We use a suite of cosmological simulations to study the mass–concentration–redshift relation, c(M, z), of dark matter haloes. Our simulations include standard Λ-cold dark matter (CDM) models, and ...additional runs with truncated power spectra, consistent with a thermal warm dark matter (WDM) scenario. We find that the mass profiles of CDM and WDM haloes are self-similar and well approximated by the Einasto profile. The c(M, z) relation of CDM haloes is monotonic: concentrations decrease with increasing virial mass at fixed redshift, and decrease with increasing redshift at fixed mass. The mass accretion histories (MAHs) of CDM haloes are also scale-free, and can be used to infer concentrations directly. These results do not apply to WDM haloes: their MAHs are not scale-free because of the characteristic scale imposed by the power spectrum suppression. Further, the WDM c(M, z) relation is non-monotonic: concentrations peak at a mass scale dictated by the truncation scale, and decrease at higher and lower masses. We show that the assembly history of a halo can still be used to infer its concentration, provided that the total mass of its progenitors is considered (the ‘collapsed mass history’; CMH), rather than just that of its main ancestor. This exploits the scale-free nature of CMHs to derive a simple scaling that reproduces the mass–concentration–redshift relation of both CDM and WDM haloes over a vast range of halo masses and redshifts. Our model therefore provides a robust account of the mass, redshift, cosmology and power spectrum dependence of dark matter halo concentrations.
We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial ...Fourier mode amplitudes are fixed to the ensemble average power spectrum) and paired (with initial modes exactly out of phase). We measure the power spectrum, monopole and quadrupole redshift-space correlation functions, halo mass function and reduced bispectrum at z = 1. By these measures, predictions from a fixed pair can be as precise on non-linear scales as an average over 50 traditional simulations. The fixing procedure introduces a non-Gaussian correction to the initial conditions; we give an analytic argument showing why the simulations are still able to predict the mean properties of the Gaussian ensemble. We anticipate that the method will drive down the computational time requirements for accurate large-scale explorations of galaxy bias and clustering statistics, and facilitating the use of numerical simulations in cosmological data interpretation.
The properties of cosmic velocity fields Hahn, Oliver; Angulo, Raul E; Abel, Tom
Monthly notices of the Royal Astronomical Society,
12/2015, Letnik:
454, Številka:
4
Journal Article
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Understanding the velocity field is very important for modern cosmology: it gives insights to structure formation in general, and also its properties are crucial ingredients in modelling ...redshift-space distortions and in interpreting measurements of the kinetic Sunyaev–Zeldovich effect. Unfortunately, characterizing the velocity field in cosmological N-body simulations is inherently complicated by two facts. (i) The velocity field becomes manifestly multivalued after shell crossing and has discontinuities at caustics. This is due to the collisionless nature of dark matter. (ii) N-body simulations sample the velocity field only at a set of discrete locations, with poor resolution in low-density regions. In this paper, we discuss how the associated problems can be circumvented by using a phase-space interpolation technique. This method provides extremely accurate estimates of the cosmic velocity fields and its derivatives, which can be properly defined without the need of the arbitrary ‘coarse-graining’ procedure commonly used. We explore in detail the configuration-space properties of the cosmic velocity field on very large scales and in the highly non-linear regime. In particular, we characterize the divergence and curl of the velocity field, present their one-point statistics, analyse the Fourier-space properties, and provide fitting formulae for the velocity divergence bias relative to the non-linear matter power spectrum. We furthermore contrast some of the interesting differences in the velocity fields of warm and cold dark matter models. We anticipate that the high-precision measurements carried out here will help to understand in detail the dynamics of dark matter and the structures it forms.
Warm dark matter (WDM) cosmologies are a viable alternative to the cold dark matter (CDM) scenario. Unfortunately, an accurate scrutiny of the WDM predictions with N-body simulations has proven ...difficult due to numerical artefacts. Here, we report on cosmological simulations that, for the first time, are devoid of those problems, and thus are able to accurately resolve the WDM halo mass function well below the cut-off. We discover a complex picture, with perturbations at different evolutionary stages populating different ranges in the halo mass function. On the smallest mass scales we can resolve, identified objects are typically centres of filaments that are starting to collapse. On intermediate mass scales, objects typically correspond to fluctuations that have collapsed and are in the process of relaxation, whereas the high-mass end is dominated by objects similar to haloes identified in CDM simulations. We then explicitly show how the formation of low-mass haloes is suppressed, which translates into a strong cut-off in the halo mass function. This disfavours some analytic formulations that predict a halo mass function that would extend well below the free streaming mass. We argue for a more detailed exploration of the formation of the smallest structures expected to form in a given cosmology, which, we foresee, will advance our overall understanding of structure formation.
