Galaxy Correlation Functions Provide a More Robust Cosmological Standard Ruler.

view Abstract Citations (28) References (44) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Cluster-Cluster Correlation in Hybrid Models Jing, Y. P. ; Mo, H. J. ; Boerner, G. ; Fang, L. Z. Abstract Using N-body simulations, we have calculated the two-point correlation functions of the clusters of galaxies (ξ_cc_) in a set of hybrid (CDM + HDM + baryon) models. The galaxies are identified as density peaks above certain thresholds, to match the observed two-point correlation function of galaxies on scales <~10 h^-1^ Mpc. The clusters of galaxies are identified such that their number density is the same as that of Abell clusters. It is found that both the coherence length (the largest scale where ξ_cc_ remains positive) and the amplitude of ξ_cc_ increase systematically with the power of the initial density spectrum on large scales. For one model in which the power on large scales is sufficient to match the two-point angular correlation function of galaxies of the APM survey, ξ_cc_has a correlation length r_0_ = 23.0 +/- 0.9 h^-1^ Mpc and remains positive for r <~70 h^-1^ Mpc with a weak dependence on the richness of clusters, in good agreement with observations. Our results suggest that the observed large correlation length of Abell clusters, which is sometimes considered to be due to contaminations, should be expected in models which have enough power to explain the recent observations of galaxy clustering and motions on large scales. Publication: The Astrophysical Journal Pub Date: July 1993 DOI: 10.1086/172847 Bibcode: 1993ApJ...411..450J Keywords: Angular Correlation; Astronomical Models; Dark Matter; Galactic Clusters; Interacting Galaxies; Many Body Problem; Galactic Evolution; Galactic Structure; Universe; Astrophysics; COSMOLOGY: DARK MATTER; GALAXIES: CLUSTERING; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; METHODS: NUMERICAL full text sources ADS |

Unveiling the physics behind the accelerating expansion of the Universe, which was discovered in 1998, is one of the most challenging tasks in modern sciences. In theory, the cosmic acceleration may result from the fact that approximately two thirds energy density of the Universe is provided by Dark Energy, a yet unknown energy component, or imply that general relativity, the most successful theory of gravity within the solar system established by Einstein, may need to be extended on cosmological scales. In principle, the scenarios of energy and modified gravity can yield identical cosmic expansion history, but predict different structure growth. Therefore, this dark degeneracy can be broken by studying the evolution history of the cosmic structure with large galaxy surveys. Galaxy surveys is one of the key probes for energy and gravity, which can be used to reconstruct the history of cosmic expansion and structure growth using baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) respectively. BAO is a specific three-dimensional clustering pattern of galaxies due to interactions between photons and baryons in the early Universe. Back in the early cosmic epochs, photons scattered with electrons and electrons interacted with protons, making photons and protons (baryonic matter) glued together. There are two opposite forces exerting on this tightly coupled plasma: the pressure of photons and gravity acting on baryons. Similar to what happens to a vibrating spring vertically fixed on the ground, the photon-baryon plasma underwent Oscillations, propagating waves in the same way as the sound does. Therefore, this physical process is called Baryonic Acoustic Oscillations. The effect of the BAO is to push galaxies apart until at a specific time, called the cosmic recombination, when the temperature of the Universe becomes so low that no more photon-baryon interaction can happen. Since then, the separation among galaxies is frozen at a characteristic scale, which is about 150 Mpc depending on the energy content of the Universe, making it a standard ruler to be used to infer the expansion history of the Universe, thus BAO is one of the key probes for the nature of energy. RSD is another special three-dimensional clustering pattern of galaxies, but it is due to local motions of the galaxies under gravity. Suppose galaxies only co-move with the cosmic background without moving locally, the clustering of galaxies should be isotropic, in other words, there are same number of galaxy pairs along or across lines of sight of the observer. However, this is not the case in the real world. Galaxies move towards nearby galaxies due to gravity, thus they have velocities. As we infer galaxies positions from their line-of-sight velocities in astronomy, the peculiar velocities can distort galaxies positions, which results in a distortion, called Redshift Space Distortions, in the 3D clustering of galaxies. RSD plays a key role in cosmology as it can directly be used to infer the nature of gravity (remember the peculiar motion is caused by gravity!). The Baryonic Oscillation Spectroscopic Survey (BOSS) program, part of the Sloan Digital Sky Survey (SDSS)-III project, is the largest completed galaxy survey in the world. BOSS has enabled us to investigate energy and gravity to a unprecedented precision, which has implied a 3.5 sigma evidence for the dynamics of energy. Ongoing and forthcoming galaxy surveys including the extended Baryonic Oscillation Spectroscopic Survey (eBOSS), Dark Energy Spectroscopic Instrument (DESI) and Prime Focus Spectrograph (PFS), will be able to probe the Universe at higher redshifts with much higher precision, which will be providing key observational support for the study of cosmic acceleration.

