Two-point Correlation Function Research Articles

Statistical anisotropy in galaxy ellipticity correlations

As well as the galaxy number density and peculiar velocity, the galaxy intrinsic alignment can be used to test the cosmic isotropy. We study distinctive impacts of the isotropy breaking on the configuration-space two-point correlation functions (2PCFs) composed of the spin-2 galaxy ellipticity field. For this purpose, we build a formalism for general types of the isotropy-violating 2PCFs and a methodology to efficiently compute them by generalizing the polypolar spherical harmonic decomposition approach to the spin-weighted version. As a demonstration, we analyze the 2PCFs when the matter power spectrum has a well-known g *-type isotropy-breaking term (induced by, e.g., dark vector fields). We then confirm that some anisotropic distortions indeed appear in the 2PCFs and their shapes rely on a preferred direction causing the isotropy violation, d̂. Such a feature can be a distinctive indicator for testing the cosmic isotropy. Comparing the isotropy-violating 2PCFs computed with and without the plane parallel (PP) approximation, we find that, depending on d̂, the PP approximation is no longer valid when an opening angle between the directions towards target galaxies is 𝒪(1°) for the density-ellipticity and velocity-ellipticity cross correlations and around 10° for the ellipticity auto correlation. This suggests that an accurate test for the cosmic isotropy requires the formulation of the 2PCF without relying on the PP approximation.

Tomographic Alcock–Paczyński Test with Redshift-space Correlation Function: Evidence for the Dark Energy Equation-of-state Parameter w > −1

The apparent shape of galaxy clustering depends on the adopted cosmology used to convert observed redshift to comoving distance, the r(z) relation, as it changes the line elements along and across the line of sight differently. The Alcock–Paczyński (AP) test exploits this property to constrain the expansion history of the universe. We present an extensive review of past studies on the AP test. We adopt an extended AP test method introduced by Park et al., which uses the full shape of redshift-space two-point correlation function (CF) as the standard shape, and apply it to the Sloan Digital Sky Survey DR7, BOSS, and eBOSS LRG samples covering the redshift range up to z = 0.8. We calibrate the test against the nonlinear cosmology-dependent systematic evolution of the CF shape using Multiverse simulations. We focus on examining whether or not the flat Lambda cold dark matter (ΛCDM) concordance model is consistent with observation. We constrain the flat wCDM model to have and from our AP test alone, which is significantly tighter than the constraints from the BAO or SNe Ia methods by a factor of 3–6. When the AP test result is combined with the recent BAO and SNe Ia results, we obtain and . This puts a strong tension with the flat ΛCDM model with w = −1 at the 4.2σ level. Consistency with w = −1 is obtained only when the Planck cosmic microwave background (CMB) observation is combined. It remains to be seen whether this tension between observations of galaxy distribution at low redshifts and CMB anisotropy at the decoupling epoch becomes greater in future studies and leads us to a new paradigm of cosmology.

Mapping the milky way’s stellar halo with 2D data

ABSTRACT We propose a new method for measuring the spatial density distribution of the stellar halo of the Milky Way. Our method is based on a pairwise statistic of the distribution of stars in the sky, the angular two-point correlation function (ATPCF). The ATPCF utilizes two-dimensional data of stars only and is therefore immune to the large uncertainties in the determination of distances to stars. We test our method using mock stellar data coming from various models including the single power-law (SPL) and the broken power-law (BPL) density profiles. We also test the influence of axisymmetric flattening factors using both constant and varying values. We find that the ATPCF is a powerful tool for recovering the spatial distributions of the stellar haloes in our models. We apply our method to observational data from the type ab RR Lyrae catalogue in the Catalina Survey Data Release 1. In the 3-parameter BPL model, we find that $s_{1}=2.46_{-0.20}^{+0.18}, s_{2}=3.99_{-1.33}^{+0.75}$, and $r_{0}=31.11_{-5.88}^{+7.61}$, which are in good agreement with previous results. We also find that introducing an extra parameter, the radially varying flattening factor, greatly improves our ability to model accurately the observed data distribution. This implies perhaps that the stellar halo of the Milky Way should be regarded as oblate.

