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 Hubble flow around the Local Group

We use updated data on distances and velocities of galaxies in the proximity of the Local Group (LG) in order to establish properties of the local Hubble flow. For 30 neighbouring galaxies with distances  0.7 < D _LG < 3.0  Mpc, the local flow is characterized by the Hubble parameter   H _loc= (78 ± 2) km s⁻¹ Mpc⁻¹  , the mean-square peculiar velocity  σ_v= 25 km s⁻¹  , corrected for errors of radial velocity measurements  (∼4 km s⁻¹)  and distance measurements  (∼10 km s⁻¹)  , as well as the radius of the zero-velocity surface   R ₀= (0.96 ± 0.03)  Mpc. The minimum value for σ_v is achieved when the barycentre of the LG is located at the distance   D_c = (0.55 ± 0.05) D _M31  towards Andromeda galaxy (M31) corresponding to the Milky Way (MW)-to-M31 mass ratio   M _MW/ M _M31≃ 4/5  . In the reference frame of the 30 galaxies at 0.7–3.0 Mpc, the LG barycentre has a small peculiar velocity  ∼(24 ± 4) km s⁻¹  towards the Sculptor constellation. The derived value of R ₀ corresponds to the total mass   M _T(LG) = (1.9 ± 0.2) 10¹² M_⊙  with  Ω_m= 0.24  and a topologically flat universe, a value in good agreement with the sum of virial mass estimates for the MW and M31.     

The Gunn–Peterson effect and the Lyman alpha forest

We show that spatial correlations in a stochastic large-scale velocity field in an otherwise smooth intergalactic medium (homogeneous comoving density) superposed on the general Hubble flow may cause a 'line-like' structure in QSO spectra similar to the population of unsaturated Lyα forest lines which usually are attributed to individual clouds with 10¹¹ ≲ N _{H i}  5 × 10¹³ cm⁻². Therefore there is no clear observational distinction between a diffuse intergalactic medium and discrete intergalactic clouds. It follows that the H  i density in the diffuse intergalactic medium might be substantially underestimated if it is determined from the observed intensity distribution near the apparent continuum in high-resolution spectra of QSOs. Our tentative estimate implies a diffuse neutral hydrogen opacity τ_GP ∼ 0.3 at z  ∼ 3 and a current baryon density Ω_IGM ≃ 0.08, assuming a Hubble constant H ₀ = 70 km s⁻¹ Mpc⁻¹.     

H 0 from an orientation-unbiased sample of Sunyaev–Zel'dovich and X-ray clusters

We have observed the Sunyaev–Zel'dovich (SZ) effect in a sample of five moderate-redshift clusters with the Ryle Telescope, and used them in conjunction with X-ray imaging and spectral data from ROSAT and ASCA to measure the Hubble constant. This sample was chosen with a strict X-ray flux limit using both the Bright Cluster Sample and the Northern ROSAT All-Sky Survey (RASS) cluster catalogues to be well above the surface brightness limit of the RASS, and hence to be unbiased with respect to the orientation of the cluster. This controls a major potential systematic effect in the SZ/X-ray method of measuring H ₀. Taking the weighted geometric mean of the results and including the main sources of error, namely the noise in the SZ measurement, the uncertainty in the X-ray temperatures and the unknown ellipticity and substructure of the clusters, we find   H ₀= 59⁺¹⁰₋₉ (random)⁺⁸₋₇(systematic) km s⁻¹ Mpc⁻¹  assuming a standard cold dark matter model with  Ω_M= 1.0, Ω_Λ= 0.0  or   H ₀= 66⁺¹¹₋₁₀ ⁺⁹₋₈ km  s⁻¹ Mpc⁻¹  if  Ω_M= 0.3, Ω_Λ= 0.7  .     

