Two-point Autocorrelation Function Research Articles

Derivation of the nonequilibrium generalized Langevin equation from a time-dependent many-body Hamiltonian.

It has become standard practice to describe systems that remain far from equilibrium even in their steady state by Langevin equationswith colored noise which is chosen independently from the friction contribution. Since these Langevin equationsare typically not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space we derive the nonequilibrium generalized Langevin equation(GLE) for an arbitrary phase-space dependent observable A from a generic many-body Hamiltonian with a time-dependent external force h(t) acting on the same observable A. This is the same Hamiltonian from which the standard fluctuation-dissipation theorem is derived, which reflects the generality of our approach. The observable A could, for example, be the position of an atom, of a molecule or of a macroscopic object, the distance between two such entities or a more complex phase-space function such as the reaction coordinate of a chemical reaction or of the folding of a protein. The Hamiltonian could, for example, describe a fluid, a solid, a viscoelastic medium, or even a turbulent inhomogeneous environment. The GLE, which is a closed-form equationof motion for the observable A, is obtained in explicit form to all orders in h(t) and without restrictions on the type of many-body Hamiltonian or the observable A. If the dynamics of the observable A corresponds to a Gaussian process, the resultant GLE has a similar form as the equilibrium Mori GLE, and in particular the friction memory kernel is given by the two-point autocorrelation function of the sum of the complementary and the external force h(t). This is a nontrivial and useful result, as many observables that characterize nonequilibrium systems display Gaussian statistics. For non-Gaussian nonequilibrium observables correction terms appear in the GLE and in the relation between the force autocorrelation and the friction memory kernel, which are explicitly given in terms of cubic correlation functions of A. Interpreting the external force h(t) as a stochastic process, we derive nonequilibrium corrections to the fluctuation-dissipation theorem and present methods to extract all GLE parameters from experimental or simulation time-series data, thus making our nonequilibrium GLE a practical tool to study and model general nonequilibrium systems.

Turbulent flow over aligned cylindrical obstacles

Turbulent flow and boundary-layer (BL) characteristics over cylindrical obstacles have been understudied compared to the flow dynamics around cubic roughness in the urban BL literature. Using large-eddy simulation, we investigate a turbulent BL flow developed over two vertically oriented cylindrical obstacles aligned downstream. For widely separated cylinders, the wake flow undergoes periodic oscillations akin to vortex shedding behind an isolated cylinder. As the height-to-width aspect ratio (AR) of the canyon bounded by the cylinders increases, the streamline geometry exhibits a clear transition from isolated to wake interference and skimming regimes. Two-point autocorrelation functions of velocities confirm a strong coupling of canyon flow with the roughness sublayer for wider canyons, while with evident decoupling as the canyon narrows. The length scales, which measure the spatial correlation in the flow, decrease in both lateral and vertical directions with increasing AR. Turbulent kinetic energy and momentum fluxes below the roughness sublayer present pronounced monotonic scaling with AR (with R-squared values up to 0.84 and 0.98, respectively), resulting in a consistent variation in the surface roughness aerodynamic parameters, the roughness length (z0) and zero-plane displacement (d), with AR. Quantitative differences in the results with respect to those well-established for street canyons are analyzed, with the similarities highlighted. The results offer insights into boundary-layer flow parameterization concerning cylinder-occupied surface roughness.

Shedding light on low-surface-brightness galaxies in dark energy surveys with transformer models

