Galaxy Bias Parameter Research Articles

The three-point function in large-scale structure: redshift distortions and galaxy bias

We study the behavior of the three-point correlation function xi_3 of dark matter and mock galaxies, concentrating on the effects of redshift-space distortions and the determination of galaxy bias parameters in current redshift galaxy surveys. On large scales, redshift space distortions tend to wash out slightly the configuration dependence of the reduced 3-point function Q3 ~ xi_3/xi_2^2. On smaller scales (< 10 Mpc/h), Q3 develops a characteristic U-shape anisotropy between elongated and open triangles due to the effects of velocity dispersion. We show that this shape is quite universal, very weakly dependent on scale, initial spectral index or cosmological parameters and should be detectable in current galaxy surveys even if affected by shot-noise or galaxy bias. We present a detailed method for obtaining constraints on galaxy bias parameters from measurements of Q3 in current galaxy redshift surveys, based on the eigenmode analysis similar to the one developed for the bispectrum. We show that our method recovers the bias parameters introduced into mock galaxies by a HOD prescription and is also able to handle potential systematics in the case when a smaller number than ideal of mock catalogs is used to estimate the covariance matrix. We find that current redshift surveys (e.g. SDSS or 2dFGRS) are just about large enough to get interesting new constraints on bias.

Galaxy bias and halo-occupation numbers from large-scale clustering

We show that current surveys have at least as much signal to noise in higher-order statistics as in the power spectrum at weakly nonlinear scales. We discuss how one can use this information to determine the mean of the galaxy halo occupation distribution (HOD) using only large-scale information, through galaxy bias parameters determined from the galaxy bispectrum and trispectrum. After introducing an averaged, reasonably fast to evaluate, trispectrum estimator, we show that the expected errors on linear and quadratic bias parameters can be reduced by at least 20-40%. Also, the inclusion of the trispectrum information, which is sensitive to "three-dimensionality" of structures, helps significantly in constraining the mass dependence of the HOD mean. Our approach depends only on adequate modeling of the abundance and large-scale clustering of halos and thus is independent of details of how galaxies are distributed within halos. This provides a consistency check on the traditional approach of using two-point statistics down to small scales, which necessarily makes more assumptions. We present a detailed forecast of how well our approach can be carried out in the case of the SDSS.

The Clustering Dipole of the Local Universe from the Two Micron All Sky Survey

The unprecedented sky coverage and photometric uniformity of the Two Micron All Sky Survey (2MASS) provides a rich resource for investigating the galaxies populating the local universe. A full characterization of the large-scale clustering distribution is important for theoretical studies of structure formation. 2MASS offers an all-sky view of the local galaxy population at 2.15 μm, unbiased by young stellar light and minimally affected by dust. We use 2MASS to map the local distribution of galaxies, identifying the largest structures in the nearby universe. The inhomogeneity of these structures causes an acceleration on the Local Group of galaxies, which can be seen in the dipole of the cosmic microwave background (CMB). We find that the direction of the 2MASS clustering dipole is 16° from the CMB dipole, confirming that the local galaxy distribution accelerates the Local Group. From the magnitude of the dipole, we find a value of the linear bias parameter b = 1.06 ± 0.17 in the Ks band. Thus, the linear bias parameter of Ks-selected galaxies is similar to the bias parameter found in other wave bands.

An Inversion Method for Measuring β in Large‐Redshift Surveys

A precision method for determining the value of β = Ω/b, where b is the galaxy bias parameter, is presented. In contrast to other existing techniques that focus on estimating this quantity by measuring distortions in the redshift-space galaxy-galaxy correlation function or power spectrum, this method removes the distortions by reconstructing the real-space density field and determining the value of β that results in a symmetric signal. To remove the distortions, the method modifies the amplitudes of a Fourier plane-wave expansion of the survey data parameterized by β. This technique is not dependent on the small-angle/plane-parallel approximation and can make full use of large-redshift survey data. It has been tested using simulations with four different cosmologies and returns the value of β to ±0.031, more than a factor of 2 improvement over existing techniques.

