arXiv subjects

G. Chon

Publications and source records attributed to G. Chon.

At least 37 records · Page 2Linked to original sources

arXiv2024

Euclid preparation. Exploring the properties of proto-clusters in the Simulated Euclid Wide Survey

Galaxy proto-clusters are receiving an increased interest since most of the processes shaping the structure of clusters of galaxies and their galaxy population are happening at early stages of their formation. The Euclid Survey will provide a unique opportunity to discover a large number of proto-clusters over a large fraction of the sky (14 500 square degrees). In this paper, we explore the expected observational properties of proto-clusters in the Euclid Wide Survey by means of theoretical models and simulations. We provide an overview of the predicted proto-cluster extent, galaxy density profiles, mass-richness relations, abundance, and sky-filling as a function of redshift. Useful analytical approximations for the functions of these properties are provided. The focus is on the redshift range z= 1.5 to 4. We discuss in particular the density contrast with which proto-clusters can be observed against the background in the galaxy distribution if photometric galaxy redshifts are used as supplied by the ESA Euclid mission together with the ground-based photometric surveys. We show that the obtainable detection significance is sufficient to find large numbers of interesting proto-cluster candidates. For quantitative studies, additional spectroscopic follow-up is required to confirm the proto-clusters and establish their richness.

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arXiv2024

A detailed study of the very-high-energy Crab pulsar emission with the LST-1

Context: There are currently three pulsars firmly detected by imaging atmospheric Cherenkov telescopes (IACTs), two of them reaching TeV energies, challenging models of very-high-energy (VHE) emission in pulsars. More precise observations are needed to better characterize pulsar emission at these energies. The LST-1 is the prototype of the Large-Sized Telescope, that will be part of the Cherenkov Telescope Array Observatory (CTAO). Its improved performance over previous IACTs makes it well suited for studying pulsars. Aims: To study the Crab pulsar emission with the LST-1, improving and complementing the results from other telescopes. These observations can also be used to characterize the potential of the LST-1 to study other pulsars and detect new ones. Methods: We analyzed a total of $\sim$103 hours of gamma-ray observations of the Crab pulsar conducted with the LST-1 in the period from September 2020 to January 2023. The observations were carried out at zenith angles less than 50 degrees. A new analysis of the Fermi-LAT data was also performed, including $\sim$14 years of observations. Results: The Crab pulsar phaseogram, long-term light-curve, and phase-resolved spectra are reconstructed with the LST-1 from 20 GeV to 450 GeV for P1 and up to 700 GeV for P2. The pulsed emission is detected with a significance of 15.2$σ$. The two characteristic emission peaks of the Crab pulsar are clearly detected (>10$σ$), as well as the so-called bridge emission (5.7$σ$). We find that both peaks are well described by power laws, with spectral indices of $\sim$3.44 and $\sim$3.03 respectively. The joint analysis of Fermi-LAT and LST-1 data shows a good agreement between both instruments in the overlapping energy range. The detailed results obtained in the first observations of the Crab pulsar with LST-1 show the potential that CTAO will have to study this type of sources.

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arXiv2023

RXCJ1111.6+4050 galaxy cluster: the observational evidence of a transitional fossil group

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 TNG 3.5m telescope 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 $644 \pm 56$ km/s and $410 \pm 123$ km/s, which yield dynamical masses of M$_{200}$=$1.9 \pm 0.4 \times10^{14}$ M$_{\odot}$ and $0.6 \pm 0.4 \times 10^{14}$ M$_{\odot}$ for the main system and substructure, respectively. RXCJ1111 presents an elongation in the North-South direction and a gradient of 250-350 km/s/Mpc in the velocity field, 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 $Δm_{12} \ge 1.8$, so it fits the "fossil-like" definition of a galaxy group. Mass estimates derived from X-ray and optical are in good agreement when two galaxy components are considered separately. 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 almost aligned with the line-of-sight. This merging model would explain the slight increase found in the T$_X$ 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.

