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.     

Maximum likelihood estimates of the two- and three-dimensional power spectra of the APM Galaxy Survey

We estimate the two- and three-dimensional power spectra, P ₂( K ) and P ₃( k ), of the galaxy distribution by applying a maximum likelihood estimator to pixel maps of the APM Galaxy Survey. The analysis provides optimal estimates of the power spectra and of their covariance matrices if the fluctuations are assumed to be Gaussian. Our estimates of P ₂( K ) and P ₃( k ) are in good agreement with previous work, but we find that the errors at low wavenumbers have been underestimated in some earlier studies. If the galaxy power spectrum is assumed to have the same shape as the mass power spectrum, then the APM maximum likelihood P ₃( k ) estimates at k ≤0.19  h  Mpc⁻¹ constrain the amplitude and shape parameter of a scale-invariant CDM model to lie within the 2 σ ranges 0.74≤( σ ₈)_g≤1.28 and 0.06≤Γ≤0.46 . Using the Galactic extinction estimates of Schlegel, Finkbeiner & Davis, we show that Galactic obscuration has a negligible effect on galaxy clustering over most of the area of the APM Galaxy Survey.     

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 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 real- and redshift-space density distribution functions for large-scale structure in the spherical collapse approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the p -order hierarchical amplitudes S _p , in both real and redshift space. We compare our results with numerical simulations, focusing on the     standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for     , where σ _L is the linearly evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for     . Numerical simulations also yield a simple empirical relation between the real-space PDF and the redshift-space PDF: we find that for     , the redshift-space PDF, [ P δ _{( z )}], is, to a good approximation, a simple rescaling of the real-space PDF, P [ δ ], i.e.,     where σ and σ _{( z )} are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the ΛCDM model. It breaks down for SCDM at     , but provides a good fit to the ΛCDM models for σ _L as large as 0.8.     

Study of corrections to the dust model via perturbation theory

This work reports on the application of the Eulerian perturbation theory to a recently proposed model of cosmological structure formation by gravitational instability. Its physical meaning is discussed in detail and put in perspective of previous works. The model incorporates in a systematic fashion corrections to the popular dust model owing to multistreaming and, more generally, the small-scale, virialized degrees of freedom. It features a time-dependent length-scale L ( t ) estimated to be   L / r ₀10^-1  [ r ₀( t ) is the non-linear scale, at which   ²=1]  . The model provides a new angle on the dust model and allows us to overcome some of its limitations. Thus, the scale L ( t ) works as a physically meaningful short-distance cut-off for the divergences appearing in the perturbation expansion of the dust model when there is too much initial power on small scales. The model also incorporates the generation of vorticity by tidal forces; according to the perturbational result, the filtered vorticity for standard cold dark matter initial conditions should be significant today only at scales below 1  h ¹ Mpc.     

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.     

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.     

A critical-density closed universe in BransDicke theory

In a BransDicke (BD) cosmological model, the energy density associated with some scalar field decreases as a ^{2[( o +1/2)/( _o +1)]} with the scalefactor a ( t ) of the universe, giving matter with an equation of state In this model, the universe could be closed but still have a non-relativistic matter density corresponding to its critical value, _o =1. Different cosmological expressions, such as luminosity distance, angular diameter, number count and ratio of the redshift thicknessangular size, are determined in terms of the redshift for this model.     

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.     

Power spectrum shape from peculiar velocity data

We constrain the velocity power spectrum shape parameter Γ in linear theory using the nine bulk flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for Γ was found after marginalizing over the power spectrum amplitude  σ₈Ω^0.6_m  using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise σ_* was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large-scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint  Γ= 0.13^+0.09_−0.05  . This value is lower than, but consistent with, values obtained using redshift surveys and cosmic microwave background data.     

Non-linear redshift distortions: the two-point correlation function

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ _s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ _s . While the deviations are insignificant for the monopole ξ ₀, the hexadecapole ξ ₄ exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ ₄ deviate from the linear predictions by a factor of two on the scale of ∼10  h ⁻¹ Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.     

Apocalypse soon

Based upon a simple vacuum Lagrangian, comprising cosmological and quadratic scalar field terms, a cosmological model is presented the history of which is indistinguishable from that of an innocuous low-density cold dark matter (CDM) universe, but the future of which is very much shorter. For sensible values of the deceleration parameter (0< q ₀<1), its age is greater than 85 per cent of the Hubble time, thus resolving the current version of the age crisis, which appears to be that t ₀∼1/ H ₀ while q ₀ is significantly positive.     

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.     

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.     

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.     

Survival and disruption of subsystems during a cold collapse

Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses under its own gravity. At the first collapse of the cluster, most of the clumps are destroyed, but some survive. In order to find the condition for the clumps to survive, we made a systematic study in two-parameter space: the number of the clumps N _c and the size of the clump r _v . We obtained the condition N _c ≫ 1 and n _k  ≥ 1, where n _k is related to r _v and the initial radius of the cluster R _ini through the relation R _ini/ r _v  = 2 N ^{( n k +5)/6}_c. A simple analytical argument supports the numerical result. This n _k corresponds to the index of the power spectrum of the density fluctuation in the cosmological hierarchical clustering, and thus our result may suggest that in the systems smaller than 2/Ω h ²)Mpc, the first violent collapse is strong enough to sweep away all the substructures that exist before the collapse.     

Multiple frequency analysis of the large-amplitude SX Phoenicis star BL Camelopardalis

A multifrequency analysis of the SX Phoenicis star BL Camelopardalis is presented on the basis of new high-speed photometry, along with fitting a total of 136 maxima. BL Cam is a multiple periodic pulsator. We find f ₀=25.5768, f ₁=25.2982, f ₂=25.8622, f ₃=31.5912, f ₄=25.1065, f ₅=25.5147 and f ₆=25.6188 cycle d⁻¹ together with the harmonics 51.1513 and 76.7268 cycle d⁻¹ and combination frequencies f ₀+ f ₁, f ₀+ f ₂ and f ₀+ f ₃. The new frequency solution represents the light curves of BL Cam quite well. The observed minus calculated (O-C) analysis indicates that the fundamental frequency is in good agreement with the results of Fourier analysis.     

Self-similar spherical collapse with non-radial motions

We derive the asymptotic mass profile near the collapse centre of an initial spherical density perturbation, δ ∝ M ^{− ε} , of collisionless particles with non-radial motions. We show that angular momenta introduced at the initial time do not affect the mass profile. Alternatively, we consider a scheme in which a particle moves on a radial orbit until it reaches its turnaround radius, r ∗. At turnaround the particle acquires an angular momentum L =ℒ√ GM _* r _* per unit mass, where M ∗ is the mass interior to r ∗. In this scheme, the mass profile is M ∝ r ^{3/(1+3 ε )} for all ε >0 , in the region r / r _t ≪ℒ , where r _t is the current turnaround radius. If ℒ≪1 then the profile in the region ℒ≪ r / r _t ≪1 is M ∝ r for ε <2/3 , and remains M ∝ r ^{3/(1+3 ε )} for ε ≥2/3 . The derivation relies on a general property of non-radial orbits which is that the ratio of the pericentre to apocentre is constant in a force field k ( t ) r ⁿ with k ( t ) varying adiabatically.     

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.