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.     

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.     

The kinematics and zero-point of the log P–〈MK〉 relation for Galactic RR Lyrae variables via statistical parallax

We use accurate absolute proper motions and Two-Micron All-Sky Survey   K_s   -band apparent magnitudes for 364 Galactic RR Lyrae variables to determine the kinematical parameters of the Galactic RR Lyrae population and constrain the zero-point of the   K_s   -band period–luminosity relation for these stars via statistical parallax. We find the mean velocities of the halo- and thick-disc RR Lyrae populations in the solar neighbourhood to be  [ U ₀(Halo), V ₀(Halo), W ₀(Halo)]= (−12 ± 10, −217 ± 9, −6 ± 6) km s⁻¹  and  [ U ₀(Disc), V ₀(Disc), W ₀(Disc)]= (−15 ± 7, −44 ± 7, −25 ± 5) km s⁻¹  , respectively, and the corresponding components of the velocity-dispersion ellipsoids,  [σ V_R (Halo), σ V _θ(Halo), σ W (Halo)]= (167 ± 9, 86 ± 6, 78 ± 5) km s⁻¹  and  [σ V_R (Disc), σ V _θ(Disc), σ W (Disc)]= (55 ± 7, 44 ± 6, 30 ± 4) km s⁻¹  , respectively. The fraction of thick-disc stars is estimated at  0.25 ± 0.03  . The corrected infrared period–luminosity relation is     , implying a Large Magellanic Cloud (LMC) distance modulus of  18.27 ± 0.08  and a solar Galactocentric distance of  7.58 ± 0.40 kpc  . Our results suggest no or slightly prograde rotation for the population of halo RR Lyraes in the Milky Way.     

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.     

The 2dF Galaxy Redshift Survey: luminosity functions by density environment and galaxy type

We use the 2dF Galaxy Redshift Survey to measure the dependence of the b _J-band galaxy luminosity function on large-scale environment, defined by density contrast in spheres of radius  8  h ⁻¹ Mpc  , and on spectral type, determined from principal component analysis. We find that the galaxy populations at both extremes of density differ significantly from that at the mean density. The population in voids is dominated by late types and shows, relative to the mean, a deficit of galaxies that becomes increasingly pronounced at magnitudes brighter than   M _{b J}−5log₁₀ h ≲−18.5  . In contrast, cluster regions have a relative excess of very bright early-type galaxies with   M _{b J}−5log₁₀ h ≲−21  . Differences in the mid- to faint-end population between environments are significant: at   M _{b J}−5log₁₀ h =−18  early- and late-type cluster galaxies show comparable abundances, whereas in voids the late types dominate by almost an order of magnitude. We find that the luminosity functions measured in all density environments, from voids to clusters, can be approximated by Schechter functions with parameters that vary smoothly with local density, but in a fashion that differs strikingly for early- and late-type galaxies. These observed variations, combined with our finding that the faint-end slope of the overall luminosity function depends at most weakly on density environment, may prove to be a significant challenge for models of galaxy formation.     

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 .     

An asteroseismic signature of helium ionization

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent γ is a superposition of two decaying periodic functions of frequency ν, with 'frequencies' that are approximately twice the acoustic depths of the centres of the He  i and He  ii ionization regions. That variation is probably best exhibited in the second frequency difference  Δ₂ν _{n ,  l} ≡ν _{n −1,  l} − 2ν _{n ,  l} +ν _{n +1,  l}   . We show how an analytic approximation to the variation of γ leads to a simple representation of this oscillatory contribution to Δ₂ν which can be used to characterize the γ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize γ, not merely to find a formula for Δ₂ν that reproduces the data.     

Optimal filters for the construction of the ensemble pulsar time

An algorithm of the ensemble pulsar time based on the optimal Wiener filtration method has been constructed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the atomic clock and the pulsar itself. Filters were designed using the cross- and auto-covariance functions of the timing residuals. The method has been applied to the timing data of millisecond pulsars PSR B1855+09 and B1937+21 and allowed the filtering out of the atomic-scale component from the pulsar data. Direct comparison of the terrestrial time TT(BIPM06) and the ensemble pulsar time PT_ens revealed that the fractional instability of TT(BIPM06)−PT_ens is equal to  σ _z = (0.8 ± 1.9) × 10⁻¹⁵  . Based on the  σ _z   statistics of TT(BIPM06)−PT_ens, a new limit of the energy density of the gravitational wave background was calculated to be equal to  Ω_g h ²∼ 3 × 10⁻⁹  .     

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.     

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.     

