Cluster Number Counts Research Articles

Impact of systematic errors in Sunyaev–Zel’dovich surveys of galaxy clusters

Future high-resolution microwave background measurements hold the promise of detectinggalaxy clusters throughout our Hubble volume through their Sunyaev–Zel’dovich (SZ)signature, down to a given limiting flux. The number density of galaxy clusters is highlysensitive to cluster mass through fluctuations in the matter power spectrum,as well as redshift through the comoving volume and the growth factor. Thissensitivity in principle allows tight constraints on such quantities as the equation ofstate of dark energy and the neutrino mass. We evaluate the ability of futurecluster surveys to measure these quantities when combined with Planck-like CMBdata. Using a simple effective model for uncertainties in the cluster mass–SZ fluxrelation, we evaluate systematic shifts in cosmological constraints from cluster SZsurveys. We find that a systematic bias of 10% in cluster mass measurements cangive rise to shifts in cosmological parameter estimates at levels larger than the1σ statistical errors. Systematic errors are unlikely to be detected from the massand redshift dependence of cluster number counts alone; increasing survey sizehas only a marginal effect. Implications for upcoming experiments are discussed.

XBootes: An X‐Ray Survey of the NDWFS Bootes Field. II. The X‐Ray Source Catalog

We present results from a Chandra survey of the nine square degree Bootes field of the NOAO Deep Wide-Field Survey (NDWFS). This XBootes survey consists of 126 separate contiguous ACIS-I observations each of approximately 5000 seconds in duration. These unique Chandra observations allow us to search for large scale structure and to calculate X-ray source statistics o ver a wide, contiguous field of view with arcsecond angular resolution and uniform coverage. Optical spectroscopic follow-up observations and the rich NDWFS data set will allow us to identify and classify these X-ray selected sources. Using wavelet decomposition, we detect 4642 point sources with n $\ge$ 2 counts. In order to keep our detections ~99% reliable, we limit our list to sources with n $\ge$ 4 counts. The full 0.5--7 keV band n $\ge$ 4 count list has 3293 point sources. In addition to the point sources, 43 extended sources have been detected consistent, with the depth of these observations and the number counts of clusters. We present here the X-ray catalog for the XBootes survey, including source positions, X-ray fluxes, hardness ratios and their uncertainties. We calculate and present the differential number of sources per flux densit y interval, $N(S)$, for the point sources.

TheXMM-Newton/2dF survey - VIII. The extended X-ray sources

We present a sample of eight extended X-ray sources detected in the wide-field (~2.3 deg^2), bright (2-10 ksec) XMM-Newton/2dF survey, reaching a flux limit of ~2 X 10^{-14} erg/s/cm^2. Of these, seven are identified as secure X-ray clusters in the soft 0.3-2 keV band using a standard wavelet algorithm on either the PN or the MOS images. Spectroscopic or photometric redshifts are available for five clusters, spanning a range between 0.12 and 0.68. The X-ray spectral fittings show temperatures between 1 and 4.6 keV, characteristic of poor clusters and groups of galaxies. We derive for the first time the XMM-Newton cluster number count log N-log S distribution albeit with poor statistics. Both the log N-\log S and the Luminosity-Temperature relation are in good agreement with previous ROSAT results.

Self-calibration of cluster dark energy studies: Observable-mass distribution

The exponential sensitivity of cluster number counts to the properties of the dark energy implies a comparable sensitivity to not only the mean but also the actual_distribution_ of an observable mass proxy given the true cluster mass. For example a 25% scatter in mass can provide a ~50% change in the number counts at z~2 for the upcoming SPT survey. Uncertainty in the scatter of this amount would degrade dark energy constraints to uninteresting levels. Given the shape of the actual mass function, the properties of the distribution may be internally monitored by the shape of the_observable_ mass function. An arbitrary evolution of the scatter of a mass-independent Gaussian distribution may be self-calibrated to allow a measurement of the dark energy equation of state of Delta w ~0.1. External constraints on the mass_variance_ of the distribution that are more accurate than Delta var < 0.01 at z~1 can further improve constraints by up to a factor of 2. More generally, cluster counts and their sample variance measured as a function of the observable provide internal consistency checks on the assumed form of the observable-mass distribution that will protect against misinterpretation of the dark energy constraints.