The asymptotic homogenization evaluation of effective mechanical property of the C/C-ZrC composite by the reconstruction technique

In this framework, we formulate a procedure to reconstruct the structure of general random 3D braid heterogeneous media based on transformation of Gaussian random fields, where the correlation of the underlying Gaussian field is determined explicitly rather than through iterative methods. The reconstructed media can meet the key microstructural information contained in the micrographs and two-point correlation function of the reference media. A robust and efficient algorithm is the operation for accurate determination the effective physical properties from a local heterogeneous material based on the methods of asymptotic homogenization and the finite element. Comparison of the present result to the experimental data from the literature shows a good agreement. The correlation length, Gaussian complexity, representative volume element size and mesh size are investigated and selected to highlight the importance of morphologically realistic microstructures. The effective properties of 3D braid composites are evaluated numerically and the respective effect of the volume fraction and relative material parameters of the reinforcement is assessed numerically. This breakthrough is the possibility to design, predict properties, and even manufacture materials not only with the help of experiments but also with computer science.

Cosmological constraints with the linear point from the BOSS survey

ABSTRACT The Linear Point (LP), defined as the mid-point between the baryon acoustic oscillation (BAO) peak and the associated left dip of the two-point correlation function (2PCF), ξ(s), is proposed as a new standard ruler which is insensitive to non-linear effects. In this paper, we use a Bayesian sampler to measure the LP and estimate the corresponding statistical uncertainty, and then perform cosmological parameter constraints with LP measurements. Using the Patchy mock catalogues, we find that the measured LPs are consistent with theoretical predictions at 0.6 per cent level. We find constraints with mid-points identified from the rescaled 2PCF (s2ξ) more robust than those from the traditional LP based on ξ, as the BAO peak is not always prominent when scanning the cosmological parameter space, with the cost of 2–4 per cent increase of statistical uncertainty. This problem can also be solved by an additional data set that provides strong parameter constraints. Measuring LP from the reconstructed data slightly increases the systematic error but significantly reduces the statistical error, resulting in more accurate measurements. The 1 σ confidence interval of distance scale constraints from LP measurements are 20–30 per cent larger than those of the corresponding BAO measurements. For the reconstructed Sloan Digital Sky Survey Data Release 12 data, the constraints on H0 and Ωm in a flat-Lambda cold dark matter framework with the LP are generally consistent with those from BAO. When combined with Planck cosmic microwave background data, we obtain $H_0=68.02_{-0.37}^{+0.36}$ ${\rm km}\, {\rm s}^{-1}\, {\rm Mpc}^{-1}$ and $\Omega _{\rm m}=0.3055_{-0.0048}^{+0.0049}$ with the LP.

Late-time correlators and complex geodesics in de Sitter space

We study two-point correlation functions of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator valid for large mass and at late times. This expression involves a sum over two complex conjugate geodesics that correctly reproduces the large-mass, late-time limit of the exact two-point function in the Bunch-Davies vacuum. The exponential decay of the late-time correlator is associated to the timelike part of the complex geodesics. We emphasize that the late-time exponential decay is in tension with the finite maximal entropy of empty de Sitter space, and we briefly discuss how non-perturbative corrections might resolve this paradox.

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

Can multipartite entanglement be characterized by two-point connected correlation functions?

We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.

MUSEQuBES: the relation between Ly α emitters and C iv absorbers at z ≈ 3.3

ABSTRACT We present a detailed study of the column density and covering fraction profiles of C iv absorption around 86 redshift z ≈ 3.3 Ly α emitters (LAEs) detected in eight Multi-Unit Spectroscopic Explorer (MUSE) fields of 1 arcmin × 1 arcmin centred on eight bright background quasars as part of the MUSE Quasar-field Blind Emitters Survey (MUSEQuBES). Using Voigt profile fitting of all the C iv absorbers detected along these eight sightlines, we generated a ‘blind’ absorber catalogue consisting of 489 C iv absorption components. We cross-matched this blind C iv catalogue with the MUSE-detected LAE catalogue and found a significant enhancement of C iv components within ≈±400 $\rm km\, s^{-1}$ of the systemic redshifts of the LAEs. Neither the C iv column density (N) nor the Doppler parameter (b) of individual C iv components shows any significant anticorrelation with impact parameter (ρ) of the LAEs in the 68 percentile range of 90 ≤ ρ ≤ 230 physical kpc (pkpc). We find a covering fraction of ≈60 per cent for a threshold $N(\rm{C{\small IV}})$ of 1012.5 cm−2, which is roughly twice as high as in random regions. The C iv covering fraction remains constant at $\approx\!{50}{{\ \rm per\, cent}}$ for impact parameters in the range of 150–250 pkpc (≈3–6R200). Using the covering fraction profile, we constrain the LAE–C iv absorber two-point correlation function, and obtain $r_0 = 3.4^{+1.1}_{-1.0}$ comoving Mpc and $\gamma = 1.2^{+0.2}_{-0.3}$ for a threshold $N(\rm{C{\small IV}})$ of 1013.0 cm−2. The C iv covering fraction is found to be enhanced for the LAEs that are part of a ‘pair/group’ compared to the isolated ones.

