Three-dimensional Correlation Function Research Articles

Optimal data compression for Lyman-α forest cosmology

ABSTRACT The Lyman-α three-dimensional correlation functions have been widely used to perform cosmological inference using the baryon acoustic oscillation scale. While the traditional inference approach employs a data vector with several thousand data points, we apply near-maximal score compression down to tens of compressed data elements. We show that carefully constructed additional data beyond those linked to each inferred model parameter are required to preserve meaningful goodness of fit tests that guard against unknown systematics, and to avoid information loss due to non-linear parameter dependences. We demonstrate, on suites of realistic mocks and Data Release 16 data from the Extended Baryon Oscillation Spectroscopic Survey, that our compression approach is lossless and unbiased, yielding a posterior that is indistinguishable from that of the traditional analysis. As an early application, we investigate the impact of a covariance matrix estimated from a limited number of mocks, which is only well conditioned in compressed space.

Dark Energy Survey Year 3 results: Measurement of the baryon acoustic oscillations with three-dimensional clustering

The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, $\xi_{\rm p}$ to measure the Baryonic Acoustic Oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range $ 0.6 < z_{\rm p } < 1.1 $ over a footprint of $4108 \, \mathrm{deg}^2 $. Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-$z$ approximation. To increase the signal-to-noise of the measurements, a Gaussian stacking window function is adopted in place of the commonly used top-hat. Using the full sample, $ D_{\rm M}(z_{\rm eff} ) / r_{\rm s} $, the ratio between the comoving angular diameter distance and the sound horizon, is constrained to be $ 19.00 \pm 0.67 $ (top-hat) and $ 19.15 \pm 0.58 $ (Gaussian) at $z_{\rm eff} = 0.835$. The constraint is weaker than the angular correlation $w$ constraint ($18.84 \pm 0.50$) because the BAO signals are heterogeneous across redshift. When a homogeneous BAO-signal sub-sample in the range $ 0.7 < z_{\rm p } < 1.0 $ ($z_{\rm eff} = 0.845$) is considered, $\xi_{\rm p} $ yields $ 19.80 \pm 0.67 $ (top-hat) and $ 19.84 \pm 0.53 $ (Gaussian). The latter is mildly stronger than the $w$ constraint ($19.86 \pm 0.55 $). We find that the $\xi_{\rm p} $ results are more sensitive to photo-$z$ errors than $w$ because $\xi_{\rm p}$ keeps the three-dimensional clustering information causing it to be more prone to photo-$z$ noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. $\xi_{\rm p}$ and the angular statistics such as $w$ have their own pros and cons, and they serve an important crosscheck with each other.

Direct cosmological inference from three-dimensional correlations of the Lyman α forest

ABSTRACT When performing cosmological inference, standard analyses of the Lyman α (Ly α) three-dimensional correlation functions only consider the information carried by the distinct peak produced by baryon acoustic oscillations (BAO). In this work, we address whether this compression is sufficient to capture all the relevant cosmological information carried by these functions. We do this by performing a direct fit to the full shape, including all physical scales without compression, of synthetic Ly α autocorrelation functions and cross-correlations with quasars at effective redshift zeff = 2.3, assuming a DESI-like survey, and providing a comparison to the classic method applied to the same data set. Our approach leads to a $3.5{{\ \rm per\ cent}}$ constraint on the matter density ΩM, which is about three to four times better than what BAO alone can probe. The growth term fσ8(zeff) is constrained to the $10{{\ \rm per\ cent}}$ level, and the spectral index ns to $\sim 3-4{{\ \rm per\ cent}}$. We demonstrate that the extra information resulting from our ‘direct fit’ approach, except for the ns constraint, can be traced back to the Alcock–Paczynski effect and redshift space distortion information.

The Glauber Model And Flow Analysis with Pb-Pb Collisions at

This work presents data analysis on Pb-Pb collisions with in centrality 40%-50%. Introduction and Monte-Carlo simulation results on the Glauber model are presented, which shed light on the initial geometric configuration of heavy ion collisions. Three-dimensional correlation function is plotted, and Fourier decomposition is carried out in order to obtain elliptic flow. Based on the assumption that non-flow effect is less prominent in long-range area, we separate it from the second Fourier decomposition of two-particle correlation function by making polynomial curve fitting.

