arXiv subjects

Will J. Percival

Publications and source records attributed to Will J. Percival.

At least 235 records · Page 13Linked to original sources

arXiv2007

Galaxy peculiar velocities and evolution-bias

Galaxy bias can be split into two components: a formation-bias based on the locations of galaxy creation, and an evolution-bias that details their subsequent evolution. In this letter we consider evolution-bias in the peaks model. In this model, galaxy formation takes place at local maxima in the density field, and we analyse the subsequent peculiar motion of these galaxies in a linear model of structure formation. The peak restriction yields differences in the velocity distribution and correlation between the galaxy and the dark matter fields, which causes the evolution-bias component of the total bias to evolve in a scale-dependent way. This mechanism naturally gives rise to a change in shape between galaxy and matter correlation functions that depends on the mean age of the galaxy population. This model predicts that older galaxies would be more strongly biased on large scales compared to younger galaxies. Our arguments are supported by a Monte-Carlo simulation of galaxy pairs propagated using the Zel'dovich-approximation for describing linear peculiar galaxy motion.

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arXiv2007

Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS

We introduce a method to constrain general cosmological models using Baryon Acoustic Oscillation (BAO) distance measurements from galaxy samples covering different redshift ranges, and apply this method to analyse samples drawn from the SDSS and 2dFGRS. BAO are detected in the clustering of the combined 2dFGRS and SDSS main galaxy samples, and measure the distance--redshift relation at z=0.2. BAO in the clustering of the SDSS luminous red galaxies measure the distance--redshift relation at z=0.35. The observed scale of the BAO calculated from these samples and from the combined sample are jointly analysed using estimates of the correlated errors, to constrain the form of the distance measure D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3). Here D_A is the angular diameter distance, and H(z) is the Hubble parameter. This gives r_s/D_V(0.2)=0.1980+/-0.0058 and r_s/D_V(0.35)=0.1094+/-0.0033 (1sigma errors), with correlation coefficient of 0.39, where r_s is the comoving sound horizon scale at recombination. Matching the BAO to have the same measured scale at all redshifts then gives D_V(0.35)/D_V(0.2)=1.812+/-0.060. The recovered ratio is roughly consistent with that predicted by the higher redshift SNLS supernovae data for Lambda cosmologies, but does require slightly stronger cosmological acceleration at low redshift. If we force the cosmological model to be flat with constant w, then we find Om_m=0.249+/-0.018 and w=-1.004+/-0.089 after combining with the SNLS data, and including the WMAP measurement of the apparent acoustic horizon angle in the CMB.

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arXiv2006

Measuring the matter density using baryon oscillations in the SDSS

We measure the cosmological matter density by observing the positions of baryon acoustic oscillations in the clustering of galaxies in the Sloan Digital Sky Survey (SDSS). We jointly analyse the main galaxies and LRGs in the SDSS DR5 sample, using over half a million galaxies in total. The oscillations are detected with 99.74% confidence (3.0sigma assuming Gaussianity) compared to a smooth power spectrum. When combined with the observed scale of the peaks within the CMB, we find a best-fit value of Omega_m=0.256+0.029-0.024 (68% confidence interval), for a flat Lambda cosmology when marginalising over the Hubble parameter and the baryon density. This value of the matter density is derived from the locations of the baryon oscillations in the galaxy power spectrum and in the CMB, and does not include any information from the overall shape of the power spectra. This is an extremely clean cosmological measurement as the physics of the baryon acoustic oscillation production is well understood, and the positions of the oscillations are expected to be independent of systematics such as galaxy bias.

