arXiv subjects

G. Efstathiou

Publications and source records attributed to G. Efstathiou.

At least 163 records · Page 9Linked to original sources

arXiv2004

A Maximum Likelihood Analysis of the Low CMB Multipoles from WMAP

The amplitudes of the quadrupole and octopole measured from the Wilkinson Microwave Anisotropy Probe (WMAP) appear to be lower than expected according to the concordance Lambda CDM cosmology. However, the pseudo-Cl estimator used by the WMAP team is non-optimal. In this paper, we discuss the effects of Galactic cuts on pseudo-Cl and quadratic maximum likelihood estimators. An application of a quadratic maximum likelihood estimator to Galaxy subtracted maps produced by the WMAP team and Tegmark, de Oliveira-Costa and Hamilton (2003) shows that the amplitudes of the low multipoles are stable to different Galactic cuts. In particular, the quadrupole and octopole amplitudes are found to lie in the ranges 176 - 250 (micro K)**2 794 - 1183 (micro K)**2 (and more likely to be at the upper ends of these ranges) rather than the values of 123 (micro K)**2 and 611 (micro K)**2 found by the WMAP team. These results indicate that the discrepancy with the concordance Lambda CDM model at low multipoles is not particularly significant and is in the region of a few percent. This conclusion is consistent with an analysis of the low amplitude of the angular correlation function computed from quadratic maximum likelihood power spectrum estimates.

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arXiv2004

Myths and Truths Concerning Estimation of Power Spectra

It is widely believed that maximum likelihood estimators must be used to provide optimal estimates of power spectra. Since such estimators require require of order N_d^3 operations they are computationally prohibitive for N_d greater than a few tens of thousands. Because of this, a large and inhomogeneous literature exists on approximate methods of power spectrum estimation. These range from manifestly sub-optimal, but computationally fast methods, to near optimal but computationally expensive methods. Furthermore, much of this literature concentrates on the power spectrum estimates rather than the equally important problem of deriving an accurate covariance matrix. In this paper, I consider the problem of estimating the power spectrum of cosmic microwave background (CMB) anisotropies from large data sets. Various analytic results on power spectrum estimators are derived, or collated from the literature, and tested against numerical simulations. An unbiased hybrid estimator is proposed that combines a maximum likelihood estimator at low multipoles and pseudo-C_\ell estimates at high multipoles. The hybrid estimator is computationally fast, nearly optimal over the full range of multipoles, and returns an accurate and nearly diagonal covariance matrix for realistic experimental configurations (provided certain conditions on the noise properties of the experiment are satisfied). It is argued that, in practice, computationally expensive methods that approximate the N_d^3 maximum likelihood solution are unlikely to improve on the hybrid estimator, and may actually perform worse. The results presented here can be generalised to CMB polarization and to power spectrum estimation using other types of data, such as galaxy clustering and weak gravitational lensing.

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arXiv2004

Galaxy groups in the 2dFGRS: the group-finding algorithm and the 2PIGG catalogue

The construction of a catalogue of galaxy groups from the 2-degree Field Galaxy Redshift Survey (2dFGRS) is described. Groups are identified by means of a friends-of-friends percolation algorithm which has been thoroughly tested on mock versions of the 2dFGRS generated from cosmological N-body simulations. The tests suggest that the algorithm groups all galaxies that it should be grouping, with an additional 40% of interlopers. About 55% of the ~190000 galaxies considered are placed into groups containing at least two members of which ~29000 are found. Of these, ~7000 contain at least four galaxies, and these groups have a median redshift of 0.11 and a median velocity dispersion of 260km/s. This 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue represents the largest available homogeneous sample of galaxy groups. It is publicly available on the WWW.

