Halo Bias Research Articles

Velocity and mass bias in the distribution of dark matter haloes

The non-linear, scale-dependent bias in the mass distribution of galaxies and the underlying dark matter is a key systematic affecting the extraction of cosmological parameters from galaxy clustering. Using 95 million halos from the Millennium-XXL N-body simulation, we find that the mass bias is scale independent only for $k<0.1 h{\rm Mpc}^{-1}$ today ($z=0$) and for $k<0.2 h{\rm Mpc}^{-1}$ at $z=0.7$. We test analytic halo bias models against our simulation measurements and find that the model of Tinker et al. 2005 is accurate to better then 5% at $z=0$. However, the simulation results are better fit by an ellipsoidal collapse model at $z=0.7$. We highlight, for the first time, another potentially serious systematic due to a sampling bias in the halo velocity divergence power spectra which will affect the comparison between observations and any redshift space distortion model which assumes dark matter velocity statistics with no velocity bias. By measuring the velocity divergence power spectra for different sized halo samples, we find that there is a significant bias which increases with decreasing number density. This bias is approximately 20% at $k=0.1h$Mpc$^{-1}$ for a halo sample of number density $\bar{n} = 10^{-3} (h/$Mpc$)^3$ at both $z=0$ and $z=0.7$ for the velocity divergence auto power spectrum. Given the importance of redshift space distortions as a probe of dark energy and the on-going major effort to advance models for the clustering signal in redshift space, our results show this velocity bias introduces another systematic, alongside scale-dependent halo mass bias, which cannot be neglected.

Halo bias in mixed dark matter cosmologies

The large-scale distribution of cold dark matter halos is generally assumed to trace the large-scale distribution of matter. In a universe with multiple types of matter fluctuations, as is the case with massive neutrinos, the relation between the halo field and the matter fluctuations may be more complicated. We develop a method for calculating the bias factor relating fluctuations in the halo number density to fluctuations in the mass density in the presence of multiple fluctuating components of the energy density. In the presence of massive neutrinos we find a small but pronounced feature in the halo bias near the neutrino free-streaming scale. The neutrino feature is a small step with amplitude that increases with halo mass and neutrino mass density. The scale-dependent halo bias lessens the suppression of the small-scale halo power spectrum and should therefore weaken constraints on neutrino mass from the galaxy auto-power spectrum and correlation function. On the other hand, the feature in the bias is itself a novel signature of massive neutrinos that can be studied independently.

Planck2013 results. XXX. Cosmic infrared background measurements and implications for star formation

We present new measurements of CIB anisotropies using Planck. Combining HFI data with IRAS, the angular auto- and cross frequency power spectrum is measured from 143 to 3000 GHz, and the auto-bispectrum from 217 to 545 GHz. The total areas used to compute the CIB power spectrum and bispectrum are about 2240 and 4400 deg^2, respectively. After careful removal of the contaminants, and a complete study of systematics, the CIB power spectrum and bispectrum are measured with unprecedented signal to noise ratio from angular multipoles ell~150 to 2500, and ell~130 to 1100, respectively. Two approaches are developed for modelling CIB power spectrum anisotropies. The first approach takes advantage of the unique measurements by Planck at large angular scales, and models only the linear part of the power spectrum, with a mean bias of dark matter halos hosting dusty galaxies at a given redshift weighted by their contribution to the emissivities. The second approach is based on a model that associates star-forming galaxies with dark matter halos and their subhalos, using a parametrized relation between the dust-processed infrared luminosity and (sub-)halo mass. The two approaches simultaneously fit all auto- and cross- power spectra very well. We find that the star formation history is well constrained up to z~2. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies. We also find that CIB galaxies have warmer temperatures as redshift increases. The CIB bispectrum is steeper than that expected from the power spectrum, although well fitted by a power law; this gives some information about the contribution of massive halos to the CIB bispectrum.

