Reconstructed Density Field Research Articles

Covariance of the redshift-space matter power spectrum after reconstruction

We explore the covariance of redshift-space matter power spectra after a standard density-field reconstruction. We derive perturbative formula of the covariance at the tree-level order and find that the amplitude of the off-diagonal components from the trispectrum decreases by reconstruction. Using a large set of N-body simulations, we also find the similar reduction of the off-diagonal components of the covariance and thereby the signal-to-noise ratio (S/N) of the post-reconstructed (post-rec) power spectra significantly increases compared to the pre-reconstructed spectra. This indicates that the information leaking to higher-order statistics come back to the two-point statistics by reconstruction. Interestingly, the post-rec spectra have higher S/N than the linear spectrum with Gaussian covariance when the scale of reconstruction characterized with the smoothing scale of the shift field is below ~10Mpc/h where the trispectrum becomes negative. We demonstrate that the error of the growth rate estimated from the monopole and quadrupole components of the redshift-space matter power spectra significantly improves by reconstruction. We also find a similar improvement of the growth rate even when taking into account the super-sample covariance, while the reconstruction cannot correct for the field variation of the super-sample modes.

Combining full-shape and BAO analyses of galaxy power spectra: a 1.6% CMB-independent constraint on H0

We present cosmological constraints from a joint analysis of the pre- and post-reconstruction galaxy power spectrum multipoles from the final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). Geometric constraints are obtained from the positions of BAO peaks in reconstructed spectra, which are analyzed in combination with the unreconstructed spectra in a full-shape (FS) likelihood using a joint covariance matrix, giving stronger parameter constraints than FS-only or BAO-only analyses. We introduce a new method for obtaining constraints from reconstructed spectra based on a correlated theoretical error, which is shown to be simple, robust, and applicable to any flavor of density-field reconstruction. Assuming ΛCDM with massive neutrinos, we analyze clustering data from two redshift bins zeff=0.38,0.61 and obtain 1.6% constraints on the Hubble constant H0, using only a single prior on the current baryon density ωb from Big Bang Nucleosynthesis (BBN) and no knowledge of the power spectrum slope ns. This gives H0 = 68.6±1.1 km s−1Mpc−1, with the inclusion of BAO data sharpening the measurement by 40%, representing one of the strongest current constraints on H0 independent of cosmic microwave background data, comparable with recent constraints using BAO data in combination with other data-sets. Restricting to the best-fit slope ns from Planck (but without additional priors on the spectral shape), we obtain a 1% H0 measurement of 67.8± 0.7 km s−1Mpc−1. Finally, we find strong constraints on the cosmological parameters from a joint analysis of the FS, BAO, and Planck data. This sets new bounds on the sum of neutrino masses ∑ mν < 0.14 eV (at 95% confidence) and the effective number of relativistic degrees of freedom Neff = 2.90+0.15−0.16, though contours are not appreciably narrowed by the inclusion of BAO data.

Perturbation theory for the redshift-space matter power spectra after reconstruction

We derive the one-loop perturbative formula of the redshift-space matter power spectrum after density field reconstruction in the Zeldovich approximation. We find that the reconstruction reduces the amplitudes of nonlinear one-loop perturbative terms significantly by partially erasing the nonlinear mode-coupling between density and velocity fields. In comparison with N-body simulations, we find that both the monopole and quadrupole spectra of reconstructed matter density fields agree with the one-loop perturbation theory up to higher wavenumber than those before reconstruction. We also evaluate the impact on cosmic growth rate assuming the survey volume and the number density like the Baryon Oscillation Spectroscopic Survey and find that the total error, including statistical and systematic ones due to one-loop approximation, decreases by half.