Peculiar velocities and the mean density parameter

We study the peculiar velocity field inferred from the Mark III spirals using a new method of analysis. We estimate optimal values of Tully-Fisher scatter and zero-point offset, and we derive the 3-dimensional rms peculiar velocity ($\sigma_v$) of the galaxies in the samples analysed. We check our statistical analysis using mock catalogs derived from numerical simulations of CDM models considering measurement uncertainties and sampling variations. Our best determination for the observations is $\sigma_v= (660\pm50) km/s$. We use the linear theory relation between $\sigma_v$, the density parameter $\Omega$, and the galaxy correlation function $\xi(r)$ to infer the quantity $\beta =\Omega^{0.6}/b = 0.60^{+0.13}_{-0.11}$ where $b$ is the linear bias parameter of optical galaxies and the uncertainties correspond to bootstrap resampling and an estimated cosmic variance added in quadrature. Our findings are consistent with the results of cluster abundances and redshift space distortion of the two-point correlation function. These statistical measurements suggest a low value of the density parameter $\Omega \sim 0.4$ if optical galaxies are not strongly biased tracers of mass.

Cosmology in the Next Millennium: Combining Microwave Anisotropy Probe and Sloan Digital Sky Survey Data to Constrain Inflationary Models

The existence of primordial adiabatic Gaussian random-phase density fluctuations is a generic prediction of inflation. The properties of these fluctuations are completely specified by their power spectrum, A(k). The basic cosmological parameters and the primordial power spectrum together completely specify predictions for the cosmic microwave background radiation anisotropy and large-scale structure. Here we show how we can strongly constrain both A(k) and the cosmological parameters by combining data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow A(k) to be a free function, and thus probe features in the primordial power spectrum on all scales. If we assume that the cosmological parameters are known a priori and that galaxy bias is linear and scale-independent, and if we neglect nonlinear redshift distortions, the primordial power spectrum in 20 steps in log k to k≤0.5 h Mpc-1 can be determined to ~16% accuracy for k~0.01 h Mpc-1, and to ~1% accuracy for k~0.1 h Mpc-1. The uncertainty in the primordial power spectrum increases by a factor of up to 3 on small scales if we solve simultaneously for the dimensionless Hubble constant h, the cosmological constant Λ, the baryon fraction Ωb, the reionization optical depth τri, and the effective bias between the matter density field and the redshift-space galaxy density field beff. Alternately, if we restrict A(k) to be a power law, we find that inclusion of the SDSS data breaks the degeneracy between the amplitude of the power spectrum and the optical depth inherent in the MAP data, significantly reduces the uncertainties in the determination of the matter density and the cosmological constant, and allows a determination of the galaxy bias parameter. Thus, combining the MAP and SDSS data allows the independent measurement of important cosmological parameters, and a measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early universe, and providing clues to the correct inflationary model.

Modelling the redshift-space distortion of galaxy clustering

We use a set of large, high-resolution cosmological N-body simulations to examine the redshift-space distortions of galaxy clustering on scales of order 10–200 h−1Mpc. Galaxy redshift surveys currently in progress will, on completion, allow us to measure the quadrupole distortion in the 2-point correlation function, ξ(σ, π), or its Fourier transform, the power spectrum P(k, μ), to a high degree of accuracy. On these scales we typically find a positive quadrupole, as expected for coherent infall on to overdense regions and outflow from underdense regions, but the distortion is substantially weaker than that predicted by pure linear theory. We assess two models that may be regarded as refinements to linear theory, the Zel’dovich approximation and a dispersion model in which the non-linear velocities generated by the formation of virialized groups and clusters are treated as random perturbations to the velocities predicted by linear theory. We find that neither provides an adequate physical description of the clustering pattern. If used to model redshift-space distortions on scales for 10 < λ < 200 h−1 Mpc the estimated value of β [β = f(Ω0) / b where f(Ω0) ≈ Ω0.60 and b is the galaxy bias parameter] is liable to systematic errors of the order of 10 per cent or more. We discuss how such systematics can be avoided by (i) development of a more complete model of redshift distortions and (ii) the direct use of galaxy catalogues generated from non-linear N-body simulations.