Context. Low-surface-brightness galaxies (LSBGs), which are defined as galaxies that are fainter than the night sky, play a crucial role in our understanding of galaxy evolution and in cosmological models. Upcoming large-scale surveys, such as Rubin Observatory Legacy Survey of Space and Time and Euclid, are expected to observe billions of astronomical objects. In this context, using semiautomatic methods to identify LSBGs would be a highly challenging and time-consuming process, and automated or machine learning-based methods are needed to overcome this challenge. Aims. We study the use of transformer models in separating LSBGs from artefacts in the data from the Dark Energy Survey (DES) Data Release 1. Using the transformer models, we then search for new LSBGs from the DES that the previous searches may have missed. Properties of the newly found LSBGs are investigated, along with an analysis of the properties of the total LSBG sample in DES. Methods. We created eight different transformer models and used an ensemble of these eight models to identify LSBGs. This was followed by a single-component Sérsic model fit and a final visual inspection to filter out false positives. Results. Transformer models achieved an accuracy of ~94% in separating the LSBGs from artefacts. In addition, we identified 4083 new LSBGs in DES, adding an additional ~17% to the LSBGs already known in DES. This also increased the number density of LSBGs in DES to 5.5 deg−2. The new LSBG sample consists of mainly blue and compact galaxies. We performed a clustering analysis of the LSBGs in DES using an angular two-point auto-correlation function and found that LSBGs cluster more strongly than their high-surface-brightness counterparts. This effect is driven by the red LSBG. We associated 1310 LSBGs with galaxy clusters and identified 317 ultradiffuse galaxies among them. We found that these cluster LSBGs are getting bluer and larger in size towards the edge of the clusters when compared with those in the centre. Conclusions. Transformer models have the potential to be equivalent to convolutional neural networks as state-of-the-art algorithms in analysing astronomical data. The significant number of LSBGs identified from the same dataset using a different algorithm highlights the substantial impact of our methodology on our capacity to discover LSBGs. The reported number density of LSBGs is only a lower estimate and can be expected to increase with the advent of surveys with better image quality and more advanced methodologies.

Spectral Form Factor and Dynamical Localization.

Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical transport time of the momentum diffusion is greater than the Heisenberg time. The transport time is typically computed from the corresponding classical dynamics. In this paper, we present an alternative approach based purely on the study of spectral fluctuations of the quantum system. The information about the transport times is encoded in the spectral form factor, which is the Fourier transform of the two-point spectral autocorrelation function. We compute large samples of the energy spectra (of the order of 106 levels) and spectral form factors of 22 stadium billiards with parameter values across the transition between the localized and extended eigenstate regimes. The transport time is obtained from the point when the spectral form factor transitions from the non-universal to the universal regime predicted by random matrix theory. We study the dependence of the transport time on the parameter value and show the level repulsion exponents, which are known to be a good measure of dynamical localization, depend linearly on the transport times obtained in this way.

Modelling the growth and evolution of statistically significant populations of intergranular fission gas bubbles by IPM

The time-evolution of an intergranular bubble population is considered using the Included Phase Model (IPM). The model considers the generation and coupled transport of vacancies and gas atoms driven by interfacial energy, elasticity, and internal energy in a framework that admits complex interface morphology. The model predicts overpressure, bubble growth, coarsening, and coalescence leading to the formation of interconnected high-aspect-ratio bubbles on the grain face. The computational efficiency of this model is leveraged to simulate sets of 250 bubbles over time, which compare well with the CAGR-UOX-SWELL SEM measurements and the established SIFGRS model. Analysis of the simulation results highlights the importance of the bubble density as an indicator of bubble structure formed by coalescence and suggests that the two-point autocorrelation function captures the formation of an interconnected network which could improve release thresholds.

Random sequential adsorption of rounded rectangles, isosceles and right triangles

We studied random sequential adsorption (RSA) of three classes of polygons with rounded corners: rectangles, isosceles triangles, and orthogonal triangles. Using the algorithm that enables the generation of strictly saturated RSA packing, we systematically determined the mean saturated packing fraction for RSA configurations built by these shapes. The main aim was to find the figure that forms the densest random configuration. Although for rounded rectangles the packing fractions were lower than for discorectangles, the densities reached for some rounded isosceles and right triangles exceeded the highest known two-dimensional packing fraction for configurations built of unoriented monodisperse objects. The microstructural properties of several packings were discussed in terms of the two-point density autocorrelation function.