EFFECTS OF LARGE-SCALE ENVIRONMENT ON THE ASSEMBLY HISTORY OF CENTRAL GALAXIES

We examine whether large-scale environment affects the mass assembly history of their central galaxies. To facilitate this, we constructed dark matter halo merger trees from a cosmological N-body simulation and calculated the formation and evolution of galaxies using a semi-analytic method. We confirm earlier results that smaller halos show a notable difference in formation time with a mild dependence on large-scale environment. However, using a semi-analytic model, we found that on average the growth rate of the stellar mass of central galaxies is largely insensitive to large-scale environment. Although our results show that the star formation rate (SFR) and the stellar mass of central galaxies in smaller halos are slightly affected by the assembly bias of halos, those galaxies are faint, and the difference in the SFR is minute, and therefore it is challenging to detect it in real galaxies given the current observational accuracy. Future galaxy surveys, such as the BigBOSS experiment and the Large Synoptic Survey Telescope, which are expected to provide observational data for fainter objects, will provide a chance to test our model predictions.

Nonlinear structure formation in nonlocal gravity

We study the nonlinear growth of structure in nonlocal gravity models with the aid of N-body simulation and the spherical collapse and halo models. We focus on a model in which the inverse-squared of the d'Alembertian operator acts on the Ricci scalar in the action. For fixed cosmological parameters, this model differs from ΛCDM by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength ∼ 6% larger today). Compared to ΛCDM today, in the nonlocal model, massive haloes are slightly more abundant (by ∼ 10% at M ∼ 1014 M⊙/h) and concentrated ≈ 8% enhancement over a range of mass scales), but their linear bias remains almost unchanged. We find that the Sheth-Tormen formalism describes the mass function and halo bias very well, with little need for recalibration of free parameters. The fitting of the halo concentrations is however essential to ensure the good performance of the halo model on small scales. For k ≳ 1 h/Mpc, the amplitude of the nonlinear matter and velocity divergence power spectra exhibits a modest enhancement of ∼ 12% to 15%, compared to ΛCDM today. This suggests that this model might only be distinguishable from ΛCDM by future observational missions. We point out that the absence of a screening mechanism may lead to tensions with Solar System tests due to local time variations of the gravitational strength, although this is subject to assumptions about the local time evolution of background averaged quantities.

Nonlocal halo bias with and without massive neutrinos

Understanding the biasing between the clustering properties of halos and the underlying dark matter distribution is important for extracting cosmological information from ongoing and upcoming galaxy surveys. While on sufficiently large scales the halo overdensity is a local function of the mass density fluctuations, on smaller scales the gravitational evolution generates nonlocal terms in the halo density field. We characterize the magnitude of these contributions at third order in perturbation theory by identifying the coefficients of the nonlocal invariant operators, and extend our calculation to include nonlocal (Lagrangian) terms induced by a peak constraint. We apply our results to describe the scale dependence of halo bias in cosmologies with massive neutrinos. The inclusion of gravity-induced nonlocal terms and, especially, a Lagrangian ${k}^{2}$ contribution is essential to reproduce the numerical data accurately. We use the peak-background split to derive the numerical values of the various bias coefficients from the excursion set peak mass function. For neutrino masses in the range $0\ensuremath{\le}\ensuremath{\sum}_{i}{m}_{{\ensuremath{\nu}}_{i}}\ensuremath{\le}0.6\text{ }\text{ }\mathrm{eV}$, we are able to fit the data with a precision of a few percents up to $k=0.3h\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ without any free parameter.

On the systematic errors of cosmological-scale gravity tests using redshift-space distortion: non-linear effects and the halo bias

Redshift-space distortion (RSD) observed in galaxy redshift surveys is a powerful tool to test gravity theories on cosmological scales, but the systematic uncertainties must carefully be examined for future surveys with large statistics. Here we employ various analytic models of RSD and estimate the systematic errors on measurements of the structure growth-rate parameter, fσ8, induced by non-linear effects and the halo bias with respect to the dark matter distribution, by using halo catalogues from 40 realizations of 3.4 × 108 comoving h−3 Mpc3 cosmological N-body simulations. We consider hypothetical redshift surveys at redshifts z = 0.5, 1.35 and 2, and different minimum halo mass thresholds in the range of 5.0 × 1011–2.0 × 1013 h−1 M⊙. We find that the systematic error of fσ8 is greatly reduced to ∼5 per cent level, when a recently proposed analytical formula of RSD that takes into account the higher order coupling between the density and velocity fields is adopted, with a scale-dependent parametric bias model. Dependence of the systematic error on the halo mass, the redshift and the maximum wavenumber used in the analysis is discussed. We also find that the Wilson–Hilferty transformation is useful to improve the accuracy of likelihood analysis when only a small number of modes are available in power spectrum measurements.