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arXiv2004

Galaxy groups in the 2dFGRS: the luminous content of the groups

The 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue of ~29000 objects is used to study the luminous content of galaxy systems of various sizes. Mock galaxy catalogues constructed from cosmological simulations are used to gauge the accuracy with which intrinsic group properties can be recovered. A Schechter function is found to be a reasonable fit to the galaxy luminosity functions in groups of different mass in the real data. The characteristic luminosity L* is larger for more massive groups. However, the mock data show that the shape of the recovered luminosity function is expected to differ from the true shape, and this must be allowed for when interpreting the data. The variation of halo mass-to-light ratio with group size is studied in both these wavebands. A robust trend of increasing M/L with increasing group luminosity is found in the 2PIGG data. From groups with L_bj=10^{10}Lsol to those 100 times more luminous, the typical bj-band M/L increases by a factor of 5, whereas the rf-band M/L grows by a factor of 3.5. These trends agree well with the simulations, which also predict a minimum M/L on a scale corresponding to the Local Group. Our data indicate that if such a minimum exists, then it must occur at L<~10^{10}Lsol, below the range accurately probed by the 2PIGG catalogue. According to the mock data, the bj M/Ls of the largest groups are expected to be approximately 1.1 times the global value. Assuming that this correction applies to the real data yields an estimate of Omega_m=0.26+/-0.03 (statistical).

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arXiv2003

The Planck High Frequency Instrument, a 3rd generation CMB experiment, and a full sky submillimeter survey

The High Frequency Instrument (HFI) of Planck is the most sensitive CMB experiment ever planned. Statistical fluctuations (photon noise) of the CMB itself will be the major limitation to the sensitivity of the CMB channels. Higher frequency channels will measure galactic foregrounds. Together with the Low Frequency Instrument, this will make a unique tool to measure the full sky and to separate the various components of its spectrum. Measurement of the polarization of these various components will give a new picture of the CMB. In addition, HFI will provide the scientific community with new full sky maps of intensity and polarization at six frequencies, with unprecedented angular resolution and sensitivity. This paper describes the logics that prevailed to define the HFI and the performances expected from this instrument. It details several features of the HFI design that have not been published up to now.

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arXiv2003

The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe

We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses.

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arXiv2003

Is the Low CMB Quadrupole a Signature of Spatial Curvature?

The temperature anisotropy power spectrum measured with the Wilkinson Microwave Anisotropy Probe (WMAP) at high multipoles is in spectacular agreement with an inflationary Lambda-dominated cold dark matter cosmology. However, the low order multipoles (especially the quadrupole) have lower amplitudes than expected from this cosmology, indicating a need for new physics. Here we speculate that the low quadrupole amplitude is associated with spatial curvature. We show that positively curved models are consistent with the WMAP data and that the quadrupole amplitude can be reproduced if the primordial spectrum truncates on scales comparable to the curvature scale.

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arXiv2003

Stable clustering, the halo model and nonlinear cosmological power spectra

We present the results of a large library of cosmological N-body simulations, using power-law initial spectra. The nonlinear evolution of the matter power spectra is compared with the predictions of existing analytic scaling formulae based on the work of Hamilton et al. The scaling approach has assumed that highly nonlinear structures obey `stable clustering' and are frozen in proper coordinates. Our results show that, when transformed under the self-similarity scaling, the scale-free spectra define a nonlinear locus that is clearly shallower than would be required under stable clustering. Furthermore, the small-scale nonlinear power increases as both the power-spectrum index n and the density parameter Omega decrease, and this evolution is not well accounted for by the previous scaling formulae. This breakdown of stable clustering can be understood as resulting from the modification of dark-matter haloes by continuing mergers. These effects are naturally included in the analytic `halo model' for nonlinear structure; using this approach we are able to fit both our scale-free results and also our previous CDM data. This approach is more accurate than the commonly-used Peacock--Dodds formula and should be applicable to more general power spectra. Code to evaluate nonlinear power spectra using this method is available from http://as1.chem.nottingham.ac.uk/~res/software.html Following publication, we will make the power-law simulation data available through the Virgo website http://www.mpa-garching.mpg.de/Virgo

