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DOE OSTI2022

Mapping variations of redshift distributions with probability integral transforms

We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials

Properties of soft materials are influenced by their anisotropic structuring under nonequilibrium fields. Although anisotropic structure-property relationships have been extensively explored theoretically, comparison to experiments requires determination of the microstructural orientation probability distribution function (OPDF) of microstructural elements. Small angle scattering (SAS) measurements encode information about the OPDF, but tools to navigate this connection are incomplete. Here, we develop and validate an explicit framework to link arbitrary OPDFs to SAS measurements. Specifically, we propose, validate, and apply a method, maximum a posteriori scattering inference (MAPSI), whereby the OPDF may be obtained from SAS measurements using a Bayesian estimation method. Using this method, we obtain estimates of the full 3D OPDF for two model semidilute fd-virus (rodlike) dispersions at concentrations that are approximately equal to and twice the overlap concentration. From the OPDF, we calculate its second and fourth moments and compare these to predictions for a dilute suspension of rigid rods and to a recent theory for semidilute suspensions. Finally, we use both the theoretical and measured moments to calculate the stress, both for dilute and semidilute suspensions. These predictions are not only compared to each other, but also to measured values of the shear stress, and point to new insights into the behavior of suspensions of highly elongated particles in the transition between dilute and semidilute behavior. We also use this new framework to provide perspective on the connection between scalar parameterizations of scattering and the OPDF that have frequently been used in the past. Here, the new tools developed in this work provide an unprecedented path toward experimental validation of dynamical theories of rodlike colloids and polymers, and for measurement of nonequilibrium structures and stresses of other complex fluids and soft materials with SAS.

36 MATERIALS SCIENCE↗

NASA NTRS2007

Space Radiation Risk Assessment for Future Lunar Missions

For lunar exploration mission design, radiation risk assessments require the understanding of future space radiation environments in support of resource management decisions, operational planning, and a go/no-go decision. The future GCR flux was estimated as a function of interplanetary deceleration potential, which was coupled with the estimated neutron monitor rate from the Climax monitor using a statistical model. A probability distribution function for solar particle event (SPE) occurrence was formed from proton fluence measurements of SPEs occurred during the past 5 solar cycles (19-23). Large proton SPEs identified from impulsive nitrate enhancements in polar ice for which the fluences are greater than 2 10(exp 9) protons/sq cm for energies greater than 30 MeV, were also combined to extend the probability calculation for high level of proton fluences. The probability with which any given proton fluence level of a SPE will be exceeded during a space mission of defined duration was then calculated. Analytic energy spectra of SPEs at different ranks of the integral fluences were constructed over broad energy ranges extending out to GeV, and representative exposure levels were analyzed at those fluences. For the development of an integrated strategy for radiation protection on lunar exploration missions, effective doses at various points inside a spacecraft were calculated with detailed geometry models representing proposed transfer vehicle and habitat concepts. Preliminary radiation risk assessments from SPE and GCR were compared for various configuration concepts of radiation shelter in exploratory-class spacecrafts.

Kim, Myung-Hee Y.↗

NASA NTRS2011

The Impacts of an Observationally-Based Cloud Fraction and Condensate Overlap Parameterization on a GCM's Cloud Radiative Effect

It has been shown that the details of how cloud fraction overlap is treated in GCMs has substantial impact on shortwave and longwave fluxes. Because cloud condensate is also horizontally heterogeneous at GCM grid scales, another aspect of cloud overlap should in principle also be assessed, namely the vertical overlap of hydrometeor distributions. This type of overlap is usually examined in terms of rank correlations, i.e., linear correlations between hydrometeor amount ranks of the overlapping parts of cloud layers at specific separation distances. The cloud fraction overlap parameter and the rank correlation of hydrometeor amounts can be both expressed as inverse exponential functions of separation distance characterized by their respective decorrelation lengths (e-folding distances). Larger decorrelation lengths mean that hydrometeor fractions and probability distribution functions have high levels of vertical alignment. An analysis of CloudSat and CALIPSO data reveals that the two aspects of cloud overlap are related and their respective decorrelation lengths have a distinct dependence on latitude that can be parameterized and included in a GCM. In our presentation we will contrast the Cloud Radiative Effect (CRE) of the GEOS-5 atmospheric GCM (AGCM) when the observationally-based parameterization of decorrelation lengths is used to represent overlap versus the simpler cases of maximum-random overlap and globally constant decorrelation lengths. The effects of specific overlap representations will be examined for both diagnostic and interactive radiation runs in GEOS-5 and comparisons will be made with observed CREs from CERES and CloudSat (2B-FLXHR product). Since the radiative effects of overlap depend on the cloud property distributions of the AGCM, the availability of two different cloud schemes in GEOS-5 will give us the opportunity to assess a wide range of potential cloud overlap consequences on the model's climate.