Reconstructing large-scale structure with neutral hydrogen surveys

Upcoming 21-cm intensity surveys will use the hyperfine transition in emission to map out neutral hydrogen in large volumes of the universe. Unfortunately, large spatial scales are completely contaminated with spectrally smooth astrophysical foregrounds which are orders of magnitude brighter than the signal. This contamination also leaks into smaller radial and angular modes to form a foreground wedge, further limiting the usefulness of 21-cm observations for different science cases, especially cross-correlations with tracers that have wide kernels in the radial direction. In this paper, we investigate reconstructing these modes within a forward modeling framework. Starting with an initial density field, a suitable bias parameterization and non-linear dynamics to model the observed 21-cm field, our reconstruction proceeds by {combining} the likelihood of a forward simulation to match the observations (under given modeling error and a data noise model) {with the Gaussian prior on initial conditions and maximizing the obtained posterior}. For redshifts z=2 and 4, we are able to reconstruct 21cm field with cross correlation, rc > 0.8 on all scales for both our optimistic and pessimistic assumptions about foreground contamination and for different levels of thermal noise. The performance deteriorates slightly at z=6. The large-scale line-of-sight modes are reconstructed almost perfectly. We demonstrate how our method also provides a technique for density field reconstruction for baryon acoustic oscillations, outperforming standard methods on all scales. We also describe how our reconstructed field can provide superb clustering redshift estimation at high redshifts, where it is otherwise extremely difficult to obtain dense spectroscopic samples, as well as open up a wealth of cross-correlation opportunities with projected fields (e.g. lensing) which are restricted to modes transverse to the line of sight.

Particle density estimation with grid-projected and boundary-corrected adaptive kernels

The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the improved nature of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the “true” particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a “hybrid” approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE.

The impact of wrong assumptions in BAO reconstruction

The process of density field reconstruction enhances the statistical power of distance scale measurements using baryon acoustic oscillations (BAO). During this process a fiducial cosmology is assumed in order to convert sky coordinates and redshifts into distances; fiducial bias and redshift-space-distortion parameters are also assumed in this procedure. We analytically assess the impact of incorrect cosmology and bias assumptions on the post-reconstruction power spectra using low-order Lagrangian perturbation theory, deriving general expressions for the incorrectly reconstructed spectra. We find that the BAO peak location appears to shift only by a negligible amount due to wrong assumptions made during reconstruction. However, the shape of the BAO peak and the quadrupole amplitude can be affected by such errors (at the percent- and five-percent-level respectively), which potentially could cause small biases in parameter inference for future surveys; we outline solutions to such complications.

Discussion of laser interferometric vibrometry for the determination of heat release fluctuations in an unconfined swirl-stabilized flame

Fluctuations in heat release, hot and cold spots convected by the flow and sound waves are all related to density fluctuations, a number easily detected by interferometry. Same as chemiluminescence, interferometry is a line-of-sight method and therefore needs optical access and tomographic reconstruction of density fields. In this work we discuss the use of Laser Interferometric Vibrometry (LIV) as an alternative or extension to chemiluminescence when detecting heat release fluctuations in the flame, convection of hot and cold spots in the non-reacting flow field and sound waves emitted from a 3.4 kW turbulent, unconfined swirl-stabilized methane/air flame under perfectly premixed conditions. For this discussion local temperatures, local ratios of heat release and local Gladstone-Dale constants are determined and their influence on the result discussed. Global and local fluctuations in heat release rate recorded by LIV and chemiluminescence are compared, resulting in the same global values if local temperature fields and local equivalence ratios are used for LIV data evaluation. In contrast, local fluctuations in OH* chemiluminescence emission are influenced by turbulence and strain in this type of flame.

Application of the iterative reconstruction to simulated galaxy fields

We apply an iterative reconstruction method to galaxy mocks in redshift space obtained from $N$-body simulations. Comparing the two-point correlation functions for the reconstructed density field, we find that although the performance is limited by shot noise and galaxy bias compared to the matter field, the iterative method can still reconstruct the initial linear density field from the galaxy field better than the standard method both in real and in redshift space. Furthermore, the iterative method is able to reconstruct both the monopole and quadrupole more precisely, unlike the standard method. We see that as the number density of galaxies gets smaller, the performance of reconstruction gets worse due to the sparseness. However, the precision in the determination of bias ($\sim20\%$) hardly impacts on the reconstruction processes.

