Galaxy Clustering Statistics Research Articles

Improving the accuracy of halo mass based statistics for fast approximate N-body simulations

ABSTRACT Approximate N-body methods, such as fastpm and cola, have been successful in modelling halo and galaxy clustering statistics, but their low resolution on small scales is a limitation for applications that require high precision. Full N-body simulations can provide better accuracy but are too computationally expensive for a quick exploration of cosmological parameters. This paper presents a method for correcting distinct haloes identified in fast N-body simulations, so that various halo statistics improve to a percent level accuracy. The scheme seeks to find empirical corrections to halo properties such that the virial mass is the same as that of a corresponding halo in a full N-body simulation. The modified outer density contour of the corrected halo is determined on the basis of the fastpm settings and the number of particles inside the halo. This method only changes some parameters of the halo finder, and does not require any extra CPU-cost. We demonstrate that the adjusted halo catalogues of fastpm simulations significantly improve the precision of halo mass-based statistics from redshifts $z=0.0$ to 1.0, and that our calibration can be applied to different cosmologies without needing to be recalibrated.

Modeling neutrino-induced scale-dependent galaxy clustering for photometric galaxy surveys

The increasing statistical precision of photometric redshift surveys requires improved accuracy of theoretical predictions for large-scale structure observables to obtain unbiased cosmological constraints. In ΛCDM cosmologies, massive neutrinos stream freely at small cosmological scales, suppressing the small-scale power spectrum. In massive neutrino cosmologies, galaxy bias modeling needs to accurately relate the scale-dependent growth of the underlying matter field to observed galaxy clustering statistics. In this work, we implement a computationally efficient approximation of the neutrino-induced scale-dependent bias (NISDB). Through simulated likelihood analyses of Dark Energy Survey Year 3 (DESY3) and Legacy Survey of Space and Time Year 1 (LSSTY1) synthetic data that contain an appreciable NISDB, we examine the impact of linear galaxy bias and neutrino mass modeling choices on cosmological parameter inference. We find model misspecification of the NISDB approximation and neutrino mass models to decrease the constraining power of photometric galaxy surveys and cause parameter biases in the cosmological interpretation of future surveys. We quantify these biases and devise mitigation strategies.

The Aemulus Project. VI. Emulation of Beyond-standard Galaxy Clustering Statistics to Improve Cosmological Constraints

There is untapped cosmological information in galaxy redshift surveys in the nonlinear regime. In this work, we use the Aemulus suite of cosmological N-body simulations to construct Gaussian process emulators of galaxy clustering statistics at small scales (0.1–50 h −1 Mpc) in order to constrain cosmological and galaxy bias parameters. In addition to standard statistics—the projected correlation function w p(r p), the redshift-space monopole of the correlation function ξ 0(s), and the quadrupole ξ 2(s)—we emulate statistics that include information about the local environment, namely the underdensity probability function P U(s) and the density-marked correlation function M(s). This extends the model of Aemulus III for redshift-space distortions by including new statistics sensitive to galaxy assembly bias. In recovery tests, we find that the beyond-standard statistics significantly increase the constraining power on cosmological parameters of interest: including P U(s) and M(s) improves the precision of our constraints on Ωm by 27%, σ 8 by 19%, and the growth of structure parameter, f σ 8, by 12% compared to standard statistics. We additionally find that scales below ∼6 h −1 Mpc contain as much information as larger scales. The density-sensitive statistics also contribute to constraining halo occupation distribution parameters and a flexible environment-dependent assembly bias model, which is important for extracting the small-scale cosmological information as well as understanding the galaxy–halo connection. This analysis demonstrates the potential of emulating beyond-standard clustering statistics at small scales to constrain the growth of structure as a test of cosmic acceleration.

