Real-space Correlation Function Research Articles

Euclid preparation

Aims. We validate a semi-analytical model for the covariance of the real-space two-point correlation function of galaxy clusters. Methods. Using 1000 PINOCCHIO light cones mimicking the expected Euclid sample of galaxy clusters, we calibrated a simple model to accurately describe the clustering covariance. Then, we used this model to quantify the likelihood-analysis response to variations in the covariance, and we investigated the impact of a cosmology-dependent matrix at the level of statistics expected for the Euclid survey of galaxy clusters. Results. We find that a Gaussian model with Poissonian shot-noise does not correctly predict the covariance of the two-point correlation function of galaxy clusters. By introducing a few additional parameters fitted from simulations, the proposed model reproduces the numerical covariance with an accuracy of 10%, with differences of about 5% on the figure of merit of the cosmological parameters Ωm and σ8. We also find that the covariance contains additional valuable information that is not present in the mean value, and the constraining power of cluster clustering can improve significantly when its cosmology dependence is accounted for. Finally, we find that the cosmological figure of merit can be further improved when mass binning is taken into account. Our results have significant implications for the derivation of cosmological constraints from the two-point clustering statistics of the Euclid survey of galaxy clusters.

Multi-directional neutron dark-field imaging with single absorption grating

Neutron dark-field imaging is a powerful technique for investigating the microstructural properties of materials through high-resolution full-field mapping of small-angle scattering. However, conventional neutron dark-field imaging utilizing Talbot–Lau interferometers is limited to probing only one scattering direction at a time. Here, we introduce a novel multi-directional neutron dark-field imaging approach that utilizes a single absorption grating with a two-dimensional pattern to simultaneously probe multiple scattering directions. The method is demonstrated to successfully resolve fiber orientations in a carbon compound material as well as the complex morphology of the transformed martensitic phase in additively manufactured stainless steel dogbone samples after mechanical deformation. The latter results reveal a preferential alignment of transformed domains parallel to the load direction, which is verified by EBSD. The measured real-space correlation functions are in good agreement with those extracted from the EBSD map. Our results demonstrate that multi-directional neutron dark-field imaging is overcoming significant limitations of conventional neutron dark-field imaging in assessing complex heterogeneous anisotropic microstructures and providing quantitative structural information on multiple length scales.

A high-performance implementation of atomistic spin dynamics simulations on x86 CPUs

Atomistic spin dynamics simulations provide valuable information about the energy spectrum of magnetic materials in different phases, allowing one to identify instabilities and the nature of their excitations. However, the time cost of evaluating the spin-spin correlation functions in real space increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. In this work, we propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel, which results in further performance improvements of 44% - 71% on several relatively large lattice sizes when compared to the implementation that uses the GEMM subroutine in OpenBLAS, which is the state-of-the-art open source library for Basic Linear Algebra Subroutine (BLAS).

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.

Galaxy clustering from the bottom up: a streaming model emulator I

ABSTRACT In this series of papers, we present a simulation-based model for the non-linear clustering of galaxies based on separate modelling of clustering in real space and velocity statistics. In the first paper, we present an emulator for the real-space correlation function of galaxies, whereas the emulator of the real-to-redshift space mapping based on velocity statistics is presented in the second paper. Here, we show that a neural network emulator for real-space galaxy clustering trained on data extracted from the dark quest suite of N-body simulations achieves sub-per cent accuracies on scales 1 < r < 30 $h^{-1} \, \mathrm{Mpc}$, and better than 3 per cent on scales r < 1 $h^{-1}\, \mathrm{Mpc}$ in predicting the clustering of dark-matter haloes with number density 10−3.5$(h^{-1}\, \mathrm{Mpc})^{-3}$, close to that of SDSS LOWZ-like galaxies. The halo emulator can be combined with a galaxy–halo connection model to predict the galaxy correlation function through the halo model. We demonstrate that we accurately recover the cosmological and galaxy–halo connection parameters when galaxy clustering depends only on the mass of the galaxies’ host halos. Furthermore, the constraining power in σ8 increases by about a factor of 2 when including scales smaller than 5 $h^{-1} \, \mathrm{Mpc}$. However, when mass is not the only property responsible for galaxy clustering, as observed in hydrodynamical or semi-analytic models of galaxy formation, our emulator gives biased constraints on σ8. This bias disappears when small scales (r < 10 $h^{-1}\, \mathrm{Mpc}$) are excluded from the analysis. This shows that a vanilla halo model could introduce biases into the analysis of future data sets.

