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1.
We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ2  analysis. The  χ2  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f nl parameter is constrained to  −8 < f nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.  相似文献   

2.
We show how the excursion set moving barrier model for halo abundances may be generalized to the local non-Gaussian f nl model. Our estimate assumes that the distribution of step sizes depends on f nl, but that they are otherwise uncorrelated. Our analysis is consistent with previous results for the case of a constant barrier, and highlights some implicit assumptions. It also clarifies the basis of an approximate analytic solution to the moving barrier problem in the Gaussian case, and shows how it might be improved.  相似文献   

3.
The algorithm ztrace of Monaco & Efstathiou is applied to the IRAS PSCz catalogue to reconstruct the initial conditions of our local Universe with a resolution down to ~5  h 1 Mpc. The one-point probability distribution function (PDF) of the reconstructed initial conditions is consistent with the assumptions that: (i) IRAS galaxies trace mass on scales of ~5  h 1 Mpc and (ii) the statistics of the primordial density fluctuations are Gaussian. We use simulated PSCz catalogues, constructed from N -body simulations with Gaussian initial conditions, to show that local non-linear bias can cause the recovered initial PDF (assuming no bias) to be non-Gaussian. However, for plausible bias models, the distortions of the recovered PDF would be difficult to detect using the volume finely sampled by the PSCz catalogue. So, for Gaussian initial conditions, a range of bias models remain compatible with our PSCz reconstruction results.  相似文献   

4.
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5.
We look for a non-Gaussian signal in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter f NL. We apply a third-order estimator of the needlet coefficients skewness and compute the  χ2  statistics of its distribution. We obtain  −80 < f NL < 120  at 95 per cent confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of f NL based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three-point correlation function in needlet space: the constraints on f NL improve to  −50 < f NL < 110  at 95 per cent confidence level.  相似文献   

6.
We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the p -order hierarchical amplitudes S p , in both real and redshift space. We compare our results with numerical simulations, focusing on the     standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for     , where σ L is the linearly evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for     . Numerical simulations also yield a simple empirical relation between the real-space PDF and the redshift-space PDF: we find that for     , the redshift-space PDF, [ P δ ( z )], is, to a good approximation, a simple rescaling of the real-space PDF, P [ δ ], i.e.,     where σ and σ ( z ) are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the ΛCDM model. It breaks down for SCDM at     , but provides a good fit to the ΛCDM models for σ L as large as 0.8.  相似文献   

7.
We present a new calculation for the evolution of the one-point probability distribution function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman–Kolmogorov equation and second-order Eulerian perturbation theory we propagate the initial density distribution into the non-linear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependence on the initial perturbation spectrum. We compare our results with other approximations to the one-point PDF, and with N -body simulations. We find that our distribution accurately models the evolution of the one-point PDF of dark matter.  相似文献   

8.
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9.
We make use of three-dimensional clustering analysis, inertia tensor methods, and the minimal spanning tree technique to estimate some physical and statistical characteristics of the large-scale galaxy distribution and, in particular, of the sample of overdense regions seen in the Las Campanas Redshift Survey (LCRS). Our investigation provides additional evidence for a network of structures found in our core sampling analysis of the LCRS : a system of rich sheet-like structures, which in turn surround large underdense regions criss-crossed by a variety of filamentary structures.
We find that the overdense regions contain ∼40–50 per cent of LCRS galaxies and have proper sizes similar to those of nearby superclusters. The formation of such structures can be roughly described as a non-linear compression of protowalls of typical cross-sectional size ∼ 20–25  h −1 Mpc; this scale is ∼5 times the conventional value for the onset of non-linear clustering – to wit, r 0, the autocorrelation length for galaxies.
The comparison with available simulations and theoretical estimates shows that the formation of structure elements with parameters similar to those observed is presently possible only in low-density cosmological models, Ωm h ∼0.2–0.3, with a suitable large-scale bias between galaxies and dark matter.  相似文献   

10.
We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both non-linear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with exponential wings. The model is easily extended to study how the statistic depends on the type of particle used to trace the velocity field (dark matter particles, dark matter haloes, galaxies), and on the density of the environment in which the test particles are located. Comparisons with simulations suggest that our model is accurate. We also show that the evolution of the peculiar velocities depends on the local, rather than the global, density. Since clusters populate denser regions on average, using cluster velocities with the linear theory scaling may lead to an overestimate of the global value of Ω0. Conversely, using linear theory with the global value of Ω0 to scale cluster velocities from the initial to the present time results in an underestimate of their true velocities. In general, however, the directions of motions of haloes are rather well described by linear theory. Our results help to simplify models of redshift-space distortions considerably.  相似文献   