Oreopoulos, Lazaros↗

NASA NTRSDate not supplied

Inter-Calibrating the CERES SW Instrument Fluxes Using Deep Convective Clouds(DCC) Within the Same Sun-Synchronous Orbit

The NASA CERES EBAF product provides the scientific community observed TOA fluxes to monitor the Earth’s energy imbalance and to validate climate models. To provide a seamless EBAF 24-year record, the CERES instrument calibration must be stable and consistent across satellite records. Once the Terra and Aqua spacecraft are decommissioned at the end of 2025, the CERES project will rely on CERES instrument observations on the SNPP and NOAA-20 1:30 PM sun-synchronous orbits. The SNPP and NOAA-20 satellite orbit placement will prevent any time matched observations for inter-calibration efforts. The future Libera instrument, which will continue the CERES record and scheduled for launch in 2028 onboard the NOAA-22 satellite, will also need to be inter-calibrated without the aid of time-matched observations. Deep convective clouds (DCC) are the most Lambertian, brightest, tropical Earth invariant targets located at the tropopause making them ideal to radiometrically scale the CERES SW observed radiance to a common reference. The SNPP, NOAA-20 and future NOAA-22 satellites are in the same 16-day repeatable orbits, allowing the DCC targets to be observed with the same angular configuration. The empirically derived SNPP CERES SW channel Bidirectional Reflectance Distribution Function (BRDF) can be easily be applied to the NOAA-20 CERES SW channel radiances since they observe the nearly the same DCC systems. The DCC BRDF corrected radiances are analyzed collectively into radiance probability distribution functions (PDF). By comparing the PDF statistics, the SNPP and NOAA-20 CERES SW channel can be inter-calibrated. The inter-calibration coefficients are validated with the CERES instrument calibration team coefficients to optimize the methodology.

David Doelling↗

DOE OSTI2014

Faraday dispersion functions of galaxies

The Faraday dispersion function (FDF), which can be derived from an observed polarization spectrum by Faraday rotation measure synthesis, is a profile of polarized emissions as a function of Faraday depth. We study intrinsic FDFs along sight lines through face-on Milky Way like galaxies by means of a sophisticated galactic model incorporating three-dimensional MHD turbulence, and investigate how much information the FDF intrinsically contains. Since the FDF reflects distributions of thermal and cosmic-ray electrons as well as magnetic fields, it has been expected that the FDF could be a new probe to examine internal structures of galaxies. We, however, find that an intrinsic FDF along a sight line through a galaxy is very complicated, depending significantly on actual configurations of turbulence. We perform 800 realizations of turbulence and find no universal shape of the FDF even if we fix the global parameters of the model. We calculate the probability distribution functions of the standard deviation, skewness, and kurtosis of FDFs and compare them for models with different global parameters. Our models predict that the presence of vertical magnetic fields and the large-scale height of cosmic-ray electrons tend to make the standard deviation relatively large. In contrast, the differences in skewness and kurtosis are relatively less significant.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

A course-grained model for polyethylene glycol polymer

A coarse-grained (CG) model of polyethylene glycol (PEG) was developed and implemented in CG molecular dynamics (MD) simulations of PEG chains with degree of polymerization (DP) 20 and 40. In the model, two repeat units of PEG are grouped as one CG bead. Atomistic MD simulation of PEG chains with DP = 20 was first conducted to obtain the bonded structural probability distribution functions (PDFs) and nonbonded pair correlation function (PCF) of the CG beads. The bonded CG potentials are obtained by simple inversion of the corresponding PDFs. The CG nonbonded potential is parameterized to the PCF using both an inversion procedure based on the Ornstein-Zernike equation with the Percus-Yevick approximation (OZPY{sup -1}) and a combination of OZPY{sup -1} with the iterative Boltzmann inversion (IBI) method (OZPY{sup -1}+IBI). As a simple one step method, the OZPY{sup -1} method possesses an advantage in computational efficiency. Using the potential from OZPY{sup -1} as an initial guess, the IBI method shows fast convergence. The coarse-grained molecular dynamics (CGMD) simulations of PEG chains with DP = 20 using potentials from both methods satisfactorily reproduce the structural properties from atomistic MD simulation of the same systems. The OZPY{sup -1}+IBI method yields better agreement than the OZPY{sup -1} method alone. The new CG model and CG potentials from OZPY{sup -1}+IBI method was further tested through CGMD simulation of PEG with DP = 40 system. No significant changes are observed in the comparison of PCFs from CGMD simulations of PEG with DP = 20 and 40 systems indicating that the potential is independent of chain length.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Numerical simulations of quiet sun magnetism: On the contribution from a small-scale dynamo