Structure of turbulence in temporal planar jets

A detailed analysis of the structure of turbulence in a temporal planar turbulent jet is reported. Instantaneous snapshots of the flow and three-dimensional spatial correlation functions are considered. It is found that the flow is characterized by large-scale spanwise vortices whose motion is felt in the entire flow field. Superimposed to this large-scale motion, a hierarchy of turbulent structures is present. The most coherent ones take the form of quasi-streamwise vortices and high and low streamwise velocity streaks. The topology of these interacting structures is analyzed by quantitatively addressing their shape and size in the different flow regions. Such information is recognized to be relevant for a structural description of the otherwise disorganized motion in turbulent free-shear flows and can be used for the assessment of models based on coherent structure assumptions. Finally, the resulting scenario provides a phenomenological description of the elementary processes at the basis of turbulence in free-shear flows.

UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

ABSTRACT Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h−1 Mpc)3 Horizon hydrodynamic simulation to a (1 h−1 Gpc)3N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving nq ≈ 10−5h3 Mpc−3 placed either in massive haloes or randomly. On scales of 10–30 h−1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ123/(ξ12ξ13 + ξ12ξ23 + ξ13ξ23) ≈ −4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h−1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h−1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ −3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h−1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h−1 Mpc the predicted SNR is lower by a factor of ∼3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

On the structure of the self-sustaining cycle in separating and reattaching flows

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

Bose-Einstein correlations in pp, pPb , and PbPb collisions at sNN=0.9–7 TeV

Quantum statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at $\sqrt{s}=$ 0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the LHC. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum ($k_\mathrm{T}$) and the charged-particle multiplicity in the event. For all systems, the extracted correlation radii steadily increase with the event multiplicity, and decrease with increasing $k_\mathrm{T}$. The radii are in the range 1-5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and $k_\mathrm{T}$ largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy.

Femtoscopy with Identified Hadrons in pp, pPb, and PbPb Collisions in CMS

Short-range correlations of identified charged hadrons in pp ( s = 0.9, 2.76, and 7 TeV), pPb ( s NN = 5.02 TeV), and peripheral PbPb collisions ( s NN = 2.76 TeV) are studied with the CMS detector at the LHC. Charged pions, kaons, and protons at low momentum and in laboratory pseudorapidity | η | &lt; 1 are identified via their energy loss in the silicon tracker. The two-particle correlation functions show effects of quantum statistics, Coulomb interaction, and also indicate the role of multi-body resonance decays and mini-jets. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as a function of transverse pair momentum, k T , and the charged-particle multiplicity of the event. The extracted radii are in the range 1–5 fm, reaching highest values for very high multiplicity pPb, also for similar multiplicity PbPb collisions, and decrease with increasing k T . The dependence of radii on multiplicity and k T largely factorizes and appears to be insensitive to the type of the colliding system and center-of-mass energy.

Modeling of two-particle femtoscopic correlations at top RHIC energy

The spatial and temporal characteristics of particle emitting source produced in particle and/or nuclear collisions can be measured by using two-particle femtoscopic correlations. These correlations arise due to quantum statistics, Coulomb and strong final state interactions. In this paper we report on the calculations of like-sign pion femtoscopic correlations produced in p+p, p+Au, d+Au, Au+Au at top RHIC energy using Ultra Relativistic Quantum Molecular Dynamics Model (UrQMD). Three-dimensional correlation functions are constructed using the Bertsch-Pratt parametrization of the two-particle relative momentum. The correlation functions are studied in several transverse mass ranges. The emitting source radii of charged pions, Rout, Rside, Rlong, are obtained from Gaussian fit to the correlation functions and compared to data from the STAR and PHENIX experiments.

Precise clustering and density evolution of redMaPPer galaxy clusters versus MXXL simulation

We construct a large, redshift complete sample of distant galaxy clusters by correlating Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12) redshifts with clusters identified with the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm. Our spectroscopic completeness is 97% for ~ 7,000 clusters within the redMaPPer selection limit, $z \leqslant$ 0.325, so that our cluster correlation functions are much more precise than earlier work and not suppressed by photometric redshifts. We derive an accurate power-law mass-richness relation from the observed abundance with respect to the mass function from Millennium XXL (MXXL) simulation, adjusted to the Planck weighted cosmology. The number density of clusters is found to decline by 20% over the range 0.1 $< z <$ 0.3, in good agreement with the evolution predicted by MXXL. Our projected three-dimensional correlation function scales with richness, $\lambda$, rising from $r_0=$ 14 h$^{-1}$ Mpc at $\lambda\simeq$ 25, to $r_0=$ 22 h$^{-1}$ Mpc at $\lambda\simeq$ 60, with a gradient that matches MXXL when applying our mass-richness relation, whereas the observed amplitude of the correlation function at $\left<z\right>=$ 0.24 exceeds the MXXL prediction by 20% at the $\simeq$ 2.5$\sigma$ level. This tension cannot be blamed on spurious, randomly located clusters as this would reduce the correlation amplitude. Full consistency between the correlation function and the abundances is achievable for the pre-Planck values of $\sigma_8=$ 0.9, $\Omega_m=$ 0.25, and h = 0.73, matching the improved distance ladder estimate of the Hubble constant.