11.
We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξJ, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S J  = ξ J /ξ J −12. We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.  相似文献   

12.
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13.
In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ξ J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J -point functions. We argue that for the hierarchical ratios S J , these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N -body simulations, which turn out to be in very good agreement up to scales where σ ≲ 1.  相似文献   

14.
Using N -body simulations with a large set of massless test particles, we compare the predictions of two theories of violent relaxation, the well-known Lynden-Bell theory and the more recent theory by Nakamura. We derive 'weakened' versions of both the theories in which we use the whole equilibrium coarse-grained distribution function     as a constraint instead of the total energy constraint. We use these weakened theories to construct expressions for the conditional probability   Ki (τ)  that a test particle initially at the phase-space coordinate τ would end-up in the i th macro-cell at equilibrium. We show that the logarithm of the ratio   Rij (τ) ≡ Ki (τ)/ Kj (τ)  is directly proportional to the initial phase-space density   f 0(τ)  for the Lynden-Bell theory and inversely proportional to   f 0(τ)  for the Nakamura theory. We then measure   Rij (τ)  using a set of N -body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both the theories are at odds with the numerical results, both qualitatively and quantitatively.  相似文献   

15.
We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ s . While the deviations are insignificant for the monopole ξ 0, the hexadecapole ξ 4 exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ 4 deviate from the linear predictions by a factor of two on the scale of ∼10  h −1 Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.  相似文献   

16.
We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f 0. Our method uses importance sampling to find the sampling DF f s that minimizes the mean-square formal errors in a given set of projections of the DF f 0. The result is a multimass N -body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal.  相似文献   

17.
We calculate the secondary anisotropies in the cosmic microwave background (CMB) produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows us to determine self-consistently the beginning ( z i≈30), the duration ( δz ≈20) and the (non-linear) evolution of the reionization process for a critical density cold dark matter (CDM) model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, C χ , and obtain the power spectrum of the anisotropies, C ℓ, in the range 5000<ℓ<106. The power spectrum has a broad maximum around ℓ≈30 000, where it reaches the value 2×10−12. We also show that the ionization correlation function C χ is not Gaussian, but at separation angles θ ≲10−4 rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted for both C χ and C ( θ ). Detection of signals as above will be possible with future millimetre-wavelength interferometers like the Atacama Large Millimeter Array (ALMA) , which appears as an optimum instrument to search for signatures of inhomogeneous reionization.  相似文献   

18.
We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ cold dark matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a spherical overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement when differences in particle and grid resolution are accounted for. Voids very clearly correspond to minima in the smoothed initial density field. Apart from a very weak dependence on the mass resolution, the rescaled mass profiles of voids in the different simulations agree remarkably well. We find a universal void mass profile of the form  ρ(< r )/ρ( r eff) ∝ exp[( r / r eff)α]  , where r eff is the effective radius of a void and  α∼ 2  . The mass function of haloes in voids is steeper than that of haloes that populate denser regions. In addition, the abundances of void haloes seem to evolve somewhat more strongly between redshifts ∼1 and 0 than the global abundances of haloes.  相似文献   

19.
We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N -body simulations. In particular, we focus on the topological properties of the 'cosmic web', quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non-linearities with different values of the usual non-Gaussianity parameter f NL. In the weakly non-linear regime (the amplitude of mass density fluctuations σ0 < 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when | f NL| < 1000. In the non-linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non-Gaussian effect remains comparable to the perturbative prediction. When smaller-scale information is included, the influence of primordial non-Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non-Gaussianity with  | f NL| = 50  is comparable to the sample variance of mass density fields with a volume of 0.125( h −1 Gpc)3 when they are smoothed by Gaussian filter at a scale of 5  h −1 Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.  相似文献   

20.
The cumulant correlators, C pq , are statistical quantities that generalize the better-known S p parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the C pq for projected clustering data, such as that obtained from the Automatic Plate Measuring (APM) survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogues, finding very good agreement. We extend the idea of cumulant correlators to multipoint generalized cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly non-linear regime to express the generalized cumulant correlators in terms of the underlying 'tree amplitudes' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogues and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that a three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical Ansatz of Bernardeau & Schaeffer with extended and hyper-extended perturbation theory to infer values of the tree amplitudes in the highly non-linear regime.  相似文献   

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