Bias Of Dark Matter Halos Research Articles

Galaxy clustering measurements out to redshift z ˜ 8 from Hubble Legacy Fields

ABSTRACT We present a novel approach for measuring the two-point correlation function of galaxies in narrow pencil beam surveys with varying depths. Our methodology is utilized to expand high-redshift galaxy clustering investigations up to z ∼ 8 by analysing a comprehensive sample consisting of Ng = 160 Lyman break galaxy candidates obtained through optical and near-infrared photometric data within the CANDELS GOODS data sets from the Hubble Space Telescope Legacy Fields. For bright sources with MUV < −19.8, we determine a galaxy bias of b = 9.33 ± 4.90 at $\overline{z} = 7.7$ and a correlation length of r0 = 10.74 ± 7.06 $h^{-1}\, \mathrm{Mpc}$. We obtain similar results for the XDF, with a galaxy bias measurement of b = 8.26 ± 3.41 at the same redshift for a slightly fainter sample with a median luminosity of MUV = −18.4. By comparing with dark-matter halo bias and employing abundance matching, we deduce a characteristic halo mass of Mh ∼ 1011.5 M⊙ and a duty cycle close to unity. To validate our approach for variable-depth data sets, we replicate the analysis in a region with near-uniform depth using a standard two-point correlation function estimator, yielding consistent outcomes. Our study not only provides a valuable tool for future utilization in JWST data sets but also suggests that the clustering of early galaxies continues to increase with redshift beyond z ≳ 8, potentially contributing to the existence of protocluster structures observed in early JWST imaging and spectroscopic surveys at z ≳ 8.

The Halo Bias inside Cosmic Voids

The bias of dark matter halos and galaxies is a crucial quantity in many cosmological analyses. In this work, using large cosmological simulations, we explore the halo mass function and halo bias within cosmic voids. For the first time to date, we show that they are scale dependent along the void profile, and provide a predictive theoretical model of both the halo mass function and halo bias inside voids, recovering for the latter a 1% accuracy against simulated data. These findings may help shed light on the dynamics of halo formation within voids and improve the analysis of several void statistics from ongoing and upcoming galaxy surveys.

The impact of massive neutrinos on halo assembly bias

Using the publicly available Quijote simulations, we present the first measurements of the assembly bias of dark matter halos in N-body simulations which include massive neutrinos. We focus on the dependence of the linear bias b_1 on three halo properties: 1) concentration c, 2) spin λ, and 3) ellipticity s. Although these simulations cover a large volume, superior to any future surveys, we do not detect any effect of neutrinos on the relations b1(c), b1(λ) and b1(s) at fixed halo mass. We further study the dependence of halo properties and environment on neutrinos, finding these quantities to be impacted by neutrino masses at the same level as assembly bias. We find that the effect of neutrinos on spin and shape can be largely attributed to the change in the cold dark matter σ8 in neutrinos simulations, which is not the case for concentration.

A robust measurement of the first higher-derivative bias of dark matter halos

We present a new simulation technique in which any chosen mode k of the density contrast field can be amplified by an amplitude Δ. These amplified-mode simulations allow us to study the response of the halo density field to a long-wavelength mode other than the DC mode. In this sense they are a generalization of the separate-universe simulations to finite-wavelength modes. In particular, we use these simulations to obtain robust measurements of the first higher-derivative bias of dark matter halos b∇2δ. We find a negative bias at all mass considered, roughly following the −RL2(M) relation, the Lagrangian radius of halos squared, as naively expected. We compare our results with those obtained from a fit to the 1-loop halo-matter power spectrum, as well as with the recent results from Abidi and Baldauf (2018), and to the prediction from the peak theory.