Femtoscopic measurements in p + Pb collisions at [formula omitted] with ATLAS at the LHC

Recent measurements in two-particle correlations in p+Pb collisions suggest collective behavior reminiscent of that observed in Pb+Pb. Femtoscopic measurements may provide useful insight on this behavior because they image the spatio-temporal size of the particle emitting region. This proceeding presents identical-pion Hanbury Brown and Twiss (HBT) measurements from ATLAS using one- and three-dimensional correlation functions. Pions are identified using dE/dx measured in the pixel detector. Correlation functions and the resulting HBT radii are shown as a function of pair momentum (kT) and collision centrality.

Redshift-space clustering of SDSS galaxies – luminosity dependence, halo occupation distribution, and velocity bias

We present the measurements and modelling of the small-to-intermediate scale (0.1--25 Mpc/h) projected and three-dimensional (3D) redshift-space two-point correlation functions (2PCFs) of local galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 7. We find a clear dependence of galaxy clustering on luminosity in both projected and redshift spaces, generally being stronger for more luminous samples. The measurements are successfully interpreted within the halo occupation distribution (HOD) framework with central and satellite velocity bias parameters to describe galaxy kinematics inside haloes and to model redshift-space distortion (RSD) effects. In agreement with previous studies, we find that more luminous galaxies reside in more massive haloes. Including the redshift-space 2PCFs helps tighten the HOD constraints. Moreover, we find that luminous central galaxies are not at rest at the halo centres, with the velocity dispersion about 30% that of the dark matter. Such a relative motion may reflect the consequence of galaxy and halo mergers, and we find that central galaxies in lower mass haloes tend to be more relaxed with respect to their host haloes. The motion of satellite galaxies in luminous samples is consistent with their following that of the dark matter. For faint samples, satellites tends to have slower motion, with velocity dispersion inside haloes about 85% that of the dark matter. We discuss possible applications of the velocity bias constraints on studying galaxy evolution and cosmology. In the appendix, we characterize the distribution of galaxy redshift measurement errors, which is well described by a Gaussian-convolved double exponential distribution.

Instrumentation on multi-scaled scattering of bio-macromolecular solutions.

The design, construction and initial tests on a combined laser light scattering and synchrotron X-ray scattering instrument can cover studies of length scales from atomic sizes in Angstroms to microns and dynamics from microseconds to seconds are presented. In addition to static light scattering (SLS), dynamic light scattering (DLS), small angle X-ray scattering (SAXS) and wide angle X-ray diffraction (WAXD), the light scattering instrument is being developed to carry out studies in mildly turbid solutions, in the presence of multiple scattering. Three-dimensional photon cross correlation function (3D-PCCF) measurements have been introduced to couple with synchrotron X-ray scattering to study the structure, size and dynamics of macromolecules in solution.

Large-scale 3D galaxy correlation function and non-Gaussianity

We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when fNL is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.

Freeze-out dynamics via charged kaon femtoscopy insNN=200GeV central Au + Au collisions

We present measurements of three-dimensional correlation functions of like-sign low transverse momentum kaon pairs from sqrt(sNN)=200 GeV Au+Au collisions. A Cartesian surface-spherical harmonic decomposition technique was used to extract the kaon source function. The latter was found to have a three-dimensional Gaussian shape and can be adequately reproduced by Therminator event generator simulations with resonance contributions taken into account. Compared to the pion one, the kaon source function is generally narrower and does not have the long tail along the pair transverse momentum direction. The kaon Gaussian radii display a monotonic decrease with increasing transverse mass m_T over the interval of 0.55<=m_T<=1.15 GeV/c^2. While the kaon radii are adequately described by the m_T-scaling in the outward and sideward directions, in the longitudinal direction the lowest m_T value exceeds the expectations from a pure hydrodynamical model prediction.