Evolution of dynamical signature in the X-cube fracton topological order

As an unconventional realization of topological orders with an exotic interplay of topology and geometry, fracton (topological) orders feature subextensive topological ground state degeneracy and subdimensional excitations that are movable only within a certain subspace. It has been known in the exactly solvable three-dimensional X-cube model that universally represents the type-I fracton orders, that mobility constraints on subdimensional excitations originate from the absence of spatially deformable string-like operators. To unveil the interplay of topology and geometry, in this paper, we study the dynamical signature in the X-cube model in the presence of external Zeeman fields via large-scale quantum Monte Carlo simulation and stochastic analytic continuation. We compute both real-space correlation functions and dynamic structure factors of subdimensional excitations (i.e., fractons, lineons, and planons) in the fracton phase and their evolution into the trivial paramagnetic phase by increasing external fields. We find in the fracton phase, that the correlation functions and the spectral functions show clear anisotropy exactly caused by the underlying mobility constraints. On the other hand, the external fields successfully induce quantum fluctuations and offer mobility to excitations along the subspace allowed by mobility constraints. These numerical results provide the evolution of a dynamical signature of subdimensional particles in fracton orders, indicating that the mobility constraints on local dynamical properties of subdimensional excitations are deeply related to the existence of fracton topological order. The results will also be helpful in potential experimental identifications in spectroscopy measurements such as neutron scattering and nuclear magnetic resonance.

Solving small-scale clustering problems in approximate light-cone mocks

ABSTRACT Realistic light-cone mocks are important in the clustering analyses of large galaxy surveys. For simulations where only the snapshots are available, it is common to create approximate light-cones by joining together the snapshots in spherical shells. We assess the two-point clustering measurements of central galaxies in approximate light-cones built from the Millennium-XXL simulation, which are constructed using different numbers of snapshots. The monopole and quadrupole of the real-space correlation function is strongly boosted on small scales below 1 h−1 Mpc, due to some galaxies being duplicated at the boundaries between snapshots in the light-cone. When more snapshots are used, the total number of duplicated galaxies is approximately constant, but they are pushed to smaller separations. The effect of this in redshift space is small, as long as the snapshots are cut into shells in real space. Randomly removing duplicated galaxies is able to reduce the excess clustering signal. Including satellite galaxies will reduce the impact of the duplicates, since many small-scale pairs come from satellites in the same halo. Galaxies that are missing from the light-cone at the boundaries can be added to the light-cone by having a small overlap between each shell. This effect will impact analyses that use very small-scale clustering measurements, and when using mocks to test the impact of fibre collisions.

Dark energy survey year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space

ABSTRACT We present cosmological constraints from the analysis of angular power spectra of cosmic shear maps based on data from the first three years of observations by the Dark Energy Survey (DES Y3). Our measurements are based on the pseudo-Cℓ method and complement the analysis of the two-point correlation functions in real space, as the two estimators are known to compress and select Gaussian information in different ways, due to scale cuts. They may also be differently affected by systematic effects and theoretical uncertainties, making this analysis an important cross-check. Using the same fiducial Lambda cold dark matter model as in the DES Y3 real-space analysis, we find ${S_8 \equiv \sigma _8 \sqrt{\Omega _{\rm m}/0.3} = 0.793^{+0.038}_{-0.025}}$, which further improves to S8 = 0.784 ± 0.026 when including shear ratios. This result is within expected statistical fluctuations from the real-space constraint, and in agreement with DES Y3 analyses of non-Gaussian statistics, but favours a slightly higher value of S8, which reduces the tension with the Planck 2018 constraints from 2.3σ in the real space analysis to 1.5σ here. We explore less conservative intrinsic alignments models than the one adopted in our fiducial analysis, finding no clear preference for a more complex model. We also include small scales, using an increased Fourier mode cut-off up to $k_{\rm max}={5}\, {h}\, {\rm Mpc}^{-1}$, which allows to constrain baryonic feedback while leaving cosmological constraints essentially unchanged. Finally, we present an approximate reconstruction of the linear matter power spectrum at present time, found to be about 20 per cent lower than predicted by Planck 2018, as reflected by the lower S8 value.