Clustering of CODEX clusters

Context. The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies. Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the 0.1 < z < 0.3 and 0.3 < z < 0.5 redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length r0 = 18.7 ± 1.1 and slope γ = 1.98 ± 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Ωm0 = 0.22−0.03+0.04 and S8 = σ8(Ωm0/0.3)0.5 = 0.85−0.08+0.10 with estimated additional systematic errors of σΩm0 = 0.02 and σS8 = 0.20. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving Ωm0 = 0.25 ± 0.01 and σ8 = 0.81−0.02+0.01 with an estimated additional systematic error of σΩm0 = 0.07 and σσ8 = 0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES). IV. Spatial Clustering and Halo Masses of Submillimeter Galaxies

Abstract We analyze an extremely deep 450 μm image (1σ = 0.56 mJy beam−1) of a ≃300 arcmin2 area in the CANDELS/COSMOS field as part of the Sub-millimeter Common User Bolometric Array-2 Ultra Deep Imaging EAO Survey. We select a robust (signal-to-noise ratio ≥4) and flux-limited (≥4 mJy) sample of 164 submillimeter galaxies (SMGs) at 450 μm that have K-band counterparts in the COSMOS2015 catalog identified from radio or mid-infrared imaging. Utilizing this SMG sample and the 4705 K-band-selected non-SMGs that reside within the noise level ≤1 mJy beam−1 region of the 450 μm image as a training set, we develop a machine-learning classifier using K-band magnitude and color–color pairs based on the 13-band photometry available in this field. We apply the trained machine-learning classifier to the wider COSMOS field (1.6 deg2) using the same COSMOS2015 catalog and identify a sample of 6182 SMG candidates with similar colors. The number density, radio and/or mid-infrared detection rates, redshift and stellar-mass distributions, and the stacked 450 μm fluxes of these SMG candidates, from the S2COSMOS observations of the wide field, agree with the measurements made in the much smaller CANDELS field, supporting the effectiveness of the classifier. Using this SMG candidate sample, we measure the two-point autocorrelation functions from z = 3 down to z = 0.5. We find that the SMG candidates reside in halos with masses of ≃(2.0 ± 0.5) × 1013 h −1 M ☉ across this redshift range. We do not find evidence of downsizing that has been suggested by other recent observational studies.

The bahamas project: effects of a running scalar spectral index on large-scale structure

ABSTRACT Recent analyses of the cosmic microwave background (CMB) and the Lyman α forest indicate a mild preference for a deviation from a power-law primordial matter power spectrum (a so-called running). We introduce an extension to the bahamas suite of simulations to explore the effects that a running scalar spectral index has on large-scale structure (LSS), using Planck CMB constraints to initialize the simulations. We focus on five key statistics: (i) the non-linear matter power spectrum (ii) the halo mass function; (iii) the halo two-point autocorrelation function; (iv) total mass halo density profiles; and (v) the halo concentration–mass relation. We find that the matter power spectrum in a Planck-constrained running cosmology is affected on all k-scales examined in this study. These effects on the matter power spectrum should be detectable with upcoming surveys such as LSST and Euclid. A positive running cosmology leads to an increase in the mass of galaxy groups and clusters, with the favoured negative running leading to a decrease in mass of lower mass ($M \lesssim 10^{13} \, \textrm{M}_{\odot }$) haloes, but an increase for the most massive ($M \gtrsim 10^{13} \, \textrm{M}_{\odot }$) haloes. Changes in the mass are generally confined to $5\rm {-}10{{\ \rm per\ cent}}$ which, while not insignificant, cannot by itself reconcile the claimed tension between the primary CMB and cluster number counts. We also demonstrate that the observed effects on LSS due to a running scalar spectral index are separable from those of baryonic effects to typically a few per cent precision.