We present a series of radiative MHD simulations addressing the origin and distribution of the mixed polarity magnetic field in the solar photosphere. To this end, we consider numerical simulations that cover the uppermost 2-6 Mm of the solar convection zone and we explore scales ranging from 2 km to 25 Mm. We study how the strength and distribution of the magnetic field in the photosphere and subsurface layers depend on resolution, domain size, and boundary conditions. We find that 50% of the magnetic energy at the τ = 1 level comes from fields with the less than 500 G strength and that 50% of the energy resides on scales smaller than about 100 km. While the probability distribution functions are essentially independent of resolution, properly describing the spectral energy distribution requires grid spacings of 8 km or smaller. The formation of flux concentrations in the photosphere exceeding 1 kG requires a mean vertical field strength greater than 30-40 G at τ = 1. The filling factor of kG flux concentrations increases with overall domain size as the magnetic field becomes organized by larger, longer-lived flow structures. A solution with a mean vertical field strength of around 85 G at τ = 1 requires a subsurface rms field strength increasing with depth at the same rate as the equipartition field strength. We consider this an upper limit for the quiet Sun field strength, which implies that most of the convection zone is magnetized close to the equipartition. We discuss these findings in view of recent high-resolution spectropolarimetric observations of quiet Sun magnetism.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

TIME-VARYING DYNAMICAL STAR FORMATION RATE

We present numerical evidence of dynamic star formation in which the accreted stellar mass grows superlinearly with time, roughly as t {sup 2}. We perform simulations of star formation in self-gravitating hydrodynamic and magnetohydrodynamic turbulence that is continuously driven. By turning the self-gravity of the gas in the simulations on or off, we demonstrate that self-gravity is the dominant physical effect setting the mass accretion rate at early times before feedback effects take over, contrary to theories of turbulence-regulated star formation. We find that gravitational collapse steepens the density profile around stars, generating the power-law tail on what is otherwise a lognormal density probability distribution function. Furthermore, we find turbulent velocity profiles to flatten inside collapsing regions, altering the size-line width relation. This local flattening reflects enhancements of turbulent velocity on small scales, as verified by changes to the velocity power spectra. Our results indicate that gas self-gravity dynamically alters both density and velocity structures in clouds, giving rise to a time-varying star formation rate. We find that a substantial fraction of the gas that forms stars arrives via low-density flows, as opposed to accreting through high-density filaments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

DETERMINING AGES OF APOGEE GIANTS WITH KNOWN DISTANCES

We present a sample of 705 local giant stars observed using the New Mexico State University 1 m telescope with the Sloan Digital Sky Survey-III/Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph, for which we estimate stellar ages and the local star formation history (SFH). The high-resolution (R ∼ 22,500), near infrared (1.51–1.7 μm) APOGEE spectra provide measurements of stellar atmospheric parameters (temperature, surface gravity, [M/H], and [α/M]). Due to the smaller uncertainties in surface gravity possible with high-resolution spectra and accurate Hipparcos distance measurements, we are able to calculate the stellar masses to within 30%. For giants, the relatively rapid evolution up the red giant branch allows the age to be constrained by the mass. We examine methods of estimating age using both the mass–age relation directly and a Bayesian isochrone matching of measured parameters, assuming a constant SFH. To improve the SFH prior, we use a hierarchical modeling approach to constrain the parameters of the model SFH using the age probability distribution functions of the data. The results of an α-dependent Gaussian SFH model show a clear age–[α/M] relation at all ages. Using this SFH model as the prior for an empirical Bayesian analysis, we determine ages for individual stars. The resulting age–metallicity relation is flat, with a slight decrease in [M/H] at the oldest ages and a ∼0.5 dex spread in metallicity across most ages. For stars with ages ≲1 Gyr we find a smaller spread, consistent with radial migration having a smaller effect on these young stars than on the older stars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