The secondary spin bias of dark matter haloes

We investigate the role of angular momentum in the clustering of dark matter haloes. We make use of data from two high-resolution N-body simulations spanning over four orders of magnitude in halo mass, from $10^{9.8}$ to $10^{14}\ h^{-1}\ \text{M}_\odot$. We explore the hypothesis that mass accretion in filamentary environments alters the angular momentum of a halo, thereby driving a correlation between the spin parameter $\lambda$ and the strength of clustering. However, we do not find evidence that the distribution of matter on large scales is related to the spin of haloes. We find that a halo's spin is correlated with its age, concentration, sphericity, and mass accretion rate. Removing these correlations strongly affects the strength of secondary spin bias at low halo masses. We also find that high spin haloes are slightly more likely to be found near another halo of comparable mass. These haloes that are found near a comparable mass neighbour - a \textit{twin} - are strongly spatially biased. We demonstrate that this \textit{twin bias}, along with the relationship between spin and mass accretion rates, statistically accounts for halo spin secondary bias.

Halo assembly bias and the tidal anisotropy of the local halo environment

We study the role of the local tidal environment in determining the assembly bias of dark matter haloes. Previous results suggest that the anisotropy of a halo's environment (i.e, whether it lies in a filament or in a more isotropic region) can play a significant role in determining the eventual mass and age of the halo. We statistically isolate this effect using correlations between the large-scale and small-scale environments of simulated haloes at $z=0$ with masses between $10^{11.6}\lesssim (m/h^{-1}M_{\odot})\lesssim10^{14.9}$. We probe the large-scale environment using a novel halo-by-halo estimator of linear bias. For the small-scale environment, we identify a variable $\alpha_R$ that captures the $\textit{tidal anisotropy}$ in a region of radius $R=4R_{\textrm{200b}}$ around the halo and correlates strongly with halo bias at fixed mass. Segregating haloes by $\alpha_R$ reveals two distinct populations. Haloes in highly isotropic local environments ($\alpha_R\lesssim0.2$) behave as expected from the simplest, spherically averaged analytical models of structure formation, showing a $\textit{negative}$ correlation between their concentration and large-scale bias at $\textit{all}$ masses. In contrast, haloes in anisotropic, filament-like environments ($\alpha_R\gtrsim0.5$) tend to show a $\textit{positive}$ correlation between bias and concentration at any mass. Our multi-scale analysis cleanly demonstrates how the overall assembly bias trend across halo mass emerges as an average over these different halo populations, and provides valuable insights towards building analytical models that correctly incorporate assembly bias. We also discuss potential implications for the nature and detectability of galaxy assembly bias.

Late time sky as a probe of steps and oscillations in primordial Universe

The standard model of cosmology with nearly Gaussian, isotropic, scale invariant and adiabatic initial conditions describes the cosmological observations well. However, the study of any deviation from the mentioned conditions will open up a new horizon to the physics of early universe. In this work, we study the effect of the oscillatory and step-like features in potentials of inflationary models in late time large scale structure observations. Mainly we study the matter power spectrum, number density of the structures, dark matter halo bias and specifically CMB lensing. We show that the oscillatory models can introduce some degeneracy with late time effects on BAO scale. We also conclude that high frequency oscillatory models which are favored by Planck data do not have significant effect on the non linear structure formation. Finally we show that inflationary models with step functions which deviates from the standard model in small scales l ⩽ 1 Mpc can be constrained by future experiments via CMB lensing. We propose the idea that CMB lensing is a bias independent observation which can be used as a small scale physics probe due to distribution of the lenses in low redshifts. Meantime this model can alter the prediction of the cosmological model for the number density of small structures and can be used as a probable explanation for galactic scale crisis of ΛCDM.

Verifying the consistency relation for the scale-dependent bias from local primordial non-Gaussianity

We measure the large-scale bias of dark matter halos in simulations with non-Gaussian initial conditions of the local type, and compare this bias to the response of the mass function to a change in the primordial amplitude of fluctuations. The two are found to be consistent, as expected from physical arguments, for three halo-finder algorithms which use different Spherical Overdensity (SO) and Friends-of-Friends (FoF) methods. On the other hand, we find that the commonly used prediction for universal mass functions, that the scale-dependent bias is proportional to the first-order Gaussian Lagrangian bias, does not yield a good agreement with the measurements. For all halo finders, high-mass halos show a non-Gaussian bias suppressed by 10-15% relative to the universal mass function prediction. For SO halos, this deviation changes sign at low masses, where the non-Gaussian bias becomes larger than the universal prediction.