Transport dynamics of complex fluids

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids. In our approach, the environment-coupled diffusion kernel and its time correlation function (TCF) are the essential quantities that determine transport dynamics and characterize mobility fluctuation of complex fluids; their time profiles are directly extractable from a model-free analysis of the MSD and NGP or, with greater computational expense, from the two-point and four-point velocity autocorrelation functions. We construct a general, explicit model of the diffusion kernel, comprising one unbound-mode and multiple bound-mode components, which provides an excellent approximate description of transport dynamics of various complex fluidic systems such as supercooled water, colloidal beads diffusing on lipid tubes, and dense hard disk fluid. We also introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents an unexplored direction for quantitative understanding of transport and transport-coupled processes in complex disordered media.

The Clustering of High-redshift (2.9 ≤ z ≤ 5.1) Quasars in SDSS Stripe 82

Abstract We present a measurement of the two-point autocorrelation function of photometrically selected high-z quasars over ∼100 deg2 on the Sloan Digital Sky Survey Stripe 82 field. Selection is performed using three machine-learning algorithms in a six-dimensional optical/mid-infrared color space. Optical data from the Sloan Digital Sky Survey are combined with overlapping deep mid-infrared data from the Spitzer IRAC Equatorial Survey and the Spitzer-HETDEX Exploratory Large-Area survey. Our selection algorithms are trained on the colors of known high-z quasars. The selected quasar sample consists of 1378 objects and contains both spectroscopically confirmed quasars and photometrically selected quasar candidates. These objects span a redshift range of 2.9 ≤ z ≤ 5.1 and are generally fainter than i = 20.2, a regime that has lacked sufficient number density to perform autocorrelation function measurements of photometrically classified quasars. We compute the angular correlation function of these data, marginally detecting quasar clustering. We fit a single power law with an index of δ = 1.39 ± 0.618 and amplitude of θ 0 = 0.′71 ± 0.′546 . A dark matter model is fit to the angular correlation function to estimate the linear bias. At the average redshift of our survey ( ), the bias is b = 6.78 ± 1.79. Using this bias, we calculate a characteristic dark matter halo mass of 1.70–9.83 . Our bias estimate suggests that quasar feedback intermittently shuts down the accretion of gas onto the central supermassive black hole at early times. If confirmed, these results hint at a level of luminosity dependence in the clustering of quasars at high-z.

FAINT SUBMILLIMETER GALAXIES IDENTIFIED THROUGH THEIR OPTICAL/NEAR-INFRARED COLORS. I. SPATIAL CLUSTERING AND HALO MASSES

ABSTRACT The properties of submillimeter galaxies (SMGs) that are fainter than the confusion limit of blank-field single-dish surveys ( 2 mJy) are poorly constrained. Using a newly developed color selection technique, Optical-Infrared Triple Color (OIRTC), that has been shown to successfully select such faint SMGs, we identify a sample of 2938 OIRTC-selected galaxies, dubbed Triple Color Galaxies (TCGs), in the UKIDSS-UDS field. We show that these galaxies have a median 850 μm flux of mJy (equivalent to a star formation rate SFR yr−1 based on spectral energy distribution fitting), representing the first large sample of faint SMGs that bridges the gap between bright SMGs and normal star-forming galaxies in S 850 and L IR. We assess the basic properties of TCGs and their relationship with other galaxy populations at . We measure the two-point autocorrelation function for this population and derive a typical halo mass of log10( ) , , and at , 2–3, and 3–5, respectively. Together with the bright SMGs ( mJy) and a comparison sample of less far-infrared luminous star-forming galaxies, we find a lack of dependence between spatial clustering and S 850 (or SFR), suggesting that the difference between these populations may lie in their local galactic environment. Lastly, on the scale of at we find a tentative enhancement of the clustering of TCGs over the comparison star-forming galaxies, suggesting that some faint SMGs are physically associated pairs, perhaps reflecting a merging origin in their triggering.

