectroscopic training sample. This approach requires deep imaging data, but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the debiasing method and confirm our finding by applying it to real-world weak-lensing data sets (COSMOS and KiDS+VIKING-450).

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arXiv2020

AMICO galaxy clusters in KiDS-DR3: Evolution of the luminosity function between z=0.1 and z=0.8

By means of the $r$-band luminosity function (LF) of galaxies in a sample of about 4000 clusters detected by the cluster finder AMICO in the KiDS-DR3 area of about 400 deg$^2$, we studied the evolution with richness and redshift of the passive evolving (red), star-forming (blue), and total galaxy populations. This analysis was performed for clusters in the redshift range [0.1,0.8] and in the mass range [$10^{13} M_{\odot}$,$10^{15} M_{\odot}$]. To compute LFs, we binned the luminosity distribution in magnitude and statistically subtracted the background. Then, we divided the cluster sample in bins of both redshift and richness/mass. We stacked LF counts in each 2D bin for the total, red, and blue galaxy populations; finally, we fitted the stacked LF with a Schechter function and studied the trend of its parameters with redshift and richness/mass. We found a passive evolution with $z$ for the bright part of the LF for the red and total populations and no significant trends for the faint galaxies. The mass/richness dependence is clear for the density parameter $Φ_{\star}$, increasing with richness, and for the total population faint end, which is shallower in the rich clusters.

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arXiv2020

Euclid preparation: IX. EuclidEmulator2 -- Power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations

We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. Percent-level accurate emulation is now supported in the eight-dimensional parameter space of $w_0w_a$CDM$+\sum m_ν$models between redshift $z=0$ and $z=3$ for spatial scales within the range 0.01 $h$/Mpc $\leq k \leq$ 10 $h$/Mpc. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (1) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy and the metric field, (2) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (3) we run over 250 high-resolution simulations with $3000^3$ particles in boxes of 1 (Gpc/$h$)${}^3$ volumes based on paired-and-fixed initial conditions and (4) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter $w_a$ significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors like Halofit, HMCode and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of 1% or better for 0.01 $h$/Mpc $\leq k \leq$ 10 $h$/Mpc and $z\leq3$ compared to high-resolution dark matter only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2 .

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arXiv2020

Euclid preparation: VIII. The Complete Calibration of the Colour-Redshift Relation survey: VLT/KMOS observations and data release

The Complete Calibration of the Colour-Redshift Relation survey (C3R2) is a spectroscopic effort involving ESO and Keck facilities designed to empirically calibrate the galaxy colour-redshift relation - P(z|C) to the Euclid depth (i_AB=24.5) and is intimately linked to upcoming Stage IV dark energy missions based on weak lensing cosmology. The aim is to build a spectroscopic calibration sample that is as representative as possible of the galaxies of the Euclid weak lensing sample. In order to minimise the number of spectroscopic observations to fill the gaps in current knowledge of the P(z|C), self-organising map (SOM) representations of the galaxy colour space have been constructed. Here we present the first results of an ESO@ VLT Large Programme approved in the context of C3R2, which makes use of the two VLT optical and near-infrared multi-object spectrographs, FORS2 and KMOS. This paper focuses on high-quality spectroscopic redshifts of high-z galaxies observed with the KMOS spectrograph in the H- and K-bands. A total of 424 highly-reliable z are measured in the 1.3<=z<=2.5 range, with total success rates of 60.7% in the H-band and 32.8% in the K-band. The newly determined z fill 55% of high and 35% of lower priority empty SOM grid cells. We measured Halpha fluxes in a 1."2 radius aperture from the spectra of the spectroscopically confirmed galaxies and converted them into star formation rates. In addition, we performed an SED fitting analysis on the same sample in order to derive stellar masses, E(B-V), total magnitudes, and SFRs. We combine the results obtained from the spectra with those derived via SED fitting, and we show that the spectroscopic failures come from either weakly star-forming galaxies (at z<1.7, i.e. in the H-band) or low S/N spectra (in the K-band) of z>2 galaxies.