Clusters of galaxies in the microwave band: Influence of the motion of the Solar System

We consider the changes of the SZ cluster brightness, flux and number counts induced by the motion of the Solar System with respect to the frame defined by the cosmic microwave background (CMB). These changes are connected to the Doppler effect and aberration and exhibit a strong spectral and spatial dependence. The correction to the SZ cluster brightness and flux has an amplitude and spectral dependence, which is similar to the first order cluster peculiar velocity correction to the thermal SZ effect and hence may lead to a ∼10% correction to the kinetic SZ effect. Due to the change in the received cluster CMB flux, the motion of the Solar System induces a dipolar asymmetry in the observed number of clusters above a given flux level. Similar effects were discussed for γ-ray bursts and radio galaxies, but here, due to the very peculiar frequency-dependence of the thermal SZ effect, the number of observed clusters in one direction of the sky can be both decreased or increased depending on the frequency band.

Cosmic Data Fusion

We compare and combine likelihood functions of the cosmological parameters Ωm, h and σ8 from the CMB, type Ia supernovae and from probes of large scale structure. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat ACDM cosmology with a scale-invariant adiabatic initial power spectrum. First we consider three data sets that directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a “biasing” relation: peculiar velocities, CMB and supernovae. We assume a baryonic fraction as inferred from Big-Bang Nucleosynthesis and find that all three data sets agree well, overlapping significantly at the 2σ level. This therefore justifies a joint analysis, in which we find a joint best fit point and 95% confidence limits of Ωm = 0.28 (0.17, 0.39), h = 0.74 (0.64, 0.86), and σ8 = 1.17 (0.98,1.37). Secondly we extend our earlier work on combining CMB, supernovae, cluster number counts, IRAS galaxy redshift survey data to include BOOMERANG and MAXIMA-1 data and to allow a free Ωbh2. We find that, given our assumption of a scale invariant initial power spectrum (n = 1), we obtain the robust result of Ωbh2 = 0.031 ± 0.03, which is dominated by the CMB constraint.

Self-calibration of cluster dark energy studies: Counts in cells

Cluster number counts can constrain the properties of dark energy if and only if the evolution in the relationship between observable quantities and the cluster mass can be calibrated. Next generation surveys with $\ensuremath{\sim}{10}^{4}$ clusters will have sufficient statistics to enable some degree of self-calibration. The excess variance of counts due to the clustering of clusters provides such an opportunity and can be measured from the survey without additional observational cost. It can minimize the degradation in dark energy constraints due to an unknown power-law evolution in the mass-observable relation improving constraints on the dark energy equation of state by a factor of 2 or more to $\ensuremath{\sigma}(w)=0.06$ for a deep $4000{\mathrm{deg}}^{2}$ survey.

S–Z anisotropy and cluster counts: consistent selection of σ8 and the temperature–mass relation

The strong dependence of the mass variance parameter, σ 8, on the adopted cluster mass–temperature relation is explored. A recently compiled X-ray cluster catalog and various mass–temperature relations are used to derive the corresponding values of σ 8. Calculations of the power spectrum of the CMB anisotropy induced by the Sunyaev–Zeldovich effect and cluster number counts are carried out in order to assess the need for a consistent choice of the mass–temperature scaling and the parameter σ 8. We find that the consequences of inconsistent choice of the mass–temperature relation and σ 8 could be quite substantial, including a considerable mis-estimation of the magnitude of the power spectrum and cluster number counts. Our results can partly explain the large scatter between published estimates of the power spectrum and number counts. We also show that the range of values of the power-law index in the scaling C ℓ∼ σ 8 6−7 deduced in previous studies is likely overestimated; we obtain a more moderate dependence, C ℓ∼ σ 8 4.

Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (D_A) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X-ray and/or SZ (Sunyaev-Zel'dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg^2 SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Omega_m can be determined within about 25%, Omega_Lambda within 20%, and w within 16%. We show that combined dN/dz + D_A constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in D_A. We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz + D_A constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut--offs in the range 0.5 < z < 1.