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arXiv2006

The shape of the SDSS DR5 galaxy power spectrum

We present a Fourier analysis of the clustering of galaxies in the combined Main galaxy and Luminous Red Galaxy (LRG) Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) sample. The aim of our analysis is to consider how well we can measure the cosmological matter density using the signature of the horizon at matter-radiation equality embedded in the large-scale power spectrum. The new data constrains the power spectrum on scales 100--600h^-1Mpc with significantly higher precision than previous analyses of just the SDSS Main galaxies, due to our larger sample and the inclusion of the LRGs. This improvement means that we can now reveal a discrepancy between the shape of the measured power and linear CDM models on scales 0.01<k<0.15hMpc^-1, with linear model fits favouring a lower matter density (Omega_m=0.22+/-0.04) on scales 0.01<k<0.06hMpc^-1 and a higher matter density (Omega_m=0.32+/-0.01) when smaller scales are included, assuming a flat LCDM model with h=0.73 and n_s=0.96. This discrepancy could be explained by scale-dependent bias and, by analysing subsamples of galaxies, we find that the ratio of small-scale to large-scale power increases with galaxy luminosity, so all of the SDSS galaxies cannot trace the same power spectrum shape over 0.01<k<0.2hMpc^-1. However, the data are insufficient to clearly show a luminosity-dependent change in the largest scale at which a significant increase in clustering is observed, although they do not rule out such an effect. Significant scale-dependent galaxy bias on large-scales, which changes with the r-band luminosity of the galaxies, could potentially explain differences in our Omega_m estimates and differences previously observed between 2dFGRS and SDSS power spectra and the resulting parameter constraints.

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arXiv2006

Likelihood methods for the combined analysis of CMB temperature and polarisation power spectra

We consider the shape of the likelihood and posterior surfaces to be used when fitting cosmological models to CMB temperature and polarisation power spectra measured from experiments. In the limit of an all-sky survey with Gaussian distributed pixel noise we show that the true combined likelihood of the four CMB power spectra (TT, TE, EE & BB) has a Wishart distribution and we discuss the properties of this function. We compare various fits to the posterior surface of the Cls, both in the case of a single auto-power spectrum and for a combination of temperature and polarisation data. In the latter case, it is important that the fits can accurately match the Wishart distribution in the limit of near full-sky coverage. Simple extensions of auto-power spectrum fits to include polarisation data generally fail to match correlations between the different power spectra in this limit. Directly fitting pixel values on large scales, as undertaken by the WMAP team in their analysis of the 3 year data, avoids the complications of characterising the shape of the posterior for the power spectra. Finally we demonstrate the importance of the likelihood distribution on analytic marginalisation, and provide a formula for analytic marginalisation over a calibration error given an all-sky survey.

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arXiv2006

Cosmological constraints from galaxy clustering

In this manuscript I review the mathematics and physics that underpins recent work using the clustering of galaxies to derive cosmological model constraints. I start by describing the basic concepts, and gradually move on to some of the complexities involved in analysing galaxy redshift surveys, focusing on the 2dF Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky survey (SDSS). Difficulties within such an analysis, particularly dealing with redshift space distortions and galaxy bias are highlighted. I then describe current observations of the CMB fluctuation power spectrum, and consider the importance of measurements of the clustering of galaxies in light of recent experiments. Finally, I provide an example joint analysis of the latest CMB and large-scale structure data, leading to a set of parameter constraints.

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arXiv2005

Cosmological structure formation in a homogeneous dark energy background

There is now strong evidence that the current energy density of the Universe is dominated by dark energy with an equation of state w<-1/3, which is causing accelerated expansion. The build-up of structure within such Universes is subject to significant ongoing study, particularly through the spherical collapse model. This paper aims to review and consolidate progress for cosmologies in which the dark energy component remains homogeneous on the scales of the structures being modelled. The equations presented are designed to allow for dark energy with a general time-varying equation of state w(a). In addition to reviewing previous work, a number of new results are introduced: A new fitting formula for the linear growth factor in constant w cosmologies is given. A new formalism for determining the critical density for collapse is presented based on the initial curvature of the perturbation. The commonly used approximation to the critical density for collapse based on the linear growth factor is discussed for a general dark energy equation of state. Virialisation within such cosmologies is also considered, and the standard assumption that energy is conserved between turn-around and virialisation is questioned and limiting possiblities are presented.

