The cosmic microwave background for a nearly flat compact hyperbolic universe

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy and an extra spatially constant dark energy X -component are considered. The general solution of the Friedmann equation for the cosmic scalefactor a ( η ) is given for the four-component models in terms of the Weierstrass ℘-function. The lower parts of the angular power spectra C _l of the CMB anisotropy are computed for nearly flat models with Ω_tot≤0.95. It is shown that the particular compact fundamental cell that is considered in this paper leads to a suppression in C _l for l ≲10 and Ω_tot≲0.9.     

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.     

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.     

Cosmic microwave background anisotropies resulting from feedback-regulated inhomogeneous reionization

We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z _i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C _χ , and obtain the power spectrum of the anisotropies, C _ℓ, in the range 5000<ℓ<10⁶. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10⁻¹². We also show that the ionization correlation function C _χ is not Gaussian, but at separation angles θ ≲10⁻⁴ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C _χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.     

Bulk viscosity of mixed nucleon–hyperon–quark matter in neutron stars

We calculate the coefficient of bulk viscosity by considering the non-leptonic weak interactions in the cores of hybrid stars with both hyperons and quarks. We first determine the dependence of the production rate of neutrons on the reaction rate of quarks in the non-leptonic processes, that is,  Γ _n = K _s Γ _s +Γ_Λ+ 2Γ_Σ−  . The conversion rate,   K _s   , in our scenario is a complicated function of baryon number density. We also consider the medium effect of quark matter on bulk viscosity. Using these results, we estimate the limiting rotation of the hybrid stars, which may suppress the r-mode instability more effectively. Hybrid stars should be the candidates for the extremely rapid rotators.     

Mass-to-light ratio gradients in early-type galaxy haloes

Owing to the fact that the near future should see a rapidly expanding set of probes of the halo masses of individual early-type galaxies, we introduce a convenient parameter for characterizing the halo masses from both observational and theoretical results:  ∇_ℓϒ  , the logarithmic radial gradient of the mass-to-light ratio. Using halo density profiles from Λ-cold dark matter (CDM) simulations, we derive predictions for this gradient for various galaxy luminosities and star formation efficiencies  ε_SF  . As a pilot study, we assemble the available  ∇_ℓϒ  data from kinematics in early-type galaxies – representing the first unbiased study of halo masses in a wide range of early-type galaxy luminosities – and find a correlation between luminosity and  ∇_ℓϒ  , such that the brightest galaxies appear the most dark-matter dominated. We find that the gradients in most of the brightest galaxies may fit in well with the ΛCDM predictions, but that there is also a population of fainter galaxies whose gradients are so low as to imply an unreasonably high star formation efficiency  ε_SF > 1  . This difficulty is eased if dark haloes are not assumed to have the standard ΛCDM profiles, but lower central concentrations.     

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

Temperature correlations in a compact hyperbolic universe

The effect of a non-trivial topology on the temperature correlations of the cosmic microwave background (CMB) in a small compact hyperbolic universe with volume comparable to the cube of the curvature radius is investigated. Because the bulk of large-angle CMB fluctuations are produced at the late epoch in low-Ω₀ models, the effect of a long-wavelength cut-off owing to the periodic structure does not lead to significant suppression of large-angle power as in compact flat models. The angular power spectra are consistent with COBE data for Ω₀0.1.     

Mixed three-point correlation functions of the non-linear integrated Sachs–Wolfe effect and their detectability

In this paper, I investigate the family of mixed three-point correlation functions  〈τ ^q γ^{3− q} 〉, q = 0, 1, 2  , between the integrated Sachs–Wolfe (iSW) temperature perturbation τ and the galaxy overdensity γ as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of non-linearly evolving cosmological structures. Both the iSW-effect and the galaxy overdensity are derived in hyperextended perturbation theory to second order and I emphasize the different parameter sensitivities of the linear and non-linear iSW-effect. I examine the configuration dependence of the relevant bispectra, quantify their sensitivities and discuss their degeneracies with respect to the cosmological parameters  Ω_m, σ₈, h   and the dark energy equation of state parameter w . I give detection significances for combining Planck CMB data and galaxy sample of a survey like Dark UNiverse Explorer (DUNE) by using a quadratic approximation for the likelihood with Λ cold dark matter (ΛCDM) as the fiducial cosmology: the combination of Planck with DUNE should be able to reach a cumulative signal-to-noise ratio of ≃0.6 for the bispectrum  〈τγ²〉  up to ℓ= 2000, which is too weak to be detected. The most important noise source is the primary CMB fluctuations as the Poisson noise in the galaxy number density is almost negligible for a survey like DUNE.     