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arXiv2019

Euclid preparation: V. Predicted yield of redshift 7<z<9 quasars from the wide survey

We provide predictions of the yield of $7 8$ may be selected from Euclid $OYJH$ photometry alone, but selection over the redshift interval $7 7.5$ should be found in the DR1 data release, expected in 2024. It will be possible to determine the bright-end slope of the QLF, $7<z<8$, $M_{1450}<-25$, using 8m class telescopes to confirm candidates, but follow-up with JWST or E-ELT will be required to measure the faint-end slope. Contamination of the candidate lists is predicted to be modest even at $J_{AB}\sim23$. The precision with which $k$ can be determined over $7<z<8$ depends on the value of $k$, but assuming $k=-0.72$ it can be measured to a 1 sigma uncertainty of 0.07.

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arXiv2019

Estimating the galaxy two-point correlation function using a split random catalog

The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data-data pair counts to data-random and random-random pair counts, where random-random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random-random pairs, and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.

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arXiv2019

The VIMOS Public Extragalactic Redshift Survey (VIPERS) -- Environment-size relation of massive passive galaxies at 0.5 < z < 0.8

We use the statistics of the VIPERS survey to investigate the relation between the surface mean stellar mass density Sigma=Mstar/(2*pi*Re^2) of massive passive galaxies (MPGs, Mstar>10^11 Msun) and their environment in the redshift range 0.5 2*10^11 Msun, we find an excess of MPGs with low Sigma and a deficit of high-Sigma MPGs in the densest regions wrt other environments. We interpret this result as due to the migration of some high-Sigma MPGs (<1% of the total population of MPGs) into low-Sigma MPGs, probably through mergers or cannibalism of small satellites. In summary, our results imply that the accretion of satellite galaxies has a marginal role in the mass-assembly history of most MPGs. We have previously found that the number density of VIPERS massive star-forming galaxies (MSFGs) declines rapidily from z=0.8 to z=0.5, which mirrors the rapid increase in the number density of MPGs. This indicates that the MSFGs at z>0.8 migrate to the MPG population. Here, we investigate the Sigma-delta relation of MSFGs at z>0.8 and find that it is consistent within 1 sigma with that of low-Sigma MPGs at z<0.8. Thus, the results of this and our previous paper show that MSFGs at z>0.8 are consistent in terms of number and environment with being the progenitors of low-Sigma MPGs at z<0.8.

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arXiv2018

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Unsupervised classification with photometric redshifts: a method to accurately classify large galaxy samples without spectroscopic information

Techniques to classify galaxies solely based on photometry will be necessary for future large cosmology missions, such as Euclid or LSST. However, the precision of classification is always lower in photometric surveys and can be systematically biased with respect to classifications based upon spectroscopic data. We verified how precisely the detailed classification scheme introduced by Siudek et al. (2018, hereafter: S1) for galaxies at z~0.7 could be reproduced if only photometric data are available. We applied the Fisher Expectation-Maximization (FEM) unsupervised clustering algorithm to 54,293 VIPERS galaxies working in a parameter space of reliable photometric redshifts and 12 corresponding rest-frame magnitudes. The FEM algorithm distinguishes four main groups: (1) red, (2) green, (3) blue, and (4) outliers. Each group is further divided into 3, 3, 4, and 2 subclasses, respectively. The accuracy of reproducing galaxy classes using spectroscopic data is high: 92%, 84%, 96% for red, green, and blue classes, respectively, except for dusty star-forming galaxies. The presented verification of the photometric classification demonstrates that large photometric samples can be used to distinguish different galaxy classes at z > 0.5 with an accuracy provided so far only by spectroscopic data except for particular galaxy classes.