LiquidDiffract: software for liquid total scattering analysis

LiquidDiffract is an open source, Python-based graphical application for X-ray total scattering analysis of liquids and disordered solids. The software implements procedures to obtain information on macroscopic bulk properties and local atomic-scale structure of monatomic or polyatomic samples from X-ray total scattering data. LiquidDiffract provides an easy to use interface with tools to perform background subtraction; calculation, normalisation, and refinement of the reciprocal-space structure factor and real-space correlation functions; and the extraction of structural information such as bond lengths, coordination number, and bulk density. The software is well suited to investigations of amorphous materials at extreme conditions, such as studies of high-pressure melt structure, polyamorphic phase transitions, and liquid equations of state. The open-source distribution and graphical interface will be of particular benefit to researchers who are new to the field. In this article we describe the distribution, system requirements, and installation of LiquidDiffract, and detail the data processing workflow and underlying numerical methods.

Quantification of dark-field effects in single-shot grid-based x-ray imaging

Dark-field (DF) x-ray imaging (DFXI) is a technology that can obtain information relating to the small-angle x-ray scattering of a sample. In this paper, we report on the quantification of DF effects by measuring the real space correlation function of scattering samples in a single-shot grid-based x-ray imaging setup that enables a simple approach to DFXI. The experimental measurements of the DF effects in our imaging setup were in good agreement with the theoretical quantification over the entire range of test conditions, thus verifying its effectiveness for single-shot grid-based DFXI. Consequently, we were able to clearly understand the associated particle-scale selectivity, which can help us determine suitable applications for single-shot grid-based x-ray DFXI.

Cosmic Voids and BAO with relative baryon-CDM perturbations

ABSTRACT We study the statistics of various large-scale structure tracers in gravity-only cosmological simulations including baryons and cold dark matter (CDM) initialized with two different transfer functions, and simulated as two distinct fluids. This allows us to study the impact of baryon-CDM relative perturbations on these statistics. In particular, we focus on the statistics of cosmic voids, as well as on the matter and halo real-space 2-point correlation function and baryon acoustic oscillations (BAO) peak. We find that the void size function is affected at the 1–2 per cent level at maximum, and that the impact is more important at higher redshift, while the void density profile and void bias are roughly unaffected. We do not detect a sizeable impact of relative baryon-CDM perturbations on the real-space correlation functions of matter and haloes or the BAO peak, which is in line with results from previous works. Our results imply that it would be hard to use voids or real-space correlation functions to constrain baryon-CDM relative perturbations, but also that we might not have to include them in models for the analysis of future cosmological surveys data.

Antiphase domain growth: Correlation functions and structure factors in the scaling regime

We study the coarsening of three-dimensional antiphase domain structures via Monte Carlo simulations. Linear lattice dimensions of $N=1024$ enable us to reach a scaling regime covering about 2.5 orders of magnitude of linear scale. With short-range interactions on cubic lattices at temperatures of $0.75\phantom{\rule{0.16em}{0ex}}{T}_{\text{c}}$, the resulting antiphase domain structures are isotropic, which allows us to describe the real-space correlation functions by a common function scaled by a time-dependent parameter. We compare abstract Potts models and realistic models of atomic order in compounds and show that those with same ground-state degeneracy $q$ lead to equivalent antiphase domain structures, while the scaling functions for different $q$ show slight but significant deviations. Finally, we quantitatively discuss notions of real-space scale (specific interface area) and reciprocal-space scale (superstructure peak width) and thus give numerically exact values for the corresponding parameter $K$ of the Scherrer equation.

A numerical study of the statistics of roughness parameters for fluctuating interfaces

Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results show that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.

Nanoscale heterogeneity, hydrogen bonding and their temperature dependence in cholinium phenylalaninate bio-ionic liquid

