Galaxy two-point correlation function in general relativity

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 |

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.

Embedded random matrix ensembles with k-body interactions are well established to be appropriate for many quantum systems. For these ensembles the two point correlation function is not yet derived, though these ensembles are introduced 50 years back. Two-point correlation function in eigenvalues of a random matrix ensemble is the ensemble average of the product of the density of eigenvalues at two eigenvalues, say E and E^{'}. Fluctuation measures such as the number variance and Dyson-Mehta Δ_{3} statistic are defined by the two-point function and so also the variance of the level motion in the ensemble. Recently, it is recognized that for the embedded ensembles with k-body interactions the one-point function (ensemble averaged density of eigenvalues) follows the so called q-normal distribution. With this, the eigenvalue density can be expanded by starting with the q-normal form and using the associated q-Hermite polynomials He_{ζ}(x|q). Covariances S_{ζ}S_{ζ^{'}}[over ¯] (overline representing ensemble average) of the expansion coefficients S_{ζ} with ζ≥1 here determine the two-point function as they are a linear combination of the bivariate moments Σ_{PQ} of the two-point function. Besides describing all these, in this paper formulas are derived for the bivariate moments Σ_{PQ} with P+Q≤8, of the two-point correlation function, for the embedded Gaussian unitary ensembles with k-body interactions [EGUE(k)] as appropriate for systems with m fermions in N single particle states. Used for obtaining the formulas is the SU(N) Wigner-Racah algebra. These formulas with finite N corrections are used to derive formulas for the covariances S_{ζ}S_{ζ^{'}}[over ¯] in the asymptotic limit. These show that the present work extends to all k values, the results known in the past in the two extreme limits with k/m→0 (same as q→1) and k=m (same as q=0).

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.

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.

Despite many independent estimates, there has been little consensus reached as to the form of the two-point angular correlation function of galaxies. The two-point angular correlation function for the recently completed Edinburgh-Durham Southern Galaxy Catalogue. This galaxy survey consists of digitized COSMOS scans for 60 UK Schmid fields centred at the South Galactic Pole. The w(θ) results from the catalogue are presented at four depths: b j = 17.5, 18.5, 19.5 and 20.3

We show how a characteristic length scale imprinted in the galaxy two-point correlation function, dubbed the "linear point," can serve as a comoving cosmological standard ruler. In contrast to the baryon acoustic oscillation peak location, this scale is constant in redshift and is unaffected by nonlinear effects to within 0.5 percent precision. We measure the location of the linear point in the galaxy correlation function of the LOWZ and CMASS samples from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) Collaboration. We combine our linear-point measurement with cosmic-microwave-background constraints from the Planck satellite to estimate the isotropic-volume distance D_{V}(z), without relying on a model-template or "reconstruction" method. We find D_{V}(0.32)=1264±28 Mpc and D_{V}(0.57)=2056±22 Mpc, respectively, consistent with the quoted values from the BOSS Collaboration. This remarkable result suggests that all the distance information contained in the baryon acoustic oscillations can be conveniently compressed into the single length associated with the linear point.

We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy–velocity cross-correlation in configuration space. We consider standard estimators of the velocity autocorrelation function, ψ1 and ψ2, the two-point galaxy correlation function, ξgg, and introduce a new estimator of the galaxy–velocity cross-correlation function, ψ3. By including pair counts measured from random catalogues of velocities and positions sampled from distributions characteristic of the true data, we find that the variance in the galaxy–velocity cross-correlation function is significantly reduced. Applying a covariance analysis and χ2 minimization procedure to these statistics, we determine estimates and errors for the normalized growth rate fσ8 and the parameter β = f/b, where b is the galaxy bias factor. We test this framework on mock hemisphere data sets for redshift z &amp;lt; 0.1 with realistic velocity noise constructed from the l-picola simulation code, and find that we are able to recover the fiducial value of fσ8 from the joint combination of ψ1 + ψ2 + ψ3 + ξgg, with 15 per cent accuracy from individual mocks. We also recover the fiducial fσ8 to within 1σ regardless of the combination of correlation statistics used. When we consider all four statistics together we find that the statistical uncertainty in our measurement of the growth rate is reduced by $59{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ2, by $53{{\ \rm per\ cent}}$ compared to the same analysis only considering ψ1, and by $52{{\ \rm per\ cent}}$ compared to the same analysis jointly considering ψ1 and ψ2.

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S.Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

Padmanabhan has suggested a model to relate the non-linear two-point correlation function to the linear two-point correlation function. In this paper, we extend this model in two directions: (1) by averaging over the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between nonlinear and linear correlation functions; (2) by using a physically motivated Ansatz, we generalize the model to N-ppoint correlation functions and relate the non-linear, volume averaged N-point correlation function with the linearly extrapolated volume averaged two-point correlation function evaluated at a different scale. We compare the point of transition between the different regimes obtained from our model with that from numerical simulations, and show that the spectral dependence of the scaling relations seen in the simulations can be easily understood. A comparison of the calculated form of with the simulations shows reasonable agreement. We discuss several implications of the results.