Spherical bispectrum: a novel visualization scheme for facilitating comparisons

Recent developments of Perturbation Theory (PT), specifically the Effective Field Theory of Large Scale Structure (EFTofLSS) and its equivalents, have proven powerful in analyzing galaxy clustering statistics such as the galaxy power spectrum and bispectrum. To further this pursuit, we have devised a novel spherical-bispectrum visualization scheme that collapses configuration dependencies to highlight the scale dependence of the bispectrum. The resulting one-dimensional curves facilitate the comparison between different bispectra, for example, from simulation and PT calculation. Using the new scheme, we present a quantitative analysis of the accuracy of PT modeling by comparing PT's analytical prediction to the result from a suite of Quijote simulations. Specifically, we determine k NL, the wavenunmber below which the analytical prediction matches well with the N-body result by inspectingboth leading order (LO) and next-to-leading order (NLO) power spectrum and bispectrum at redshifts z = 0, 0.5, 1, 2, 3. We also quantify the binning effect in Fourier space and show that an appropriate correction must be applied to the analytic predictions in order to compare them with the discrete Fourier transform results obtained from N-body-simulation or real data.

First Constraints on Growth Rate from Redshift-space Ellipticity Correlations of SDSS Galaxies at 0.16 < z < 0.70

We report the first constraints on the growth rate of the universe, f(z)σ 8(z), with intrinsic alignments (IAs) of galaxies. We measure the galaxy density-intrinsic ellipticity cross-correlation and intrinsic ellipticity autocorrelation functions over 0.16 < z < 0.7 from luminous red galaxies (LRGs) and LOWZ and CMASS galaxy samples in the Sloan Digital Sky Survey (SDSS) and SDSS-III BOSS survey. We detect clear anisotropic signals of IA due to redshift-space distortions. By combining measured IA statistics with the conventional galaxy clustering statistics, we obtain tighter constraints on the growth rate. The improvement is particularly prominent for the LRG, which is the brightest galaxy sample and known to be strongly aligned with underlying dark matter distribution; using the measurements on scales above 10 h −1 Mpc, we obtain (68% confidence level) from the clustering-only analysis and with clustering and IA, meaning 19% improvement. The constraint is in good agreement with the prediction of general relativity, f σ 8 = 0.4937 at z = 0.34. For LOWZ and CMASS samples, the improvement of constraints on f σ 8 is found to be 10% and 3.5%, respectively. Our results indicate that the contribution from IA statistics for cosmological constraints can be further enhanced by carefully selecting galaxies for a shape sample.

H i HOD. I. The Halo Occupation Distribution of H i Galaxies

The next generation of galaxy surveys will provide more precise measurements of galaxy clustering than have previously been possible. The 21 cm radio signals that are emitted from neutral atomic hydrogen (H i) gas will be detected by large-area radio surveys such as the Widefield Australian Square Kilometre Array (SKA) Pathfinder L-band Legacy All-sky Blind Survey and SKA, and deliver galaxy positions and velocities that can be used to measure galaxy clustering statistics. However, to harness this information to improve our cosmological understanding and learn about the physics of dark matter and dark energy, we need to accurately model the manner in which galaxies detected in H i trace the underlying matter distribution of the universe. For this purpose, we develop a new H i-based halo occupation distribution (HOD) model, which makes predictions for the number of galaxies present in dark matter halos conditional on their H i mass. The parameterized HOD model is fit and validated using the Dark Sage semi-analytic model, where we show that the HOD parameters can be modeled by simple linear and quadratic functions of the H i mass. However, we also find that the clustering predicted by the HOD depends sensitively on the radial distributions of the H i galaxies within their host dark matter halos, which does not follow the Navarro–Frenk–White profile in the Dark Sage simulation. As such, this work enables—for the first time—a simple prescription for placing galaxies of different H i masses within dark matter halos in a way that is able to reproduce the H i mass-dependent galaxy clustering and H i mass function simultaneously and without requiring knowledge of the optical properties of the galaxies. Further efforts are required to demonstrate that this model can be used to produce large ensembles of mock galaxy catalogs for upcoming surveys.

Distinguishing between ΛCDM and f(R) gravity models using halo ellipticity correlations in simulations

ABSTRACT There is a growing interest in utilizing intrinsic alignment (IA) of galaxy shapes as a geometric and dynamical probe of cosmology. In this paper, we present the first measurements of IA in a modified gravity model using the gravitational shear-intrinsic ellipticity correlation (GI) and intrinsic ellipticity-ellipticity correlation (II) functions of dark-matter haloes from f(R) gravity simulations. By comparing them with the same statistics measured in Lambda cold dark matter (ΛCDM) simulations, we find that the IA statistics in different gravity models show distinguishable features, with a trend similar to the case of conventional galaxy clustering statistics. Thus, the GI and II correlations are found to be useful in distinguishing between the ΛCDM and f(R) gravity models. More quantitatively, IA statistics enhance detectability of the imprint of f(R) gravity on large-scale structures by $\sim 40{{\ \rm per\ cent}}$ when combined with the conventional halo clustering in redshift space. We also find that the correlation between the axial ratio and orientation of haloes becomes stronger in f(R) gravity than that in ΛCDM. Our results demonstrate the usefulness of IA statistics as a probe of gravity beyond a consistency test of ΛCDM and general relativity.

