Galaxy Bias Factor Research Articles

Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample

The cosmological information extracted from photometric surveys is most robust when multiple probes of the large scale structure of the Universe are used. Two of the most sensitive probes are the clustering of galaxies and the tangential shear of background galaxy shapes produced by those foreground galaxies, so-called galaxy-galaxy lensing. Combining the measurements of these two two-point functions leads to cosmological constraints that are independent of the way galaxies trace matter (the galaxy bias factor). The optimal choice of foreground, or lens, galaxies is governed by the joint, but conflicting requirements to obtain accurate redshift information and large statistics. We present cosmological results from the full 5000 deg2 of the Dark Energy Survey’s first three years of observations (Y3) combining those two-point functions, using for the first time a magnitude-limited lens sample (MagLim) of 11 million galaxies, especially selected to optimize such combination, and 100 million background shapes. We consider two flat cosmological models, the Standard Model with dark energy and cold dark matter (ΛCDM) a variation with a free parameter for the dark energy equation of state (wCDM). Both models are marginalized over 25 astrophysical and systematic nuisance parameters. In ΛCDM we obtain for the matter density Ωm=0.320−0.034+0.041 and for the clustering amplitude S8≡σ8(Ωm/0.3)0.5=0.778−0.031+0.037, at 68% C.L. The latter is only 1σ smaller than the prediction in this model informed by measurements of the cosmic microwave background by the Planck satellite. In wCDM we find Ωm=0.32−0.046+0.044, S8=0.777−0.051+0.049 and dark energy equation of state w=−1.031−0.379+0.218. We find that including smaller scales, while marginalizing over nonlinear galaxy bias, improves the constraining power in the Ωm−S8 plane by 31% and in the Ωm−w plane by 41% while yielding consistent cosmological parameters from those in the linear bias case. These results are combined with those from cosmic shear in a companion paper to present full DES-Y3 constraints from the three two-point functions (3×2pt).10 MoreReceived 3 June 2021Accepted 13 October 2022DOI:https://doi.org/10.1103/PhysRevD.106.103530© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmological parametersCosmologyDark energyDark matterGravitational lensesLarge scale structure of the UniverseSky surveysGravitation, Cosmology & Astrophysics

CFHTLenS: Galaxy bias as function of scale, stellar mass, and colour

Galaxy models predict a tight relation between the clustering of galaxies and dark matter on cosmological scales, but predictions differ notably in the details. We used this opportunity and tested two semi-analytic models by the Munich and Durham groups with data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). For the test we measured the scale-dependent galaxy bias factor b(k) and correlation factor r(k) from linear to non-linear scales of k ≈ 10 h Mpc−1 at two redshifts z̄ = 0.35, 0.51 for galaxies with stellar mass between 5 × 109 and 3 × 1011 h70−2 M⊙. Our improved gravitational lensing technique accounts for the intrinsic alignment of sources and the magnification of lens galaxies for better constraints for the galaxy-matter correlation r(k). Galaxy bias in CFHTLenS increases with k and stellar mass; it is colour-dependent, revealing the individual footprints of galaxy types. Despite a reasonable model agreement for the relative change with both scale and galaxy properties, there is a clear conflict for b(k) with no model preference: the model galaxies are too weakly clustered. This may flag a model problem at z ≳ 0.3 for all stellar masses. As in the models, however, there is a high correlation r(k) between matter and galaxy density on all scales, and galaxy bias is typically consistent with a deterministic bias on linear scales. Only our blue and low-mass galaxies of about 7 × 109 h70−2 M⊙ at z̄ = 0.51 show, contrary to the models, a weak tendency towards a stochastic bias on linear scales where rls = 0.75 ± 0.14 (stat.) ± 0.06 (sys.). This result is of interest for cosmological probes, such as EG, that rely on a deterministic galaxy bias. We provide Monte Carlo realisations of posterior constraints for b(k) and r(k) in CFHTLenS for every galaxy sample in this paper at the CDS.

Improving estimates of the growth rate using galaxy–velocity correlations: a simulation study

ABSTRACT 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 < 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.

