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NASA NTRS2002

VEXT: A Virtual Observatory Exploration Toolkit

This final report consists of two main parts. The first is taken from a paper by the PiCA (Pittsburgh Computational Astrostatistics) Group which describes our ongoing work in fast computation of n-point correlation functions. We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kd-trees which are decorated with cached sufficient statistics thus allowing for orders of magnitude speed-ups over the naive non-tree-based implementation of correlation functions. We further discuss the use of controlled approximations within the computation which allows for further acceleration. In summary, our algorithm now makes it possible to compute exact, all-pairs, measurements of the two, three and four-point correlation functions for cosmological data sets like the Sloan Digital Sky Survey and the next generation of Cosmic Microwave Background experiments. The second part summarizes the progress made by the PiCA Group in this area through the AISR grant.

Schneider, Jeff↗

NASA NTRS1989

Three-point correlations of galaxy clusters

A relation between two- and three-point correlation functions similar to that of galaxies is presently established by estimating the irreducible angular three-point correlation function of Abell clusters in distance classes 5 and 6, for Galactic latitudes below 40 deg. The shape of the three-point correlation function is fully consistent with the quadratic scaling law found by Groth and Peebles (1977) for galaxies. The three-point correlation function is inconsistent with the expectations from biasing.

Toth, Gabor↗

DOE OSTI2019

Water Dynamics in Nanoporous Silica: Ultrafast Vibrational Spectroscopy and Molecular Dynamics Simulations

Nanoporous silica materials are important in catalysis, energy, and materials applications in which water is an essential component. System performance is intimately connected to the water dynamics occurring in the confined environment. However, the dynamics and associated structures of water in nanoporous silica have proven challenging to measure and predict. Here, confined water dynamics are examined via the ultrafast infrared spectroscopy of selenocyanate (SeCN – ) dissolved in the hydrated ~2.4 nm silica mesopores of MCM41. Polarization selective pump–probe and two-dimensional infrared measurements on the CN stretching mode of SeCN – are used to probe the effect of confinement on orientational relaxation and spectral diffusion dynamics. Here, the dynamics of SeCN – provide information on the surrounding water hydrogen bond dynamics. The long CN stretch lifetime (~36 ps), relative to the water hydroxyl stretch (<2 ps), significantly extends the time scales that can be accessed. Complete orientational relaxation (C 2 (t), orientational correlation function) and spectral diffusion (C ω (t), frequency–frequency correlation function) dynamics are presented and compared to the simulated time correlation functions in a model silica pore of the same size. A slow decay component not present in the bulk liquid is observed in both experiments, indicating that the hydrogen bond dynamics are significantly altered by confinement. The simulations reveal a qualitative difference in the functional dependence of C 2 (t;d) and C ω (t;d) on d, the distance from the interface. The former becomes exponentially faster with distance while the latter makes an abrupt transition from slower to faster dynamics midway between the surface and pore center, d ≅ 6 Å.

14 SOLAR ENERGY↗

DOE OSTI2014

An infinite set of Ward identities for adiabatic modes in cosmology

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — the q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: The role of the three-gluon correlator

Here, we study the Sivers asymmetry in semi-inclusive hadron production in deep inelastic scattering. We concentrate on the contribution from the photon-gluon fusion channel at O(α em 2 α s ), where three-gluon correlation functions play a major role within the twist-3 collinear factorization formalism. We establish the correspondence between such a formalism with three-gluon correlation functions and the usual transverse momentum-dependent (TMD) factorization formalism at moderate hadron transverse momenta. We derive the coefficient functions used in the usual TMD evolution formalism related to the quark Sivers function expansion in terms of the three-gluon correlation functions. We further perform the next-to-leading order calculation for the transverse momentum-weighted spin-dependent differential cross section and identify the off-diagonal contribution from the three-gluon correlation functions to the QCD collinear evolution of the twist-3 Qiu-Sterman function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Strong Clustering of Lyman Break Galaxies around Luminous Quasars at Z ∼ 4