The Effects of Relativistic Corrections on Cosmological Parameter Estimations from Sunyaev‐Zeldovich Effect Cluster Surveys

Sunyaev-Zeldovich effect (SZE) cluster surveys are anticipated to yield tight constraints on cosmological parameters, such as the equation of state of dark energy. In this paper, we study the effect of relativistic corrections of the thermal SZE on the cluster number counts expected from a cosmological model and thus, assuming that other cosmological parameters are known to high accuracies, on the determination of the w-parameter and σ8 from an SZE cluster survey, where w = p/ρ (with p the pressure and ρ the density of dark energy) and σ8 is the rms of the extrapolated linear density fluctuation smoothed over 8 Mpc h-1. For the purpose of illustrating the effects of relativistic corrections, our analyses mainly focus on ν = 353 GHz and Slim = 30 mJy, where ν and Slim are the observing frequency and the flux limit of a survey, respectively. These observing parameters are relevant to the Planck survey. It is found that from two measurable quantities, the total number of SZE clusters and the number of clusters with redshift z ≥ 0.5, σ8 and w can be determined to a level of ±1% and ±8%, respectively, with 1 σ uncertainties from a survey of 10,000 deg2. Relativistic effects are important in determining the central values of σ8 and w. If we choose the two quantities calculated relativistically from the flat cosmological model with σ8 = 0.8284 and w = -0.75 as input, the derived σ8 and w would be 0.819 and -0.81, respectively, if relativistic effects are wrongly neglected. The location of the resulting σ8 and w in the σ8-w plane is outside the 3 σ region around the real central σ8 and w.

Self-consistency and calibration of cluster number count surveys for dark energy

Cluster number counts offer sensitive probes of the dark energy if and only if the_evolution_ of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding consistency in the counts as a function of the observable. In the context of a constant dark energy equation of state, known initial fluctuation amplitude expected from the CMB, universal underlying mass function, and an idealized selection, we find that the ambiguity from the normalization of the mass-observable relationships, or an extrapolation of external mass-observable determinations from higher masses, can be largely eliminated with a sufficiently deep survey, even allowing for an arbitrary evolution. More generally, number counts as a function of both the redshift and the observable enable strong consistency tests on assumptions made in modelling the mass-observable relations and cosmology.

A deep cluster survey in Chandra archival data. First results

I present the first results of a search for clusters of galaxies in Chandra ACIS pointed observations at high galactic latitude with exposure times larger than 10 ks. The survey is being carried out using the Voronoi Tessellation and Percolation technique, which is particularly suited for the detection and accurate quantification of extended and/or low surface brightness emission in X-ray imaging observations. A new catalogue of 36 cluster candidates has been created from 5.55 deg 2 of surveyed area. Five of these candidates have already been associated to visible enhancements of the projected galaxy distribution in low deepness DSS-II fields and are probably low-to moderate redshift systems. Three of the candidates have been identified in previous ROSAT-based surveys. I show that a significative fraction (30-40%) of the candidate clusters are probably intermediate to high redshift systems. In this paper I publish the catalogue of these first candidate clusters. I also derive the number counts of clusters and compare it with the results of deep ROSAT-based cluster surveys.

Expected Number Counts of Radio Galaxy Clusters

Clusters of galaxies may contain radio sources if they still experience successive mergers at present. This has been confirmed by radio observations that about 30% of nearby clusters possess radio halos. We present a theoretical prediction of radio cluster counts using a semi-analytic approach which incorporates the empirical correlation between radio power and dynamical mass of clusters, and the cluster mass function described by the Press-Schechter formalism. The total population of radio clusters over the whole sky and their redshift distribution are given.

Probing dark energy: Methods and strategies

The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3 of the critical density, is very smoothly distributed, and has large negative pressure. Its nature is very much unknown. Most of its discernible consequences follow from its effect on evolution of the expansion rate of the Universe, which in turn affects the growth of density perturbations and the age of the Universe, and can be probed by the classical kinematic cosmological tests. Absent a compelling theoretical model (or even a class of models), we describe the dark energy by an effective equation-of-state w=p_X/\rho_X which is allowed to vary with time. We describe and compare different approaches for determining w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies and clusters, and CMB anisotropy, focusing particular attention on the use of a sample of several thousand type Ia supernova with redshifts z\lesssim 1.7, as might be gathered by the proposed SNAP satellite. Among other things, we derive optimal strategies for constraining cosmological parameters using type Ia supernovae. While in the near term CMB anisotropy will provide the first measurements of w, supernovae and number counts appear to have the most potential to probe dark energy.