Disentangling interacting dark energy cosmologies with the three-point correlation function

We investigate the possibility of constraining coupled dark energy (cDE) cosmologies using the three-point correlation function (3PCF). Making use of the CoDECS N-body simulations, we study the statistical properties of cold dark matter (CDM) haloes for a variety of models, including a fiducial $\Lambda$CDM scenario and five models in which dark energy (DE) and CDM mutually interact. We measure both the halo 3PCF, $\zeta(\theta)$, and the reduced 3PCF, $Q(\theta)$, at different scales ($2<r\,[$Mpc\h$]<40$) and redshifts ($0\leq z\leq2$). In all cDE models considered in this work, $Q(\theta)$ appears flat at small scales (for all redshifts) and at low redshifts (for all scales), while it builds up the characteristic V-shape anisotropy at increasing redshifts and scales. With respect to the $\Lambda $CDM predictions, cDE models show lower (higher) values of the halo 3PCF for perpendicular (elongated) configurations. The effect is also scale-dependent, with differences between $\Lambda$CDM and cDE models that increase at large scales. We made use of these measurements to estimate the halo bias, that results in fair agreement with the one computed from the two-point correlation function (2PCF). The main advantage of using both the 2PCF and 3PCF is to break the bias$-\sigma_{8}$ degeneracy. Moreover, we find that our bias estimates are approximately independent of the assumed strength of DE coupling. This study demonstrates the power of a higher-order clustering analysis in discriminating between alternative cosmological scenarios, for both present and forthcoming galaxy surveys, such as e.g. BOSS and Euclid.

Renormalized halo bias

This paper provides a systematic study of renormalization in models of halo biasing. Building on work of McDonald, we show that Eulerian biasing is only consistent with renormalization if non-local terms and higher-derivative contributions are included in the biasing model. We explicitly determine the complete list of required bias parameters for Gaussian initial conditions, up to quartic order in the dark matter density contrast and at leading order in derivatives. At quadratic order, this means including the gravitational tidal tensor, while at cubic order the velocity potential appears as an independent degree of freedom. Our study naturally leads to an effective theory of biasing in which the halo density is written as a double expansion in fluctuations and spatial derivatives. We show that the bias expansion can be organized in terms of Galileon operators which aren't renormalized at leading order in derivatives. Finally, we discuss how the renormalized bias parameters impact the statistics of halos.

Study on decision making model on information presentation by client’s management: an experimental test on halo and recency effect

Auditing is a process to verify financial statements that require a high degree of professional skepticism from auditors. However, auditors individually have cognitive limitation in processing information. Overall assessment potentially leads to halo effect that will influence auditors’ decision making. On the other hand, the sequence and type of information presentation affect primacy and recency effect. Our experimental research design manipulated the information about client (convincing or unconvincing), type of information presentation (step by step and end of sequence), sequence of presentation (positive-negative, negative-positive) and length of information (long and short). The subjects of experiment were students who had taken auditing courses. The results shows that (1) there was higher halo bias when individuals had convincing clients than unconvincing clients, (2) there was halo and primacy effects when individuals had convincing clients and information was presented simultaneously and sequentially, (3) there was halo and primacy effects when individuals had convincing clients and information was presented both with positive-negative and negative-positive sequences and both with short and long series.

Statistics of dark matter halos in the excursion set peak framework

We derive approximated, yet very accurate analytical expressions for the abundance and clustering properties of dark matter halos in the excursion set peak framework; the latter relies on the standard excursion set approach, but also includes the effects of a realistic filtering of the density field, a mass-dependent threshold for collapse, and the prescription from peak theory that halos tend to form around density maxima. We find that our approximations work excellently for diverse power spectra, collapse thresholds and density filters. Moreover, when adopting a cold dark matter power spectra, a tophat filtering and a mass-dependent collapse threshold (supplemented with conceivable scatter), our approximated halo mass function and halo bias represent very well the outcomes of cosmological N-body simulations.