Clustering of red sequence galaxies in the fourth data release of the Kilo-Degree Survey

We present a sample of luminous red sequence galaxies as the basis for a study of the large-scale structure in the fourth data release of the Kilo-Degree Survey. The selected galaxies are defined by a red sequence template, in the form of a data-driven model of the colour-magnitude relation conditioned on redshift. In this work, the red sequence template was built using the broad-band optical+near infrared photometry of KiDS-VIKING and the overlapping spectroscopic data sets. The selection process involved estimating the red sequence redshifts, assessing the purity of the sample and estimating the underlying redshift distributions of redshift bins. After performing the selection, we mitigated the impact of survey properties on the observed number density of galaxies by assigning photometric weights to the galaxies. We measured the angular two-point correlation function of the red galaxies in four redshift bins and constrain the large-scale bias of our red sequence sample assuming a fixed ΛCDM cosmology. We find consistent linear biases for two luminosity-threshold samples (‘dense’ and ‘luminous’). We find that our constraints are well characterised by the passive evolution model.

Euclidpreparation

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set ofEuclid-like mocks, derived fromN-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ωm,σ8) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses withEuclid. The data used in this analysis are publicly released with the paper.

Small-scale dynamo with finite correlation times.

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behavior, but they are based on simplifying assumptions. For instance, the well-known Kazantsev model assumes an incompressible flow that is δ-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equationfor the longitudinal two-point magnetic correlation function in real space to first order in the correlation time τ and for an arbitrary degree of compressibility (DOC). This generalized Kazantsev equationencapsulates the original Kazantsev equation. In the limit of small Strouhal numbers St∝τ we use the Wentzel-Kramers-Brillouin approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e., M_{k}(k)∼k^{3/2}. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity and the DOC together.

Small-scale clustering of BOSS galaxies: dependence on luminosity, colour, age, stellar mass, specific star formation rate, and other properties

ABSTRACT We measure and analyse galaxy clustering and the dependence on luminosity, colour, age, stellar mass, and specific star formation rate using Baryon Oscillation Spectroscopic Survey (BOSS) galaxies at 0.48 < z < 0.62. We fit the monopole and quadrupole moments of the two-point correlation function and its projection on scales of 0.1–60.2 h−1 Mpc, after having split the catalogue in a variety of ways. We find that the clustering dependence is consistent with previous well-established results showing the broad trends expected: For example, that brighter, redder, older, more massive and quenched galaxies are more strongly clustered. We also investigate the dependence on additional parameters previously derived from stellar population synthesis model fits to the spectra. We find that galaxy clustering depends on look-back formation time at a low level, while it has little dependence on metallicity. To understand the physics behind these trends, we fit the clustering with a simulation-based emulator to simultaneously model cosmology and galaxy bias using a halo occupation distribution framework. After marginalizing parameters determining the background cosmology, galaxy bias, and a scaling parameter to decouple halo velocity field, we find that the growth rate of large-scale structure as determined by the redshift space distortions is consistent with previous analysis using the full sample, and we do not find evidence that cosmological constraints depend systematically on galaxy selection. This demonstrates that cosmological inference using small-scale clustering measurements is robust to changes in the catalogue selection.