Evidence for an environment-dependent shift in the baryon acoustic oscillation peak

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric assumes comoving spatial rigidity of metrical properties. The curvature term in comoving coordinates is environment independent and cannot evolve. In the standard model, structure formation is interpreted accordingly: structures average out on the chosen metrical background, which remains rigid in comoving coordinates despite nonlinear structure growth. The latter claim needs to be tested, since it is a hypothesis that is not derived using general relativity. We introduce a test of the comoving rigidity assumption by measuring the two-point autocorrelation function on comoving scales – assuming FLRW comoving spatial rigidity – in order to detect shifts in the baryon acoustic oscillation (BAO) peak location for luminous red galaxy (LRG) pairs of the Sloan Digital Sky Survey Data Release 7. In tangential directions, subsets of pairs overlapping with superclusters or voids show the BAO peak. The tangential BAO peak location for overlap with Nadathur & Hotchkiss superclusters is 4.3 ± 1.6 h−1 Mpc less than that for LRG pairs unselected for supercluster overlap, and 6.6 ± 2.8 h−1 Mpc less than that of the complementary pairs. Liivamägi et al. superclusters give corresponding differences of 3.7 ± 2.9 h−1 Mpc and 6.3 ± 2.6 h−1 Mpc, respectively. We have found moderately significant evidence (Kolmogorov–Smirnov tests suggest very significant evidence) that the BAO peak location for supercluster-overlapping pairs is compressed by about 6 per cent compared to that of the complementary sample, providing a potential challenge to FLRW models and a benchmark for predictions from models based on an averaging approach that leaves the spatial metric a priori unspecified.

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 of cold gas. We analyze the {\em 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 found halos have some distinct properties worth noting. The masses of found quasar hosts decrease with decreasing redshift, with the mass thresholds being $[(2-5)\times 10^{12}, (2-5)\times 10^{11}, (1-3)\times 10^{11}]\msun$ for median luminosities of $\sim[10^{46}, 10^{46}, 10^{45}]$erg/s 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 $z\ge 2-3$ but increasingly dominated by lower mass satellite halos experiencing major interactions towards lower redshift. But below $z=1$ satellite halos in groups more massive than $\sim 2\times 10^{13}\msun$ 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 $z\sim 2$ would be hosted by halos of mass $\sim 5\times 10^{11}\msun$ in this model, compared to $\sim 3\times 10^{12}\msun$ previously thought, which would help reconcile with the observed, otherwise puzzling high covering fractions for Lyman limit systems around quasars.

On the clustering of compact galaxy pairs in dark matter haloes

We analyze the clustering of photometrically selected galaxy pairs by using the halo-occupation distribution (HOD) model. We measure the angular two-point auto-correlation function, $\omega(\theta)$, for galaxies and galaxy pairs in three volume-limited samples and develop an HOD to model their clustering. Our results are successfully fit by these HOD models, and we see the separation of "1-halo" and "2-halo" clustering terms for both single galaxies and galaxy pairs. Our clustering measurements and HOD model fits for the single galaxy samples are consistent with previous results. We find that the galaxy pairs generally have larger clustering amplitudes than single galaxies, and the quantities computed during the HOD fitting, e.g., effective halo mass, $M_{eff}$, and linear bias, $b_{g}$, are also larger for galaxy pairs. We find that the central fractions for galaxy pairs are significantly higher than single galaxies, which confirms that galaxy pairs are formed at the center of more massive dark matter haloes. We also model the clustering dependence of the galaxy pair correlation function on redshift, galaxy type, and luminosity. We find early-early pairs (bright galaxy pairs) cluster more strongly than late-late pairs (dim galaxy pairs), and that the clustering does not depend on the luminosity contrast between the two galaxies in the compact group.