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arXiv2023

More relaxed intracluster gas than galaxies in clusters in quasi-equilibrium

During cluster mergers, the intracluster gas and member galaxies undergo dynamic evolution, but at different timescales and reach different states. We collect 24 galaxy clusters in quasi-equilibrium state as indicated by the X-ray image, and calculate the cluster orientations and three kinds of dynamical parameters, i.e., the normalized centroid offset, the sphere index and the ellipticity, for these clusters from the distributions of member galaxies and also the intracluster gas. We find consistent alignments for the orientations estimated from the two components. However, the three kinds of dynamical parameters indicated by member galaxies are systematically larger than those derived from the gas component, suggesting that the gas component is more relaxed than member galaxies. Differences of dynamical features between the intracluster gas and member galaxies are independent of cluster mass and concentration. We conclude that the intracluster gas reaches the dynamic equilibrium state earlier than the almost collisionless member galaxies.

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arXiv2022

XMM-Newton study of six massive, X-ray luminous galaxy clusters systems in the redshift range z = 0.25 to 0.5

Massive galaxy clusters are interesting astrophysical and cosmological study objects, but are relatively rare. In the redshift range z = 0.25 to 0.5 which is, for example, a favourable region for gravitational lensing studies, about 100 such systems are known. Most of them have been studied in X-rays. In this paper we study the six remaining massive clusters in this redshift interval in the highly complete CLASSIX survey which have so far not been observed with sufficiently deep exposures in X-rays. With data from our new XMM-Newton observations we characterise their structures, derive X-ray properties such as the X-ray luminosity and intra-cluster medium temperature and estimate their gas and total masses. We find that one cluster, RXCJ1230.7+3439, is dynamically young with three distinct substructures in the cluster outskirts and RXCJ1310.9+2157/RXCJ1310.4+2151 is a double cluster system. Mass determination is difficult in the systems with substructure. We therefore discuss several methods of mass estimation including scaling relations. In summary we find that five of the six study targets are indeed massive clusters as expected, while the last cluster RXCJ2116.2-0309 is a close projection of a distant and a nearby cluster which has led to a previous overestimation of its mass. In the XMM-Newton observation fields we also find three low redshift clusters close to the targets which are also analysed and described here. In the field of RXCJ2116.2-0309 we discover serendipitously a highly variable X-ray source which has decreased its flux within a year by more than a factor of eight. This source is most probably an AGN.

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arXiv2022

The dynamical state of RXCJ1230.7+3439: a multi-substructured merging galaxy cluster

We analyse the kinematical and dynamical state of the galaxy cluster RXCJ1230.7+3439, at z=0.332, using 93 new spectroscopic redshifts of galaxies acquired at the 3.6m TNG telescope and from SDSS DR16 public data. We find that RXCJ1230 appears as a clearly isolated peak in the redshift space, with a global line-of-sight velocity dispersion of $1004_{-122}^{+147}$ km s$^{-1}$, and showing a very complex structure with the presence of three subclusters. Our analyses confirm that the three substructures detected are in a pre-merger phase, where the main interaction takes place with the south-west subclump. We compute a velocity dispersion of $σ_\textrm{v} \sim 1000$ and $σ_\textrm{v} \sim 800$ km s$^{-1}$ for the main cluster and the south-west substructure, respectively. The central main body and south-west substructure differ by $\sim 870$ km s$^{-1}$ in the LOS velocity. From these data, we estimate a dynamical mass of $M_{200}= 9.0 \pm 1.5 \times 10^{14}$ M$_{\odot}$ and $4.4 \pm 3.3 \times 10^{14}$ M$_{\odot}$ for the RXCJ1230 main body and south-west clump, respectively, which reveals that the cluster will suffer a merging characterized by a 2:1 mass ratio impact. We solve a two-body problem for this interaction and find that the most likely solution suggests that the merging axis lies almost contained in the plane of the sky and the subcluster will fully interact in $\sim0.3$ Gyr. The comparison between the dynamical masses and those derived from X-ray data reveals a good agreement within errors (differences $\sim 15$\%), which suggests that the innermost regions ($<r_{500}$) of the galaxy clumps are almost in hydrostatical equilibrium. To summarize, RXCJ1230 is a young but also massive cluster in a pre-merging phase accreeting other galaxy systems from its environment.