Higher moments of primordial non-Gaussianity and N-bodysimulations

We perform cosmological N-body simulations with non-Gaussian initial conditions generated from two independent fields. The dominant contribution to the perturbations comes from a purely Gaussian field, but we allow the second field to have local non-Gaussianity that need not be weak. This scenario allows us to adjust the relative importance of non-Gaussian contributions beyond the skewness, producing a scaling of the higher moments different from (and stronger than) the scaling in the usual single field local ansatz. We compare semi-analytic prescriptions for the non-Gaussian mass function, large scale halo bias, and stochastic bias against the simulation results. We discuss applications of this work to large scale structure measurements that can test a wider range of models for the primordial fluctuations than is usually explored.

Measuring non-local Lagrangian peak bias

We investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the nonlocal ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a 1-point cross-correlation technique to measure bias factors associated with 2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order nonlocal contributions. We can reproduce our measurement of \chi_{10} if we allow for an offset between the Lagrangian halo center-of-mass and the peak position. The sign and magnitude of \chi_{10} is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 10^13 Msun/h, but could become relevant at larger halo masses. For the second nonlocal bias \chi_{01} however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from nonlocal Lagrangian contributions induced by nonspherical collapse.

A halo bias function measured deeply into voids without stochasticity

We study the relationship between dark-matter haloes and matter in the MIP $N$-body simulation ensemble, which allows precision measurements of this relationship, even deeply into voids. What enables this is a lack of discreteness, stochasticity, and exclusion, achieved by averaging over hundreds of possible sets of initial small-scale modes, while holding fixed large-scale modes that give the cosmic web. We find (i) that dark-matter-halo formation is greatly suppressed in voids; there is an exponential downturn at low densities in the otherwise power-law matter-to-halo density bias function. Thus, the rarity of haloes in voids is akin to the rarity of the largest clusters, and their abundance is quite sensitive to cosmological parameters. The exponential downturn appears both in an excursion-set model, and in a model in which fluctuations evolve in voids as in an open universe with an effective $\Omega_m$ proportional to a large-scale density. We also find that (ii) haloes typically populate the average halo-density field in a super-Poisson way, i.e. with a variance exceeding the mean; and (iii) the rank-order-Gaussianized halo and dark-matter fields are impressively similar in Fourier space. We compare both their power spectra and cross-correlation, supporting the conclusion that one is roughly a strictly-increasing mapping of the other. The MIP ensemble especially reveals how halo abundance varies with `environmental' quantities beyond the local matter density; (iv) we find a visual suggestion that at fixed matter density, filaments are more populated by haloes than clusters.

Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are expressed as infinite sums over velocity moment correlators in real space, as is the case for the density power spectrum in redshift space. We compute each correlator using Eulerian perturbation theory (PT) and halo biasing model and compare the resulting redshift-space velocity statistics to those measured from N-body simulations for both dark matter and halos. We find that in redshift space linear theory predictions for the density-momentum cross power spectrum as well as for the momentum auto spectrum fail to predict the N-body results at very large scales. On the other hand, our nonlinear PT prediction for these velocity statistics, together with real-space power spectrum for dark matter from simulations, improves the accuracy for both dark matter and halos. We also present the same analysis in configuration space, computing the redshift-space pairwise mean infall velocities and velocity correlation function and compare to nonlinear PT.