The ROSAT-ESO flux limited X-ray (REFLEX) galaxy cluster survey. I. The construction of the cluster sample

We discuss the construction of an X-ray flux-limited sample of galaxy clusters, the REFLEX survey catalogue, to be used for cosmological studies. This cluster identification and redshift survey was conducted in the frame of an ESO key programme and is based on candidates selected from the southern part of the ROSAT All-Sky Survey (RASS). For the first cluster candidate selection from a flux-limited RASS source list, we make use of optical data from the COSMOS digital catalogue produced from the scans of the UK-Schmidt plates. To ensure homogeneity of the sample construction process, this selection is based only on this one well-defined optical data base. The nature of the candidates selected in this process is subsequently checked by a more detailed evaluation of the X-ray and optical source properties and available literature data. The final identification and the redshift is then based on optical spectroscopic follow-up observations. In this paper we document the process by which the primary cluster candidate catalogue is constructed prior to the optical follow-up observations. We describe the reanalysis of the RASS source catalogue which enables us to impose a proper flux limit cut to the X-ray source list without introducing a severe bias against extended sources. We discuss the correlation of the X-ray and optical (COSMOS) data to find galaxy density enhancements at the RASS X-ray source positions and the further evaluation of the nature of these cluster candidates. Based also on the results of the follow-up observations we provide a statistical analysis of the completeness and contamination of the final cluster sample and show results on the cluster number counts. The final sample of identified X-ray clusters reaches a flux limit of 3 10-12 erg s-1 cm-2 in the 0.1-2.4 keV band and comprises 452 clusters in an area of 4.24 ster. The results imply a completeness of the REFLEX cluster sample well in excess of 90% . We also derive for the first time an upper limit of less than 9% for the number of clusters which may feature a dominant contribution to the X-ray emission from AGN. This accuracy is sufficient for the use of this cluster sample for cosmological tests.

The Northern ROSAT All‐Sky (NORAS) Galaxy Cluster Survey. I. X‐Ray Properties of Clusters Detected as Extended X‐Ray Sources

In the construction of an X-ray-selected sample of galaxy clusters for cosmological studies, we have assembled a sample of 495 X-ray sources found to show extended X-ray emission in the first processing of the ROSAT All-Sky Survey. The sample covers the celestial region with declination ? ? 0? and Galactic latitude |bII| ? 20? and comprises sources with a count rate ?0.06 counts s-1 and a source extent likelihood of L ? 7. In an optical follow-up identification program we find 378 (76%) of these sources to be clusters of galaxies.?????It was necessary to reanalyze the sources in this sample with a new X-ray source characterization technique to provide more precise values for the X-ray flux and source extent than obtained from the standard processing. This new method, termed growth curve analysis (GCA), has the advantage over previous methods in its ability to be robust, to be easy to model and to integrate into simulations, to provide diagnostic plots for visual inspection, and to make extensive use of the X-ray data. The source parameters obtained assist the source identification and provide more precise X-ray fluxes. This reanalysis is based on data from the more recent second processing of the ROSAT Survey. We present a catalog of the cluster sources with the X-ray properties obtained as well as a list of the previously flagged extended sources that are found to have a noncluster counterpart. We discuss the process of source identification from the combination of optical and X-ray data.?????To investigate the overall completeness of the cluster sample as a function of the X-ray flux limit, we extend the search for X-ray cluster sources to the data of the second processing of the ROSAT Survey for the northern sky region between 9h and 14h in right ascension. We include the search for X-ray emission of known clusters as well as a new investigation of extended X-ray sources. In the course of this search we find X-ray emission from 85 additional Abell clusters and 56 very probable cluster candidates among the newly found extended sources. A comparison of the X-ray cluster number counts of the NORAS sample with the ROSAT-ESO Flux-limited X-Ray (REFLEX) Cluster Survey results leads to an estimate of the completeness of the NORAS sample of ROSAT All-Sky Survey (RASS) I extended clusters of about 50% at an X-ray flux of FX(0.1-2.4 keV) = 3 ? 10-12 ergs s-1 cm-2. The estimated completeness achieved by adding the supplementary sample in the study area amounts to about 82% in comparison to REFLEX. The low completeness introduces an uncertainty in the use of the sample for cosmological statistical studies that will be cured with the completion of the continuing Northern ROSAT All-Sky (NORAS) Cluster Survey project.