In the standard picture of structure formation, the first massive galaxies are expected to form at the highest peaks of the density field, which constitute the cores of massive proto-clusters. Luminous quasars (QSOs) at z ∼ 4 are the most strongly clustered population known, and should thus reside in massive dark matter halos surrounded by large overdensities of galaxies, implying a strong QSO–galaxy cross-correlation function. We observed six z ∼ 4 QSO fields with VLT/FORS, exploiting a novel set of narrow-band filters custom designed to select Lyman Break Galaxies (LBGs) in a thin redshift slice of Δz∼0.3, mitigating the projection effects that have limited the sensitivity of previous searches for galaxies around z≳4 QSOs. We find that LBGs are strongly clustered around QSOs, and present the first measurement of the QSO–LBG cross-correlation function at z ∼ 4, on scales of 0.1≲R≲9 h{sup −1} Mpc (comoving). Assuming a power-law form for the cross-correlation function ξ=(r/r{sub 0}{sup QG}){sup γ}, we measure r{sub 0}{sup QG}=8.83{sub −1.51}{sup +1.39} h{sup −1} Mpc for a fixed slope of γ=2.0. This result is in agreement with the expected cross-correlation length deduced from measurements of the QSO and LBG auto-correlation function, and assuming a deterministic bias model. We also measure a strong auto-correlation of LBGs in our QSO fields, finding r{sub 0}{sup GG}=21.59{sub −1.69}{sup +1.72} h{sup −1} Mpc for a fixed slope of γ=1.5, which is ∼4 times larger than the LBG auto-correlation length in blank fields, providing further evidence that QSOs reside in overdensities of LBGs. Our results qualitatively support a picture where luminous QSOs inhabit exceptionally massive (M{sub halo}>10{sup 12} M{sub ⊙}) dark matter halos at z ∼ 4.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Dark Energy Survey Year 1 Results: Joint Analysis of Galaxy Clustering, Galaxy Lensing, and CMB Lensing Two-point Functions

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $\Lambda$CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_{8}\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3} = 0.782^{+0.019}_{-0.025}$ and $\Omega_{\rm m}=0.260^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $\Lambda$CDM models. Combining constraints from all six two-point functions yields $S_{8}=0.776^{+0.014}_{-0.021}$ and $\Omega_{\rm m}= 0.271^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Disconnected covariance of 2-point functions in large-scale structure

Optimal analyses using the 2-point functions of large-scale structure probes require accurate covariance matrices. A covariance matrix of the 2-point function comprises the disconnected part and the connected part. While the connected covariance only becomes important on small scales, the disconnected covariance is dominant on large scales, where the survey window has a significant impact. In this work, we develop an analytical method to compute the disconnected covariance, accounting for the window effect. Derived under the flat-sky approximation, our formalism is applicable to wide surveys by swapping in the curved-sky window functions. Our method works for both the power spectrum and the correlation function, and applies to the covariances of various probes including the multipoles and the wedges of 3D clustering, the angular and the projected statistics of clustering and shear, as well as the cross covariances between different probes. We verify the analytic covariance against the sample covariance from the galaxy mock simulations in two test cases: (1) the power spectrum multipole covariance, and (2) the joint covariance of the projected correlation function and the correlation function multipoles. Our method achieve good agreement with the mocks, while at a negligible computational cost. Unlike mocks, our analytic covariance is free of sampling noise, which often leads to numerical problems and the need to inflate the errors. In addition, our method can use the best-fit power spectrum as input, in contrast to the standard procedure of using a fiducial model that may deviate significantly from the truth. We also show that a naive diagonal power spectrum covariance underestimates the signal-to-noise ratio compared to our analytic covariance. The code that accompanies this paper is available at https://github.com/eelregit/covdisc.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Fourier band-power E/B-mode estimators for cosmic shear