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arXiv2003

Reconstructing the primordial power spectrum

We reconstruct the shape of the primordial power spectrum from the latest cosmic microwave background data, including the new results from the Wilkinson Microwave Anisotropy Probe (WMAP), and large scale structure data from the two degree field galaxy redshift survey (2dFGRS). We tested four parameterizations taking into account the uncertainties in four cosmological parameters. First we parameterize the initial spectrum by a tilt and a running spectral index, finding marginal evidence for a running spectral index only if the first three WMAP multipoles (ell=2,3,4) are included in the analysis. Secondly, to investigate further the low CMB large scale power, we modify the conventional power-law spectrum by introducing a scale above which there is no power. We find a preferred position of the cut at k_c ~ 3e-4 /Mpc although k_c=0 (no cut) is not ruled out. Thirdly we use a model independent parameterization, with 16 bands in wavenumber, and find no obvious sign of deviation from a power law spectrum on the scales investigated. Furthermore the values of the other cosmological parameters defining the model remain relatively well constrained despite the freedom in the shape of the initial power spectrum. Finally we investigate a model motivated by double inflation, in which the power spectrum has a break between two characteristic wavenumbers. We find that if a break is required to be in the range 0.01 < k Mpc <0.1 then the ratio of amplitudes across the break is constrained to be 1.23 +/- 0.14. Our results are consistent with a power law spectrum that is featureless and close to scale invariant over the wavenumber range 0.005 ~< k Mpc ~< 0.15, with a hint of a decrease in power on the largest scales.

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arXiv2003

The 2dF Galaxy Redshift Survey: galaxy clustering per spectral type

We have calculated the two-point correlation functions in redshift space, xi(sigma,pi), for galaxies of different spectral types in the 2dF Galaxy Redshift Survey. Using these correlation functions we are able to estimate values of the linear redshift-space distortion parameter, beta = Omega_m^0.6/b, the pairwise velocity dispersion, a, and the real-space correlation function, xi(r), for galaxies with both relatively low star-formation rates (for which the present rate of star formation is less than 10% of its past averaged value) and galaxies with higher current star-formation activity. At small separations, the real-space clustering of passive galaxies is very much stronger than that of the more actively star-forming galaxies; the correlation-function slopes are respectively 1.93 and 1.50, and the relative bias between the two classes is a declining function of radius. On scales larger than 10 h^-1 Mpc there is evidence that the relative bias tends to a constant, b(passive)/b(active) ~ 1. This result is consistent with the similar degrees of redshift-space distortions seen in the correlation functions of the two classes -- the contours of xi(sigma,pi) require beta(active)=0.49+/-0.13, and beta(passive)=0.48+/-0.14. The pairwise velocity dispersion is highly correlated with beta. However, despite this a significant difference is seen between the two classes. Over the range 8-20 h^-1 Mpc, the pairwise velocity dispersion has mean values 416+/-76 km/s and 612+/-92 km/s for the active and passive galaxy samples respectively. This is consistent with the expectation from morphological segregation, in which passively evolving galaxies preferentially inhabit the cores of high-mass virialised regions.

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arXiv2003

Fred Hoyle: Contributions to the Theory of Galaxy Formation

I review two fundamental contributions that Fred Hoyle made to the theory of galaxy formation. Hoyle was the first to propose that protogalaxies acquired their angular momentum via tidal torques from neighbouring perturbations during a period of gravitational instability. To my knowledge, he was also the first to suggest that the masses of galaxies could be explained by the requirement that primordial gas clouds cool radiatively on a suitable timescale. Tidal torques and cooling arguments play a central role in the modern theory of galaxy formation. It is a measure of Hoyle's breadth and inventiveness that he recognised the importance of these processes at such an early stage in the history of the subject.

