PSCz superclusters: detection, shapes and cosmological implications

We study the possibility of correctly identifying, from the smooth galaxy density field of the PSC z flux-limited catalogue, high-density regions (superclusters) and recovering their true shapes in the presence of a bias introduced by the coupling between the selection function and the constant radius smoothing. We quantify such systematic biases in the smoothed PSC z density field and after applying the necessary corrections we study supercluster multiplicity and morphologies using a differential geometry definition of shape. Our results strongly suggest that filamentary morphology is the dominant feature of PSC z superclusters. Finally, we compare our results with those expected in three different cosmological models and find that the Λ cold dark matter (CDM) model (Ω_Λ=1−Ω_m=0.7) performs better than Ω_m=1 CDM models.     

Sources of contamination to weak lensing tomography: redshift-dependent shear measurement bias

The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape measurement bias on the cosmological interpretation of tomographic two-point weak lensing shear statistics.
We use a set of realistic image simulations produced by the Shear Testing Programme (STEP) collaboration to derive shape measurement bias as a function of redshift. We define biased two-point weak lensing statistics and perform a likelihood analysis for two fiducial surveys. We present a derivation of the covariance matrix for tomography in real space and a fitting formula to calibrate it for non-Gaussianity.
We find the biased aperture mass dispersion is reduced by  ∼20 per cent  at redshift ∼1, and has a shallower scaling with redshift. This effect, if ignored in data analyses, biases σ₈ and w ₀ estimates by a few per cent. The power of tomography is significantly reduced when marginalizing over a range of realistic shape measurement biases. For a Canada-France-Hawaii Telescope Legacy Survey (CFHTLS)-Wide-like survey,  [Ω_m, σ₈]  confidence regions are degraded by a factor of 2, whereas for a Kilo-Degree Survey (KIDS)-like survey the factor is 3.5. Our results are strictly valid only for KSB methods, but they demonstrate the need to marginalize over a redshift-dependent shape measurement bias in all future cosmological analyses.     

Local Group velocity versus gravity: the coherence function

In maximum-likelihood analyses of the Local Group (LG) acceleration, the object describing non-linear effects is the coherence function (CF), i.e. the cross-correlation coefficient of the Fourier modes of the velocity and gravity fields. We study the CF both analytically, using perturbation theory, and numerically, using a hydrodynamic code. The dependence of the function on Ω_m and the shape of the power spectrum is very weak. The only cosmological parameter that the CF is strongly sensitive to is the normalization σ ₈ of the underlying density field. A perturbative approximation for the function turns out to be accurate as long as σ ₈ is smaller than about 0.3. For higher normalizations we provide an analytical fit for the CF as a function of σ ₈ and the wavevector. The characteristic decoherence scale which our formula predicts is an order of magnitude smaller than that determined by Strauss et al. This implies that present likelihood constraints on cosmological parameters from analyses of the LG acceleration are significantly tighter than hitherto reported.     

Measuring Ω0 from the entropy evolution of clusters

In this paper we have extended the entropy-driven model of cluster evolution developed by Bower in order to be able to predict the evolution of galaxy clusters for a range of cosmological scenarios. We have applied this model to recent measurements of the evolution of the L _x− T normalization and X-ray luminosity function in order to place constraints on cosmological parameters. We find that these measurements alone do not select a particular cosmological framework. An additional constraint is required on the effective slope of the power spectrum to break the degeneracy that exists between this and the background cosmology. We therefore include a theoretical calculation of the Ω₀ dependence on the power spectrum, based on the cold dark matter paradigm, which infers Ω₀<0.55 (0.1<Ω₀<0.7 for Ω₀+Λ₀=1), at the 95 per cent confidence level. Alternatively, an independent measurement of the slope of the power spectrum from galaxy clustering requires Ω₀<0.6 (Ω₀<0.65 for Ω₀+Λ₀=1), again to 95 per cent confidence. The rate of entropy evolution is insensitive to the values of Ω₀ considered, although it is sensitive to changes in the distribution of the intracluster medium.     

Determination of cosmology and evolution from K-band magnitude–redshift and number count observations

We determine cosmological and evolutionary parameters from the 3CR K -band Hubble diagram and K -band number counts, assuming that the galaxies in question undergo pure luminosity evolution. Separately the two data sets are highly degenerate with respect to choice of cosmological and evolutionary parameters, but in combination the degeneracy is resolved. Of models that either are flat or have  Ω_Λ=0  , the preferred ones are close to the canonical case  Ω_{cold  matter}=1  ,  Ω_Λ=0  , with luminosity evolution amounting to 1 mag brighter at   z =1  .     