A general framework for removing point-spread function additive systematics in cosmological weak lensing analysis

ABSTRACT Cosmological weak lensing measurements rely on a precise measurement of the shear two-point correlation function (2PCF) along with a deep understanding of systematics that affect it. In this work, we demonstrate a general framework for detecting and modelling the impact of PSF systematics on the cosmic shear 2PCF and mitigating its impact on cosmological analysis. Our framework can detect PSF leakage and modelling error from all spin-2 quantities contributed by the PSF second and higher moments, rather than just the second moments, using the cross-correlations between galaxy shapes and PSF moments. We interpret null tests using the HSC Year 3 (Y3) catalogs with this formalism and find that leakage from the spin-2 combination of PSF fourth moments is the leading contributor to additive shear systematics, with total contamination that is an order-of-magnitude higher than that contributed by PSF second moments alone. We conducted a mock cosmic shear analysis for HSC Y3 and find that, if uncorrected, PSF systematics can bias the cosmological parameters Ωm and S8 by ∼0.3σ. The traditional second moment-based model can only correct for a 0.1σ bias, leaving the contamination largely uncorrected. We conclude it is necessary to model both PSF second and fourth moment contaminations for HSC Y3 cosmic shear analysis. We also reanalyse the HSC Y1 cosmic shear analysis with our updated systematics model and identify a 0.07σ bias on Ωm when using the more restricted second moment model from the original analysis. We demonstrate how to self-consistently use the method in both real space and Fourier space, assess shear systematics in tomographic bins, and test for PSF model overfitting.

Subhalo abundance matching using progenitor mass at varying redshift: two modes of stellar mass growth imprinted into the Subaru HSC galaxy clustering

ABSTRACT We propose a novel subhalo abundance matching (SHAM) model that uses the virial mass of the main progenitor of each (sub)halo Mprog as a proxy of the galaxy stellar mass M* at the time of observation. This Mprog model predicts the two-point correlation functions depending on the choice of the epoch zprog at which Mprog is quoted. With zprog as a fitting parameter, we apply the Mprog model to the angular correlation functions measured with varying stellar mass thresholds from M*, lim/(h−2 M⊙) = 1011–108.6 using a sample of galaxies at z ≃ 0.4 from the Subaru Hyper Suprime-Cam survey. The Mprog model can reproduce the observations very well over 10 h−1kpc–10 h−1Mpc. We find that, for the samples of 109.2 ≤ M*, lim/(h−2 M⊙) ≤ 1010.2, the correlation functions predicted by the widely used Vpeak model lack amplitudes at ≲1 h−1 Mpc, suggesting that Mprog is a better proxy of the galaxy stellar mass than conventional Vpeak. The zprog parameter is highest (zprog ≃ 3) for intermediate mass galaxies at M* ≃ 109.9 h−2 M⊙, and becomes smaller down to zprog ≃ 1 for both lower and higher mass galaxies. We interpret these trends as reflecting the downsizing in the in situ star formation in lower mass galaxies and the larger contribution of the ex situ stellar mass growth in higher mass galaxies.

Cosmological forecasts for future galaxy surveys with the linear point standard ruler: Toward consistent BAO analyses far from a fiducial cosmology

The linear point (LP) standard ruler was identified as the basis of a purely geometric method for exploiting the baryon acoustic oscillations (BAO). The LP exploits the BAO feature imprinted in the galaxy two-point correlation function to measure cosmological distances independent of any specific cosmological model. We forecast the expected precision of future and ongoing spectroscopic galaxy surveys to measure distances leveraging the linear point. We investigate the cosmological implications of our forecasted results. We focus in particular on a relevant working example: the detection of the late-time cosmic acceleration independent of other cosmological probes. Our findings show that, even within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ standard cosmological paradigm, estimated distances need to be reliable over a very wide parameter range in order to realize their maximum utility. This is particularly relevant if we aim to properly characterize cosmological tensions. The LP is a promising candidate approach to achieve this reliability. In contrast, widely employed procedures in BAO analysis estimate distances keeping fixed cosmological parameters to fiducial values close to cosmic-microwave-background constraints in flat-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. It is unclear whether they are purely geometric methods. Moreover, they rely on untested extrapolations to explore the parameter space away from those fiducial flat-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values. We recommend that all BAO methodologies be validated across the full range of models and parameters over which their results are quoted, first by means of linear predictions and then $N$-body simulations.