L{sub CO}{sup ′}/L{sub FIR} relations with CO rotational ladders of galaxies across the Herschel spire archive

We present a catalog of all CO (J = 4−3 through J = 13−12), [C i], and [N ii] lines available from extragalactic spectra from the Herschel SPIRE Fourier Transform Spectrometer (FTS) archive combined with observations of the low-J CO lines from the literature and from the Arizona Radio Observatory. This work examines the relationships between L {sub FIR}, L{sub CO}{sup ′}, and L {sub CO}/L {sub CO,1−0}. We also present a new method for estimating probability distribution functions from marginal signal-to-noise ratio Herschel FTS spectra, which takes into account the instrumental “ringing” and the resulting highly correlated nature of the spectra. The slopes of log(L {sub FIR}) versus log(L{sub CO}{sup ′}) are linear for all mid- to high-J CO lines and slightly sublinear if restricted to (ultra)luminous infrared galaxies ((U)LIRGs). The mid- to high-J CO luminosity relative to CO J = 1−0 increases with increasing L {sub FIR}, indicating higher excitement of the molecular gas, although these ratios do not exceed ∼180. For a given bin in L {sub FIR}, the luminosities relative to CO J = 1−0 remain relatively flat from J = 6−5 through J = 13−12, across three orders of magnitude of L {sub FIR}. A single component theoretical photodissociation region (PDR) model cannot match these flat SLED shapes, although combinations of PDR models with mechanical heating added qualitatively match the shapes, indicating the need for further comprehensive modeling of the excitation processes of warm molecular gas in nearby galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest–neighbor probability distribution function, p{sub 1}(r), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest–neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of p{sub 1}(r) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest–neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

SIMULTANEOUS ESTIMATION OF PHOTOMETRIC REDSHIFTS AND SED PARAMETERS: IMPROVED TECHNIQUES AND A REALISTIC ERROR BUDGET

We seek to improve the accuracy of joint galaxy photometric redshift estimation and spectral energy distribution (SED) fitting. By simulating different sources of uncorrected systematic errors, we demonstrate that if the uncertainties in the photometric redshifts are estimated correctly, so are those on the other SED fitting parameters, such as stellar mass, stellar age, and dust reddening. Furthermore, we find that if the redshift uncertainties are over(under)-estimated, the uncertainties in SED parameters tend to be over(under)-estimated by similar amounts. These results hold even in the presence of severe systematics and provide, for the first time, a mechanism to validate the uncertainties on these parameters via comparison with spectroscopic redshifts. We propose a new technique (annealing) to re-calibrate the joint uncertainties in the photo-z and SED fitting parameters without compromising the performance of the SED fitting + photo-z estimation. This procedure provides a consistent estimation of the multi-dimensional probability distribution function in SED fitting + z parameter space, including all correlations. While the performance of joint SED fitting and photo-z estimation might be hindered by template incompleteness, we demonstrate that the latter is “flagged” by a large fraction of outliers in redshift, and that significant improvements can be achieved by using flexible stellar populations synthesis models and more realistic star formation histories. In all cases, we find that the median stellar age is better recovered than the time elapsed from the onset of star formation. Finally, we show that using a photometric redshift code such as EAZY to obtain redshift probability distributions that are then used as priors for SED fitting codes leads to only a modest bias in the SED fitting parameters and is thus a viable alternative to the simultaneous estimation of SED parameters and photometric redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Observation of Kolmogorov turbulence due to multiscale vortices in dusty plasma experiments

We report the experimental observation of fully developed Kolmogorov turbulence originating from self-excited vortex flows in a three-dimensional (3D) dust cloud. The characteristic -5/3 scaling of 3D Kolmogorov turbulence is consistent in both the spatial and temporal energy spectra within a statistical variation of experimental data. Additionally, the 2/3 scaling in the second-order structure function further supports the presence of Kolmogorov turbulence. We also identified a slight deviation in the tails of the probability distribution functions for velocity gradients, a reflection of intermittency. The experiment showed the formation of a dust cloud in the diffused plasma region away from the electrodes. The dust rotation was observed in multiple experimental campaigns under different discharge conditions at different spatial locations and background plasma environments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions

Within the Bayesian statistical framework we infer the incompressibility K 0 , skewness J 0 and kurtosis Z 0 parameters of symmetric nuclear matter (SNM) at its saturation density ρ 0 using the constraining bands on the pressure in cold SNM in the density range of 1.3ρ 0 to 4.5ρ 0 from transport model analyses of kaon production and nuclear collective flow in relativistic heavy-ion collisions. As the default option assuming the K 0 , J 0 and Z 0 have Gaussian prior probability distribution functions (PDFs) with the means and variances of 235±30, -200±200 and -146±1728 MeV, their posterior most probable values are narrowed down to 192$^{+12}_{-16}$ MeV, -180$^{+100}_{-110}$ MeV and ${\mathrm{200}}_{-250}^{+250}$ at 68% confidence level, respectively. The results are largely independent of the prior PDFs of J 0 and Z 0 used. However, if one adopts the strong belief that the incompressibility K 0 has a uniform prior PDF within its absolute boundary of 220–260 MeV as one can find easily in the literature, the posterior most probable values of K 0 , J 0 and Z 0 shift to ${K}_{0}=22{0}_{-0}^{+6}$ MeV, ${J}_{0}=-39{0}_{-70}^{+60}$ MeV and ${Z}_{0}=60{0}_{-200}^{+200}$ MeV, respectively. While the posterior PDFs of the SNM EOS parameters depend somewhat on the prior PDF of K 0 used, the results from using different prior PDFs are qualitatively consistent. The uncertainties of all three parameters are significantly reduced especially for the J 0 and Z 0 parameters compared to their current values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2008

Determination of a Limited Scope Network's Lightning Detection Efficiency

This paper outlines a modeling technique to map lightning detection efficiency variations over a region surveyed by a sparse array of ground based detectors. A reliable flash peak current distribution (PCD) for the region serves as the technique's base. This distribution is recast as an event probability distribution function. The technique then uses the PCD together with information regarding: site signal detection thresholds, type of solution algorithm used, and range attenuation; to formulate the probability that a flash at a specified location will yield a solution. Applying this technique to the full region produces detection efficiency contour maps specific to the parameters employed. These contours facilitate a comparative analysis of each parameter's effect on the network's detection efficiency. In an alternate application, this modeling technique gives an estimate of the number, strength, and distribution of events going undetected. This approach leads to a variety of event density contour maps. This application is also illustrated. The technique's base PCD can be empirical or analytical. A process for formulating an empirical PCD specific to the region and network being studied is presented. A new method for producing an analytical representation of the empirical PCD is also introduced.

Rompala, John T.↗

DOE OSTI2011

Intermittency and geometrical statistics of three-dimensional homogeneous magnetohydrodynamic turbulence: A wavelet viewpoint

Scale-dependent and geometrical statistics of three-dimensional incompressible homogeneous magnetohydrodynamic turbulence without mean magnetic field are examined by means of the orthogonal wavelet decomposition. The flow is computed by direct numerical simulation with a Fourier spectral method at resolution 512{sup 3} and a unit magnetic Prandtl number. Scale-dependent second and higher order statistics of the velocity and magnetic fields allow to quantify their intermittency in terms of spatial fluctuations of the energy spectra, the flatness, and the probability distribution functions at different scales. Different scale-dependent relative helicities, e.g., kinetic, cross, and magnetic relative helicities, yield geometrical information on alignment between the different scale-dependent fields. At each scale, the alignment between the velocity and magnetic field is found to be more pronounced than the other alignments considered here, i.e., the scale-dependent alignment between the velocity and vorticity, the scale-dependent alignment between the magnetic field and its vector potential, and the scale-dependent alignment between the magnetic field and the current density. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations and the corresponding time-derivatives of the magnetic field are performed. It is found that the Lagrangian acceleration does not exhibit substantially stronger intermittency compared to the Eulerian acceleration, in contrast to hydrodynamic turbulence where the Lagrangian acceleration shows much stronger intermittency than the Eulerian acceleration. The Eulerian time-derivative of the magnetic field is more intermittent than the Lagrangian time-derivative of the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Testing approximate predictions of displacements of cosmological dark matter halos

We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing for all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z =0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are reconstructed at the object-by-object level.

79 ASTRONOMY AND ASTROPHYSICS↗