Large-scale assembly bias of dark matter halos

We present precise measurements of the assembly bias of dark matter halos, i.e. the dependence of halo bias on other properties than the mass, using curved “separate universe” N-body simulations which effectively incorporate an infinite-wavelength matter overdensity into the background density. This method measures the LIMD (local-in-matter-density) bias parameters bn in the large-scale limit. We focus on the dependence of the first two Eulerian biases bE1 and bE2 on four halo properties: the concentration, spin, mass accretion rate, and ellipticity. We quantitatively compare our results with previous works in which assembly bias was measured on fairly small scales. Despite this difference, our findings are in good agreement with previous results. We also look at the joint dependence of bias on two halo properties in addition to the mass. Finally, using the excursion set peaks model, we attempt to shed new insights on how assembly bias arises in this analytical model.

The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales

We investigate the spatial clustering of dark matter halos, collapsing from $1-4 \sigma$ fluctuations, in the redshift range $0 - 5$ using N-body simulations. The halo bias of high redshift halos ($z \geq 2$) is found to be strongly non-linear and scale-dependent on quasi-linear scales that are larger than their virial radii ($0.5-10$ Mpc/h). However, at lower redshifts, the scale-dependence of non-linear bias is weaker and and is of the order of a few percent on quasi-linear scales at $z \sim 0$. We find that the redshift evolution of the scale dependent bias of dark matter halos can be expressed as a function of four physical parameters: the peak height of halos, the non-linear matter correlation function at the scale of interest, an effective power law index of the {\it rms} linear density fluctuations and the matter density of the universe at the given redshift. This suggests that the scale-dependence of halo bias is not a universal function of the dark matter power spectrum, which is commonly assumed. We provide a fitting function for the scale dependent halo bias as a function of these four parameters. Our fit reproduces the simulation results to an accuracy of better than 4 % over the redshift range $0\leq z \leq 5$. We also extend our model by expressing the non-linear bias as a function of the linear matter correlation function. It is important to incorporate our results into the clustering models of dark matter halos at any redshift, including those hosting early generations of stars and galaxies before reionization.

Precision measurement of the local bias of dark matter halos

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved “separate universe” N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth & Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The prediction from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters b2(b1) and b3(b1), which work well over a range of redshifts.

Sloan Digital Sky Survey III photometric quasar clustering: probing the initial conditions of the Universe

The Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky, and delivered over a trillion pixels of imaging data. We present the large-scale clustering of 1.6 million quasars between z=0.5 and z=2.5 that have been classified from this imaging, representing the highest density of quasars ever studied for clustering measurements. This data set spans 0∼ 11,00 square degrees and probes a volume of 80 h−3 Gpc3. In principle, such a large volume and medium density of tracers should facilitate high-precision cosmological constraints. We measure the angular clustering of photometrically classified quasars using an optimal quadratic estimator in four redshift slices with an accuracy of ∼ 25% over a bin width of δl ∼ 10−15 on scales corresponding to matter-radiation equality and larger (0ℓ ∼ 2−3).Observational systematics can strongly bias clustering measurements on large scales, which can mimic cosmologically relevant signals such as deviations from Gaussianity in the spectrum of primordial perturbations. We account for systematics by employing a new method recently proposed by Agarwal et al. (2014) to the clustering of photometrically classified quasars. We carefully apply our methodology to mitigate known observational systematics and further remove angular bins that are contaminated by unknown systematics. Combining quasar data with the photometric luminous red galaxy (LRG) sample of Ross et al. (2011) and Ho et al. (2012), and marginalizing over all bias and shot noise-like parameters, we obtain a constraint on local primordial non-Gaussianity of fNL = −113+154−154 (1σ error). We next assume that the bias of quasar and galaxy distributions can be obtained independently from quasar/galaxy-CMB lensing cross-correlation measurements (such as those in Sherwin et al. (2013)). This can be facilitated by spectroscopic observations of the sources, enabling the redshift distribution to be completely determined, and allowing precise estimates of the bias parameters. In this paper, if the bias and shot noise parameters are fixed to their known values (which we model by fixing them to their best-fit Gaussian values), we find that the error bar reduces to 1σ ≃ 65. We expect this error bar to reduce further by at least another factor of five if the data is free of any observational systematics. We therefore emphasize that in order to make best use of large scale structure data we need an accurate modeling of known systematics, a method to mitigate unknown systematics, and additionally independent theoretical models or observations to probe the bias of dark matter halos.