Implications of bias evolution on measurements of the integrated Sachs–Wolfe effect: errors and biases in parameter estimation

The subject of this paper is a quantification of the impact of uncertainties in bias and bias evolution on the interpretation of measurements of the integrated Sachs–Wolfe (ISW) effect, in particular on the estimation of cosmological parameters. We carry out a Fisher matrix analysis for quantifying the degeneracies between the parameters of a dark energy cosmology and bias evolution, for the combination of the PLANCK microwave sky survey with the EUCLID main galaxy sample, where bias evolution   b ( a ) = b ₀+ (1 − a ) b_a   is modelled with two parameters b ₀ and   b_a   . Using a realistic bias model introduces a characteristic suppression of the ISW spectrum on large angular scales, due to the altered distance-weighting functions. The errors in estimating cosmological parameters if the data with evolving bias is interpreted in the framework of cosmologies with constant bias are quantified in an extended Fisher formalism. We find that the best-fitting values of all parameters are shifted by an amount comparable to the statistical accuracy: the estimation bias in units of the statistical accuracy amounts to 1.19 for Ω_m, 0.27 for σ₈ and 0.72 for w for bias evolution with   b_a = 1  . Leaving   b_a   open as a free parameter deteriorates the statistical accuracy, in particular on Ω_m and w .     

Probing quintessence: reconstruction and parameter estimation from supernovae

We explore the prospects for using future supernova observations to probe the dark energy. We focus on quintessence, an evolving scalar field that has been suggested as a candidate for the dark energy. After simulating the observations that would be expected from the proposed SuperNova / Acceleration Probe satellite ( SNAP ), we investigate two methods for extracting information concerning quintessence from such data. First, by expanding the quintessence equation of state as   w _Q ( z ) = w _Q (0) −α ln(1 + z )  , to fit the data, it is possible to reconstruct the quintessence potential for a wide range of smoothly varying potentials. Secondly, it will be possible to test the basic properties of the dark energy by constraining the parameters  Ω _Q , w _Q   and α. We show that it may be possible, for example, to distinguish between quintessence and the cosmological constant in this way. Furthermore, when supernova data are combined with other planned cosmological observations, the precision of reconstructions and parameter constraints is significantly improved, allowing a wider range of dark energy models to be distinguished.     

Constraints on cosmological anisotropy out to z= 1 from Type Ia supernovae

A combined sample of 79 high- and low-redshift Type Ia supernovae (SNe) is used to set constraints on the degree of anisotropy in the Universe out to z ≃1. First, we derive the global most probable values of matter density Ω_M, the cosmological constant Ω_Λ and the Hubble constant H ₀, and find them to be consistent with the published results from the two data sets of Riess et al. and Perlmutter et al. We then examine the Hubble diagram (HD, i.e., the luminosity–redshift relation) in different directions on the sky by utilizing spherical harmonic expansion. In particular, via the analysis of the dipole anisotropy, we divide the sky into the two hemispheres that yield the most discrepant of the three cosmological parameters, and the scatter χ _HD² in each case. The most discrepant values roughly move along the locus −4Ω_M+3Ω_Λ=1 (cf. Perlmutter et al.), but by no more than Δ≈2.5 along this line. For a perfect Friedmann–Robertson–Walker universe, Monte Carlo realizations that mimic the current set of SNe yield values higher than the measured Δ in ∼1/5 of the cases (for Ω_M). We discuss implications for the validity of the Cosmological Principle, and possible calibration problems in the SNe data sets.     

Investigating cosmological weak lensing with the ray-bundle method

Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω₀, λ ₀)=(1.0,0.0)  , the open model with  (Ω₀, λ ₀)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω₀, λ ₀)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H ₀, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ ₈, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.     

The matter power spectrum from the Lyα forest: an optical depth estimate

We measure the matter power spectrum from 31 Lyα spectra spanning the redshift range of 1.6–3.6. The optical depth, τ, for Lyα absorption of the intergalactic medium is obtained from the flux using the inversion method of Nusser & Haehnelt. The optical depth is converted to density by using a simple power-law relation,  τ∝ (1 +δ)^α  . The non-linear 1D power spectrum of the gas density is then inferred with a method that makes simultaneous use of the one- and two-point statistics of the flux and compared against theoretical models with a likelihood analysis. A cold dark matter model with standard cosmological parameters fits the data well. The power-spectrum amplitude is measured to be (assuming a flat Universe),  σ₈= (0.92 ± 0.09) × (Ω_m/0.3)^−0.3  , with α varying in the range of 1.56–1.8 with redshift. Enforcing the same cosmological parameters in all four redshift bins, the likelihood analysis suggests some evolution in the temperature–density relation and the thermal smoothing length of the gas. The inferred evolution is consistent with that expected if reionization of He  ii occurred at   z ∼ 3.2  . A joint analysis with the Wilkinson Microwave Anisotropy Probe results together with a prior on the Hubble constant as suggested by the Hubble Space Telescope key project data, yields values of Ω_m and σ₈ that are consistent with the cosmological concordance model. We also perform a further inversion to obtain the linear 3D power spectrum of the matter density fluctuations.     