Measurement of baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9

We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-α flux fluctuations at a redshift zeff = 2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of error covariance matrix estimation) and is consistent with predictions of the standard ΛCDM model. We assess the biases in our method, stability of the error covariance matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100 × (αiso − 1) = −1.6+2.0 +4.3 +7.4−2.0 −4.1 −6.8 (stat.) ±1.0 (syst.) (multiple statistical errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat ΛCDM with Ωm = 0.27, h = 0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100 × (α|| − 1) = −1.3+3.5 +7.6 +12.3−3.3 −6.7 −10.2 (stat.) ±2.0 (syst.) and 100 × (α⊥ − 1) = −2.2+7.4 +17−7.1 −15 (stat.) ±3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ∼ −0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-α sample, providing an important consistency test of the standard cosmological model in a new redshift regime.

Baryon acoustic oscillations in the Lyαforest of BOSS quasars

We report a detection of the baryon acoustic oscillation (BAO) feature in the three-dimensional correlation function of the transmitted flux fraction in the \Lya forest of high-redshift quasars. The study uses 48,640 quasars in the redshift range $2.1\le z \le 3.5$ from the Baryon Oscillation Spectroscopic Survey (BOSS) of the third generation of the Sloan Digital Sky Survey (SDSS-III). At a mean redshift $z=2.3$, we measure the monopole and quadrupole components of the correlation function for separations in the range $20\hMpc<r<200\hMpc$. A peak in the correlation function is seen at a separation equal to $(1.01\pm0.03)$ times the distance expected for the BAO peak within a concordance $\Lambda$CDM cosmology. This first detection of the BAO peak at high redshift, when the universe was strongly matter dominated, results in constraints on the angular diameter distance $\da$ and the expansion rate $H$ at $z=2.3$ that, combined with priors on $H_0$ and the baryon density, require the existence of dark energy. Combined with constraints derived from Cosmic Microwave Background (CMB) observations, this result implies $H(z=2.3)=(224\pm8){\rm km\,s^{-1}Mpc^{-1}}$, indicating that the time derivative of the cosmological scale parameter $\dot{a}=H(z=2.3)/(1+z)$ is significantly greater than that measured with BAO at $z\sim0.5$. This demonstrates that the expansion was decelerating in the range $0.7<z<2.3$, as expected from the matter domination during this epoch. Combined with measurements of $H_0$, one sees the pattern of deceleration followed by acceleration characteristic of a dark-energy dominated universe.

Fitting methods for baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9

We describe fitting methods developed to analyze fluctuations in the Lyman-α forest and measure the parameters of baryon acoustic oscillations (BAO). We apply our methods to BOSS Data Release 9. Our method is based on models of the three-dimensional correlation function in physical coordinate space, and includes the effects of redshift-space distortions, anisotropic non-linear broadening, and broadband distortions. We allow for independent scale factors along and perpendicular to the line of sight to minimize the dependence on our assumed fiducial cosmology and to obtain separate measurements of the BAO angular and relative velocity scales. Our fitting software and the input files needed to reproduce our main BOSS Data Release 9 results are publicly available.

A NEW METHOD TO CORRECT FOR FIBER COLLISIONS IN GALAXY TWO-POINT STATISTICS

In fiber-fed galaxy redshift surveys, the finite size of the fiber plugs prevents two fibers from being placed too close to one another, limiting the ability of studying galaxy clustering on all scales. We present a new method for correcting such fiber collision effects in galaxy clustering statistics based on spectroscopic observations. Our method makes use of observations in tile overlap regions to measure the contributions from the collided population, and to therefore recover the full clustering statistics. The method is rooted in solid theoretical ground and is tested extensively on mock galaxy catalogs. We demonstrate that our method can well recover the projected and the full three-dimensional redshift-space two-point correlation functions on scales both below and above the fiber collision scale, superior to the commonly used nearest neighbor and angular correction methods. We discuss potential systematic effects in our method. The statistical correction accuracy of our method is only limited by sample variance, which scales down with (the square root of) the volume probed. For a sample similar to the final SDSS-III BOSS galaxy sample, the statistical correction error is expected to be at the level of 1% on scales 0.1--30Mpc/h for the two-point correlation functions. The systematic error only occurs on small scales, caused by non-perfect correction of collision multiplets, and its magnitude is expected to be smaller than 5%. Our correction method, which can be generalized to other clustering statistics as well, enables more accurate measurements of full three-dimensional galaxy clustering on all scales with galaxy redshift surveys. (abridged)