We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off (kIR ⩽ H0) in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation (∼ 2% at 150 Mpc/h and redshift one). Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.

We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of $1.5\%-3.4\%$ for $D_V/r_d$, $1.8\% -4.2\%$ for $D_A/r_d$ and $3.7\% - 7.5\%$ for $H \ r_d$, depending on effective redshifts. We provide our BAO measurement of $D_A/r_d$ and $H \ r_d$ with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in \citet{Acacia}, in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements, and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, ξ̂(ř,řL), where řL is the location of a subvolume, and the corresponding mean overdensities, δ̄(řL). This correlation, which we call the “integrated three-point function”, iζ(r)≡⟨ξ̂(ř,řL)δ̄(řL)⟩, measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The iζ(r) measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of iζ(r). The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters (b1 and b2), as well as on the amplitude and linear growth rate of matter fluctuations (σ8 and f). Combining iζ(r) with the constraints on b1σ8 and fσ8 from the global two-point correlation function and that on σ8 from the weak lensing signal of BOSS galaxies, we measure b2=0.41±0.41 (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.

Extraction of the Baryon Acoustic Oscillations (BAO) to per cent level accuracy is challenging and demands an understanding of many potential systematics to an accuracy well below 1 per cent, in order to ensure that they do not combine significantly when compared to statistical error of the BAO measurement. Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 (DR11) reaches a distance measurement with ?1 per cent statistical error and this prompts an extensive search for all possible sub-per cent level systematic errors which could previously be safely ignored. In this paper, we analyse the potential systematics in BAO fitting methodology using mocks and data from BOSS DR10 and DR11. We demonstrate the robustness of the fiducial multipole fitting methodology to be at 0.1-0.2 per cent level with a wide range of tests in mock galaxy catalogues pre- and post-reconstruction. We also find the DR10 and DR11 data from BOSS to be robust against changes in methodology at a similar level. This systematic error budget is incorporated into the BOSS DR10 and DR11 BAO measurements. Of the wide range of changes we have investigated, we find that when fitting post-reconstructed data or mocks, the only change which has an effect >0.1 per cent on the best-fitting values of distance measurements is varying the order of the polynomials to describe the broad-band terms (?0.2 per cent). Finally, we compare an alternative methodology denoted as Clustering Wedges with Multipoles, and find that it is consistent with the standard approach.

We report a detection of the baryon acousticoscillation (BAO) feature in the flux-correlation function of the Lyα forest of high-redshift quasars with a statistical significance of five standard deviations. The study uses 137 562 quasars in the redshift range 2.1 ≤ z ≤ 3.5 from the data release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-III. This sample contains three times the number of quasars used in previous studies. The measured position of the BAO peak determines the angular distance, DA(z = 2.34) and expansion rate, H(z = 2.34), both on a scale set by the sound horizon at the drag epoch, rd. We find DA/rd = 11.28 ± 0.65(1σ)+2.8-1.2 (2σ) and DH/rd = 9.18 ± 0.28(1σ) ± 0.6(2σ) where DH = c/H. The optimal combination, ~DH0.7DA0.3/rd is determined with a precision of ~2%. For the value rd = 147.4 Mpc, consistent with the cosmic microwave background power spectrum measured by Planck, we find DA(z = 2.34) = 1662 ± 96(1σ) Mpc and H(z = 2.34) = 222 ± 7(1σ) km s-1 Mpc-1. Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors. Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Lyα forest cross-correlation. The autocorrelation and cross-correlation approaches are complementary because of the quite different impact of redshift-space distortion on the two measurements. The combined constraints from the two correlation functions imply values of DA/rd that are 7% lower and 7% higher for DH/rd than the predictions of a flat ΛCDM cosmological model with the best-fit Planck parameters. With our estimated statistical errors, the significance of this discrepancy is ≈2.5σ. Appendices are available in electronic form at &lt;A href="http://www.aanda.org/10.1051/0004-6361/201423969/olm"&gt;http://www.aanda.org&lt;/A&gt;