Constraints on cosmological and biasing models using active galactic nucleus clustering

We attempt to put constraints on different cosmological and biasing models by combining the recent clustering results of X-ray sources in the local ( z ≤0.1) and distant Universe ( z ∼1) . To this end we compare the measured angular correlation function for bright (Akylas et al.) and faint (Vikhlinin & Forman) ROSAT X-ray sources respectively with those expected in three spatially flat cosmological models. Taking into account the different functional forms of the bias evolution, we find that there are two cosmological models which match the data well. In particular, low-Ω_○ cosmological models (Ω_Λ=1−Ω_○=0.7) that contain either (i) high σ ₈^mass=1.13 value with galaxy merging bias, b ( z )∝(1+ z )^1.8 or (ii) low σ ₈^mass=0.9 with non-bias, b ( z ) ≡ 1 best reproduce the AGN clustering results, while τ CDM models with different bias behaviour are ruled out at a high significance level.     

The distance–redshift equation in quintessence cosmology and the estimation of H0 through time delays

We calculate analytically and numerically the distance–redshift equation in perfect fluid quintessence models and give an accurate fit to the numerical solutions for all the values of the density parameter and the quintessence equation of state. Then we apply our solutions to the estimation of H ₀ from multiple image time delays and find that the inclusion of quintessence modifies significantly the likelihood distribution of H ₀, generally reducing the best estimate with respect to a pure cosmological constant. Marginalizing over the other parameters (Ω _m and the quintessence equation of state) we obtain H ₀=71±6 km s⁻¹ Mpc⁻¹ for an empty beam and H ₀=64±4 km s⁻¹ Mpc⁻¹ for a filled beam. These errors, however, do not take into account the uncertainty on the modelling of the lens. We also discuss the future prospects for distinguishing quintessence from a cosmological constant with time delays.     

Constraints on structure formation models from the Sunyaev–Zel'dovich effect

In the context of cold dark matter (CDM) cosmological models, we have simulated images of the brightness temperature fluctuations in the cosmic microwave background (CMB) sky owing to the Sunyaev–Zel'dovich (S–Z) effect in a cosmological distribution of clusters. We compare the image statistics with recent ATCA limits on arcmin-scale CMB anisotropy. The S–Z effect produces a generically non-Gaussian field and we compute the variance in the simulated temperature-anisotropy images, after convolution with the ATCA beam pattern, for different cosmological models. All the models are normalized to the 4-yr COBE data. We find an increase in the simulated-sky temperature variance with increase in the cosmological density parameter Ω₀. A comparison with the upper limits on the sky variance set by the ATCA appears to rule out our closed-universe model: low-Ω₀ open-universe models are preferred. The result is independent of any present day observations of σ ₈.     

The cluster abundance in cosmic string models for structure formation

We use the present observed number density of large X-ray clusters to constrain the amplitude of matter density perturbations induced by cosmic strings on the scale of 8  h ⁻¹ Mpc ( σ ₈), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of σ ₈ than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of σ ₈ results from the mild non-Gaussianity on cluster scales, where the one-point probability distribution function is well approximated by a χ ² distribution and thus has a longer tail than a Gaussian distribution. We also show that σ ₈ normalized using cluster abundance is consistent with the COBE normalization.     

The location of cosmic microwave background peaks in a universe with dark energy

The locations of the peaks of the cosmic microwave background (CMB) spectrum are sensitive indicators of cosmological parameters, yet there is no known analytic formula which accurately describes their dependence on them. We parametrize the location of the peaks as   l _m = l _A( m - φ _m )  , where l _A is the analytically calculable acoustic scale and m labels the peak number. Fitting formulae for the phase shifts φ _m for the first three peaks and the first trough are given. It is shown that in a wide range of parameter space, the acoustic scale l _A can be retrieved from actual CMB measurements of the first three peaks within 1 per cent accuracy. This can be used to speed up likelihood analysis. We describe how the peak shifts can be used to distinguish between different models of dark energy.     

Empirical distributions of galactic λ spin parameters from the Sloan Digital Sky Survey

Using simple dimensional arguments for both spiral and elliptical galaxies, we present formulae to derive an estimate of the halo spin parameter λ for any real galaxy, in terms of common observational parameters. This allows a rough estimate of λ, which we apply to a large volume-limited sample of galaxies taken from the Sloan Digital Sky Survey data base. The large numbers involved (11 597) allow the derivation of reliable λ distributions, as signal adds up significantly in spite of the errors in the inferences for particular galaxies. We find that if the observed distribution of λ is modelled with a lognormal function, as often done for this distribution in dark matter haloes that appear in cosmological simulations, we obtain parameters  λ₀= 0.04 ± 0.005  and  σ_λ= 0.51 ± 0.05  , interestingly consistent with values derived from simulations. For spirals, we find a good correlation between empirical values of λ and visually assigned Hubble types, highlighting the potential of this physical parameter as an objective classification tool.     