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arXiv2002

The 2dF Galaxy Redshift Survey: the luminosity function of cluster galaxies

We have determined the composite luminosity function (LF) for galaxies in 60 clusters from the 2dF Galaxy Redshift Survey. The LF spans the range $-22.5<M_{b_{\rm J}}<-15$, and is well-fitted by a Schechter function with ${M_{b_{\rm J}}}^{*}=-20.07\pm0.07$ and $α=-1.28\pm0.03$ ($H_0$=100 km s$^{-1}$ Mpc$^{-1}$, $Ω_M$=0.3, $Ω_Λ$=0.7). It differs significantly from the field LF of \cite{mad02}, having a characteristic magnitude that is approximately 0.3 mag brighter and a faint-end slope that is approximately 0.1 steeper. There is no evidence for variations in the LF across a wide range of cluster properties. However the LF of early-type galaxies in clusters is both brighter and steeper than its field counterpart. The differences between the field and cluster LFs for the various spectral types can be qualitatively explained by the suppression of star formation in the dense cluster environment, together with mergers to produce the brightest early-type galaxies.

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arXiv2002

Studying large-scale structure with the 2dF Galaxy Redshift Survey

The 2dF Galaxy Redshift Survey is the first to observe more than 100,000 redshifts. This allows precise measurements of many of the key statistics of galaxy clustering, in particular redshift-space distortions and the large-scale power spectrum. This paper presents the current 2dFGRS results in these areas. Redshift-space distortions are detected with a high degree of significance, confirming the detailed Kaiser distortion from large-scale infall velocities, and measuring the distortion parameter beta equiv Omega_m^{0.6}/b = 0.43 +- 0.07. The power spectrum is measured to < 10% accuracy for k > 0.02 h Mpc^{-1}, and is well fitted by a CDM model with Omega_m h = 0.20 +- 0.03 and a baryon fraction of 0.15 +- 0.07. A joint analysis with CMB data requires Omega_m = 0.29 +- 0.05, assuming scalar fluctuations, but no priors on other parameters. Two methods are used to determine the large-scale bias parameter: an internal bispectrum analysis yields b = 1.04 +- 0.11, in very good agreement with the b = 1.10 +- 0.08 obtained from a joint 2dFGRS+CMB analysis, again assuming scalar fluctuations. These figures refer to galaxies of approximate luminosity 2L^*; luminosity dependence of clustering is detected at high significance, and is well described by b/b^* = 0.85 + 0.15(L/L^*).

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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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arXiv2002

The 2dF Galaxy Redshift Survey: The b_J-band galaxy luminosity function and survey selection function

We use more than 110500 galaxies from the 2dF galaxy redshift survey (2dFGRS) to estimate the b_J-band galaxy luminosity function at redshift z=0, taking account of evolution, the distribution of magnitude measurement errors and small corrections for incompletenessin the galaxy catalogue. Throughout the interval -16.5>M- 5log h>-22, the luminosity function is accurately described by a Schechter function with M* -5log h =-19.66+/-0.07, alpha=-1.21+/-0.03 and phistar=(1.61+/-0.08) 10^{-2} h^3/Mpc^3, giving an integrated luminosity density of rho_L=(1.82+/-0.17) 10^8 h L_sol/Mpc^3 (assuming an Omega_0=0.3, Lambda_0=0.7 cosmology). The quoted errors have contributions from the accuracy of the photometric zeropoint, large scale structure in the galaxy distribution and, importantly, from the uncertainty in the appropriate evolutionary corrections. Our luminosity function is in excellent agreement with, but has much smaller statistical errors than an estimate from the Sloan Digital Sky Survey (SDSS) data when the SDSS data are accurately translated to the b_J-band and the luminosity functions are normalized in the same way. We use the luminosity function, along with maps describing the redshift completeness of the current 2dFGRS catalogue, and its weak dependence on apparent magnitude, to define a complete description of the 2dFGRS selection function. Details and tests of the calibration of the 2dFGRS photometric parent catalogue are also presented.