Multi-scale vortical structure analysis on large eddy simulation of dune wake flow

The three-dimensional dune wake flow is evaluated by large eddy simulation at a Reynolds number of 5,534, and validated by time-averaged results of particle image velocimetry measurement at a central streamwise plane. To reveal multi-scale characteristics of vortical structure, the instantaneous velocity, vorticity, and pressure were decomposed into the large-, intermediate- and small-scale components by three-dimensional wavelet multi-resolution technique, the scale of each wavelet component is quantified by two-point autocorrelation function with the central scale of 43, 20 and 9.6 mm, respectively. It is found that large-scale structure determines the formation of separation bubble and makes the most significance to the vorticity. Some intermediate-scale and small-scale streamwise vortices cause the upwelling of vortical structures, and they tend to be more active at the downstream. By visualization of pressure distribution, we can find that pressure distribution is mainly characterized by large-scale structure, and the distribution of small-scale structure can be interfered as a reason why large-scale vortical structure breaks into small vortices at the near outlet region.

3D reconstruction and design of porous media from thin sections

Characterization and design of fluid–thermal transport through random porous sintered beds is critical for improving the performance of two-phase heat transport devices such as heat pipes. Two-dimensional imaging techniques are quite well developed and commonly employed for microstructure and material characterization. In this study, we employ 2D image data (thin sections) for measuring critical microstructural features of commercial wicks for use in correlation-based prediction of transport properties. We employ a stochastic characterization methodology based on the two-point autocorrelation function, and compare the predicted properties such as particle and pore diameters and permeability with those from our previously published studies, in which 3D X-ray microtomography data was employed for reconstruction. Further, we implement a reconstruction technique for reconstructing a three-dimensional stochastic equivalent structure from the thin sections. These reconstructed domains are employed for predicting effective thermal conductivity, permeability and interfacial heat transfer coefficient in single-phase flow. The current computations are found to compare well with models and correlations from the literature, as well as our previous numerical studies. Finally, we propose a new parametrized model for the design of porous materials based on the nature of the two-point autocorrelation functions. Using this model, we reconstruct sample three-dimensional microstructures, and analyze the influence of various parameters on fluid–thermal properties of interest. With advances in additive manufacturing techniques, such an approach may eventually be employed to design intricate porous structures with properties tailored to specific applications.

Electrostatic interaction due to patch potentials on smooth conducting surfaces

We evaluate the electrostatic interaction energy between two surfaces, one flat and the other slightly curved, in terms of the two-point autocorrelation functions for patch potentials on each one of them, and of a single function $\psi$ which defines the curved surface. The resulting interaction energy, a functional of $\psi$, is evaluated up to the second order in a derivative expansion approach. We derive explicit formulae for the coefficients of that expansion as simple integrals involving the autocorrelation functions, and evaluate them for some relevant patch-potential profiles and geometries

Nurturing Lyman break galaxies: observed link between environment and spectroscopic features