Halo model and halo properties in Galileon gravity cosmologies

We investigate the performance of semi-analytical modelling of large-scale structure in Galileon gravity cosmologies using results from N-body simulations. We focus on the Cubic and Quartic Galileon models that provide a reasonable fit to CMB, SNIa and BAO data. We demonstrate that the Sheth-Tormen mass function and linear halo bias can be calibrated to provide a very good fit to our simulation results. We also find that the halo concentration-mass relation is well fitted by a power law. The nonlinear matter power spectrum computed in the halo model approach is found to be inaccurate in the mildly nonlinear regime, but captures reasonably well the effects of the Vainshtein screening mechanism on small scales. In the Cubic model, the screening mechanism hides essentially all of the effects of the fifth force inside haloes. In the case of the Quartic model, the screening mechanism leaves behind residual modifications to gravity, which make the effective gravitational strength time-varying and smaller than the standard value. Compared to normal gravity, this causes a deficiency of massive haloes and leads to a weaker matter clustering on small scales. For both models, we show that there are realistic halo occupation distributions of Luminous Red Galaxies that can match both the observed large-scale clustering amplitude and the number density of these galaxies.

MEASUREMENT OF THE HALO BIAS FROM STACKED SHEAR PROFILES OF GALAXY CLUSTERS

We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between the optical richness of galaxy clusters and their mass.

A new method to measure galaxy bias

We present a new approach for modelling galaxy/halo bias that utilizes the full non-linear information contained in the moments of the matter density field, which we derive using a set of numerical simulations. Although our method is general, we perform a case study based on the local Eulerian bias scheme truncated to second-order. Using 200 N-body simulations covering a total comoving volume of 675 (Gpc/h)^3, we measure several 2- and 3-point statistics of the halo distribution to unprecedented accuracy. We use the bias model to fit the halo-halo power spectrum, the halo-matter cross spectrum and the corresponding three bispectra for wavenumbers in the range 0.04 < k < 0.12 h Mpc^-1. We find the constraints on the bias parameters obtained using the full non-linear information differ significantly from those derived using standard perturbation theory at leading order. Hence, neglecting the full non-linear information leads to biased results for this particular scale range. We also test the validity of the second-order Eulerian local biasing scheme by comparing the parameter constraints derived from different statistics. Analysis of the halo-matter cross-correlation coefficients defined for the 2- and 3-point statistics reveals further inconsistencies contained in the second-order Eulerian bias scheme, suggesting it is too simple a model to describe halo bias with high accuracy.

Cosmic degeneracies – I. Joint N-body simulations of modified gravity and massive neutrinos

We present the first suite of cosmological N-body simulations that simultaneously include the effects of two different and theoretically independent extensions of the standard Λ cold dark matter (ΛCDM) cosmological scenario – namely an f (R) theory of modified gravity and a cosmological background of massive neutrinos – with the aim to investigate their possible observational degeneracies. We focus on three basic statistics of the large-scale matter distribution, more specifically the non-linear matter power spectrum, the halo mass function, and the halo bias. Our results show that while these two extended models separately determine very prominent and potentially detectable features in all the three statistics, when we allow them to be simultaneously at work these features are strongly suppressed. In particular, when an f (R) gravity model with fR0 = −1 × 10−4 is combined with a total neutrino mass of Σimνi = 0.4 eV, the resulting matter power spectrum, halo mass function, and bias at z = 0 are found to be consistent with the standard model's predictions at the ≲10, ≲20, and ≲5 per cent accuracy levels, respectively. Therefore, our results imply an intrinsic theoretical limit to the effective discriminating power of present and future observational data sets with respect to these widely considered extensions of the standard cosmological scenario.

Asymmetric sky from the long mode modulations

The observed dipole asymmetry in Cosmic Microwave Background radiation may have originated from the modulations of super-horizon long wavelength modes. In this work we unveil different aspects of asymmetries generated from the long wavelength mode modulations. We show that the same mechanism which leads to the observed CMB power spectrum dipole asymmetry from the long mode modulations also yields dipole asymmetry in (a): tensor perturbations power spectrum and (b): the halo bias parameter. These are different phenomena relevant to different cosmological histories but both share the same underlying mechanism in generating asymmetries in the sky. We obtain the set of consistency conditions relating the amplitude of dipole asymmetries generated on tensor perturbations and halo bias parameter to the amplitude of dipole asymmetry generated on CMB power spectrum. In addition, we show that this mechanism does not produce dipole asymmetry in acceleration expansion in $\Lambda CDM$ universe because the super-horizon curvature perturbation is conserved in this background.