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arXiv2002

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 about quintessence from such data. First, by expanding the quintessence equation of state as w_Q(z) = w_Q(0)-alpha*ln(1+z), to fit the data, it is possible to reconstruct the quintessence potential for a wide range of smoothly varying potentials. Second, it will be possible, to test the basic properties of the dark energy by constraining the parameters Omega_Q, w_Q and alpha. We show that it may be possible, for example, to distinguish between quintessence and the cosmological constant in this way. Further, 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.

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arXiv2002

The 2dF Galaxy Redshift Survey: Galaxy luminosity functions per spectral type

We calculate the optical bj luminosity function of the 2dF Galaxy Redshift Survey (2dFGRS) for different subsets defined by their spectral properties. These spectrally selected subsets are defined using a new parameter, eta, which is a linear combination of the first two projections derived from a Principal Component Analysis. This parameter eta identifies the average emission and absorption line strength in the galaxy rest-frame spectrum and hence is a useful indicator of the present star formation. We use a total of 75,000 galaxies in our calculations, chosen from a sample of high signal-to-noise ratio, low redshift galaxies observed before January 2001. We find that there is a systematic steepening of the faint end slope (alpha) as one moves from passive (alpha = -0.54) to active (alpha = -1.50) star-forming galaxies, and that there is also a corresponding faintening of the rest-frame characteristic magnitude M* - 5\log_10(h) (from -19.6 to -19.2). We also show that the Schechter function provides a poor fit to the quiescent (Type 1) LF for very faint galaxies (M - 5log_10(h) fainter than -16.0), perhaps suggesting the presence of a significant dwarf population. The luminosity functions presented here give a precise confirmation of the trends seen previously in a much smaller preliminary 2dFGRS sample, and in other surveys. We also present a new procedure for determining self-consistent K-corrections and investigate possible fibre-aperture biases.

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arXiv2002

The 2dF Galaxy Redshift Survey: The population of nearby radio galaxies at the 1 mJy level

We use redshift determinations and spectral analysis of galaxies in the 2dF Galaxy Redshift Survey to study the properties of local radio sources with $S\ge 1$ mJy. 557 objects drawn from the FIRST survey, corresponding to 2.3 per cent of the total radio sample, are found in the 2dFGRS cataloge within the area $9^h 48^m \simlt {\rm RA}({\rm 2000}) \simlt 14^h 32^m$ and $-2.77^\circ \simlt {\rm dec}({\rm 2000}) \simlt 2.25^\circ$, down to a magnitude limit $b_J= 19.45$. The excellent quality of 2dF spectra allows us to divide these sources into classes, according to their optical spectra. Radio galaxies (i.e. absorption systems, mainly belonging to the class of FR I sources, whose spectra may or may not show emission lines due to AGN activity) make up 63 per cent of the spectroscopic sample; they are characterized by relatively high radio-to-optical ratios, red colours and luminosities $10^{21}\simlt P_{1.4{\rm GHz}} W Hz^${-1}$ sr$^{-1}$ \simlt 10^{24}$. Actively star-forming galaxies instead contribute with 30 per cent to the total sample. These objects -- principally found at low redshifts ($z \simlt 0.1$) -- in general show low radio-to-optical ratios, blue colours and low radio luminosities. We also found 18 Seyfert 2 galaxies and 4 Seyfert 1's. Analysis of the local radio luminosity function shows that radio galaxies are well described by models that assume pure luminosity evolution, at least down to radio powers $P_{1.4{\rm GHz}}\simlt 10^{20.5} W Hz$^{-1}$ sr$^{-1}$ Late-type galaxies, whose relative contribution to the RLF is found to be lower than was predicted by previous work, present a luminosity function which is compatible with the IRAS galaxy LF, and therefore plausibly constitute the radio counterpart of the dusty spirals and starbursts that dominate the counts at 60 $μ$m.

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