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arXiv2020

Optical validation and characterisation of Planck PSZ1 sources at the Canary Islands observatories. II. Second year of ITP13 observations

We report new galaxy clusters previously unknown included in the PSZ1 catalogue. The results here presented have been achieved during the second year of a 2-year observational programme, the ITP13, developed at the Roque de los Muchachos Observatory (La Palma, Spain). We characterise 75 SZ sources with low SZ significance, SZ S/N$<5.32$ by performing deep optical imaging and spectroscopy in order to associate actual galaxy clusters to the SZ Planck source. We adopt robust criteria, based on the 2D-spatial distribution, richness and velocity dispersions to confirm actual optical counterparts up to $z<0.85$. At the end of the ITP13 observational programme, we study 256 SZ sources with $Dec \geq -15^{\circ}$ (212 of them completely unknown), finding optical counterparts for 152 SZ sources. The ITP13 validation programme has allowed us to update the PSZ1 purity, which is now more refined, increasing from 72\% to 83\% in the low SZ S/N regime. Our results are consistent with the predicted purity curve for the full PSZ1 catalogue and with the expected fraction of false detections caused by the non-Gaussian noise of foreground signals. Indeed, we find a strong correlation between the number of unconfirmed sources and the thermal emission of diffuse galactic dust at 857 GHz, thus increasing the fraction of false Planck SZ detections at low galactic latitudes.

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arXiv2018

Optical validation and characterization of Planck PSZ1 sources at the Canary Islands observatories. I. First year of ITP13 observations

We identify new clusters and characterize previously unknown Planck Sunyaev-Zeldovich (SZ) sources from the first Planck catalogue of SZ sources (PSZ1). The results presented here correspond to an optical follow-up observational programme developed during approximately one year (2014) at Roque de los Muchachos Observatory, using the 2.5m Isaac Newton telescope, the 3.5m Telescopio Nazionale Galileo, the 4.2m William Herschel telescope and the 10.4m Gran Telescopio Canarias. We characterize 115 new PSZ1 sources using deep optical imaging and spectroscopy. We adopt robust criteria in order to consolidate the SZ counterparts by analysing the optical richness, the 2D galaxy distribution, and velocity dispersions of clusters. Confirmed counterparts are considered to be validated if they are rich structures, well aligned with the Planck PSZ1 coordinate and show relatively high velocity dispersion. Following this classification, we confirm 53 clusters, which means that 46% of this PSZ1 subsample has been validated and characterized with this technique. Sixty-two SZ sources (54% of this PSZ1 subset) remain unconfirmed. In addition, we find that the fraction of unconfirmed clusters close to the galactic plane (at |b|<25deg) is greater than that at higher galactic latitudes (|b|>25deg), which indicates contamination produced by radio emission of galactic dust and gas clouds on these SZ detections. In fact, in the majority of the cases, we detect important galactic cirrus in the optical images, mainly in the SZ target located at low galactic latitudes, which supports this hypothesis.

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arXiv2017

Comparison of hydrostatic and dynamical masses of distant X-ray luminous galaxy clusters

The main goal of this work is to compare the results of three dynamical mass estimators to the X-ray hydrostatic values, focussing on massive galaxy clusters at intermediate redshifts $z\sim0.3$. We estimated dynamical masses with the virial theorem, the Jeans equation, and the caustic method using wide-field VIMOS spectroscopy. We investigated the role of colour selection and the impact of substructures on the dynamical estimators. The Jeans and caustic methods give consistent results, whereas the virial theorem leads to masses $\sim15\%$ larger. The Jeans, caustic, and virial masses are respectively $\sim20\%$, $\sim30\%$, and $\sim50\%$ larger than the hydrostatic values. Large scatters of $\gtrsim50\%$ are mainly due to the two outliers RXCJ0014 and RXCJ1347; excluding the latter increases the mass ratios by $\sim10\%$, giving a fractional mass bias significant at $\gtrsim2σ$. We found a correlation between the dynamical-to-hydrostatic mass ratio and two substructure indicators, suggesting a bias in the dynamical measurements. The velocity dispersions of blue galaxies are $\sim15\%$ ($\sim25\%$ after removing the substructures) larger than that of the red-sequence galaxies; using the latter leads to dynamical masses $\sim10\%-15\%$ smaller. Discarding the galaxies part of substructures reduces the masses by $\sim15\%$; the effect is larger for the more massive clusters, owing to a higher level of substructures. After the substructure analysis, the dynamical masses are in perfect agreement with the hydrostatic values and the scatters around the mean ratios are divided by $\sim2$.