The local star formation rate and radio luminosity density

We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×10²² W Hz⁻¹  and density   φ ∗=(4.8±1.1)×10⁻⁴ Mpc⁻³.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×10¹⁹ W Hz⁻¹ Mpc⁻³  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ _1.4 GHz=(2.10±0.45±0.04)×10⁻² M_⊙ yr⁻¹ Mpc⁻³  for a Salpeter initial mass function from  0.1–125 M_⊙  and Hubble constant of 50 km s⁻¹ Mpc⁻¹. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.     

Spectroscopic solution of the star QX Cas

High-resolution spectroscopic observations around the Hα line of the binary star QX Cas covering the whole orbital period are presented. Our radial velocity solution, the first ever determined, requires an eccentric orbit with the following orbital parameters: eccentricity,   e = 0.22 ± 0.01  ; longitude of periastron,  ω= 45°± 5°  ; semi-amplitudes of the radial velocity curves of the primary and secondary stars,   K ₁ sin  i = 125.8 ± 0.9 km s⁻¹  and   K ₂ sin  i = 144.8 ± 1.1 km s⁻¹  ; gamma velocity,   V ₀= 65.1 ± 0.5 km s⁻¹  ; and mass ratio,   q = 0.869 ± 0.013  . The corresponding lower limits of the masses of the components and their separation are         , and   a sin  i = 31.34 ± 0.48 R_⊙  .     

Spectroscopic and photometric observations of the eclipsing star UV Leo

High-resolution spectroscopic observations around the Hα line and BVRI photometry of the eclipsing short-period RS CVn star UV Leo are presented. The simultaneous light-curve solution and radial velocity-curve solution led to the following values of the global parameters of the binary: temperatures   T ₁= 6000 ± 100 K  and   T ₂= 5970 ± 20 K  ; masses   M ₁= 0.976 ± 0.067 M_⊙  and   M ₂= 0.931 ± 0.052 M_⊙  ; separation   a = 3.716 ± 0.048 R_⊙  ; orbital inclination     ; radii   R ₁= 1.115 ± 0.052 R_⊙  and   R ₂= 1.078 ± 0.051 R_⊙  ; equatorial velocities   V ₁= 98.8 ± 2.3 km s⁻¹  and   V ₂= 89.6 ± 2.7 km s⁻¹  . These results lead to the conclusion that the two components of UV Leo are slightly oversized for their masses and lie within the main-sequence band on the mass–radius diagram, close to the isochrone 9 × 10¹⁰ yr.     

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.     

Dark matter haloes within clusters

We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s⁻¹ within the cluster virial radius of 2 Mpc (with Hubble constant H ₀ = 50 km s⁻¹ Mpc⁻¹). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —'galaxy harassment'. Mergers between haloes do not occur inside the cluster virial radius.     

The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann–Lemaître–Robertson–Walker models

The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann–Lemaître–Robertson–Walker (FLRW) model, with     and  Ω_Λ≈ 0.73  – or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range  1.5 < z < 1.8  become available. We obtain characteristic FLRW-closed functional forms for   C = C ( z )  and     , the angular-diameter distance and the density per source counted, respectively, when  Λ≠ 0  , analogous to those we have for  Λ= 0  . More importantly, we verify that for flat FLRW models z _max– as is already known but rarely recognized – the redshift of C _max, the maximum of the angular-diameter distance, uniquely gives  Ω_Λ  , the amount of vacuum energy in the universe, independent of H ₀, the Hubble parameter. For non-flat models, determination of both z _max and C _max gives both  Ω_Λ  and Ω_M, the amount of matter in the universe, as long as we know H ₀ independently. Finally, determination of C _max automatically gives a very simple observational criterion for whether or not the universe is flat – presuming that it is FLRW.     