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.

A SECOND-ORDER BIAS MODEL FOR THE LOGARITHMIC HALO MASS DENSITY

We present an analytic model for the local bias of dark matter halos in a LCDM universe. The model uses the halo mass density instead of the halo number density and is searched for various halo mass cuts, smoothing lengths, and redshift epoches. We find that, when the logarithmic density is used, the second-order polynomial can fit the numerical relation between the halo mass distribution and the underlying matter distribution extremely well. In this model the logarithm of the dark matter density is expanded in terms of log halo mass density to the second order. The model remains excellent for all halo mass cuts (from M_{cut}=3\times10^{11}$ to $3\times10^{12}h^{-1}M_{\odot}$), smoothing scales (from $R=5h^{-1}$Mpc to $50h^{-1}$Mpc), and redshift ranges (from z=0 to 1.0) considered in this study. The stochastic term in the relation is found not entirely random, but a part of the term can be determined by the magnitude of the shear tensor.

THE COSMIC NEAR INFRARED BACKGROUND. III. FLUCTUATIONS, REIONIZATION, AND THE EFFECTS OF MINIMUM MASS AND SELF-REGULATION

Current observations suggest that the universe was reionized sometime before z~6. One way to observe this epoch of the universe is through the Near Infrared Background (NIRB), which contains information about galaxies which may be too faint to be observed individually. We calculate the angular power spectrum (C_l) of the NIRB fluctuations caused by the distribution of these galaxies. Assuming a complete subtraction of any post-reionization component, C_l will be dominated by galaxies responsible for completing reionization (e.g., z~6). The shape of C_l at high l is sensitive to the amount of non-linear bias of dark matter halos hosting galaxies. As the non-linear bias depends on the mass of these halos, we can use the shape of C_l to infer typical masses of dark matter halos responsible for completing reionization. We extend our previous study by using a higher-resolution N-body simulation, which can resolve halos down to 10^8 M_sun. We also include improved radiative transfer, which allows for the suppression of star formation in small-mass halos due to photo-ionization heating. As the non-linear bias enhances the dark-matter-halo power spectrum on small scales, we find that C_l is steeper for the case with a complete suppression of small sources or partial suppression of star formation in small halos (the minimum galaxy mass is M_min=10^9 M_sun in ionized regions and M_min=10^8 M_sun in neutral regions) than the case in which these small halos were unsuppressed. In all cases, we do not see a turn-over toward high l in the shape of l^2 C_l.

Constraints on primordial non-Gaussianity from large scale structure probes

In this paper we measure the angular power spectra Cℓ of three high-redshift large-scale structure probes: the radio sources from the NRAO VLA Sky Survey (NVSS), the quasar catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs) and the MegaZ-LRG (DR7), the final SDSS II Luminous Red Galaxy (LRG) photometric redshift survey. We perform a global analysis of the constraints on the amplitude of primordial non-Gaussianity from these angular power spectra, as well as from their cross-correlation power spectra with the cosmic microwave background (CMB) temperature map. In particular, we include non-Gaussianity of the type arising from single-field slow roll, multifields, curvaton (local type), and those which effects on the halo clustering can be described by the equilateral template (related to higher-order derivative type non-Gaussianity) and by the enfolded template (related to modified initial state or higher-derivative interactions). When combining all data sets, we obtain limits of fNL = 48±20, fNL = 50±265 and fNL = 183±95 at 68% confidence level for local, equilateral and enfolded templates, respectively. Furthermore, we explore the constraint on the cubic correction gNLϕ3 on the bias of dark matter haloes and obtain a limit of −1.2 × 105 < gNL < 11.3 × 105 at 95% confidence level.

