In cosmological N-body simulations, the representation of dark matter as discrete ‘macroparticles’ suppresses the growth of structure, such that simulations no longer reproduce linear theory on small ...scales near k
Nyquist. Marcos et al. demonstrate that this is due to sparse sampling of modes near k
Nyquist and that the often-assumed continuum growing modes are not proper growing modes of the particle system. We develop initial conditions (ICs) that respect the particle linear theory growing modes and then rescale the mode amplitudes to account for growth suppression. These ICs also allow us to take advantage of our very accurate N-body code abacus to implement second-order Lagrangian perturbation theory (2LPT) in configuration space. The combination of 2LPT and rescaling improves the accuracy of the late-time power spectra, halo mass functions, and halo clustering. In particular, we achieve 1 per cent accuracy in the power spectrum down to k
Nyquist, versus k
Nyquist/4 without rescaling or k
Nyquist/13 without 2LPT, relative to an oversampled reference simulation. We anticipate that our 2LPT will be useful for large simulations where fast Fourier transforms are expensive and that rescaling will be useful for suites of medium-resolution simulations used in cosmic emulators and galaxy survey mock catalogues. Code to generate ICs is available at https://github.com/lgarrison/zeldovich-PLT.
The baryon acoustic oscillation (BAO) feature in the clustering of matter in the universe serves as a robust standard ruler and hence can be used to map the expansion history of the universe. We use ...high force resolution simulations to analyze the effects of galaxy bias on the measurements of the BAO signal. We apply a variety of Halo Occupation Distributions (HODs) and produce biased mass tracers to mimic different galaxy populations. We investigate whether galaxy bias changes the nonlinear shifts on the acoustic scale relative to the underlying dark matter distribution presented by Seo et al. For the less biased HOD models (b < 3), we do not detect any shift in the acoustic scale relative to the no-bias case, typically 0.10% ? 0.10%. However, the most biased HOD models (b > 3) show a shift at moderate significance (0.79% ? 0.31% for the most extreme case). We test the one-step reconstruction technique introduced by Eisenstein et al. in the case of realistic galaxy bias and shot noise. The reconstruction scheme increases the correlation between the initial and final (z = 1) density fields, achieving an equivalent level of correlation at nearly twice the wavenumber after reconstruction. Reconstruction reduces the shifts and errors on the shifts. We find that after reconstruction the shifts from the galaxy cases and the dark matter case are consistent with each other and with no shift. The 1 Delta *s systematic errors on the distance measurements inferred from our BAO measurements with various HODs after reconstruction are about 0.07%-0.15%.
The combination of galaxy–galaxy lensing (GGL) with galaxy clustering is one of the most promising routes to determining the amplitude of matter clustering at low redshifts. Here, we show that ...extending clustering+GGL analyses from the linear regime down to |${\sim } 0.5 \, h^{-1}$| Mpc scales increases their constraining power considerably, even after marginalizing over a flexible model of non-linear galaxy bias. Using a grid of cosmological N-body simulations, we construct a Taylor-expansion emulator that predicts the galaxy autocorrelation ξgg(r) and galaxy-matter cross-correlation ξgm(r) as a function of σ8, Ωm, and halo occupation distribution (HOD) parameters, which are allowed to vary with large-scale environment to represent possible effects of galaxy assembly bias. We present forecasts for a fiducial case that corresponds to BOSS LOWZ galaxy clustering and SDSS-depth weak lensing (effective source density ~0.3 arcmin-2). Using tangential shear and projected correlation function measurements over |$0.5 \le r_\mathrm{ p} \le 30 \, h^{-1}$| Mpc yields a 2 per cent constraint on the parameter combination |$\sigma _8\Omega _\mathrm{ m}^{0.6}$| , a factor of two better than a constraint that excludes non-linear scales ( |$r_\mathrm{ p} \gt 2 \, h^{-1}$| Mpc, |$4 \, h^{-1}$| Mpc for γt, |$w$| p). Much of this improvement comes from the non-linear clustering information, which breaks degeneracies among HOD parameters. Increasing the effective source density to 3 arcmin-2 sharpens the constraint on |$\sigma _8\Omega _\mathrm{ m}^{0.6}$| by a further factor of two. With robust modelling into the non-linear regime, low-redshift measurements of matter clustering at the 1-per cent level with clustering+GGL alone are well within reach of current data sets such as those provided by the Dark Energy Survey.
The baryon acoustic oscillation (BAO) feature in the clustering of matter in the universe serves as a robust standard ruler and hence can be used to map the expansion history of the universe. We use ...high force resolution simulations to analyze the effects of galaxy bias on the measurements of the BAO signal. We apply a variety of Halo Occupation Distributions (HODs) and produce biased mass tracers to mimic different galaxy populations. We investigate whether galaxy bias changes the non-linear shifts on the acoustic scale relative to the underlying dark matter distribution presented by Seo et al. (2009). For the less biased HOD models (b < 3), we do not detect any shift in the acoustic scale relative to the no-bias case, typically 0.10% ± 0.10%. However, the most biased HOD models (b > 3) show a shift at moderate significance (0.79% ± 0.31% for the most extreme case). We test the one-step reconstruction technique introduced by Eisenstein et al. (2007) in the case of realistic galaxy bias and shot noise. The reconstruction scheme increases the correlation between the initial and final (z = 1) density fields achieving an equivalent level of correlation at nearly twice the wavenumber after reconstruction. Reconstruction reduces the shifts and errors on the shifts. We find that after reconstruction the shifts from the galaxy cases and the dark matter case are consistent with each other and with no shift. The 1σ systematic errors on the distance measurements inferred from our BAO measurements with various HODs after reconstruction are about 0.07%-0.15%.