A Zeldovich reconstruction method for measuring redshift space distortions using cosmic voids

Redshift space distortions (RSD) in the void-galaxy correlation $\xi^s$ provide information on the linear growth rate of structure in low density environments. Accurate modelling of these RSD effects can also allow the use of voids in competitive Alcock-Paczynski measurements. Linear theory models of $\xi^s$ are able to provide extremely good descriptions of simulation data on all scales provided the real space void positions are known. However, by reference to simulation data we demonstrate the failure of the assumptions implicit in current models of $\xi^s$ for voids identified directly in redshift space, as would be simplest using real observational data. To overcome this problem we instead propose using a density-field reconstruction method based on the Zeldovich approximation to recover the real space void positions from redshift space data. We show that this recovers the excellent agreement between theory and data for $\xi^s$. Performing the reconstruction requires an input cosmological model so, to be self-consistent, we have to perform reconstruction for every model to be tested. We apply this method to mock galaxy and void catalogues in the Big MultiDark $N$-body simulation and consistently recover the fiducial growth rate to a precision of $3.4\%$ using the simulation volume of $(2.5\;h^{-1}\mathrm{Gpc})^3$.

The environmental dependence of the baryon acoustic peak in the Baryon Oscillation Spectroscopic Survey CMASS sample

The environmental dependence of galaxy clustering encodes information about the physical processes governing the growth of cosmic structure. We analyze the baryon acoustic peak as a function of environment in the galaxy correlation function of the Baryon Oscillation Spectroscopic Survey CMASS sample. Dividing the sample into three subsets by smoothed local overdensity, we detect acoustic peaks in the six separate auto-correlation and cross-correlation functions of the sub-samples. Fitting models to these correlation functions, calibrated by mock galaxy and dark matter catalogues, we find that the inferred distance scale is independent of environment, and consistent with the result of analyzing the combined sample. The shape of the baryon acoustic feature, and the accuracy of density-field reconstruction in the Zeldovich approximation, varies with environment. By up-weighting underdense regions and down-weighting overdense regions in their contribution to the full-sample correlation function, by up to 50%, we achieve a fractional improvement of a few per cent in the precision of baryon acoustic oscillation fits to the CMASS data and mock catalogues: the scatter in the preferred-scale fits to the ensemble of mocks improves from 1.45% to 1.34% (pre-reconstruction) and 1.03% to 1.00% (post-reconstruction). These results are consistent with the notion that the acoustic peak is sharper in underdense environments.

Low redshift baryon acoustic oscillation measurement from the reconstructed 6-degree field galaxy survey.

Low-redshift measurements of baryon acoustic oscillations (BAO) measure the late-time evolution of the Universe and are a vital probe of dark energy. Over the past decade both the 6-degree Field Galaxy Survey (6dFGS) and Sloan Digital Sky Survey Main Galaxy Sample (SDSS MGS) have provided important distance constraints at [Formula: see text] < 0.3. In this paper we re-evaluate the cosmological information from the BAO detection in 6dFGS making use of halo occupation distribution (HOD)-populated COmoving Lagrangian Acceleration (COLA) mocks for an accurate covariance matrix and take advantage of the now commonly implemented technique of density field reconstruction. For the 6dFGS data, we find consistency with the previous analysis, and obtain an isotropic volume-averaged distance measurement of [Formula: see text] but with a highly non-Gaussian likelihood. We combine our measurement from both the post-reconstruction clustering of 6dFGS and SDSS MGS offering an updated constraint in this redshift regime, [Formula: see text]. This measurement tightens the constraint in comparison to the result from SDSS MGS alone, especially at the 2σ and higher significance levels. These measurements are consistent with standard Λcold dark matter (ΛCDM) and after fixing the standard ruler using a Planck prior on Ω m h 2, the joint analysis gives [Formula: see text]. This result is consistent with other BAO and Cosmic microwave background (CMB) studies but is in >2σ tension with supernova distance ladder measurements. In the near future both the Taipan Galaxy Survey and the Dark Energy Spectroscopic Instrument (DESI) will improve this measurement to [Formula: see text] at low redshift.