We examine the effects of magnitude, colour and Lyα equivalent width (EW) on the spatial distribution of z ∼ 3 Lyman break galaxies (LBGs) and report significant differences in the two-point autocorrelation functions. The results are obtained using samples of ∼10 000–55 000 LBGs from the Canada–France–Hawaii Telescope Legacy Survey Deep Fields. We find that magnitude has a larger effect on the autocorrelation function amplitude on small scales (≲1 |$h^{-1}_{70}$| Mpc, the one-halo term) and that colour is more influential on large scales (≳1 |$h^{-1}_{70}$| Mpc, the two-halo term). We find the most significant differences between autocorrelation functions for LBGs with dominant net Lyα EW in absorption (aLBGs) and dominant net Lyα EW in emission (eLBGs) determined from ≳95 per cent pure samples of each population using a photometric technique calibrated from ∼1000 spectra. The aLBG autocorrelation function has a higher two-halo amplitude than the full LBG sample and has a one-halo term departure from a power-law fit near ∼1 |$h^{-1}_{70}$| Mpc, corresponding to the virial radii of MDM ∼ 1013 M⊙ dark matter haloes. In contrast, the eLBG autocorrelation function has a one-halo term departure at ∼0.12 |$h^{-1}_{70}$| Mpc, suggesting parent haloes of MDM ∼ 1011 M⊙ and a two-halo term that exhibits a curious ‘hump’ on intermediate scales that we localize to the faintest, bluest members. The aLBG–eLBG cross-correlation function exhibits an anticorrelation component that reinforces different physical locations for a significant fraction of aLBGs and eLBGs. We introduce a ‘shell’ model for the eLBG autocorrelation function and find that the form can be reproduced assuming that a significant fraction of eLBGs have a shell-like spatial distribution. Based on the analysis of all LBG subsamples, and considering the natural asymmetric distribution of LBGs on the colour–magnitude diagram, we conclude that aLBGs are more likely to reside in group-like environments hosting multiple luminous (i′ < 26.4) LBGs whereas eLBGs are more likely to be found on group outskirts and in the field. Because Lyα is a tracer of several intrinsic properties, including morphology, the results presented here imply that the mechanisms behind the morphology–density relation at low redshift are in place at z ∼ 3 and that Lyα EW may be a key environment diagnostic. Finally, our results show that the LBG autocorrelation function amplitude is lower than the true average as a result of the spatial anticorrelation of the spectral types. This result holds broad consequences for all autocorrelation functions measured for any population that contains members residing in different environments as the average amplitude, and hence the inferred average dark matter mass, will always be underestimated.

Clustering analysis of high-redshift luminous red galaxies in Stripe 82

We present a clustering analysis of luminous red galaxies (LRGs) in Stripe 82 from the Sloan Digital Sky Survey (SDSS). We study the angular two-point autocorrelation function, w(θ), of a selected sample of over 130 000 LRG candidates via colour-cut selections in izK with the K-band coverage coming from UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS). We have used the cross-correlation technique of Newman to establish the redshift distribution of the LRGs. Cross-correlating them with SDSS quasi-stellar objects (QSOs), MegaZ-LRGs and DEEP Extragalactic Evolutionary Probe 2 (DEEP2) galaxies, implies an average redshift of the LRGs to be z ≈ 1 with space density, ng ≈ 3.20 ± 0.16 × 10−4 h3 Mpc−3. For θ ≤ 10 arcmin (corresponding to ≈10 h−1 Mpc), the LRG w(θ) significantly deviates from a conventional single power law as noted by previous clustering studies of highly biased and luminous galaxies. A double power law with a break at rb ≈ 2.4 h−1 Mpc fits the data better, with best-fitting scale length, r0, 1 = 7.63 ± 0.27 h−1 Mpc and slope γ1 = 2.01 ± 0.02 at small scales and r0, 2 = 9.92 ± 0.40 h−1 Mpc and γ2 = 1.64 ± 0.04 at large scales. Due to the flat slope at large scales, we find that a standard Λ cold dark matter (⁠|$\Lambda \rm$|CDM) linear model is accepted only at 2–3σ, with the best-fitting bias factor, b = 2.74 ± 0.07. We also fitted the halo occupation distribution (HOD) models to compare our measurements with the predictions of the dark matter clustering. The effective halo mass of Stripe 82 LRGs is estimated as Meff = 3.3 ± 0.6 × 1013 h−1 M⊙. But at large scales, the current HOD models did not help explain the power excess in the clustering signal. We then compare the w(θ) results to the results of Sawangwit et al. from three samples of photometrically selected LRGs at lower redshifts to measure clustering evolution. We find that a long-lived model may be a poorer fit than at lower redshifts, although this assumes that the Stripe 82 LRGs are luminosity-matched to the AAΩ LRGs. We find stronger evidence for evolution in the form of the z ≈ 1 LRG correlation function with the above flat two-halo slope maintaining to s ≳ 50 h− 1 Mpc. Applying the cross-correlation test of Ross et al., we find little evidence that the result is due to systematics. Otherwise, it may represent evidence for primordial non-Gaussianity in the density perturbations at early times, with flocalNL = 90 ± 30.