We measure the quasar two-point correlation function over the redshift range 2.2<z<2.8 using data from the Baryon Oscillation Spectroscopic Survey. We use a homogeneous subset of the data consisting of 27,129 quasars with spectroscopic redshifts---by far the largest such sample used for clustering measurements at these redshifts to date. The sample covers 3,600 square degrees, corresponding to a comoving volume of 9.7(Gpc/h)^3 assuming a fiducial LambdaCDM cosmology, and it has a median absolute i-band magnitude of -26, k-corrected to z=2. After accounting for redshift errors we find that the redshift space correlation function is fit well by a power-law of slope -2 and amplitude s_0=(9.7\pm 0.5)Mpc/h over the range 3<s<25Mpc/h. The projected correlation function, which integrates out the effects of peculiar velocities and redshift errors, is fit well by a power-law of slope -1 and r_0=(8.4\pm 0.6)Mpc/h over the range 4<R<16Mpc/h. There is no evidence for strong luminosity or redshift dependence to the clustering amplitude, in part because of the limited dynamic range in our sample. Our results are consistent with, but more precise than, previous measurements at similar redshifts. Our measurement of the quasar clustering amplitude implies a bias factor of b~3.5 for our quasar sample. We compare the data to models to constrain the manner in which quasars occupy dark matter halos at z~2.4 and infer that such quasars inhabit halos with a characteristic mass of <M>~10^{12}Msun/h with a duty cycle for the quasar activity of 1 per cent.

We present a new method that simultaneously solves for cosmology and galaxy bias on non-linear scales. The method uses the halo model to analytically describe the (non-linear) matter distribution, and the conditional luminosity function (CLF) to specify the halo occupation statistics. For a given choice of cosmological parameters, this model can be used to predict the galaxy luminosity function, as well as the two-point correlation functions of galaxies, and the galaxy–galaxy lensing signal, both as a function of scale and luminosity. These observables have been reliably measured from the Sloan Digital Sky Survey. In this paper, the first in a series, we present the detailed, analytical model, which we test against mock galaxy redshift surveys constructed from high-resolution numerical N-body simulations. We demonstrate that our model, which includes scale dependence of the halo bias and a proper treatment of halo exclusion, reproduces the three-dimensional galaxy–galaxy correlation and the galaxy–matter cross-correlation (which can be projected to predict the observables) with an accuracy better than 10 (in most cases 5) per cent. Ignoring either of these effects, as is often done, results in systematic errors that easily exceed 40 per cent on scales of ∼ 1 h− 1 Mpc, where the data are typically most accurate. Finally, since the projected correlation functions of galaxies are never obtained by integrating the redshift-space correlation function along the line of sight out to infinity, simply because the data only cover a finite volume, they are still affected by residual redshift-space distortions (RRSDs). Ignoring these, as done in numerous studies in the past, results in systematic errors that easily exceed 20 per cent on large scales (rp ≳ 10 h− 1 Mpc). We show that it is fairly straightforward to correct for these RRSDs, to an accuracy better than ∼ 2 per cent, using a mildly modified version of the linear Kaiser formalism.

Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter H(z) and angular diameter distance DA(z). These measurements are typically obtained from moments of the measured 2-point clustering statistics, with respect to the cosine of the angle to the line of sight mu. The position of the BAO features in each moment depends on a combination of DA(z) and H(z), and measuring the positions in two or more moments breaks this parameter degeneracy. We derive analytic formulae for the parameter combinations measured from moments given by Legendre polynomials, power laws and top-hat Wedges in μ, showing explicitly what is being measured by each in real-space for both the correlation function and power spectrum, and in redshift-space for the power spectrum. The large volume covered by modern galaxy samples means that the correlation function can be well approximated as having no correlations at different mu on the BAO scale, and that the errors on this scale are approximately independent of mu. Using these approximations, we derive the information content of various moments. We show that measurements made using either the monopole and quadrupole, or the monopole and μ2 power-law moment, are optimal for anisotropic BAO measurements, in that they contain all of the available information using two moments, the minimal number required to measure both H(z) and DA(z). We test our predictions using 600 mock galaxy samples, matched to the SDSS-III Baryon Oscillation Spectroscopic Survey CMASS sample, finding a good match to our analytic predictions. Our results should enable the optimal extraction of information from future galaxy surveys such as eBOSS, DESI and Euclid.

We measure and analyse the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) relative to the line-of-sight (LOS), for LOWZ and CMASS galaxy samples drawn from the final Data Release 12 (DR12). The LOWZ sample contains 361\,762 galaxies with an effective redshift of $z_{\rm lowz}=0.32$, and the CMASS sample 777\,202 galaxies with an effective redshift of $z_{\rm cmass}=0.57$. From the power spectrum monopole and quadrupole moments around the LOS, we measure the growth of structure parameter $f$ times the amplitude of dark matter density fluctuations $\sigma_8$ by modeling the Redshift-Space Distortion signal. When the geometrical Alcock-Paczynski effect is also constrained from the same data, we find joint constraints on $f\sigma_8$, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon $D_A(z)/r_s(z_d)$. We find $f(z_{\rm lowz})\sigma_8(z_{\rm lowz})=0.394\pm0.062$, $D_A(z_{\rm lowz})/r_s(z_d)=6.35\pm0.19$, $H(z_{\rm lowz})r_s(z_d)=(11.41\pm 0.56)\,{10^3\rm km}s^{-1}$ for the LOWZ sample, and $f(z_{\rm cmass})\sigma_8(z_{\rm cmass})=0.444\pm0.038$, $D_A(z_{\rm cmass})/r_s(z_d)=9.42\pm0.15$, $H(z_{\rm cmass})r_s(z_d)=(13.92 \pm 0.44)\, {10^3\rm km}s^{-1}$ for the CMASS sample. We find general agreement with previous BOSS DR11 measurements. Assuming the Hubble parameter and angular distance parameter are fixed at fiducial $\Lambda$CDM values, we find $f(z_{\rm lowz})\sigma_8(z_{\rm lowz})=0.485\pm0.044$ and $f(z_{\rm cmass})\sigma_8(z_{\rm cmass})=0.436\pm0.022$ for the LOWZ and CMASS samples, respectively.

It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions that do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.

We present a pedagogical systematic investigation of the accuracy of Eulerian and Lagrangian perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ≲3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theory to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive \U0001d4aa(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by Eulerian Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z≲4 in real space.In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price.Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.

The observed two-point correlation functions of galaxies in redshift space become anisotropic because of the geometry of the universe, as well as because of the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift z and obtain analytic formulae to infer the deceleration parameter q0, the density parameter Ω0, and the derivative of the bias parameter d ln b/dz at z = 0 in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum and thus can be applied to future redshift surveys of galaxies, including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of β0 ≡ Ω00.6/b from a galaxy redshift survey on the basis of a conventional estimator for β0, which neglects both the geometrical distortion effect and the time evolution of the parameter β(z). If the magnitude limit of the survey is as faint as 18.5 (in B band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will definitely dominate the expected statistical error for future surveys.

We describe mock data-sets generated to simulate the high-redshift quasar sample in Data Release 11 (DR11) of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). The mock spectra contain Lyα forest correlations useful for studying the 3D correlation function including Baryon Acoustic Oscillations (BAO). They also include astrophysical effects such as quasar continuum diversity and high-density absorbers, instrumental effects such as noise and spectral resolution, as well as imperfections introduced by the SDSS pipeline treatment of the raw data. The Lyα forest BAO analysis of the BOSS collaboration, described in Delubac et al. 2014, has used these mock data-sets to develop and cross-check analysis procedures prior to performing the BAO analysis on real data, and for continued systematic cross checks. Tests presented here show that the simulations reproduce sufficiently well important characteristics of real spectra. These mock data-sets will be made available together with the data at the time of the Data Release 11.