ADDGALS: Simulated Sky Catalogs for Wide Field Galaxy Surveys

We present a method for creating simulated galaxy catalogs with realistic galaxy luminosities, broadband colors, and projected clustering over large cosmic volumes. The technique, denoted Addgals (Adding Density Dependent GAlaxies to Lightcone Simulations), uses an empirical approach to place galaxies within lightcone outputs of cosmological simulations. It can be applied to significantly lower-resolution simulations than those required for commonly used methods such as halo occupation distributions, subhalo abundance matching, and semi-analytic models, while still accurately reproducing projected galaxy clustering statistics down to scales of r ∼ 100 h −1kpc . We show that Addgals catalogs reproduce several statistical properties of the galaxy distribution as measured by the Sloan Digital Sky Survey (SDSS) main galaxy sample, including galaxy number densities, observed magnitude and color distributions, as well as luminosity- and color-dependent clustering. We also compare to cluster–galaxy cross correlations, where we find significant discrepancies with measurements from SDSS that are likely linked to artificial subhalo disruption in the simulations. Applications of this model to simulations of deep wide-area photometric surveys, including modeling weak-lensing statistics, photometric redshifts, and galaxy cluster finding, are presented in DeRose et al., and an application to a full cosmology analysis of Dark Energy Survey (DES) Year 3 like data is presented in DeRose et al. We plan to publicly release a 10,313 square degree catalog constructed using Addgals with magnitudes appropriate for several existing and planned surveys, including SDSS, DES, VISTA, Wide-field Infrared Survey Explorer, and Rubin Observatory’s Legacy Survey of Space and Time.

Constraining ultralight axions with galaxy surveys

Ultralight axions and other bosons are dark matter candidates present in many high energy physics theories beyond the Standard Model. In particular, the string axiverse postulates the existence of up to \U0001d4aa(100) light scalar bosons constituting the dark sector. We test the validity of the effective field theory of large-scale structure approach to mixed ultralight axion dark matter by making our own mock galaxy catalogs and find an anisotropic ultralight axion signature in the galaxy quadrupole. We use the Fourier-space galaxy clustering statistics from the Baryon Oscillation Spectroscopic Survey (BOSS) and obtain upper bounds for the axion relic density Ω_a h2<0.004 for axions of mass 10-31 eV≤ m_a≤ 10-26 eV at 95% confidence. We also improve existing constraints by a factor of over 4.5 and 2.1 for axion masses of 10-25 eV and 10-32 eV compared to CMB alone. To improve the convergence speed of our analysis, we develop an augmented interpolation scheme allowing a fast computation of the axion contribution to the linear matter power spectrum. This method leads to a 70% reduction of the computational cost for the full Monte Carlo Markov chains analysis.

Statistics of a single sky: constrained random fields and the imprint of Bardeen potentials on galaxy clustering

ABSTRACT We explore the implications of a single observer’s viewpoint on measurements of galaxy clustering statistics. We focus on the Bardeen potentials, which imprint characteristic scale-dependent signatures in the observed galaxy power spectrum. The existence of an observer breaks homogeneity as it singles out particular field values at her/his position, like a spontaneous symmetry breaking. As a result, spatial averaging of the data must be performed while holding the Bardeen potentials fixed at the observer’s position. In practice, this can be implemented with the formalism of constrained random fields. In the traditional Cartesian Fourier decomposition, this constraint imprints a signature in the observed galaxy power spectrum at wavenumbers comparable to the fundamental mode of the survey. This effect, which is well within the cosmic variance, is the same for all observers regardless of their local environment because differences of potential solely are observable. In a spherical Bessel Fourier decomposition, this constraint affects the monopole of the observed galaxy distribution solely, like in CMB data. As a corollary, the scale dependence of the non-Gaussian bias induced by a local primordial non-Gaussianity is not significantly affected by the observer’s viewpoint.