Constraining the H i–Halo Mass Relation from Galaxy Clustering

Abstract We study the dependence of galaxy clustering on H i mass using ∼16,000 galaxies with redshift in the range of 0.0025 < z < 0.05 and H i mass of M H I > 10 8 M ☉ , drawn from the 70% complete sample of the Arecibo Legacy Fast ALFA survey. We construct subsamples of galaxies with M H I above different thresholds and make volume-limited clustering measurements in terms of three statistics: the projected two-point correlation function, the projected cross-correlation function with respect to a reference sample, and the redshift-space monopole moment. In contrast to previous studies, which found no/weak H i mass dependence, we find both the clustering amplitudes on scales above a few megaparsecs and the bias factors to increase significantly with increasing H i mass for M H I > 10 9 M ☉ . For H i mass thresholds below ∼ 10 9 M ☉ , the inferred galaxy bias factors are systematically lower than the minimum halo bias from mass-selected halo samples. We extend the simple halo model, in which the galaxy content is only determined by halo mass, by including the halo formation time as an additional parameter. A model that puts H i-rich galaxies into halos that formed late can reproduce the clustering measurements reasonably well. We present the implications of our best-fitting model on the correlation of H i mass with halo mass and formation time, as well as the halo occupation distributions and H i mass functions for central and satellite galaxies. These results are compared with the predictions from semianalytic galaxy formation models and hydrodynamic galaxy formation simulations.

Velocity–density correlations from the cosmicflows-3 distance catalogue and the 2MASS Redshift Survey

The peculiar velocity of a mass tracer is on average aligned with the dipole modulation of the surrounding mass density field. We present a first measurement of the correlation between radial peculiar velocities of objects in the cosmicflows-3 catalog and the dipole moment of the 2MRS galaxy distribution in concentric spherical shells centered on these objects. Limiting the analysis to cosmicflows-3 objects with distances of $100 \rm Mpc h^{-1}$, the correlation function is detected at a confidence level $> 4\sigma$. The measurement is found consistent with the standard $\Lambda$CDM model at $< 1.7\sigma$ level. We formally derive the constraints $0.32<\Omega^{0.55}\sigma_8<0.48$ ($68\% $ confidence level) or equivalently $0.34<\Omega^{0.55}/b<0.52$, where $b$ is the galaxy bias factor. Deeper and improved peculiar velocity catalogs will substantially reduce the uncertainties, allowing tighter constraints from this type of correlations.

The WiggleZ Dark Energy Survey: measuring the cosmic growth rate with the two-point galaxy correlation function

The growth history of large-scale structure in the Universe is a powerful probe of the cosmological model, including the nature of dark energy. We study the growth rate of cosmic structure to redshift $z = 0.9$ using more than $162{,}000$ galaxy redshifts from the WiggleZ Dark Energy Survey. We divide the data into four redshift slices with effective redshifts $z = [0.2,0.4,0.6,0.76]$ and in each of the samples measure and model the 2-point galaxy correlation function in parallel and transverse directions to the line-of-sight. After simultaneously fitting for the galaxy bias factor we recover values for the cosmic growth rate which are consistent with our assumed $\Lambda$CDM input cosmological model, with an accuracy of around 20% in each redshift slice. We investigate the sensitivity of our results to the details of the assumed model and the range of physical scales fitted, making close comparison with a set of N-body simulations for calibration. Our measurements are consistent with an independent power-spectrum analysis of a similar dataset, demonstrating that the results are not driven by systematic errors. We determine the pairwise velocity dispersion of the sample in a non-parametric manner, showing that it systematically increases with decreasing redshift, and investigate the Alcock-Paczynski effects of changing the assumed fiducial model on the results. Our techniques should prove useful for current and future galaxy surveys mapping the growth rate of structure using the 2-dimensional correlation function.

The WiggleZ Dark Energy Survey: the selection function and z= 0.6 galaxy power spectrum