We calculate the two-point correlation function for a sample of ringed galaxies. Results are similar to that of general field galaxies. We also find evidence that these galaxies form very large scale structures.

We examine the effect of redshift space distortions on the galaxy two-point\ncorrelation function $\\xi(r_p,\\pi)$ as a function of separations parallel\n($r_p$) and perpendicular ($\\pi$) to the line of sight. We find that the\nrelative velocity dispersion of pairs of IRAS galaxies is $\\sigma(r)=\n317^{+40}_{-49}$ \\kms at $r=1 \\mpc$, consistent with previous estimates derived\nfrom optically selected galaxy catalogues. Unfortunately, the use of this\nresult to estimate $\\Omega$ via the Cosmic Virial Theorem is thwarted by large\nsystematic uncertainties. We also fit for the mean relative streaming velocity\nof pairs, $v_{12}(r)$, which describes the growth of fluctuations on both\nlinear and nonlinear scales. We find that $v_{12}(r) = 167^{+99}_{-67}$ \\kms at\n$r=4$\\mpc, so that on average, approximately half the Hubble expansion velocity\nof pairs at this separation is canceled by infall. At $r=10$\\mpc, the amplitude\nof the streaming is lower and $v_{12}(r) = 109^{+64}_{-47} \\kms$. Linear\nperturbation theory then implies that $\\Omega^{0.6}/b =0.45^{+0.27}_{-0.18}$ on\nscales $\\sim 10-15 \\mpc$. The amplitude of $v_{12}(r)$ is sensitive to the\nassumed shape of $\\sigma(r)$; if the latter deviates substantially from a\nvirialized form on small scale, our best fit amplitude of $v_{12}(r)$ can\ndeviate by a factor of two.\n

The anisotropies in the galaxy two-point correlation function measured from redshift survey exhibits deviations from the predictions of the linear theory of redshift space distortion on scales as large as 20 h -1 Mpc where we expect linear theory to hold in real space. Any attempt at analysing the anisotropies in the redshift correlation function and determining the linear distortion parameter β requires these deviations to be correctly modelled and taken into account. These deviations are usually attributed to galaxy random motions and these are incorporated in the analysis through a phenomenological model in which the linear redshift correlation is convolved with the random pairwise velocity distribution function along the line of sight. We show that a substantial fraction of the deviations arise from non-linear effects in the mapping from real to redshift space caused by the coherent flows. Models that incorporate this effect provide as good a fit to N-body results as the phenomenological model which only includes the effect of random motions. We find that the pairwise velocity dispersions predicted by all of the models that we have considered are in excess of the values determined directly from the N-body simulations. This indicates a shortcoming in our understanding of the statistical properties of peculiar velocities and their relation to redshift distortion.

Reconstruction of three-dimensional heterogeneous media from a single two-dimensional section via co-occurrence correlation function

view Abstract Citations (36) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Galaxy mergers and active nuclei. I - The luminosity function. II - Cosmological evolution Roos, N. Abstract Theoretical models of active-galactic-nucleus (AGN) formation in galaxies with massive central black holes by the repopulation of stellar loss-cone orbits during galaxy mergers are investigated. A local AGN bolometric luminosity function is calculated for galaxies with Galaxy-like nuclear density distributions using a merging rate based on the two-point correlation function of galaxies and shown to be qualitatively similar to the observed luminosity functions in the visible, X-ray, and radio bands, with a power-law index of -1.4 at high luminosity and a break at radio luminosity about 10 to the 44th erg/s (corresponding to an interacting-galaxy mass ratio greater than 20). The cosmological evolution of the galaxy merging rate is considered, assuming galaxy formation at z = about 3 and galactic-stellar-luminosity-dependent evolution, and found to be faster at the bright end of the galaxy luminosity function. The merger rate outside rich clusters in an expanding universe is found to vary as the inverse of cosmic time. Publication: The Astrophysical Journal Pub Date: July 1985 DOI: 10.1086/163314 Bibcode: 1985ApJ...294..479R Keywords: Black Holes (Astronomy); Cosmology; Extragalactic Radio Sources; Galactic Clusters; Galactic Evolution; Galactic Nuclei; Interacting Galaxies; Luminosity; Active Galactic Nuclei; Astronomical Models; Bivariate Analysis; Mass Ratios; Quasars; Radio Galaxies; Red Shift; Seyfert Galaxies; Stellar Orbits; Astrophysics full text sources ADS |