Density Acquisition and Aero-optics Measurement from BOS Images for a Hot Jet

Acquiring density field of a flow is important to understand the flow structure, especially for studying aero-optics. Background-oriented schlieren (BOS) is one of a flow visualization technique which can obtain density field of the flow. Using BOS images density gradient can be acquired quantitatively and density field can be obtained when additional numerical method is applied. In this paper, density field of a hot jet is reconstructed from BOS images by assuming the jet as asymmetric flow and applying adaptive Fourier–Hankel Abel method. Reconstructed density field is evaluated by comparing with wavefront of the optical wave propagating through the hot jet. Optical path difference (OPD) is calculated from the reconstructed density field and compared with Shack–Hartmann (S–H) sensor measured OPD map. OPD obtained from the reconstructed density field and S–H sensor show similar tendency, especially when results are time averaged and turbulence characteristics are removed. Comparing RMS OPD of each time-averaged result show 8.8% error, which is within reasonable range. Thus, it seems that the density field acquisition using BOS technique is reliable for the hot jet flow.

The quasi-linear nearby Universe

The local Universe provides a unique opportunity for testing cosmology and theories of structure formation. To facilitate this opportunity we present a new method for the reconstruction of the quasi-linear matter density and velocity fields from galaxy peculiar velocities and apply it to the Cosmicflows-2 data. The method consists of constructing an ensemble of cosmological simulations, constrained by the standard cosmological model and the observational data. The quasi-linear density field is the geometric mean and variance of the fully non-linear density fields of the simulations. The main nearby clusters (Virgo, Centaurus, Coma), superclusters (Shapley, Perseus-Pisces) and voids (Dipole Repeller) are robustly reconstructed. Galaxies are born biased with respect to the underlying dark matter distribution. Using our quasi-linear framework we demonstrate that the luminosity-weighted density field derived from the 2M++ redshift compilations is non-linearly biased with respect to the matter density field. The bias diminishes in the linear regime.

Theoretical Systematics of Future Baryon Acoustic Oscillation Surveys

Future Baryon Acoustic Oscillation surveys aim at observing galaxy clustering over a wide range of redshift and galaxy populations at great precision, reaching tenths of a percent, in order to detect any deviation of dark energy from the $\LCDM$ model. We utilize a set of paired quasi-\Nb\, FastPM simulations that were designed to mitigate the sample variance effect on the BAO feature and evaluated the BAO systematics as precisely as $\sim 0.01\%$. We report anisotropic BAO scale shifts before and after density field reconstruction in the presence of redshift-space distortions over a wide range of redshift, galaxy/halo biases, and shot noise levels. We test different reconstruction schemes and different smoothing filter scales, and introduce physically-motivated BAO fitting models. For the first time, we derive a Galilean-invariant infrared resummed model for halos in real and redshift space. We test these models from the perspective of robust BAO measurements and non-BAO information such as growth rate and nonlinear bias. We find that pre-reconstruction BAO scale has moderate fitting-model dependence at the level of $0.1\%-0.2\%$ for matter while the dependence is substantially reduced to less than $0.07\%$ for halos. We find that post-reconstruction BAO shifts are generally reduced to below $0.1\%$ in the presence of galaxy/halo bias and show much smaller fitting model dependence. Different reconstruction conventions can potentially make a much larger difference on the line-of-sight BAO scale, upto $0.3\%$. Meanwhile, the precision (error) of the BAO measurements is quite consistent regardless of the choice of the fitting model or reconstruction convention.