Cosmological implications of galaxy clusters in X-ray, millimeter, and submillimeter bands

Cosmological implications of clusters of galaxies are discussed with particular attention to their importance in probing the cosmological parameters. More specifically we compute the number counts of clusters of galaxies, Log N -Log S relation, in X-ray and submm bands on the basis of the Press-Schechter theory. As an important step toward breaking the degeneracy among the viable cosmological models, we observed the most luminous X-ray cluster RXJ1347-1145 in three bands (21 and 43 GHz in the Nobeyama Radio Observatory, Japan, and 350 GHz in the J. C. Maxwell telescope at Mauna Kea, Hawaii). We report on the preliminary results which are in good agreement with the profile of the Sunayev - Zel'dovich effect predicted on the basis of the previous X-ray observation of the cluster.

Number Counts of Clusters of Galaxies in X-ray and Submm Bands

We compute the number counts of clusters of galaxies, the logN-logS relation, in several X-ray and submm bands on the basis of the Press—Schechter theory (Kitayama et al. 1998). We pay particular attention to a set of theoretical models which well reproduce the ROSAT 0.5–2 keV band logN-logS (Ebeling et al. 1997; Rosati et al. 1997), and explore possibilities to further constrain the models from future observations with ASCA and/or at submm bands. The latter is closely related to the European PLANCK mission and the Japanese LMSA project. We exhibit that one can break the degeneracy in an acceptable parameter region on the Ω0–σ8 plane by combining the ROSAT logN-logS and the submm number counts. Models which reproduce the ROSAT band logN-logS will have N(&gt; S) ∼ (150–300)(S/10−12 erg cm−2 s−) −1.3 str−1 at S ≳ 10−12 erg cm−2 s−1 in the ASCA 2–10 keV band, and N(&gt; Sv) ∼ (102–104)(Sv/100 mJy)−1.5 str−1 at Sv ≳ 100m J y in the submm (0.85mm) band. The amplitude of the logN-logS is very sensitive to the model parameters in the submm band. We also compute the redshift evolution of the cluster number counts and compare with that of the X-ray brightest Abell-type clusters (Ebeling et al. 1996). The results, although still preliminary, point to low density (Ω0 ∼ 0.3) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT logN-logS.

Cosmological Implications of Number Counts of Clusters of Galaxies: log N–log S in X-Ray and Submm Bands

We have computed the number counts of clusters of galaxies, the log N–log S relations, in X-ray and submm bands based on the Press-Schechter theory. We paid particular attention to a set of theoretical models which well reproduce the ROSAT soft X-ray log N–log S, and explored possibilities to further constrain the models from future observations in hard X-ray and submm bands. The former is closely related to the ASCA, AXAF, and Astro-E missions, while the latter to the PLANCK and LMSA projects. We have shown that one can break the degeneracy in an acceptable parameter region on the Ω0–σ8 plane by combining the X-ray and submm number counts. Models which reproduce the ROSAT 0.5–2 keV band log N–log S will have N(&amp;gt; S) ∼ (150–300)(S/10−12 erg cm−2 s−1)−1.3 str−1 at S ≳ 10−12 erg cm−2 s−1 in the 2–10 keV band, and N(&amp;gt; Sv) ∼ (102–104)(Sv/100 mJy)−1.5 str−1 at Sv ≳ 100 mJy in the submm (0.85 mm) band. The amplitude of log N–log S is very sensitive to the model parameters in the submm band. We also computed the redshift evolution of the cluster number counts and compared it with that of the X-ray brightest Abell-type clusters. The results, although still preliminary, point to low density (Ω0 ∼ 0.3) universes. The contribution of clusters to the X-ray and submm background radiations is shown to be insignificant in any model compatible with the ROSAT log N–log S relation.

Results from the ROSAT Deep Cluster Survey

AbstractDeep X‐ray surveys of galaxy clusters covering large solid angles offer ideal samples for studying the evolution of the large scale structure in the Universe. I review here some recent results from the ROSAT Deep Cluster Survey (RDCS), particularly, on the study of the evolution of the abundance of galaxy clusters over a large redshift range. The optical identification of RDCS sources have revealed a significant fraction of clusters at &gt;z &gt; 0.5. The observed X‐ray Luminosity Function out to z ⋍ 0.8 and the faint cluster number counts from the RDCS, when combined with previous results of the Einstein Extended Medium Sensitivity Survey, provide a much improved observational picture of the evolution of clusters in the X‐ray band, revealing a slowly evolving population of galaxy clusters since at least z ⋍ 0.8. The theoretical interpretation of these findings in the framework of theories of structure formation will still be subject of much debate in the years to come. The construction of large samples of clusters out to z ∽ 1 and beyond appears to be a challenging task even with the next generation of X‐ray satellites (AXAF, XMM).