Scale-dependent non-Gaussianity as a generalization of the local model

We generalize the local model of primordial non-Gaussianity by promoting the parameter fNL to a general scale-dependent function fNL(k). We calculate the resulting bispectrum and the effect on the bias of dark matter halos, and thus the extent to which fNL(k) can be measured from the large-scale structure observations. By calculating the principal components of fNL(k), we identify scales where this form of non-Gaussianity is best constrained and estimate the overlap with previously studied local and equilateral non-Gaussian models.

The bias and mass function of dark matter haloes in non-Markovian extension of the excursion set theory

The excursion set theory based on spherical or ellipsoidal gravitational collapse provides an elegant analytic framework for calculating the mass function and the large-scale bias of dark matter haloes. This theory assumes that the perturbed density field evolves stochastically with the smoothing scale and exhibits Markovian random walks in the presence of a density barrier. Here, we derive an analytic expression for the halo bias in a new theoretical model that incorporates non-Markovian extension of the excursion set theory with a stochastic barrier. This model allows us to handle non-Markovian random walks and to calculate perturbatively these corrections to the standard Markovian predictions for the halo mass function and halo bias. Our model contains only two parameters: κ, which parametrizes the degree of non-Markovianity and whose exact value depends on the shape of the filter function used to smooth the density field, and a, which parametrizes the degree of stochasticity of the barrier. Appropriate choices of κ and a in our new model can lead to a closer match to both the halo mass function and the halo bias in the latest N-body simulations than the standard excursion set theory.

Large-scale bias of dark matter halos

We build a simple analytical model for the bias of dark matter halos that applies to objects defined by an arbitrary density threshold, $200\leq\deltas\leq 1600$, and that provides accurate predictions from low-mass to high-mass halos. We point out that it is possible to build simple and efficient models, with no free parameter for the halo bias, by using integral constraints that govern the behavior of low-mass and typical halos, whereas the properties of rare massive halos are derived through explicit asymptotic approaches. We also describe how to take into account the impact of halo motions on their bias, using their linear displacement field. We obtain a good agreement with numerical simulations for the halo mass functions and large-scale bias at redshifts $0\leq z \leq 2.5$, for halos defined by a nonlinear density threshold $200\leq\deltas\leq 1600$. We also evaluate the impact on the halo bias of two common approximations, i) neglecting halo motions, and ii) linearizing the halo two-point correlation.

Primordial non-Gaussianity from the covariance of galaxy cluster counts

It has recently been proposed that the large-scale bias of dark matter halos depends sensitively on primordial non-Gaussianity of the local form. In this paper we point out that the strong scale dependence of the non-Gaussian halo bias imprints a distinct signature on the covariance of cluster counts. We find that using the full covariance of cluster counts results in improvements on constraints on the non-Gaussian parameter ${f}_{\mathrm{NL}}$ of 3 (1) orders of magnitude relative to cluster counts ($\mathrm{\text{counts}}+\mathrm{\text{clustering variance}}$) constraints alone. We forecast ${f}_{\mathrm{NL}}$ constraints for the upcoming Dark Energy Survey in the presence of uncertainties in the mass-observable relation, halo bias, and photometric redshifts. We find that the Dark Energy Survey can yield constraints on non-Gaussianity of $\ensuremath{\sigma}({f}_{\mathrm{NL}})\ensuremath{\sim}1--5$ even for relatively conservative assumptions regarding systematics. Excess of correlations of cluster counts on scales of hundreds of megaparsecs would represent a smoking-gun signature of primordial non-Gaussianity of the local type.