GEOMAX: beyond linear compression for three-point galaxy clustering statistics

ABSTRACT We present the GEOMAX algorithm and its python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximizes the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the 68 per cent credible intervals for the inferred parameters (b1, b2, f, σ8) by 50.4, 56.1, 33.2, and 38.3 per cent with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over 100 galaxy mocks to test the statistical significance of the improvements. On average, GEOMAX performs ∼15 per cent better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data sets such as DESI, Euclid, PFS, and SKA.

Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.

Improving Geometric and Dynamical Constraints on Cosmology with Intrinsic Alignments of Galaxies

Abstract We show that the spatial correlation of the intrinsic alignments (IAs) of galaxies, measured in galaxy redshift surveys, offers a precision route to improve the geometrical and dynamical constraints on cosmology. The IA has been treated as a contaminant against cosmological probes such as weak gravitational lensing experiments. However, the large-scale correlation of IAs is expected to follow the coherent large-scale matter inhomogeneities. Here, making use of its anisotropic nature, we show that the large-scale IA correlations help to improve the measurements of the geometric distances and growth of structure. In combination with the conventional galaxy clustering statistics, we find that constraints on equation-of-state parameter for dark energy and Hubble parameter can be tighter than those from the clustering statistics alone by a factor of more than 1.5.

Testing the accuracy of halo occupation distribution modelling using hydrodynamic simulations

ABSTRACT Halo models provide a simple and computationally inexpensive way to investigate the connection between galaxies and their dark matter haloes. However, these models rely on the assumption that the role of baryons can easily be parametrized in the modelling procedure. We aim to examine the ability of halo occupation distribution (HOD) modelling to reproduce the galaxy clustering found in two different hydrodynamic simulations, Illustris and EAGLE. For each simulation, we measure several galaxy clustering statistics on two different luminosity threshold samples. We then apply a simple five parameter HOD, which was fit to each simulation separately, to the corresponding dark matter-only simulations, and measure the same clustering statistics. We find that the halo mass function is shifted to lower masses in the hydrodynamic simulations, resulting in a galaxy number density that is too high when an HOD is applied to the dark matter-only simulation. However, the exact way in which baryons alter the mass function is remarkably different in the two simulations. After applying a correction to the halo mass function in each simulation, the HOD is able to accurately reproduce all clustering statistics for the high luminosity sample of galaxies. For the low luminosity sample, we find evidence that in addition to correcting the halo mass function, including spatial, velocity, and assembly bias parameters in the HOD is necessary to accurately reproduce clustering statistics.

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering

Abstract We perform an ensemble of N-body simulations with 20483 particles for 101 flat wCDM cosmological models sampled based on a maximin distance sliced Latin hypercube design. By using the halo catalogs extracted at multiple redshifts in the range of z = [0,1.48], we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo–matter cross-correlation, and halo autocorrelation as a function of halo masses, redshift, separations, and cosmological models based on principal component analysis and Gaussian process regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of N-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo–matter cross-correlation, relevant for galaxy–galaxy weak lensing, with an accuracy better than 2% and the halo autocorrelation, relevant for galaxy clustering correlation, with an accuracy better than 4%. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the concentration–mass relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo–galaxy connection, such as the halo occupation distribution at the equation level, instead of using the mock catalogs to make accurate predictions of galaxy clustering statistics, such as galaxy–galaxy weak lensing and the projected correlation function for any model within the wCDM cosmologies, in a few CPU seconds.

De Sitter universe described by a binary mixture with a variable cosmological constant λ $\lambda $

We have constructed a self-consistent system of Bianchi Type VI0 cosmology, and mingling of perfect fluid and dark energy in five dimensions. The usual equation of state \(p = \gamma \rho \) with \(\gamma \in [0, 1]\) is chosen by the perfect fluid. The dark energy assumed to be chosen is taken into consideration to be either the quintessence or Chaplygin gas. The same solutions pertaining to the corresponding the field equations of Einstein are obtained as a quadrature. State parameter’s equations for dark energy \(\omega \) is found to be consistent enough with the recent observations of SNe Ia data (SNe Ia data with CMBR anisotropy) and galaxy clustering statistics. Here our models predict that the rate of expansion of Universe would increase with passage of time. The cosmological constant \(\varLambda \) is traced as a declining function of time and it gets nearer to a small positive value later on which is supported by the results from the current supernovae Ia observations. Also a detail discussion is made on the physical and geometrical aspects of the models.