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arXiv2005

Imaging of SDSS z>6 quasar fields: gravitational lensing, companion galaxies and the host dark matter halos

We have undertaken deep optical imaging observations of three 6.2<z<6.5 quasar fields in the i' and z' filters. These data are used to search for foreground galaxies which are gravitationally lensing the quasars and distant galaxies physically associated with the quasars. Foreground galaxies are found closer than 5 arcsec from the lines-of-sight of two of the three quasars. However, the faintness of these galaxies suggests they have fairly low masses and provide only weak magnifications (mu<1.1). No convincing galaxies physically associated with the quasars are found and the number of i'-band dropouts is consistent with that found in random fields. We consider the expected dark matter halo masses which host these quasars under the assumption that a correlation between black hole mass and dark matter halo mass exists. We show that the steepness of the high-mass tail of the halo mass function at this redshift, combined with realistic amounts of scatter in this correlation, lead to expected halo masses substantially lower than previously believed. This analysis can explain the lack of companion galaxies found here and the low dynamical mass recently published for one of the quasars.

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arXiv2005

The extragalactic sub-mm population: predictions for the SCUBA Half-Degree Extragalactic Survey (SHADES)

We present predictions for the angular correlation function and redshift distribution for SHADES, the SCUBA HAlf-Degree Extragalactic Survey, which will yield a sample of around 300 sub-mm sources in the 850 micron waveband in two separate fields. Complete and unbiased photometric redshift information on these sub-mm sources will be derived by combining the SCUBA data with i) deep radio imaging already obtained with the VLA, ii) guaranteed-time Spitzer data at mid-infrared wavelengths, and iii) far-infrared maps to be produced by BLAST, the Balloon-borne Large-Aperture Sub-millimeter Telescope. Predictions for the redshift distribution and clustering properties of the final anticipated SHADES sample have been computed for a wide variety of models, each constrained to fit the observed number counts. Since we are dealing with around 150 sources per field, we use the sky-averaged angular correlation function to produce a more robust fit of a power-law shape w(theta)=(theta/A)^{-delta} to the model data. Comparing the predicted distributions of redshift and of the clustering amplitude A and slope delta, we find that models can be constrained from the combined SHADES data with the expected photometric redshift information.

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arXiv2004

Markov-chain reconstruction of the 2dF Galaxy Redshift Survey real-space power spectrum

The real-space power spectrum of L* galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov-Chain Monte-Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a Spherical Harmonics decomposition of the 2dFGRS overdensity field (described in Percival et al. 2004) with 16 real-space power spectrum values and linear redshift-space distortion parameter β(L*,0). The recovered marginalised band-powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17 dimensional likelihood hyper-surface in order to allow the likelihood to be quickly estimated given a set of model band-powers and β(L*,0). The likelihood surface is not well approximated by a multi-variate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band-power has a Gaussian distribution in a combination of the band-power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full Spherical Harmonics procedure. All of the data are made publically available (from http://www.roe.ac.uk/~wjp/, enabling the Spherical Harmonics decomposition of the 2dFGRS of Percival et al. (2004) to be easily used as a cosmological constraint.

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arXiv2004

A search for the first massive galaxy clusters

We have obtained deep, multi-band imaging observations around three of the most distant known quasars at redshifts z>6. Standard accretion theory predicts that the supermassive black holes present in these quasars were formed at a very early epoch. If a correlation between black hole mass and dark matter halo mass is present at these early times, then these rare supermassive black holes will be located inside the most massive dark matter halos. These are therefore ideal locations to search for the first clusters of galaxies. We use the Lyman-break technique to identify star-forming galaxies at high redshifts. Our observations show no overdensity of star-forming galaxies in the fields of these quasars. The lack of (dust-free) luminous starburst companions indicates that the quasars may be the only massive galaxies in their vicinity undergoing a period of intense activity.