Measuring Ω0 using cluster evolution

The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Ω₀. Recent ASCA data are used to quantify this evolution as measured by the cluster X-ray temperature function. A χ² minimization fit to the cumulative temperature function, as well as a maximum-likelihood estimate (which requires additional assumptions about cluster luminosities), leads to the estimate Ω₀ ≈ 0.45 ± 0.25 (1σ statistical error). Various systematic uncertainties are considered, none of which significantly enhances the probability that Ω₀ = 1. These conclusions hold for models with or without a cosmological constant, i.e., with Λ₀ = 0 or Λ₀ = 1 − Ω₀. The statistical uncertainties are at least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place an upper limit on Ω₀ is also presented and tentatively applied, with the result that Ω₀  1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.     

ASCA observations of deep ROSAT fields — III. The discovery of an obscured Type 2 AGN at z = 0.67

We report on the discovery of a narrow-emission-line object at z  = 0.672 detected in a deep ASCA survey. The object, AXJ 0341.4–4453, has a flux in the 2–10 keV band of 1.1 ± 0.27 × 10⁻¹³ erg s⁻¹ cm⁻², corresponding to a luminosity of 1.8 × 10⁴⁴ erg s⁻¹ ( q ₀ = 0.5, H ₀ = 50 km s⁻¹ Mpc⁻¹). It is also marginally detected in the ROSAT 0.5–2 keV band with a flux 5.8 × 10⁻¹⁵ erg s⁻¹ cm⁻². Both the ASCA data alone and the combined ROSAT/ASCA data show a very hard X-ray spectrum, consistent with either a flat power law (α < 0.1) or photoelectric absorption with a column of n _H > 4 × 10²² cm⁻² (α = 1). The optical spectrum shows the high-ionization, narrow emission lines typical of a Seyfert 2 galaxy. We suggest that this object may be typical of the hard sources required to explain the remainder of the X-ray background at hard energies.     

The pattern speed of the OH/IR stars in the Milky Way

We show how the continuity equation can be used to determine pattern speeds in the Milky Way Galaxy (MWG). This method, first discussed by Tremaine & Weinberg in the context of external galaxies, requires projected positions, ( l , b ), and line-of-sight velocities for a spatially complete sample of relaxed tracers. If the local standard of rest (LSR) has a zero velocity in the radial direction ( u _LSR), then the quantity that is measured is  Δ V ≡Ω_p R ₀- V _LSR  , where Ω_p is the pattern speed of the non-axisymmetric feature, R ₀ is the distance of the Sun from the Galactic centre and V _LSR is the tangential motion of the LSR, including the circular velocity. We use simple models to assess the reliability of the method for measuring a single, constant pattern speed of either a bar or spiral in the inner MWG. We then apply the method to the OH/IR stars in the ATCA/VLA OH 1612-MHz survey of Sevenster et al., finding  Δ V =252±41 km s^-1,  if   u _LSR=0  . Assuming further that   R ₀=8 kpc  and   V _LSR=220 km s^-1,  this gives  Ω_p=59±5 km s^-1 kpc^-1  with a possible systematic error of perhaps 10 km s⁻¹ kpc⁻¹. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.     

Predicting the peculiar velocities of nearby PSCz galaxies using the Least Action Principle

We use the Least Action Principle to predict the peculiar velocities of PSC z galaxies inside cz =2000 km s⁻¹. Linear theory is used to account for tidal effects to cz =15 000 km s⁻¹, and we iterate galaxy positions to account for redshift distortions. As the Least Action Principle is valid beyond linear theory, we can predict reliable peculiar velocities even for very nearby galaxies (i.e., cz ≤500 km s⁻¹). These predicted peculiar velocities are then compared with the observed velocities of 12 galaxies with Cepheid distances. The combination of the PSC z galaxy survey (with its large sky coverage and uniform selection) with the accurate Cepheid distances makes this comparison relatively free from systematic effects. We find that galaxies are good tracers of the mass, even at small (≤10  h ⁻¹ Mpc) scales; under the assumption of no biasing, 0.25≤ β ≤0.75 (at 90 per cent confidence). We use the reliable predicted peculiar velocities to estimate the Hubble constant H ₀ from the local volume without 'stepping up' the distance ladder, finding a confidence range of 65–75 km s⁻¹ Mpc⁻¹ (at 90 per cent confidence).     