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w ₀ =  p _x0/ρ_x0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.     

The edge-on spiral gravitational lens B1600+434

We present new observations of the gravitational lens (GL) system B1600+434, strongly suggesting that the lens is an edge-on spiral galaxy. These observations are used to constrain the mass model of the system, in particular the oblateness and velocity dispersion of the dark matter halo around the lensing galaxy. From an analytical model we find a lower limit on the halo oblateness q _halo=( c/a )_ρ≳0.4; more detailed numerical models give a lower limit of q _halo≳0.5. We determine an average halo velocity dispersion of σ_halo=190±15 km s⁻¹ over all non-singular isothermal elliptical (NIE) halo models. Constraining the models to larger and more massive discs decreases this average by only 10 km s⁻¹. A lower limit of σ_halo≳150 km s⁻¹ is found, even for disc masses larger than the mass inside the Einstein radius. This lower limit indicates the need for a massive dark matter halo, contributing at least half of the mass inside the Einstein radius. Time-delay calculations give (54±3)/ h ₅₀ d for the NIE halo model and (70±4)/ h ₅₀ d for the modified Hubble profile (MHP) halo model. Although the time delay for both NIE and MHP halo models is well constrained on our parameter grid, it strongly depends on the halo surface density profile. We furthermore find that the presence of a flat luminous mass distribution can severely alter the statistical properties of the lens.     

CDM models with a BSI step-like primordial spectrum and a cosmological constant

A class of spatially flat models with cold dark matter (CDM), a cosmological constant and a broken-scale-invariant (BSI) step-like primordial (initial) spectrum of adiabatic perturbations, generated in an exactly solvable inflationary model where the inflaton potential has a rapid change of its first derivative at some point, is confronted with existing observational data on angular fluctuations of the CMB temperature, galaxy clustering and peculiar velocities of galaxies. If we locate the step in the initial spectrum at k  ≃ 0.05  h Mpc⁻¹, where a feature in the spectrum of Abell clusters of galaxies was found that could reflect a property of the initial spectrum, and if the large-scale flat plateau of the spectrum is normalized according to the COBE data, the only remaining parameter of the spectrum is p — the ratio of amplitudes of the metric perturbations between the small-scale and large-scale flat plateaux. Allowed regions in the plane of parameters (Ω = 1 − Ω_Λ,  H ₀) satisfying all data have been found for p lying in the region (0.8–1.7). Especially good agreement of the form of the present power spectrum in this model with the form of the cluster power spectrum is obtained for the inverted step ( p  < 1,  p  = 0.7–0.8), when the initial spectrum has slightly more power on small scales.     

Decay of the vacuum energy into cosmic microwave background photons

We examine the possibility of the decay of the vacuum energy into a homogeneous distribution of a thermalized cosmic microwave background (CMB), which is characteristic of an adiabatic vacuum energy decay into photons. It is shown that observations of the primordial density fluctuation spectrum, obtained from CMB and galaxy distribution data, restrict the possible decay rate. When photon creation due to an adiabatic vacuum energy decay takes place, the standard linear temperature dependence   T ( z ) = T ₀(1 + z )  is modified, where T ₀ is the present CMB temperature, and can be parametrized by a modified CMB temperature dependence     . From the observed CMB and galaxy distribution data, a strong limit on the maximum value of the decay rate is obtained by placing a maximum value  β_max≃ 3.4 × 10⁻³  on the β parameter.     

Variance and skewness in the FIRST survey

We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function ( counts in cells ). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function w (θ), the variance Ψ₂ and skewness Ψ₃ of the distribution for the various subsamples chosen on different criteria. Both w (θ) and Ψ₂ show power-law behaviour with an amplitude corresponding to a spatial correlation length of r ₀ ∼ 10  h ⁻¹Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through Ψ₃ =  S ₃(Ψ₂)^α, with α = 1.9 ± 0.1, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and the skewness are consistent with realistic models of galaxy clustering.     

An asteroseismic study of the β Cephei star 12 Lacertae: multisite spectroscopic observations, mode identification and seismic modelling

We present the results of a spectroscopic multisite campaign for the β Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high-resolution high S/N spectra gathered with eight different telescopes in a time span of 11 months. In addition, we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the slowly pulsating B-stars (SPB)-like g -mode with frequency 0.3428 d⁻¹ reported before is detected in our spectroscopy. We identify the four main modes as  (ℓ₁, m ₁) = (1, 1), (ℓ₂, m ₂) = (0, 0), (ℓ₃, m ₃) = (1, 0)  and  (ℓ₄, m ₄) = (2, 1)  for   f ₁= 5.178 964 d⁻¹, f ₂= 5.334 224 d⁻¹, f ₃= 5.066 316 d⁻¹  and   f ₄= 5.490 133 d⁻¹  , respectively. Our seismic modelling shows that f ₂ is likely the radial first overtone and that the core overshooting parameter  α_ov  is lower than 0.4 local pressure scale heights.     