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arXiv2018

The VIMOS Public Extragalactic Redshift Survey (VIPERS). The complexity of galaxy populations at 0.4< z<1.3 revealed with unsupervised machine-learning algorithms

Various galaxy classification schemes have been developed so far to constrain the main physical processes regulating evolution of different galaxy types. In the era of a deluge of astrophysical information and recent progress in machine learning, a new approach to galaxy classification becomes imperative. We employ a Fisher Expectation-Maximization unsupervised algorithm working in a parameter space of 12 rest-frame magnitudes and spectroscopic redshift. The model (DBk) and the number of classes (12) were established based on the joint analysis of standard statistical criteria and confirmed by the analysis of the galaxy distribution with respect to a number of classes and their properties. This new approach allows us to classify galaxies based just on their redshifts and UV-NIR spectral energy distributions. The FEM unsupervised algorithm has automatically distinguished 12 classes: 11 classes of VIPERS galaxies and an additional class of broad-line AGNs. After a first broad division into blue, green and red categories we obtained a further sub-division into three red, three green, and five blue galaxy classes. The FEM classes follow the galaxy sequence from the earliest to the latest types that is reflected in their colours (which are constructed from rest-frame magnitudes used in classification procedure) but also their morphological, physical, and spectroscopic properties (not included in the classification scheme). We demonstrate that the members of each class share similar physical and spectral properties. In particular, we are able to find three different classes of red passive galaxy populations. Thus, we demonstrate the potential of an unsupervised approach to galaxy classification and we retrieve the complexity of galaxy populations at z~0.7, a task that usual simpler colour-based approaches cannot fulfil.

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arXiv2018

The XXL Survey XX: The 365 cluster catalogue

In the currently debated context of using clusters of galaxies as cosmological probes, the need for well-defined cluster samples is critical. The XXL Survey has been specifically designed to provide a well characterised sample of some 500 X-ray detected clusters suitable for cosmological studies. The main goal of present article is to make public and describe the properties of the cluster catalogue in its present state, as well as of associated catalogues as super-clusters and fossil groups. We release a sample containing 365 clusters in total. We give the details of the follow-up observations and explain the procedure adopted to validate the cluster spectroscopic redshifts. Considering the whole XXL cluster sample, we have provided two types of selection, both complete in a particular sense: one based on flux-morphology criteria, and an alternative based on the [0.5-2] keV flux within one arcmin of the cluster centre. We have also provided X-ray temperature measurements for 80$\%$ of the clusters having a flux larger than 9$\times$10$^{-15}$$\rm \thinspace erg \, s^{-1} \, cm^{-2}$. Our cluster sample extends from z$\sim$0 to z$\sim$1.2, with one cluster at z$\sim$2. Clusters were identified through a mean number of six spectroscopically confirmed cluster members. Our updated luminosity function and luminosity-temperature relation are compatible with our previous determinations based on the 100 brightest clusters, but show smaller uncertainties. We also present an enlarged list of super-clusters and a sample of 18 possible fossil groups. This intermediate publication is the last before the final release of the complete XXL cluster catalogue when the ongoing C2 cluster spectroscopic follow-up is complete. It provides a unique inventory of medium-mass clusters over a 50~\dd\ area out to z$\sim$1.

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arXiv2018

The VIMOS Public Extragalactic Redshift Survey (VIPERS): Unbiased clustering estimate with VIPERS slit assignment

The VIPERS galaxy survey has measured the clustering of $0.5<z<1.2$ galaxies, enabling a number of measurements of galaxy properties and cosmological redshift-space distortions (RSD). Because the measurements were made using one-pass of the VIMOS instrument on the Very Large Telescope (VLT), the galaxies observed only represent approximately 47\% of the parent target sample, with a distribution imprinted with the pattern of the VIMOS slitmask. Correcting for the effect on clustering has previously been achieved using an approximate approach developed using mock catalogues. Pairwise inverse probability (PIP) weighting has recently been proposed by Bianchi & Percival to correct for missing galaxies, and we apply it to mock VIPERS catalogues to show that it accurately corrects the clustering for the VIMOS effects, matching the clustering measured from the observed sample to that of the parent. We then apply PIP-weighting to the VIPERS data, and fit the resulting monopole and quadrupole moments of the galaxy two-point correlation function with respect to the line-of-sight, making measurements of RSD. The results are close to previous measurements, showing that the previous approximate methods used by the VIPERS team are sufficient given the errors obtained on the RSD parameter.