In this article, by employing atomistic molecular dynamics (MD) simulations, we examine the origin of nanoscale structural organization in cholinium phenylalaninate ([Ch][Phe]) biocompatible ionic liquid (IL), in which the [Phe]− anion possesses aromatic ring as its side chain. We attempt to deduce the bulk structure of [Ch][Phe] through simulated X-ray scattering structure function (S(q)), its partial components, real-space correlation functions and hydrogen bond analysis. While the simulated S(q) successfully captures the experimentally observed prepeak, resembling nanoscale heterogeneity, in the S(q) of [Ch][Phe] around q = 0.4 Å−1 at ambient conditions, the temperature dependence of the prepeak in the S(q) shows an unusual behavior. The intensity of the prepeak increases with increasing the temperature, contrary to many imidazolium cation-based ILs, but similar to several ammonium and phosphonium cation-based ILs. Multiple judicial decompositions of the total S(q)s clearly reveal that while [Phe]tail− − [Phe]tail− and [Ch]+ − [Phe]head− correlations are most prominent contributors and indicators of the prepeak, a balance of three major interactions lays down the observation of the nanoscale heterogeneity in this IL. Spatial distribution function analysis also corroborates with these observations, where the segregations of polar groups in polar domains and apolar groups in apolar domains are clearly observed. Our analysis reveals that the increase in the prepeak intensity is because of the increase in all the correlations responsible for the origin of prepeak on increasing the temperature. Hydrogen bond analysis performed through angle-resolved radial distribution functions reveals that only one type of hydrogen bond is present in [Ch][Phe] in which [Ch]+ acts as hydrogen bond donor via its hydroxyl hydrogen and [Phe]− as acceptor via its oxygen atoms. Weakening of this hydrogen bond and enhancement in [Phe]tail− − [Phe]tail− correlation with increasing the temperature are also observed.

A Semianalytic Model of the Pairwise Velocity Distribution between Dark Matter Halos

Abstract We study the probability distribution function (PDF) of relative velocity between two different dark matter halos (i.e., pairwise velocity) with high-resolution cosmological N-body simulations. We revisit a non-Gaussian framework to predict pairwise velocity statistics developed in Tinker. We investigate the pairwise velocity PDFs over a wide range of halo masses of 1012.5 ≲ M [h −1 M ⊙] ≲ 1015 and redshifts of 0 < z < 1. At a given set of masses, redshift, and separation length between two halos, our model requires three parameters to set the pairwise velocity PDF, whereas previous non-Gaussian models in the literature assumed four or more free parameters. At length scales of 5 < r [h −1 Mpc] < 40, our model predicts the mean and dispersion of the pairwise velocity for dark matter halos with masses of 1012.5 ≲ M [h −1 M ⊙] ≲ 1013.5 at 0.3 < z < 1 with a 5%-level precision. We demonstrate that our model of the pairwise velocity PDF provides an accurate mapping of the two-point clustering of massive-galaxy-sized halos at scales of O(10)h −1 Mpc between redshift and real space for a given real-space correlation function. For a mass-limited halo sample with masses greater than 1013.5 h −1 M ⊙ at z = 0.55, our model can explain the monopole and quadrupole moments of the redshift-space two-point correlations with a precision better than 5% at the scales of 5−40 and 10–30 h −1 Mpc, respectively. Our model of the pairwise velocity PDF will give a detailed explanation of the statistics of massive galaxies at intermediate scales in redshift surveys.

Effective real-space correlations of crystal lattice vibrations

Effective phonon fields coupled to a temperature-dependent permeability tensor are introduced to model empirical thermodynamic functions of crystal lattices and the temperature variation of Debye-Waller factors inferred by X-ray, γ-ray or neutron diffraction. The permeabilities generate a varying Debye temperature and a temperature-dependent spectral cutoff in the partition function as well as an effective temperature-dependent oscillator mass, to be calculated from diffraction and heat capacity data. The zero-point internal energy of the phonon field is extracted from low-temperature Debye-Waller B-factor measurements. The varying spectral cutoff, Debye temperature and oscillator mass determine the temperature evolution of real-space correlation functions. Closed integral representations are derived for the effective two-point function correlating isotropic lattice vibrations in monatomic cubic crystals as well as for the reduced four-point function correlating fluctuations around the mean-squared atomic displacement. The correlations are long-range with power-law tails and become oscillatory at low temperature. The formalism is illustrated with the correlation functions of copper.

Iterative removal of redshift-space distortions from galaxy clustering

ABSTRACT Observations of galaxy clustering are made in redshift space, which results in distortions to the underlying isotropic distribution of galaxies. These redshift-space distortions (RSDs) not only degrade important features of the matter density field, such as the baryonic acoustic oscillation (BAO) peaks, but also pose challenges for the theoretical modelling of observational probes. Here, we introduce an iterative non-linear reconstruction algorithm to remove RSD effects from galaxy clustering measurements, and assess its performance by using mock galaxy catalogues. The new method is found to be able to recover the real-space galaxy correlation function with an accuracy of $\sim \!1{{\ \rm per\ cent}}$, and restore the quadrupole accurately to 0, on scales $s\gtrsim 20\,h^{-1}\, {\rm Mpc}$. It also leads to an improvement in the reconstruction of the initial density field, which could help to accurately locate the BAO peaks. An ‘internal calibration’ scheme is proposed to determine the values of cosmological parameters, as a part of the reconstruction process, and possibilities to break parameter degeneracies are discussed. RSD reconstruction can offer a potential way to simultaneously extract the cosmological parameters, initial density field, real-space galaxy positions, and large-scale peculiar velocity field (of the real Universe), making it an alternative to standard perturbative approaches in galaxy clustering analysis, bypassing the need for RSD modelling.