The redshift evolution of clustering in the Hubble Deep Field

We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto, Lanzetta & Yahil. By dividing the catalogue into redshift bins of width Δ z =0.4 we measured the angular correlation function w ( θ ) as a function of redshift up to z ∼4.8. From these measurements we derive the trend of the correlation length r ₀. We find that r ₀( z ) is roughly constant with look-back time up to z ≃2, and then increases to higher values at z ≳2.4. We estimate the values of r ₀, assuming ξ ( r , z )=[ r r ₀( z )]^{− γ} , γ =1.8 and various geometries. For Ω₀=1 we find r ₀( z =3)≃7.00±4.87  h ⁻¹ Mpc, in good agreement with the values obtained from analysis of the Lyman break galaxies.     

Evolution of the dark matter distribution with three-dimensional weak lensing

We present a direct detection of the growth of large-scale structure, using weak gravitational lensing and photometric redshift data from the COMBO-17 survey. We use deep R -band imaging of two  0.5 × 0.5 deg²  fields, affording shear estimates for over 52 000 galaxies; we combine these with photometric redshift estimates from our 17-band survey, in order to obtain a 3D shear field. We find theoretical models for evolving matter power spectra and correlation functions, and fit the corresponding shear correlation functions to the data as a function of redshift. We detect the evolution of the power at the 4.7σ level given reasonable priors, and measure the rate of evolution for  0 < z < 1  . We also fit correlation functions to our 3D data as a function of cosmological parameters σ₈ and  Ω_Λ  . We find joint constraints on  Ω_Λ  and σ₈, demonstrating an improvement in accuracy by ≃40 per cent over that available from 2D weak lensing for the same area.     

Covariance of dark energy parameters and sound speed constraints from large H i surveys

An interesting probe of the nature of dark energy is the measure of its sound speed, c _s. We review the significance for constraining sound speed models of dark energy using large neutral hydrogen (H  i ) surveys with the square kilometre array (SKA). Our analysis considers the effect on the sound speed measurement that arises from the covariance of c _s with the dark energy density, Ω_de, and a time-varying equation of state,   w ( a ) = w ₀+ (1 − a ) w _a   . We find that the approximate degeneracy between dark energy parameters that arises in power spectrum observations is lifted through redshift tomography of the H  i -galaxy angular power spectrum, resulting in sound speed constraints that are not severely degraded. The cross-correlation of the galaxy and the integrated Sachs Wolfe (ISW) effect spectra contributes approximately 10 per cent of the information that is needed to distinguish variations in the dark energy parameters, and most of the discriminating signal comes from the galaxy auto-correlation spectrum. We also find that the sound speed constraints are weakly sensitive to the H  i bias model. These constraints do not improve substantially for a significantly deeper H  i survey since most of the clustering sensitivity to sound speed variations arises from   z ≲ 1.5  . A detection of models with sound speeds close to zero,   c _s≲ 0.01,  is possible for dark energy models with   w ≳−0.9  .     

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 2dF Galaxy Redshift Survey: the nature of the relative bias between galaxies of different spectral type

We present an analysis of the relative bias between early- and late-type galaxies in the Two-degree Field Galaxy Redshift Survey (2dFGRS) – as defined by the η parameter of Madgwick et al., which quantifies the spectral type of galaxies in the survey. We calculate counts in cells for flux-limited samples of early- and late-type galaxies, using approximately cubical cells with sides ranging from 7 to  42 h ⁻¹ Mpc  . We measure the variance of the counts in cells using the method of Efstathiou et al., which we find requires a correction for a finite volume effect equivalent to the integral constraint bias of the autocorrelation function. Using a maximum-likelihood technique we fit lognormal models to the one-point density distribution, and develop methods of dealing with biases in the recovered variances resulting from this technique. We then examine the joint density distribution function,   f (δ_E, δ_L)  , and directly fit deterministic bias models to the joint counts in cells. We measure a linear relative bias of ≈1.3, which does not vary significantly with ℓ. A deterministic linear bias model is, however, a poor approximation to the data, especially on small scales  (ℓ≤ 28  h ⁻¹ Mpc)  where deterministic linear bias is excluded at high significance. A power-law bias model with index   b ₁≈ 0.75  is a significantly better fit to the data on all scales, although linear bias becomes consistent with the data for  ℓ≳ 40  h ⁻¹ Mpc  .