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arXiv2018

The XXL Survey: XVI. The clustering of X-ray selected galaxy clusters at z~0.3

Galaxy clusters trace the highest density peaks in the large-scale structure of the Universe. Their clustering provides a powerful probe that can be exploited in combination with cluster mass measurements to strengthen the cosmological constraints provided by cluster number counts. We investigate the spatial properties of a homogeneous sample of X-ray selected galaxy clusters from the XXL survey, the largest programme carried out by the XMM-Newton satellite. The measurements are compared to $Λ$-cold dark matter predictions, and used in combination with self-calibrated mass scaling relations to constrain the effective bias of the sample, $b_{eff}$, and the matter density contrast, $Ω_{\rm M}$. We measured the angle-averaged two-point correlation function of the XXL cluster sample. The analysed catalogue consists of $182$ X-ray selected clusters from the XXL second data release, with median redshift $\langle z \rangle=0.317$ and median mass $\langle M_{500} \rangle\simeq1.3\cdot10^{14} M_\odot$. A Markov chain Monte Carlo analysis is performed to extract cosmological constraints using a likelihood function constructed to be independent of the cluster selection function. Modelling the redshift-space clustering in the scale range $10<r\,[$\Mpch$]<40$, we obtain $Ω_{\rm M}=0.27_{-0.04}^{+0.06}$ and $b_{eff}=2.73_{-0.20}^{+0.18}$. This is the first time the two-point correlation function of an X-ray selected cluster catalogue at such relatively high redshifts and low masses has been measured. The XXL cluster clustering appears fully consistent with standard cosmological predictions. The analysis presented in this work demonstrates the feasibility of a cosmological exploitation of the XXL cluster clustering, paving the way for a combined analysis of XXL cluster number counts and clustering.

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arXiv2017

The VIMOS Public Extragalactic Redshift Survey (VIPERS). AGN feedback in [NeV] emitters

Using an unconventional single line diagnostic that unambiguously identifies AGNs in composite galaxies we report statistical differences in the properties (stellar age, [OII] luminosity, colour) between active and inactive galaxies at 0.62<z<1.2 extracted from the VIMOS Public Extragalactic Redshift Survey (VIPERS). The nuclear activity is probed by the high-ionization [NeV] emission line and along with their parent samples, the galaxies are properly selected according to their stellar mass, redshift, and colour distributions. We report younger underlying stellar ages and higher [OII] luminosities of active galaxies in the green valley and in the blue cloud compared to control samples. We observe higher fractions of green galaxies hosting AGN activity at progressively bluer (r-K) colours. Depending on the location of the host galaxy in the NUVrK colour diagram we find higher AGN fractions in massive blue galaxies and in the least massive red galaxies, in agreement with the picture that black holes vary their properties when hosted in either star-forming or passive galaxies. Exactly where the fast quenching processes are expected to play a role, we identify a novel class of active galaxies in the blue cloud with signatures typical for a suddenly suppression of their star formation activity after a burst happening in the recent past. Their optical spectra resemble those of post-starburst galaxies, that would never be identified in a spectroscopic search using classical selection techniques. Broadly, these active galaxies selected on the [NeV] line are not commonly represented in shallow X-ray, mid-IR, or classical line diagnostics. If we consider that our results are limited by the shallow observational limits and rapid AGN variability, the impact of AGN feedback on galaxy formation and evolution may represent an important channel of fast-transiting galaxies moving to the red sequence.

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arXiv2017

The VIMOS Public Extragalactic Redshift Survey (VIPERS): An unbiased estimate of the growth rate of structure at $\mathbf{\left =0.85}$ using the clustering of luminous blue galaxies