N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling ...collisionless systems. We introduce a new approach to simulate the gravitational evolution of cold collisionless fluids by solving the Vlasov–Poisson equations in terms of adaptively refineable ‘Lagrangian phase–space elements’. These geometrical elements are piecewise smooth maps between Lagrangian space and Eulerian phase–space and approximate the continuum structure of the distribution function. They allow for dynamical adaptive splitting to accurately follow the evolution even in regions of very strong mixing. We discuss in detail various one-, two- and three-dimensional test problems to demonstrate the performance of our method. Its advantages compared to N-body algorithms are: (i) explicit tracking of the fine-grained distribution function, (ii) natural representation of caustics, (iii) intrinsically smooth gravitational potential fields, thus (iv) eliminating the need for any type of ad hoc force softening. We show the potential of our method by simulating structure formation in a warm dark matter scenario. We discuss how spurious collisionality and large-scale discreteness noise of N-body methods are both strongly suppressed, which eliminates the artificial fragmentation of filaments. Therefore, we argue that our new approach improves on the N-body method when simulating self-gravitating cold and collisionless fluids, and is the first method that allows us to explicitly follow the fine-grained evolution in six-dimensional phase–space.
The abundance of galaxy clusters can constrain both the geometry and growth of structure in our Universe. However, this probe could be significantly complicated by recent claims of ...non-universality–non-trivial dependences with respect to the cosmological model and redshift. In this work, we analyse the dependence of the mass function on the way haloes are identified and establish if this can cause departures from universality. In order to explore this dependence, we use a set of different N-body cosmological simulations (Le SBARBINE simulations), with the latest cosmological parameters from the Planck collaboration; this first suite of simulations is followed by a lower resolution set, carried out with different cosmological parameters. We identify dark matter haloes using a spherical overdensity algorithm with varying overdensity thresholds (virial, 2000, 1000, 500, 200 ρc and 200 ρb) at all redshifts. We notice that, when expressed in terms of the rescaled variable ν, the mass function for virial haloes is a nearly universal as a function of redshift and cosmology, while this is clearly not the case for the other overdensities we considered. We provide fitting functions for the halo mass function parameters as a function of overdensity, that allow us to predict, to within a few per cent accuracy, the halo mass function for a wide range of halo definitions, redshifts and cosmological models. We then show how the departures from universality associated with other halo definitions can be derived by combining the universality of the virial definition with the expected shape of the density profile of haloes.
We explore the cosmological constraints from cosmic shear using a new way of modelling the non-linear matter correlation functions. The new formalism extends the method of Angulo & White, which ...manipulates outputs of N-body simulations to represent the 3D non-linear mass distribution in different cosmological scenarios. We show that predictions from our approach for shear two-point correlations at 1–300 arcmin separations are accurate at the ∼10 per cent level, even for extreme changes in cosmology. For moderate changes, with target cosmologies similar to that preferred by analyses of recent Planck data, the accuracy is close to ∼5 per cent. We combine this approach with a Monte Carlo Markov chain sampler to explore constraints on a Λ cold dark matter model from the shear correlation functions measured in the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS). We obtain constraints on the parameter combination σ8(Ωm/0.27)0.6 = 0.801 ± 0.028. Combined with results from cosmic microwave background data, we obtain marginalized constraints on σ8 = 0.81 ± 0.01 and Ωm = 0.29 ± 0.01. These results are statistically compatible with previous analyses, which supports the validity of our approach. We discuss the advantages of our method and the potential it offers, including a path to model in detail (i) the effects of baryons, (ii) high-order shear correlation functions, and (iii) galaxy–galaxy lensing, among others, in future high-precision cosmological analyses.