Large-scale clustering of buried X-ray AGN: Trends in AGN obscuration and redshift evolution

Aims. In order to test active galactic nucleus (AGN) unification and evolutionary models, we measured the AGN clustering properties as a function of AGN obscuration defined in terms of hydrogen column density, NH. In addition to measuring the clustering of unobscured (NH < 1022 cm−2) and moderately obscured (1022 ≤ NH < 1023.5) AGNs, we also targeted highly obscured sources (NH ≥ 1023.5) up to redshifts of z = 3. Methods. We have compiled one of the largest samples of X-ray-selected AGNs from a total of eight deep XMM/Chandra and multiwavelength surveys. We measured the clustering as a function of both AGN obscuration and redshift using the projected two-point correlation function, wp(rp). We modeled the large-scale clustering signal, measured the AGN bias, b(z, NH), and interpreted it in terms of the typical AGN host dark matter halo, Mhalo(z, NH). Results. We find no significant dependence of AGN clustering on obscuration, suggesting similar typical masses of the hosting halos as a function of NH. This result matches expectations of AGN unification models, in which AGN obscuration depends mainly on the viewing angle of the obscuring torus. We measured, for the first time, the clustering of highly obscured AGNs and find that these objects reside in halos with typical mass log Mhalo = 12.98−0.22+0.17[h−1 M⊙] (12.28−0.19+0.13) at low z ∼ 0.7 (high z ∼ 1.8) redshifts. We find that irrespective of obscuration, an increase in AGN bias with redshift is slower than the expectation for a constant halo mass and instead follows the growth rate of halos, known as the passive evolution track. This implies that for those AGNs the clustering is mainly driven by the mass growth rate of the hosting halos and galaxies across cosmic time.

Mass bias and cosmological constraints from Planck cluster clustering

Aims. We analysed the 3D clustering of the Planck sample of Sunyaev–Zeldovich (SZ) selected galaxy clusters, focusing on the redshift-space two-point correlation function (2PCF). We compared our measurements to theoretical predictions of the standard Λ cold dark matter (ΛCDM) cosmological model, deriving an estimate of the Planck mass bias, bSZ, and cosmological parameters. Methods. We measured the 2PCF of the sample in the cluster-centric radial range r ∈ [10, 150] h−1 Mpc, considering 920 galaxy clusters with redshift z ≤ 0.8. A Markov chain Monte Carlo analysis was performed to constrain bSZ, assuming priors on cosmological parameters from Planck cosmic microwave background (CMB) results. We also adopted priors on bSZ from external data sets to constrain the cosmological parameters Ωm and σ8. Results. We obtained (1−bSZ) = 0.62−0.11+0.14, which agrees with the value required to reconcile primary CMB and cluster count observations. By adopting priors on (1 − bSZ) from external data sets, we derived results on Ωm that fully agree and are competitive, in terms of uncertainties, with those derived from cluster counts. This confirms the importance of including clustering in cosmological studies in order to fully exploit the information from galaxy cluster statistics. On the other hand, we found that σ8 is not constrained.

Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model

Quantum annealing is a contender to solve combinatorial optimization problems based on quantum dynamics. While significant efforts have been undertaken to investigate the quality of the solutions and the required run times, much less attention has been paid to understanding the dynamics of quantum annealing and the process leading to the solution during the sweep itself. In this comprehensive study, we investigate various aspects of the quantum annealing dynamics using different approaches. We perform quantum annealing, simulated quantum annealing, and classical annealing on several hundred instances of the Sherrington-Kirkpatrick model with intermediate system sizes up to 22 spins using numerical simulations. We observe qualitative differences between the quantum and classical methods, in particular at intermediate times, where a peak in the fidelity, also known as diabatic bump, appears for hard instances. Furthermore, we investigate the two-point correlation functions, which feature differences at intermediate times as well. At short times, however, the methods are similar again, which can be explained by relating the short-time expansion of quantum annealing to a high-temperature expansion, thus allowing one in principle to find the classical solution already at short times, albeit at prohibitive sampling cost.

Holographic two-point functions in a disorder system

We study the holographic dual of two-point correlation functions for nonconformal field theories. We first take into account a Lifshitz geometry as the dual of a Lifshitz field theory which may appear at a critical or IR fixed point. We explicitly show the holographic relation between a Lifshitz geometry and a Lifshitz field theory by calculating two-point correlators and equation of state parameter on both sides. We also investigate a disorder deformation, which allows a UV conformal field theory to flow into a new IR Lifshitz field theory. In this deformed theory, we investigate an anomalous dimension representing the change of an operator's scaling dimension along the RG flow.