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arXiv2017

From the core to the outskirts: structure analysis of three massive galaxy clusters

The hierarchical model of structure formation is a key prediction of the Lambda cold dark matter model, which can be tested by studying the large-scale environment and the substructure content of massive galaxy clusters. We present here a detailed analysis of the clusters RXCJ0225.9-4154, RXCJ0528.9-3927, and RXCJ2308.3-0211, as part of a sample of massive X-ray luminous clusters located at intermediate redshifts. We used a multiwavelength analysis, combining WFI photometric observations, VIMOS spectroscopy, and the X-ray surface brightness maps. We investigated the optical morphology of the clusters, we looked for significant counterparts in the residual X-ray emission, and we ran several tests to assess their dynamical state. We correlated the results to define various substructure features, to study their properties, and to quantify their influence on simple dynamical mass estimators. RXCJ0225 has a bimodal core, and two massive galaxy groups are located in its immediate surroundings; they are aligned in an elongated structure that is also detected in X-rays. RXCJ0528 is located in a poor environment; an X-ray centroid shift and the presence of two central BCGs provide mild evidence for a recent and active dynamical history. RXCJ2308 has complex central dynamics, and it is found at the core of a superstes-cluster. The complexity of the cluster's central dynamics reflects the richness of its large-scale environment: RXCJ0225 and RXCJ2308 present a mass fraction in substructures larger than the typical 0.05-0.15, whereas the isolated cluster RXCJ0528 does not have any major substructures within its virial radius. The largest substructures are found in the cluster outskirts. The optical morphology of the clusters correlates with the orientation of their BCG, and with the position of the main axes of accretion.

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arXiv2016

Planck Intermediate Results. XXXVI. Optical identification and redshifts of Planck SZ sources with telescopes in the Canary Islands Observatories

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).

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arXiv2015

Comparison of Sunyaev-Zel'dovich measurements from Planck and from the Arcminute Microkelvin Imager for 99 galaxy clusters

We present observations and analysis of a sample of 123 galaxy clusters from the 2013 Planck catalogue of Sunyaev-Zel'dovich sources with the Arcminute Microkelvin Imager (AMI), a ground-based radio interferometer. AMI provides an independent measurement with higher angular resolution, 3 arcmin compared to the Planck beams of 5-10 arcmin. The AMI observations thus provide validation of the cluster detections, improved positional estimates, and a consistency check on the fitted 'size' ($θ_{s}$) and 'flux' ($Y_{\rm tot}$) parameters in the Generalised Navarro, Frenk and White (GNFW) model. We detect 99 of the clusters. We use the AMI positional estimates to check the positional estimates and error-bars produced by the Planck algorithms PowellSnakes and MMF3. We find that $Y_{\rm tot}$ values as measured by AMI are biased downwards with respect to the Planck constraints, especially for high Planck-SNR clusters. We perform simulations to show that this can be explained by deviation from the 'universal' pressure profile shape used to model the clusters. We show that AMI data can constrain the $α$ and $β$ parameters describing the shape of the profile in the GNFW model for individual clusters provided careful attention is paid to the degeneracies between parameters, but one requires information on a wider range of angular scales than are present in AMI data alone to correctly constrain all parameters simultaneously.

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arXiv2015

Planck 2015 results. XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources

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 all-sky catalogue 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 > $10^3$ 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 Y5R500 estimates are robust to pressure-profile 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.

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arXiv2015

Planck 2013 results. XXIX. The Planck catalogue of Sunyaev-Zeldovich sources: Addendum

We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from Sunyaev-Zeldovich (SZ) effect detections using the first 15.5 months of Planck satellite observations. Addendum. We deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planck-discovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through follow-up observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (~80.6%) are spectroscopic, and associated mass estimates derived from the Y_z mass proxy. We also provide a new SZ quality flag, derived from a novel artificial neural network classification of the SZ signal, for the remaining 280 candidates. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections.