An iterative reconstruction of cosmological initial density fields

We present an iterative method to reconstruct the linear-theory initial conditions from the late-time cosmological matter density field, with the intent of improving the recovery of the cosmic distance scale from the baryon acoustic oscillations (BAOs). We present tests using the dark matter density field in both real and redshift space generated from an $N$-body simulation. In redshift space at $z = 0.5$, we find that the reconstructed displacement field using our iterative method are more than 80\% correlated with the true displacement field of the dark matter particles on scales $k < 0.10h\ {\rm Mpc}^{-1}$. Furthermore, we show that the two-point correlation function of our reconstructed density field matches that of the initial density field substantially better, especially on small scales ($< 40h^{-1}\ {\rm Mpc}$). Our redshift-space results are improved if we use an anisotropic smoothing so as to account for the reduced small-scale information along the line of sight in redshift space.

Augmented Flow Simulation Based on Tight Coupling Between Video Reconstruction and Eulerian Models

Hybrid approaches such as combining video data with pure physics-based simulation have been popular in the recent decade for computer graphics. The key motivation is to clearly retain salient advantages from both data-driven method and model-centric numerical simulation, while overcoming certain difficulties of both. The Eulerian method, which has been widely employed in flow simulation, stores variables such as velocity and density on regular Cartesian grids, thereby it could be associated with (volumetric) video data on the same domain. This paper proposes a novel method for flow simulation, which is tightly coupling video-based reconstruction with physically-based simulation and making use of meaningful physical attributes during re-simulation. First, we reconstruct the density field from a single-view video. Second, we estimate the velocity field using the reconstructed density field as prior. In the iterative process, the pressure projection can be treated as a physical constraint and the results of each step are corrected by obtained velocity field in the Eulerian framework. Third, we use the reconstructed density field and velocity field to guide the Eulerian simulation with anticipated new results. Through the guidance of video data, we can produce new flows that closely match with the real scene exhibited in data acquisition. Moreover, in the multigrid Eulerian simulation, we can generate new visual effects which cannot be created from raw video acquisition, with a goal of easily producing many more visually interesting results and respecting true physical attributes at the same time. We demonstrate salient advantages of our hybrid method with a variety of animation examples.

New method for initial density reconstruction

A theoretically interesting and practically important question in cosmology is the reconstruction of the initial density distribution provided a late-time density field. This is a long-standing question with a revived interest recently, especially in the context of optimally extracting the baryonic acoustic oscillation (BAO) signals from observed galaxy distributions. We present a new efficient method to carry out this reconstruction, which is based on numerical solutions to the nonlinear partial differential equation that governs the mapping between the initial Lagrangian and final Eulerian coordinates of particles in evolved density fields. This is motivated by numerical simulations of the quartic Galileon gravity model, which has similar equations that can be solved effectively by multigrid Gauss-Seidel relaxation. The method is based on mass conservation, and does not assume any specific cosmological model. Our test shows that it has a performance comparable to that of state-of-the-art algorithms which were very recently put forward in the literature, with the reconstructed density field over $\sim80\%$ ($50\%$) correlated with the initial condition at $k\lesssim0.6h/{\rm Mpc}$ ($1.0h/{\rm Mpc}$). With an example, we demonstrate that this method can significantly improve the accuracy of BAO reconstruction.