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 shapes of galaxies in the Sloan Digital Sky Survey

We determine the underlying shapes of spiral and elliptical galaxies in the Sloan Digital Sky Survey Data Release 6 (SDSS DR6) from the observed distribution of projected galaxy shapes, taking into account the effects of dust extinction and reddening. We assume that the underlying shapes of spirals and ellipticals are well approximated by triaxial ellipsoids. The elliptical galaxy data are consistent with oblate spheroids, with a correlation between luminosity and ellipticity: the mean values of minor to middle axis ratios are 0.41 ± 0.03 for   M _r ≈−18  ellipticals and 0.76 ± 0.04 for   M _r ≈−22.5  ellipticals. Ellipticals show almost no dependence of axial ratio on galaxy colour, implying a negligible dust optical depth.
There is a strong variation of spiral galaxy shapes with colour indicating the presence of dust. The intrinsic shapes of spiral galaxies in the SDSS DR6 are consistent with flat discs with a mean and dispersion of thickness to diameter ratio of (21 ± 2) per cent, and a face-on ellipticity, e , of  ln( e ) =−2.33 ± 0.79  . Not including the effects of dust in the model leads to discs that are systematically rounder by up to 60 per cent. More luminous spiral galaxies tend to have thicker and rounder discs than lower luminosity spirals. Both elliptical and spiral galaxies tend to be rounder for larger galaxies.
The marginalized value of the edge-on r -band dust extinction E ₀ in spiral galaxies is   E ₀≃ 0.45  mag for galaxies of median colours, increasing to   E ₀= 1  mag for   g − r > 0.9  and   E ₀= 1.9  for the luminous and most compact galaxies, with half-light radii  <2  h ⁻¹ kpc  .     

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.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.     

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.     

Clustering of luminous red galaxies – II. Small-scale redshift-space distortions

This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over  1 Gpc³  h ⁻³  for  0.15 < z < 0.47  . Here, we focus on modelling redshift-space distortions in  ξ(σ, π)  , the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called 'fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity σ₁₂ with the distance. We show how both quantities can be inferred from the  ξ(σ, π)  data. From   r ≃ 10 Mpc  h ⁻¹  to   r ≃ 1 Mpc  h ⁻¹  , both the bias and σ₁₂ are shown to increase by a factor of 2: from   b = 2  to 4 and from  σ₁₂= 400  to  800 km s⁻¹  . The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with  Ω_m= 0.25  and  σ₈= 0.85  .     

A measurement of the faint source correlation function in the GOODS and UDF surveys

We present a stable procedure for defining and measuring the two point angular autocorrelation function,   w (θ) =[θ/θ₀( V )]^−Γ  , of faint  (25 < V < 29)  , barely resolved and unresolved sources in the Hubble Space Telescope Great Observatories Origins Deep Survey and Ultra Deep Field data sets. We construct catalogues that include close pairs and faint detections. We show, for the first time, that, on subarcsec scales, the correlation function exceeds unity. This correlation function is well fit by a power law with index  Γ≈ 2.5  and a  θ₀= 10^{−0.1( V −25.8)} arcsec  . This is very different from the values of  Γ≈ 0.7  and  θ₀( r ) = 10^{−0.4( r −21.5)} arcsec  associated with the gravitational clustering of brighter galaxies. This observed clustering probably reflects the presence of giant star-forming regions within galactic-scale potential wells. Its measurement enables a new approach to measuring the redshift distribution of the faintest sources in the sky.     

Lyman continuum escape from an inhomogeneous interstellar medium

We have studied the effects of gas density inhomogeneities on the escape of ionizing Lyman continuum (Lyc) photons from Milky Way type galaxies via 3D numerical simulations using the Monte Carlo radiative transfer code crash . To this aim a comparison between a smooth Gaussian distribution (GDD) and an inhomogeneous, fractal one (FDD) has been made with realistic assumptions for the ionizing stellar sources based on available data in the solar neighbourhood. In both cases the escape fraction f _esc increases with ionization rate  ˙ _γ   (although for the FDD with a flatter slope) and they become equal at  ˙ _γ =2×10⁵⁰ s^-1  where   f _esc=0.11  . FDD allows escape fractions of the same order also at lower  ˙ _γ ,  when Lyc photon escape is sharply suppressed by GDD. Values of the escape fraction as high as 0.6 can be reached (GDD) for  ˙ _γ ≈9×10⁵⁰ s^-1  , corresponding to a star formation rate (SFR) of roughly 2 M_⊙ yr⁻¹; at this ionizing luminosity the FDD is less transparent  ( f _esc≈0.28)  . If high-redshift galaxies have gas column densities similar to local ones, and are characterized by such high SFRs and by a predominantly smooth (i.e. turbulence-free) interstellar medium, our results suggest that they should considerably contribute to – and possibly dominate – the cosmic UV background.     

WIYN Open Cluster Study – XVI. Optical/infrared photometry and comparisons with theoretical isochrones

We present combined optical/near-infrared photometry ( BVIK ) for six open clusters – M35, M37, NGC 1817, NGC 2477, NGC 2420 and M67. The open clusters span an age range from 150 Myr to 4 Gyr and have metal abundances from  [Fe/H]=−0.27  to +0.09 dex. We have utilized these data to test the robustness of theoretical main sequences constructed by several groups as denoted by the following designations – Padova, Baraffe, Y², Geneva and Siess. The comparisons of the models with the observations have been performed in the  [ M_V , ( B − V )₀], [ M_V , ( V − I )₀]  and  [ M_V , ( V − K )₀]  colour–magnitude diagrams as well as the distance-independent  [( V − K )₀, ( B − V )₀]  and  [( V − K )₀, ( V − I )₀]  two-colour diagrams. We conclude that none of the theoretical models reproduces the observational data in a consistent manner over the magnitude and colour range of the unevolved main sequence. In particular, there are significant zero-point and shape differences between the models and the observations. We speculate that the crux of the problem lies in the precise mismatch between theoretical and observational colour–temperature relations. These results underscore the importance of pursuing the study of stellar structure and stellar modelling with even greater intensity.