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arXiv2004

The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue

We present the result of a decomposition of the 2dFGRS galaxy overdensity field into an orthonormal basis of spherical harmonics and spherical Bessel functions. Galaxies are expected to directly follow the bulk motion of the density field on large scales, so the absolute amplitude of the observed large-scale redshift-space distortions caused by this motion is expected to be independent of galaxy properties. By splitting the overdensity field into radial and angular components, we linearly model the observed distortion and obtain the cosmological constraint Omega_m^{0.6} sigma_8=0.46+/-0.06. The amplitude of the linear redshift-space distortions relative to the galaxy overdensity field is dependent on galaxy properties and, for L_* galaxies at redshift z=0, we measure beta(L_*,0)=0.58+/-0.08, and the amplitude of the overdensity fluctuations b(L_*,0) sigma_8=0.79+/-0.03, marginalising over the power spectrum shape parameters. Assuming a fixed power spectrum shape consistent with the full Fourier analysis produces very similar parameter constraints.

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arXiv2003

Fourier analysis of luminosity-dependent galaxy clustering

We extend the Fourier transform based method for the analysis of galaxy redshift surveys of Feldman, Kaiser & Peacock (1994: FKP) to model luminosity-dependent clustering. In a magnitude limited survey, galaxies at high redshift are more luminous on average than galaxies at low redshift. Galaxy clustering is observed to increase with luminosity, so the inferred density field is effectively multiplied by an increasing function of radius. This has the potential to distort the shape of the recovered power spectrum. In this paper we present an extension of the FKP analysis method to incorporate this effect, and present revised optimal weights to maximize the precision of such an analysis. The method is tested and its accuracy assessed using mock catalogues of the 2-degree field galaxy redshift survey (2dFGRS). We also show that the systematic effect caused by ignoring luminosity-dependent bias was negligible for the initial analysis of the 2dFGRS of Percival et al. (2001). However, future surveys, sensitive to larger scales, or covering a wider range of galaxy luminosities will benefit from this refined method.

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arXiv2002

The bias of galaxies and the density of the universe from the 2dF galaxy redshift survey

By studying the bispectrum of the galaxy distribution in the 2dF galaxy redhsift survey (2dFGRS), we have shown that 2dFGRS galaxies are unbiased tracers of the mass distribution. This allows us the break the degeneracy intrinsic to power spectrum studies, between the matter density parameter Omega_m and the bias parameter b, and to obtain an accurate measurement of Omega_m: Omega_{m,z_{eff}}=0.27 \pm 0.06, a measurement obtained from the 2dFGRS alone, independently from other data sets. This result has to be interpreted as Omega_m at the effective redshift of the survey z_{eff}=0.17. Extrapolated at z=0 we obtain Omega_m=0.2 \pm 0.06 for the LCDM model. This constraint on the matter density parameter when combined with cosmic microwave background constraints on the flatness of the Universe, show firm evidence that the Universe is dominated by a vacuum energy component.

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arXiv2002

The clustering of halo mergers

We analyse the spatial distribution of halo merger sites using four numerical simulations with high time resolution of structure growth in a Lambda-CDM cosmology. We find no evidence for any large-scale relative bias between mergers and randomly selected haloes of the same mass at high redshift. Given a sample of galaxies that form a Poisson sampling of halo mergers, then the amplitude of the measured clustering ought to lead to a robust estimate of the median host halo mass. In the hierarchical picture of structure growth, mergers between galaxies at high redshifts are thought to create dust enshrouded starbursts leading to increased emission in the sub-mm wavebands. Hence, a measurement of the clustering strength of SCUBA galaxies, for example, can determine whether or not they are giant elliptical galaxies in the process of formation.