Cosmological implications of different baryon acoustic oscillation data

In this work, we explore the cosmological implications of different baryon acoustic oscillation (BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering (GC) statistics (hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics (hereafter BAO2). To make a comparison, we also take into account the case without BAO data (hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the $\Lambda$CDM, the $w$CDM, and the Chevallier-Polarski-Linder (CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, including its effects on parameter space, equation of state (EoS), figure of merit (FoM), deceleration-acceleration transition redshift, Hubble parameter $H(z)$, deceleration parameter $q(z)$, statefinder hierarchy $S^{(1)}_3(z)$, $S^{(1)}_4(z)$ and cosmic age $t(z)$. We find that: (1) NO BAO data always give a smallest fractional matter density $\Omega_{m0}$, a largest fractional curvature density $\Omega_{k0}$ and a largest Hubble constant $h$; in contrast, BAO1 data always give a largest $\Omega_{m0}$, a smallest $\Omega_{k0}$ and a smallest $h$. (2) For the $w$CDM and the CPL model, NO BAO data always give a largest EoS $w$; in contrast, BAO2 data always give a smallest $w$. (3) Compared with the case of BAO1, BAO2 data always give a slightly larger FoM, and thus can give a cosmological constraint with a slightly better accuracy. (4) The impacts of different BAO data on the cosmic evolution and the comic age are very small, and can not be distinguished by using various dark energy diagnosis and the cosmic age data.

Cosmological N-body simulations with suppressed variance

Abstract We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial Fourier mode amplitudes are fixed to the ensemble average power spectrum) and paired (with initial modes exactly out of phase). We measure the power spectrum, monopole and quadrupole redshift-space correlation functions, halo mass function and reduced bispectrum at z = 1. By these measures, predictions from a fixed pair can be as precise on non-linear scales as an average over 50 traditional simulations. The fixing procedure introduces a non-Gaussian correction to the initial conditions; we give an analytic argument showing why the simulations are still able to predict the mean properties of the Gaussian ensemble. We anticipate that the method will drive down the computational time requirements for accurate large-scale explorations of galaxy bias and clustering statistics, and facilitating the use of numerical simulations in cosmological data interpretation.

Recovering dark-matter clustering from galaxies with Gaussianization

The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and nonlinearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark matter power spectrum to k ~ 0.5 h/Mpc and of the initial power spectrum to k ~ 0.4 h/Mpc in certain cases at z = 0.

The same with less: the cosmic web of warm versus cold dark matter dwarf galaxies

We explore fundamental properties of the distribution of low-mass dark matter haloes within the cosmic web using warm dark matter (WDM) and cold dark matter (CDM) cosmological simulations. Using self-abundance-matched mock galaxy catalogues, we show that the distribution of dwarf galaxies in a WDM universe, wherein low-mass halo formation is heavily suppressed, is nearly indistinguishable to that of a CDM universe whose low-mass haloes are not seen because galaxy formation is suppressed below some threshold halo mass. However, if the scatter between dwarf galaxy luminosity and halo properties is large enough, low-mass CDM haloes would sometimes host relatively bright galaxies thereby populating CDM voids with the occasional isolated galaxy and reducing the numbers of completely empty voids. Otherwise, without high mass to light scatter, all mock galaxy clustering statistics that we consider – the auto-correlation function, the numbers and radial profiles of satellites, the numbers of isolated galaxies, and the probability distribution function of small voids – are nearly identical in CDM and WDM. WDM voids are neither larger nor emptier than CDM voids, when constructed from abundance-matched halo catalogues. It is thus a challenge to determine whether the CDM problem of the overabundance of small haloes with respect to the number density of observed dwarf galaxies has a cosmological solution or an astrophysical solution. However, some clues about the dark matter particle and the scatter between the properties of dwarf galaxies and their dark matter halo hosts might be found in the cosmic web of galaxies in future surveys of the local volume.