We introduce new Fourier band-power estimators for cosmic shear data analysis and E/B-mode separation. We consider both the case where one performs E/B-mode separation and the case where one does not. The resulting estimators have several nice properties which make them ideal for cosmic shear data analysis. First, they can be written as linear combinations of the binned cosmic shear correlation functions. Secondly, they account for the survey window function in real-space. Thirdly, they are unbiased by shape noise since they do not use correlation function data at zero separation. Fourthly, the band-power window functions in Fourier space are compact and largely non-oscillatory. Fifthly, they can be used to construct band-power estimators with very efficient data compression properties. In particular, we find that all of the information on the parameters Ωm, σ8 and ns in the shear correlation functions in the range of ~10–400 arcmin for single tomographic bin can be compressed into only three band-power estimates. Finally, we can achieve these rates of data compression while excluding small-scale information where the modelling of the shear correlation functions and power spectra is very difficult. Given these desirable properties, these estimators will be very useful for cosmic shear data analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Searching for low-lying multi-particle thresholds in lattice spectroscopy

We explore the Euclidean-time tails of odd-parity nucleon correlation functions in a search for the S-wave pion–nucleon scattering-state threshold contribution. The analysis is performed using 2+1 flavor 32{sup 3}×64 PACS-CS gauge configurations available via the ILDG. Correlation matrices composed with various levels of fermion source/sink smearing are used to project low-lying states. The consideration of 25,600 fermion propagators reveals the presence of more than one state in what would normally be regarded as an eigenstate-projected correlation function. This observation is in accord with the scenario where the eigenstates contain a strong mixing of single and multi-particle states but only the single particle component has a strong coupling to the interpolating field. Employing a two-exponential fit to the eigenvector-projected correlation function, we are able to confirm the presence of two eigenstates. The lower-lying eigenstate is consistent with a Nπ scattering threshold and has a relatively small coupling to the three-quark interpolating field. We discuss the impact of this small scattering-state contamination in the eigenvector projected correlation function on previous results presented in the literature. -- Highlights: • Correlation-matrix projected correlators reveal more than one state contributing. • Results are associated with strong mixing of single and multi-particle states in QCD. • A two-exponential fit confirms the presence of two QCD eigenstates. •The lower-lying eigenstate is consistent with a nucleon–pion scattering threshold. •The impact of this small contamination on the higher-lying state is examined.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Consistency relations for sharp inflationary non-Gaussian features

If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Electronic Structures and Magnetism of Zr-, Th-, and U-based Metal-Organic Frameworks (MOFs) by Density Functional Theory

Metal-organic frameworks (MOFs) have recently gained wide interest as candidate materials for nuclear waste immobilization. While the fundamental thermodynamic properties, such as the substitution energies determine the favorability of radionuclide sequestration by utilization of a MOF matrix, the studies of MOF electronic structure reveal the role of d-, and/or f-electrons on changes in physical properties of actinide-containing materials. We use density functional theory (DFT) calculations to investigate the electronic structures of Zr-, Th-, and U-MOFs, including their electronic band structures and, where appropriate, their magnetic properties. We employ various DFT methods including DFT+U, collinear spin-polarization, spin-orbit coupling, and different flavors of exchange-correlation functionals to assess the robustness to the specific exchange-correlation functional. Unlike the Zr-, and Th-MOFs, the U-MOF is found to be sensitive to electron localization and spin; hence we explore the magnetic structure of the U-MOF in further detail.

Metal-Organic Framework, MOF, Actinides, DFT↗

DOE OSTI2017

Scrambling and thermalization in a diffusive quantum many-body system

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose–Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. As a result, our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

The Alcock Paczy'nski test with Baryon Acoustic Oscillations: systematic effects for future surveys

We investigate the Alcock Paczy'nski (AP) test applied to the Baryon Acoustic Oscillation (BAO) feature in the galaxy correlation function. By using a general formalism that includes relativistic effects, we quantify the importance of the linear redshift space distortions and gravitational lensing corrections to the galaxy number density fluctuation. We show that redshift space distortions significantly affect the shape of the correlation function, both in radial and transverse directions, causing different values of galaxy bias to induce offsets up to 1% in the AP test. On the other hand, we find that the lensing correction around the BAO scale modifies the amplitude but not the shape of the correlation function and therefore does not introduce any systematic effect. Furthermore, we investigate in details how the AP test is sensitive to redshift binning: a window function in transverse direction suppresses correlations and shifts the peak position toward smaller angular scales. We determine the correction that should be applied in order to account for this effect, when performing the test with data from three future planned galaxy redshift surveys: Euclid, the Dark Energy Spectroscopic Instrument (DESI) and the Square Kilometer Array (SKA).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Efficient reconstruction and validation of heterogeneous microstructures for energy applications