Towards an optimal sampling of peculiar velocity surveys for Wiener Filter reconstructions

The Wiener Filter (WF) technique enables the reconstruction of density and velocity fields from observed radial peculiar velocities. This paper aims at identifying the optimal design of peculiar velocity surveys within the WF framework. The prime goal is to test the dependence of the quality of the reconstruction on the distribution and nature of data points. Mock datasets, extending to 250 Mpc/h, are drawn from a constrained simulation that mimics the local Universe to produce realistic mock catalogs. Reconstructed fields obtained with these mocks are compared to the reference simulation. Comparisons, including residual distributions, cell-to-cell and bulk velocities, imply that the presence of field data points is essential to properly measure the flows. The fields reconstructed from mocks that consist only of galaxy cluster data points exhibit poor quality bulk velocities. In addition, the quality of the reconstruction depends strongly on the grouping of individual data points into single points to suppress virial motions in high density regions. Conversely, the presence of a Zone of Avoidance hardly affects the reconstruction. For a given number of data points, a uniform sample does not score any better than a sample with decreasing number of data points with the distance. The best reconstructions are obtained with a grouped survey containing field galaxies: Assuming no error, they differ from the simulated field by less than 100 km/s up to the extreme edge of the catalogs or up to a distance of three times the mean distance of data points for non-uniform catalogs. The overall conclusions hold when errors are added.

Multishot echo-planar MREIT for fast imaging of conductivity, current density, and electric field distributions.

Magnetic resonance electrical impedance tomography (MREIT) sequences typically use conventional spin or gradient echo-based acquisition methods for reconstruction of conductivity and current density maps. Use of MREIT in functional and electroporation studies requires higher temporal resolution and faster sequences. Here, single and multishot echo planar imaging (EPI) based MREIT sequences were evaluated to see whether high-quality MREIT phase data could be obtained for rapid reconstruction of current density, conductivity, and electric fields. A gel phantom with an insulating inclusion was used as a test object. Ghost artifact, geometric distortion, and MREIT correction algorithms were applied to the data. The EPI-MREIT-derived phase-projected current density and conductivity images were compared with simulations and spin-echo images as a function of EPI shot number. Good agreement among measures in simulated, spin echo, and EPI data was achieved. Current density errors were stable and below 9% as the shot number decreased from 64 to 2, but increased for single-shot images. Conductivity reconstruction relative contrast ratios were stable as the shot number decreased. The derived electric fields also agreed with the simulated data. The EPI methods can be combined successfully with MREIT reconstruction algorithms to achieve fast imaging of current density, conductivity, and electric field. Magn Reson Med 79:71-82, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

The Clustering of Galaxies in the Completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmic Flows and Cosmic Web from Luminous Red Galaxies

We present a Bayesian phase-space reconstruction of the cosmic large-scale matter density and velocity fields from the SDSS-III Baryon Oscillations Spectroscopic Survey Data Release 12 (BOSS DR12) CMASS galaxy clustering catalogue. We rely on a given $\Lambda$CDM cosmology, a mesh resolution in the range of 6-10 $h^{-1}$ Mpc, and a lognormal-Poisson model with a redshift dependent nonlinear bias. The bias parameters are derived from the data and a general renormalised perturbation theory approach. We use combined Gibbs and Hamiltonian sampling, implemented in the \textsc{argo} code, to iteratively reconstruct the dark matter density field and the coherent peculiar velocities of individual galaxies, correcting hereby for coherent redshift space distortions (RSD). Our tests relying on accurate $N$-body based mock galaxy catalogues, show unbiased real space power spectra of the nonlinear density field up to $k\sim0.2\, h$ Mpc$^{-1}$, and vanishing quadrupoles down to $r\sim20\,h^{-1}$ Mpc. We also demonstrate that the nonlinear cosmic web can be obtained from the tidal field tensor based on the Gaussian component of the reconstructed density field. We find that the reconstructed velocities have a statistical correlation coefficient compared to the true velocities of each individual lightcone mock galaxy of $r\sim0.68$ including about 10% of satellite galaxies with virial motions (about $r=0.75$ without satellites). The power spectra of the velocity divergence agree well with theoretical predictions up to $k\sim0.2\,h\,{\rm Mpc}^{-1}$. This work will be especially useful to improve, e.g. BAO reconstructions, kinematic Sunyaev-Zeldovich (kSZ), integrated Sachs-Wolfe (ISW) measurements, or environmental studies.