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.     

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.     

A targeted survey for H i clouds in galaxy groups

Five galaxy groups with properties similar to those of the Local Group have been surveyed for H  i clouds with the Arecibo Telescope. In total 300 pointings have been observed on grids of approximately 2.5×1.5 Mpc² centred on the groups. The 4.5 σ detection limit on the minimal detectable H  i masses is approximately 7×10⁶ M_⊙ ( H ₀=65 km s⁻¹ Mpc⁻¹) . All detections could be attributed to optical galaxies; no significant detections of H  i clouds have been made. This null result leads to the conclusion that the total H  i mass of intragroup clouds must be less than 10 per cent of the total H  i mass of galaxy groups and less than 0.05 per cent of the dynamical mass. The recent hypothesis that Galactic high-velocity clouds are Local Group satellite galaxies is highly inconsistent with these observations.     

MERLIN/VLA imaging of the gravitational lens system B0218+357

Gravitational lenses offer the possibility of accurately determining the Hubble parameter ( H ₀) over cosmological distances, and B0218+357 is one of the most promising systems for an application of this technique. In particular this system has an accurately measured time delay (10.5±0.4 d) and preliminary mass modelling has given a value for H ₀ of 69₋₁₉⁺¹³ km s⁻¹ Mpc⁻¹. The error on this estimate is now dominated by the uncertainty in the mass modelling. As this system contains an Einstein ring it should be possible to constrain the model better by imaging the ring at high resolution. To achieve this we have combined data from MERLIN and the Very Large Array (VLA) at a frequency of 5 GHz. In particular MERLIN has been used in multifrequency mode in order to improve substantially the aperture coverage of the combined data set. The resulting map is the best that has been made of the ring and contains many new and interesting features. Efforts are currently underway to exploit the new data for lensing constraints using the LensClean algorithm.     

Principal-component analysis of the cosmic microwave background anisotropies: revealing the tensor degeneracy

A principal-component analysis of cosmic microwave background (CMB) anisotropy measurements is used to investigate degeneracies among cosmological parameters. The results show that a degeneracy with tensor modes – the 'tensor degeneracy'– dominates uncertainties in estimates of the baryon and cold dark matter densities,   ω _b=Ω_b  h ²  ,   ω _c=Ω_c  h ²  , ¹ from an analysis of CMB anisotropies alone. The principal-component analysis agrees well with a maximum-likelihood analysis of the observations, identifying the main degeneracy directions and providing an impression of the effective dimensionality of the parameter space.     

The component masses of the cataclysmic variable V347 Puppis

We present time-resolved spectroscopy and photometry of the double-lined eclipsing cataclysmic variable V347 Pup (=LB 1800). There is evidence of irradiation on the inner hemisphere of the secondary star, which we correct for using a model to give a secondary-star radial velocity of   K _R= 198 ± 5 km s⁻¹  . The rotational velocity of the secondary star in V347 Pup is found to be   v sin  i = 131 ± 5 km s⁻¹  and the system inclination is   i = 840 ± 23  . From these parameters we obtain masses of   M ₁= 0.63 ± 0.04 M_⊙  for the white dwarf primary and   M ₂= 0.52 ± 0.06 M_⊙  for the M0.5V secondary star, giving a mass ratio of   q = 0.83 ± 0.05  . On the basis of the component masses, and the spectral type and radius of the secondary star in V347 Pup, we find tentative evidence for an evolved companion. V347 Pup shows many of the characteristics of the SW Sex stars, exhibiting single-peaked emission lines, high-velocity S-wave components and phase-offsets in the radial velocity curve. We find spiral arms in the accretion disc of V347 Pup and measure the disc radius to be close to the maximum allowed in a pressureless disc.