The digital reconstruction of microstructures is necessary for simulations in fields ranging from geology to electrochemistry, but the state-of-the-art digital reconstruction techniques often compromise between resolution and field of view. It is challenging to retain detailed microstructure information in large-scale reconstructions. Here, this study investigates different aspects of the Yeong-Torquato algorithm based on correlation functions to make it more efficient. We achieve this goal by reducing the computational complexity of the chord-length distribution function and the two-point correlation function, applying the random sphere-packing method as the initial condition, and restricting potential voxel swaps to interfaces. In addition, a novel superposition parallel scheme is introduced to aid in searching for potential voxel swaps. The algorithm proposed is validated by comparing the pore-size distributions of reconstructed 3D custom battery electrodes from a sample dataset obtained from transmission X-ray microscopy. From a sample image with 200 x 200 pixels, the code can reconstruct a 300 x 300 x 300 structure in under 22 h and reconstruct a 400 x 400 x 400 structure in 43 h with eight cores.

42 ENGINEERING↗

DOE OSTI2015

A NEW MODEL FOR DARK MATTER HALOS HOSTING QUASARS

A new model for quasar-hosting dark matter halos, meeting two physical conditions, is put forth. First, significant interactions are taken into consideration to trigger quasar activities. Second, satellites in very massive halos at low redshift are removed from consideration due to their deficiency in cold gas. We analyze the Millennium Simulation to find halos that meet these two conditions and simultaneously match two-point auto-correlation functions of quasars and cross-correlation functions between quasars and galaxies at z = 0.5-3.2. The masses of the quasar hosts found decrease with decreasing redshift, with the mass thresholds being [(2-5) × 10{sup 12}, (2-5) × 10{sup 11}, (1-3) × 10{sup 11}] M {sub ☉} for median luminosities of ∼[10{sup 46}, 10{sup 46}, 10{sup 45}] erg s{sup –1} at z = (3.2, 1.4, 0.53), respectively, an order of magnitude lower than those inferred based on halo occupation distribution modeling. In this model, quasar hosts are primarily massive central halos at z ≥ 2-3 but increasingly dominated by lower mass satellite halos experiencing major interactions toward lower redshift. However, below z = 1, satellite halos in groups more massive than ∼2 × 10{sup 13} M {sub ☉} do not host quasars. Whether for central or satellite halos, imposing the condition of significant interactions substantially boosts the clustering strength compared to the total population with the same mass cut. The inferred lifetimes of quasars at z = 0.5-3.2 of 3-30 Myr are in agreement with observations. Quasars at z ∼ 2 would be hosted by halos of mass ∼5 × 10{sup 11} M {sub ☉} in this model, compared to ∼3 × 10{sup 12} M {sub ☉} previously thought, which would help reconcile with the observed, otherwise puzzling high covering fractions for Lyman limit systems around quasars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

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

Abstract 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 Ω m 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.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2000

Method for suppressing noise in measurements

Methods for suppressing noise in measurements by correlating functions based on at least two different measurements of a system at two different times. In one embodiment, a measurement operation is performed on at least a portion of a system that has a memory. A property of the system is measured during a first measurement period to produce a first response indicative of a first state of the system. Then the property of the system is measured during a second measurement period to produce a second response indicative of a second state of the system. The second measurement is performed after an evolution duration subsequent to the first measurement period when the system still retains a degree of memory of an aspect of the first state. Next, a first function of the first response is combined with a second function of the second response to form a second-order correlation function. Information of the system is then extracted from the second-order correlation function.

Carson, Paul L.↗