We measure shifts of the acoustic scale due to nonlinear growth and redshift distortions to a high precision using a very large volume of high-force-resolution simulations. We compare results from ...various sets of simulations that differ in their force, volume, and mass resolution. We find a consistency within 1.5{sigma} for shift values from different simulations and derive shift {alpha}(z) - 1 = (0.300 {+-} 0.015) %D(z)/D(0){sup 2} using our fiducial set. We find a strong correlation with a non-unity slope between shifts in real space and in redshift space and a weak correlation between the initial redshift and low redshift. Density-field reconstruction not only removes the mean shifts and reduces errors on the mean, but also tightens the correlations. After reconstruction, we recover a slope of near unity for the correlation between the real and redshift space and restore a strong correlation between the initial and the low redshifts. We derive propagators and mode-coupling terms from our N-body simulations and compare with the Zel'dovich approximation and the shifts measured from the {chi}{sup 2} fitting, respectively. We interpret the propagator and the mode-coupling term of a nonlinear density field in the context of an average and a dispersion of its complex Fourier coefficients relative to those of the linear density field; from these two terms, we derive a signal-to-noise ratio of the acoustic peak measurement. We attempt to improve our reconstruction method by implementing 2LPT and iterative operations, but we obtain little improvement. The Fisher matrix estimates of uncertainty in the acoustic scale is tested using 5000 h {sup -3} Gpc{sup 3} of cosmological Particle-Mesh simulations from Takahashi et al. At an expected sample variance level of 1%, the agreement between the Fisher matrix estimates based on Seo and Eisenstein and the N-body results is better than 10%.
We provide a novel and efficient algorithm for computing accelerations in the periodic large-N-body problem that is at the same time significantly faster and more accurate than previous methods. Our ...representation of the periodic acceleration is precisely mathematically equivalent to that determined by Ewald summation and is computed directly as an infinite lattice sum using the Newtonian kernel (|r|-1). Retaining this kernel implies that one can (i) extend the standard open boundary numerical algorithms and (ii) harness the tremendous computational speed possessed by Graphics Processing Units (GPUs) in computing Newtonian kernels straightforwardly to the periodic domain. The precise form of our direct interactions is based upon the adaptive softening length methodology introduced for open boundary conditions by Price and Monaghan. Furthermore, we describe a new Fast Multipole Method (FMM) that represents the multipoles and Taylor series as collections of pseudoparticles. Using these techniques we have computed forces to machine precision throughout the evolution of a 1 billion particle cosmological simulation with a price/performance ratio more than 100 times that of current numerical techniques operating at much lower accuracy.
We provide a novel and efficient algorithm for computing accelerations in theperiodic large-N-body problem that is at the same time significantly fasterand more accurate than previous methods. Our ...representation of theperiodic acceleration is precisely mathematically equivalent to that determinedby Ewald summation and is computed directly as an infinite lattice sum usingthe Newtonian kernel. Retaining this kernel implies that one can(i) extend the standard open boundary numerical algorithms and(ii) harness the tremendous computational speed possessed by Graphics ProcessingUnits (GPUs) in computing Newtonian kernels straightforwardly to the periodic domain.The precise form of our direct interactions is based upon the adaptive softeninglength methodology introduced for open boundary conditions by Price and Monaghan.Furthermore, we describe a new Fast Multipole Method (FMM) that represents themultipoles and Taylor series as collections of pseudoparticles. Using thesetechniques we have computed forces to machine precision throughout the evolution ofa 1 billion particle cosmological simulation with a price/performance ratio morethan 100 times that of current numerical techniques operating at much lower accuracy.
MNRAS (October 01, 2016) 461 (4): 4125-4145 In cosmological $N$-body simulations, the representation of dark matter as
discrete "macroparticles" suppresses the growth of structure, such that
...simulations no longer reproduce linear theory on small scales near $k_{\rm
Nyquist}$. Marcos et al. demonstrate that this is due to sparse sampling of
modes near $k_{\rm Nyquist}$ and that the often-assumed continuum growing modes
are not proper growing modes of the particle system. We develop initial
conditions that respect the particle linear theory growing modes and then
rescale the mode amplitudes to account for growth suppression. These ICs also
allow us to take advantage of our very accurate $N$-body code Abacus to
implement 2LPT in configuration space. The combination of 2LPT and rescaling
improves the accuracy of the late-time power spectra, halo mass functions, and
halo clustering. In particular, we achieve 1% accuracy in the power spectrum
down to $k_{\rm Nyquist}$, versus $k_{\rm Nyquist}/4$ without rescaling or
$k_{\rm Nyquist}/13$ without 2LPT, relative to an oversampled reference
simulation. We anticipate that our 2LPT will be useful for large simulations
where FFTs are expensive and that rescaling will be useful for suites of
medium-resolution simulations used in cosmic emulators and galaxy survey mock
catalogs. Code to generate initial conditions is available at
https://github.com/lgarrison/zeldovich-PLT
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