We report one of the most accurate measurements of the three-dimensional large-scale galaxy power spectrum achieved to date, using 56,159 redshifts of bright emission-line galaxies at effective redshift z=0.6 from the WiggleZ Dark Energy Survey at the Anglo-Australian Telescope. We describe in detail how we construct the survey selection function allowing for the varying target completeness and redshift completeness. We measure the total power with an accuracy of approximately 5% in wavenumber bands of dk=0.01 h/Mpc. A model power spectrum including non-linear corrections, combined with a linear galaxy bias factor and a simple model for redshift-space distortions, provides a good fit to our data for scales k < 0.4 h/Mpc. The large-scale shape of the power spectrum is consistent with the best-fitting matter and baryon densities determined by observations of the Cosmic Microwave Background radiation. By splitting the power spectrum measurement as a function of tangential and radial wavenumbers we delineate the characteristic imprint of peculiar velocities. We use these to determine the growth rate of structure as a function of redshift in the range 0.4 < z < 0.8, including a data point at z=0.78 with an accuracy of 20%. Our growth rate measurements are a close match to the self-consistent prediction of the LCDM model. The WiggleZ Survey data will allow a wide range of investigations into the cosmological model, cosmic expansion and growth history, topology of cosmic structure, and Gaussianity of the initial conditions. Our calculation of the survey selection function will be released at a future date via our website wigglez.swin.edu.au.

Metric Tests for Curvature from Weak Lensing and Baryon Acoustic Oscillations

We describe a practical measurement of the curvature of the universe which, unlike current constraints, relies purely on the properties of the Robertson-Walker metric rather than any assumed model for the dynamics and content of the universe. The observable quantity is the cross-correlation between foreground mass and gravitational shear of background galaxies, which depends on the angular diameter distances dA(zl), dA(zs), and dA(zs,zl) on the degenerate triangle formed by observer, source, and lens. In a flat universe, dA(zl,zs) = dA(zs) - dA(zl), but in curved universes an additional term ∝Ωk appears and alters the lensing observables even if dA(z) is fixed. We describe a method whereby weak-lensing data can be used to solve simultaneously for dA and the curvature. This method is completely insensitive to the equation of state of the contents of the universe, or amendments to general relativity that alter the gravitational deflection of light or the growth of structure. The curvature estimate is also independent of biases in the photometric redshift scale. This measurement is shown to be subject to a degeneracy among dA, Ωk, and the galaxy bias factors that may be broken by using the same imaging data to measure the angular scale of baryon acoustic oscillations. Simplified estimates of the accuracy attainable by this method indicate that ambitious weak-lensing + baryon-oscillation surveys would measure Ωk to an accuracy ≈0.04f(σln z/0.04)1/2, where σln z is the photometric redshift error. The Fisher-matrix formalism developed here is also useful for predicting bounds on curvature and other characteristics of parametric dark energy models. We forecast some representative error levels and compare ours to other analyses of the weak-lensing cross-correlation method. We find both curvature and parametric constraints to be surprisingly insensitive to the systematic shear calibration errors.

Projected Three‐Point Correlation Functions and Galaxy Bias

The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF, where these distortions are eliminated by integrating over the redshift dimension, as is commonly done for the two-point correlation function. The calculation of the projected 3PCF from the real-space, three-dimensional bispectrum is greatly simplified by expanding both quantities in Fourier components, analogous to Szapudi's expansion of the three-dimensional quantities in multipole components. In the weakly nonlinear regime, the bispectrum can be well represented by the first few Fourier components. There is a well-known relation between the reduced 3PCFs of matter and galaxies in the weakly nonlinear regime, which can be used to infer galaxy bias factors if the real-space three-dimensional galaxy correlation functions (two-point and three-point) can be measured. I show that the same relation holds for the reduced projected 3PCFs if these are properly defined. These results should aid determinations of galaxy bias from large redshift surveys by eliminating the complication of redshift-space distortions.

Cosmological information from quasar-galaxy correlations induced by weak lensing

The magnification bias of large-scale structures, combined with galaxy biasing, leads to a cross-correlation of distant quasars with foreground galaxies on angular scales of the order of arcminutes and larger. The amplitude and angular shape of the cross-correlation function w Q G contain information on cosmological parameters and the galaxy bias factor. While the existence of this cross-correlation has firmly been established, existing data did not allow an accurate measurement of w Q G yet, but wide area surveys like the Sloan Digital Sky Survey now provide an ideal database for measuring it. However, w Q G depends on several cosmological parameters and the galaxy bias factor. We study in detail the sensitivity of w Q G to these parameters and develop a strategy for using the data. We show that the parameter space can be reduced to the bias factor b, Ω 0 and σ 8 , and compute the accuracy with which these parameters can be deduced from SDSS data. Under reasonable assumptions, it should be possible to reach relative accuracies of the order of 5%-15% for b, Ω 0 , and σ 8 . This method is complementary to other weak-lensing analyses based on cosmic shear.