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arXiv2002

Parameter constraints for flat cosmologies from CMB and 2dFGRS power spectra

We constrain flat cosmological models with a joint likelihood analysis of a new compilation of data from the cosmic microwave background (CMB) and from the 2dF Galaxy Redshift Survey (2dFGRS). Fitting the CMB alone yields a known degeneracy between the Hubble constant h and the matter density Omega_m, which arises mainly from preserving the location of the peaks in the angular power spectrum. This `horizon-angle degeneracy' is considered in some detail and shown to follow a simple relation Omega_m h^{3.4} = constant. Adding the 2dFGRS power spectrum constrains Omega_m h and breaks the degeneracy. If tensor anisotropies are assumed to be negligible, we obtain values for the Hubble constant h=0.665 +/- 0.047, the matter density Omega_m=0.313 +/- 0.055, and the physical CDM and baryon densities Omega_c h^2 = 0.115 +/- 0.009, Omega_b h^2 = 0.022 +/- 0.002 (standard rms errors). Including a possible tensor component causes very little change to these figures; we set a upper limit to the tensor-to-scalar ratio of r<0.7 at 95% confidence. We then show how these data can be used to constrain the equation of state of the vacuum, and find w<-0.52 at 95% confidence. The preferred cosmological model is thus very well specified, and we discuss the precision with which future CMB data can be predicted, given the model assumptions. The 2dFGRS power-spectrum data and covariance matrix, and the CMB data compilation used here, are available from http://www.roe.ac.uk/~wjp/

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arXiv2002

The 2dF Galaxy Redshift Survey: The amplitudes of fluctuations in the 2dFGRS and the CMB, and implications for galaxy biasing

We compare the amplitudes of fluctuations probed by the 2dF Galaxy Redshift Survey and by the latest measurements of the Cosmic Microwave Background anisotropies. By combining the 2dFGRS and CMB data we find the linear-theory rms mass fluctuations in 8 Mpc/h spheres to be sigma_8 = 0.73 +-0.05 (after marginalization over the matter density parameter Omega_m and three other free parameters). This normalization is lower than the COBE normalization and previous estimates from cluster abundance, but it is in agreement with some revised cluster abundance determinations. We also estimate the scale-independent bias parameter of present-epoch L_s = 1.9L_* APM-selected galaxies to be b(L_s,z=0) = 1.10 +- 0.08 on comoving scales of 0.02 < k < 0.15 h/Mpc. If luminosity segregation operates on these scales, L_* galaxies would be almost un-biased, b(L_*,z=0) = 0.96. These results are derived by assuming a flat Lambda-CDM Universe, and by marginalizing over other free parameters and fixing the spectral index n=1 and the optical depth due to reionization tau=0. We also study the best fit pair (Omega_m,b), and the robustness of the results to varying n and tau. Various modelling corrections can each change the resulting b by 5-15 per cent. The results are compared with other independent measurements from the 2dFGRS itself, and from the SDSS, cluster abundance and cosmic shear.

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arXiv2002

The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe

We compute the bispectrum of the 2dF Galaxy Redshift Survey (2dFGRS) and use it to measure the bias parameter of the galaxies. This parameter quantifies the strength of clustering of the galaxies relative to the mass in the Universe. By analysing 80 million triangle configurations in the wavenumber range 0.1 < k < 0.5 h/Mpc (i.e. on scales roughly between 5 and 30 Mpc/h) we find that the linear bias parameter is consistent with unity: b_1=1.04 pm 0.11, and the quadratic (nonlinear) bias is consistent with zero: b_2=-0.054 pm 0.08. Thus, at least on large scales, optically-selected galaxies do indeed trace the underlying mass distribution. The bias parameter can be combined with the 2dFGRS measurement of the redshift distortion parameter beta = Omega_m^{0.6}/b_1, to yield Omega_m = 0.27 pm 0.06 for the matter density of the Universe, a result which is determined entirely from this survey, independently of other datasets. Our measurement of the matter density of the Universe should be interpreted as Omega_m at the effective redshift of the survey (z=0.17).

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