Abstract
We simulate neutralino dark matter (χDM) haloes from their initial collapse, at ∼ earth mass, up to a few percent solar. Our results confirm that the density profiles of the first haloes are ...described by a ∼r
−1.5 power law. As haloes grow in mass, their density profiles evolve significantly. In the central regions, they become shallower and reach on average ∼r
−1, the asymptotic form of an NFW profile. Using non-cosmological controlled simulations, we observe that temporal variations in the gravitational potential caused by major mergers lead to a shallowing of the inner profile. This transformation is more significant for shallower initial profiles and for a higher number of merging systems. Depending on the merger details, the resulting profiles can be shallower or steeper than NFW in their inner regions. Interestingly, mergers have a much weaker effect when the profile is given by a broken power law with an inner slope of −1 (such as NFW or Hernquist profiles). This offers an explanation for the emergence of NFW-like profiles: after their initial collapse, r
−1.5 χDM haloes suffer copious major mergers, which progressively shallows the profile. Once an NFW-like profile is established, subsequent merging does not change the profile anymore. This suggests that halo profiles are not universal but rather a combination of (1) the physics of the formation of the microhaloes and (2) their early merger history – both set by the properties of the dark matter particle – as well as (3) the resilience of NFW-like profiles to perturbations.
ABSTRACT
Inaccuracies in the initial conditions for cosmological N-body simulations could easily be the largest source of systematic error in predicting the non-linear large-scale structure. From the ...theory side, initial conditions are usually provided by using low-order truncations of the displacement field from Lagrangian perturbation theory, with the first- and second-order approximations being the most common ones. Here, we investigate the improvement brought by using initial conditions based on third-order Lagrangian perturbation theory (3LPT). We show that with 3LPT, truncation errors are vastly suppressed, thereby opening the portal to initializing simulations accurately as late as z = 12 (for the resolution we consider). We analyse the competing effects of perturbative truncation and particle discreteness on various summary statistics. Discreteness errors are essentially decaying modes and thus get strongly amplified for earlier initialization times. We show that late starting times with 3LPT provide the most accurate configuration, which we find to coincide with the continuum fluid limit within 1 per cent for the power- and bispectrum at z = 0 up to the particle Nyquist wavenumber of our simulations (k ∼ 3h Mpc−1). In conclusion, to suppress non-fluid artefacts, we recommend initializing simulations as late as possible with 3LPT. We make our 3LPT initial condition generator publicly available.
Galaxy formation in WMAP1 and WMAP7 cosmologies Guo, Qi; White, Simon; Angulo, Raul E ...
Monthly notices of the Royal Astronomical Society,
01/2013, Letnik:
428, Številka:
2
Journal Article
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Using the technique of Angulo & White, we scale the Millennium and Millennium II simulations of structure growth in a Λ cold dark matter (ΛCDM) universe from the cosmological parameters with which ...they were carried out (based on first-year results from the Wilkinson Microwave Anisotropy Probe, WMAP1) to parameters consistent with the seven-year WMAP data (WMAP7). We implement semi-analytic galaxy formation modelling (SAM) on both simulations in both cosmologies to investigate how the formation, evolution and clustering of galaxies are predicted to vary with cosmological parameters. The increased matter density Ωm and decreased linear fluctuation amplitude σ8 in WMAP7 have compensating effects, so that the abundance and clustering of dark haloes are predicted to be very similar to those in WMAP1 for z ≤ 3. As a result, local galaxy properties can be reproduced equally well in the two cosmologies by slightly altering galaxy formation parameters. The evolution of the galaxy populations is then also similar. In WMAP7, structure forms slightly later. This shifts the peak in cosmic star formation rate to lower redshift, resulting in slightly bluer galaxies at z = 0. Nevertheless, the model still predicts more passive low-mass galaxies than are observed. For r
p < 1 Mpc, the z = 0 clustering of low-mass galaxies is weaker for WMAP7 than for WMAP1 and closer to that observed, but the two cosmologies give very similar results for more massive galaxies and on large scales. At z > 1 galaxies are predicted to be more strongly clustered for WMAP7. Differences in galaxy properties, including clustering, in these two cosmologies are rather small out to z ∼ 3. Given that there are still considerable residual uncertainties in galaxy formation models, it is very difficult to distinguish WMAP1 from WMAP7 through observations of galaxy properties or their evolution.
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