A model of slingshot prominences in rapidly rotating stars

We analyse the spatial clustering properties of the ROSAT All-Sky Survey (RASS) 1 Bright Sample, an X-ray flux-limited catalogue of galaxy clusters selected from the southern part of the survey. The two-point correlation function ( r ) of the whole sample is well fitted (in an Einsteinde Sitter model) by the power law =( r r ₀) , with and (95.4 per cent confidence level with one fitting parameter). We use the RASS 1 Bright Sample as a first application of a theoretical model that aims to predict the clustering properties of X-ray clusters in flux-limited surveys for different cosmological scenarios. The model uses the theoretical and empirical relations between mass, temperature and X-ray cluster luminosity, and fully accounts for the redshift evolution of the underlying dark matter clustering and cluster bias factor. The comparison between observational results and theoretical predictions shows that the Einsteinde Sitter models display too low a correlation length, while models with a matter density parameter _0m=0.3 (with or without a cosmological constant) are successful in reproducing the observed clustering. The dependence of the correlation length r ₀ on the X-ray limiting flux and luminosity of the sample is generally consistent with the predictions of all our models. Quantitative agreement is however only reached for _0m=0.3 models. The model presented here can be reliably applied to future deeper X-ray cluster surveys: the study of the clustering properties will provide a useful complementary tool to the traditional cluster abundance analyses used to constrain the cosmological parameters.     

Spatial clustering of Ultra Steep Spectrum sources and galaxies

We present measurements of the clustering properties of galaxies in the field of redshift range 0.5 ≲ z ≲ 1.5 Ultra Steep Spectrum radio sources selected from the Sydney University Molonglo Sky Survey and the National Radio Astronomy Observatories Very Large Array Sky Survey. Galaxies in these USS fields were identified in deep near-infrared observations, complete down to   K _s= 20  , using the IRIS2 instrument at the Anglo-Australian Telescope. We used the redshift distribution of   K _s < 20  galaxies taken from Cimatti et al. (2002) to constrain the correlation length r ₀. We find a strong correlation signal of galaxies with   K _s < 20  around our USS sample. A comoving correlation length   r ₀= 14.0 ± 2.8  h ⁻¹ Mpc  and γ= 1.98 ± 0.15 are derived in a flat cosmological model universe.
We compare our findings with those obtained in a cosmological N -body simulation populated with galform semi-analytic galaxies. We find that clusters of galaxies with masses in the range   M = 10^13.4–14.2  h ⁻¹ M_⊙  have a cluster–galaxy cross-correlation amplitude comparable to those found between the USS hosts and galaxies. These results suggest that distant radio galaxies are excellent tracers of galaxy overdensities and pinpoint the progenitors of present day rich clusters of galaxies.     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

Constraining quasar host halo masses with the strength of nearby Lyα forest absorption

Using cosmological hydrodynamic simulations, we measure the mean transmitted flux in the Lyα forest for quasar sightlines that pass near a foreground quasar. We find that the trend of absorption with pixel quasar separation distance can be fitted using a simple power-law form including the usual correlation function parameters r ₀ and γ, so that     . From the simulations, we find the relation between r ₀ and quasar host mass, and formulate this as a way to estimate quasar host dark matter halo masses, quantifying uncertainties due to cosmological and IGM parameters, and redshift errors. With this method, we examine data for ∼9000 quasars from the Sloan Digital Sky Survey (SDSS) Data Release 5, assuming that the effect of ionizing radiation from quasars (the so-called transverse proximity effect) is unimportant (no evidence for it is seen in the data). We find that the best-fitting host halo mass for SDSS quasars with mean redshift z = 3 and absolute G -band magnitude −27.5 is  log  M /M_⊙= 12.68^+0.81_−0.67  . We also use the Lyman-Break Galaxy (LBG) and Lyα forest data of Adelberger et al. in a similar fashion to constrain the halo mass of LBGs to be  log₁₀  M /M_⊙= 11.41^+0.54_−0.59  , a factor of ∼20 lower than the bright quasars. In addition, we study the redshift distortions of the Lyα forest around quasars, using the simulations. We use the quadrupole to monopole ratio of the quasar Lyα forest correlation function as a measure of the squashing effect. We find its dependence on halo mass difficult to measure, but find that it may be useful for constraining cosmic geometry.