We use the VIPERS final data release to investigate the performance of colour-selected populations of galaxies as tracers of linear large-scale motions. We empirically select volume-limited samples of blue and red galaxies as to minimise the systematic error on the estimate of the growth rate $fσ_8$ from the anisotropy of the two-point correlation function. To this end, rather than rigidly splitting the sample into two colour classes we define the red/blue fractional contribution of each object through a weight based on the $(U-V)$ colour distribution. Using mock surveys that are designed to reproduce the observed properties of VIPERS galaxies, we find the systematic error in recovering the fiducial value of $fσ_8$ to be minimized when using a volume-limited sample of luminous blue galaxies. We model non-linear corrections via the Scoccimarro extension of the Kaiser model, finding systematic errors on $fσ_8$ of below $1-2\%$, using scales as small as 5 $h^{-1}\mathrm{Mpc}$. We interpret this result as indicating that selection of luminous blue galaxies maximises the fraction that are central objects in their dark matter haloes; this in turn minimises the contribution to the measured $ξ(r_p,π)$ from the 1-halo term, which is dominated by non-linear motions. The gain is inferior if one uses the full magnitude-limited sample of blue objects, consistent with the presence of a significant fraction of blue, fainter satellites dominated by non-streaming, orbital velocities. We measure a value of $fσ_8=0.45 \pm 0.11$ over the single redshift range $0.6\le z\le 1.0$, corresponding to an effective redshift for the blue galaxies $\left =0.85$. Including in the likelihood the potential extra information contained in the blue-red galaxy cross-correlation function does not lead to an appreciable improvement in the error bars, while it increases the systematic error.

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arXiv2017

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at $0.5 < z < 1.2$

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of $z \simeq 0.8$, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts $z=0.6$ and $z=0.86$. We obtain measurements of $fσ_8(0.6) = 0.48 \pm 0.12$ and $fσ_8(0.86) = 0.48 \pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and $σ_8$ degeneracies, providing direct measurements of $[f(0.6),σ_8(0.6)] = [0.93 \pm 0.22, 0.52 \pm 0.06]$ and $f(0.86),σ_8(0.86)] = [0.99 \pm 0.19, 0.48 \pm 0.04]$. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, $E_G$ , for the first time at $z>0.6$. We find values of $\smash{\overline{E}_G}(0.6) = 0.16 \pm 0.09$ and $\smash{\overline{E}_G}(0.86) = 0.09 \pm 0.07$, when $E_G$ is averaged over scales above $3 h^{-1} \rm{Mpc}$. We find that our $E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a ΛCDM background, although the results are consistent within $1-2σ$.

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arXiv2017

The XXL survey: first results and future

The XXL survey currently covers two 25 sq. deg. patches with XMM observations of ~10ks. We summarise the scientific results associated with the first release of the XXL data set, that occurred mid 2016. We review several arguments for increasing the survey depth to 40 ks during the next decade of XMM operations. X-ray (z<2) cluster, (z<4) AGN and cosmic background survey science will then benefit from an extraordinary data reservoir. This, combined with deep multi-$λ$ observations, will lead to solid standalone cosmological constraints and provide a wealth of information on the formation and evolution of AGN, clusters and the X-ray background. In particular, it will offer a unique opportunity to pinpoint the z>1 cluster density. It will eventually constitute a reference study and an ideal calibration field for the upcoming eROSITA and Euclid missions.

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arXiv2017

The VIMOS Public Extragalactic Redshift Survey (VIPERS). The matter density and baryon fraction from the galaxy power spectrum at redshift $0.6<z<1.1$

We use the final catalogue of the VIMOS Public Extragalactic Redshift Survey (VIPERS) to measure the power spectrum of the galaxy distribution at high redshift, presenting results that extend beyond $z=1$ for the first time. We apply an FFT technique to four independent sub-volumes comprising a total of $51,728$ galaxies at $0.6<z<1.1$ (out of the nearly $90,000$ included in the whole survey). We concentrate here on the shape of the direction-averaged power spectrum in redshift space, explaining the level of modelling of redshift-space anisotropies and the anisotropic survey window function that are needed to deduce this in a robust fashion. We then use covariance matrices derived from a large ensemble of mock datasets in order to fit the spectral data. The results are well matched by a standard $Λ$CDM model, with density parameter $Ω_M h =\smash{0.227^{+0.063}_{-0.050}}$ and baryon fraction $\smash{f_B=Ω_B/Ω_M=0.220^{+0.058}_{-0.072}}$. These inferences from the high-$z$ galaxy distribution are consistent with results from local galaxy surveys, and also with the Cosmic Microwave Background. Thus the $Λ$CDM model gives a good match to cosmic structure at all redshifts so far accessible to observational study.

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