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arXiv2014

Planck intermediate results. XXVI. Optical identification and redshifts of Planck clusters with the RTT150 telescope

We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with the Russian-Turkish 1.5-m telescope (RTT150), as a part of the optical follow-up programme undertaken by the Planck collaboration. During this time period approximately 20% of all dark and grey clear time available at the telescope was devoted to observations of Planck objects. Some observations of distant clusters were also done at the 6-m Bolshoy Telescope Azimutal'ny (BTA) of the Special Astrophysical Observatory of the Russian Academy of Sciences. In total, deep, direct images of more than one hundred fields were obtained in multiple filters. We identified 47 previously unknown galaxy clusters, 41 of which are included in the Planck catalogue of SZ sources. The redshifts of 65 Planck clusters were measured spectroscopically and 14 more were measured photometrically. We discuss the details of cluster optical identifications and redshift measurements. We also present new spectroscopic redhifts for 39 Planck clusters that were not included in the Planck SZ source catalogue and are published here for the first time.

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arXiv2014

Planck 2013 results. I. Overview of products and scientific results

The ESA's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the CMB and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the SZ effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter LCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25 sigma. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations derived from CMB data and that derived from SZ data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak.

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arXiv2014

Planck intermediate results. XIII. Constraints on peculiar velocities

Using \Planck\ data combined with the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we address the study of peculiar motions by searching for evidence of the kinetic Sunyaev-Zeldovich effect (kSZ). By implementing various filters designed to extract the kSZ generated at the positions of the clusters, we obtain consistent constraints on the radial peculiar velocity average, root mean square (rms), and local bulk flow amplitude at different depths. For the whole cluster sample of average redshift 0.18, the measured average radial peculiar velocity with respect to the cosmic microwave background (CMB) radiation at that redshift, i.e., the kSZ monopole, amounts to $72 \pm 60$ km s$^{-1}$. This constitutes less than 1% of the relative Hubble velocity of the cluster sample with respect to our local CMB frame. While the linear $Λ$CDM prediction for the typical cluster radial velocity rms at $z=0.15$ is close to 230km s$^{-1}$, the upper limit imposed by \Planck\ data on the cluster subsample corresponds to 800 km s$^{-1}$ at 95% confidence level, i.e., about three times higher. \Planck\ data also set strong constraints on the local bulk flow in volumes centred on the Local Group. There is no detection of bulk flow as measured in any comoving sphere extending to the maximum redshift covered by the cluster sample. A blind search for bulk flows in this sample has an upper limit of 254 km s$^{-1}$ (95% confidence level) dominated by CMB confusion and instrumental noise, indicating that the Universe is largely homogeneous on Gpc scales. In this context, in conjunction with supernova observations, \Planck\ is able to rule out a large class of inhomogeneous void models as alternatives to dark energy or modified gravity. The \Planck\ constraints on peculiar velocities and bulk flows are thus consistent with the $Λ$CDM scenario.

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arXiv2014

Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts

We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev--Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass $M$ and SZ signal $Y$ calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude $σ_8$ and matter density parameter $Ω_{\mathrm{m}}$ in a flat $Λ$CDM model. We test the robustness of our estimates and find that possible biases in the $Y$--$M$ relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that $σ_8=0.75\pm 0.03$, $Ω_{\mathrm{m}}=0.29\pm 0.02$, and $σ_8(Ω_{\mathrm{m}}/0.27)^{0.3} = 0.764 \pm 0.025$. The value of $σ_8$ is degenerate with the mass bias; if the latter is fixed to a value of 20% we find $σ_8(Ω_{\mathrm{m}}/0.27)^{0.3}=0.78\pm 0.01$ and a tighter one-dimensional range $σ_8=0.77\pm 0.02$. We find that the larger values of $σ_8$ and $Ω_{\mathrm{m}}$ preferred by Planck's measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the $Λ$CDM model, such as a component of massive neutrinos (abridged).

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