The n-point streaming model: how velocities shape correlation functions in redshift space

Starting from first principles, we derive the fundamental equations that relate the n-point correlation functions in real and redshift space. Our result generalises the so-called `streaming model' to higher-order statistics: the full n-point correlation in redshift-space is obtained as an integral of its real-space counterpart times the joint probability density of n−1 relative line-of-sight peculiar velocities. Equations for the connected n-point correlation functions are obtained by recursively applying the generalised streaming model for decreasing n. Our results are exact within the distant-observer approximation and completely independent of the nature of the tracers for which the correlations are evaluated. Focusing on 3-point statistics, we use an N-body simulation to study the joint probability density function of the relative line-of-sight velocities of pairs of particles in a triplet. On large scales, we find that this distribution is approximately Gaussian and that its moments can be accurately computed with standard perturbation theory. We use this information to formulate a phenomenological 3-point Gaussian streaming model. A practical implementation is obtained by using perturbation theory at leading order to approximate several statistics in real space. In spite of this simplification, the resulting predictions for the matter 3-point correlation function in redshift space are in rather good agreement with measurements performed in the simulation. We discuss the limitations of the simplified model and suggest a number of possible improvements. Our results find direct applications in the analysis of galaxy clustering but also set the basis for studying 3-point statistics with future peculiar-velocity surveys and experiments based on the kinetic Sunyaev-Zel'dovich effect.

Many-body localization of zero modes

The celebrated Dyson singularity signals the relative delocalization of single-particle wave functions at the zero-energy symmetry point of disordered systems with a chiral symmetry. Here we show that analogous zero modes in interacting quantum systems can fully localize at sufficiently large disorder, but do so less strongly than nonzero modes, as signifed by their real-space and Fock-space localization characteristics. We demonstrate this effect in a spin-1 Ising chain, which naturally provides a chiral symmetry in an odd-dimensional Hilbert space, thereby guaranteeing the existence of a many-body zero mode at all disorder strengths. In the localized phase, the bipartite entanglement entropy of the zero mode follows an area law, but is enhanced by a system-size-independent factor of order unity when compared to the nonzero modes. Analytically, this feature can be attributed to a specific zero-mode hybridization pattern on neighboring spins. The zero mode also displays a symmetry-induced even-odd and spin-orientation fragmentation of excitations, characterized by real-space spin correlation functions, which generalizes the sublattice polarization of topological zero modes in noninteracting systems, and holds at any disorder strength.

Limitations to the ‘basic’ HOD model and beyond

ABSTRACT We use the IllustrisTNG cosmological, hydrodynamical simulations to test fundamental assumptions of the mass-based halo occupation distribution (HOD) approach to modelling the galaxy–halo connection. By comparing the clustering of galaxies measured in the 300 Mpc TNG box (TNG300) with that predicted by the standard (basic) HOD model, we find that, on average, the ‘basic’ HOD model underpredicts the real-space correlation function in the TNG300 box by ∼15 per cent on scales of $1 \,\,\lt\,\, r \,\,\lt\,\, 20 \ {\rm Mpc}\, h^{-1}$, which is well beyond the target precision demanded of next-generation galaxy redshift surveys. We perform several tests to establish the robustness of our findings to systematic effects, including the effect of finite box size and the choice of halo finder. In our exploration of ‘secondary’ parameters with which to augment the ‘basic’ HOD, we find that the local environment of the halo, the velocity dispersion anisotropy, β, and the product of the half-mass radius and the velocity dispersion, σ2Rhalfmass, are the three most effective measures of assembly bias that help reconcile the ‘basic’ HOD-predicted clustering with that in TNG300. In addition, we test other halo properties such as halo spin, formation epoch, and halo concentration. We also find that at fixed halo mass, galaxies in one type of environment cluster differently from galaxies in another. We demonstrate that a more complete model of the galaxy–halo connection can be constructed if we combine both mass and local environment information about the halo.