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The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogues, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF, using a suite of ∼7000 N -body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P ∝ ρ−2, which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N -body results for small filtering scales R < 5 h−1Mpc with rms density fluctuations σ > 1. In combination with the spherical infall model that works well for small fluctuations σ < 1, the PDF is now approximated with just few per cent errors over the range of 12 orders of magnitude – a remarkable example of precision cosmology. We find that at |${\sim } 5{-}10{{\ \rm per\ cent}}$| level the PDF explicitly depends on redshift (at fixed σ) and on cosmological density parameter Ωm. We test different existing analytical approximations and find that the often-used lognormal approximation is always 3–5 times less accurate than either the double-exponential approximation or the spherical infall model. [ABSTRACT FROM AUTHOR]

ABSTRACT We study the concentration of dark matter haloes and its evolution in N-body simulations of the standard Λ cold dark matter (ΛCDM) cosmology. The results presented in this paper are based on four large N-body simulations with ∼10 billion particles each: the Millennium-I and -II, Bolshoi and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the state of the art of our current knowledge on this basic property of dark matter haloes in the ΛCDM cosmology. We find that there is consistency among the different simulation data sets, despite the different codes, numerical algorithms and halo/subhalo finders used in our analysis. We confirm a novel feature for halo concentrations at high redshifts: a flattening and upturn with increasing mass. The concentration c( M, z) as a function of mass and the redshift and for different cosmological parameters shows a remarkably complex pattern. However, when expressed in terms of the linear rms fluctuation of the density field σ( M, z), the halo concentration c(σ) shows a nearly universal simple U-shaped behaviour with a minimum at a well-defined scale at σ∼ 0.71. Yet, some small dependences with redshift and cosmology still remain. At the high-mass end (σ < 1), the median halo kinematic profiles show large signatures of infall and highly radial orbits. This c-σ( M, z) relation can be accurately parametrized and provides an analytical model for the dependence of concentration on halo mass. When applied to galaxy clusters, our estimates of concentrations are substantially larger - by a factor up to 1.5 - than previous results from smaller simulations, and are in much better agreement with results of observations. [ABSTRACT FROM AUTHOR]

Using a large sample of galaxies from the seventh data release of the Sloan Digital Sky Survey (SDSS-DR7), we have analyzed the alignment of disk galaxies around cosmic voids. We have constructed a complete sample of cosmic voids (devoid of galaxies brighter than Mr - 5 log h = -20.17) with radii larger than 10 h-1 Mpc up to redshift 0.12. Disk galaxies in shells around these voids have been used to look for particular alignments between the angular momentum of the galaxies and the radial direction of the voids. We find that disk galaxies around voids larger than ≳ 15 h-1 Mpc within distances not much larger than 5 h-1 Mpc from the surface of the voids present a significant tendency to have their angular momenta aligned with the void's radial direction with a significance ≳ 98.8% against the null hypothesis. The strength of this alignment is dependent on the void's radius and for voids with a radius ≲ 15 h-1 Mpc the distribution of the orientation of the galaxies is compatible with a random distribution. Finally, we find that this trend observed in the alignment of galaxies is similar to the one observed for the minor axis of dark matter halos around cosmic voids found in cosmological simulations, suggesting a possible link in the evolution of both components. [ABSTRACT FROM AUTHOR]

We present a general analytical formalism to calculate accurately several statistics related to underdense regions in the Universe. The statistics are computed for dark matter halo and galaxy distributions both in real space and redshift space at any redshift. Using this formalism, we found that void statistics for galaxy distributions can be obtained, to a very good approximation, assuming galaxies to have the same clustering properties as haloes above a certain mass. We deduced a relationship between this mass and that of haloes with the same accumulated number density as the galaxies. We also found that the dependence of void statistics on redshift is small. For instance, the number of voids larger than (defined to not contain galaxies brighter than ) change less than 20 per cent between and 0. However, the dependence of void statistics on σ8 and Γ is considerably larger, making them appropriate to develop tests to measure these parameters. We have shown how to efficiently construct several of these tests and discussed in detail the treatment of several observational effects. The formalism presented here along with the observed statistics extracted from current and future large galaxy redshift surveys will provide an independent measurement of the relevant cosmological parameters. Combining these measurements with those found using other methods will contribute to reduce their uncertainties. [ABSTRACT FROM AUTHOR]

The unconditional mass function (UMF) of dark matter haloes has been determined accurately in the literature, showing excellent agreement with high-resolution numerical simulations. However, this is not the case for the conditional mass function (CMF). Here, we propose a simple analytical procedure to derive the CMF by rescaling the UMF to the constrained environment using the appropriate mean and variance of the density field at the constrained point. This method introduces two major modifications with respect to the standard rescaling procedure. First of all, rather than using in the scaling procedure the properties of the environment averaged over all the conditioning regions, we implement the rescaling locally. We show that for high masses this modification may lead to substantially different results. Secondly, we modify the (local) standard rescaling procedure in such a manner as to force normalization, in the sense that when one integrates the CMF over all possible values of the constraint multiplied by their corresponding probability distribution, the UMF is recovered. In practice, we do this by replacing in the standard procedure the value (the linear density contrast for collapse) by certain adjustable effective parameter . In order to test the method, we compare our prescription with the results obtained from numerical simulations in voids. We find that when our modified rescaling is applied locally to any existing numerical fit of the UMF, and the appropriate value for is chosen, the resulting CMF is, in all cases, in very good agreement with the numerical results. Based on these results, we finally present a very accurate analytical fit to the (accumulated) CMF obtained with our procedure, as a function of the parameters that describe the conditioning region (size and mean linear density contrast), the redshift and the relevant cosmological parameters (σ8 and Γ). This analytical fit may be useful for any theoretical treatment of the large-scale structure, and has been already used successfully in regard with the statistic of voids. [ABSTRACT FROM AUTHOR]

Using the high-resolution cosmological N-body simulation MareNostrum universe we study the orientation of shape and angular momentum of galaxy-size dark matter haloes around large voids. We find that haloes located on the shells of the largest cosmic voids have angular momenta that tend to be preferentially perpendicular to the direction that joins the centre of the halo and the centre of the void. This alignment has been found in spiral galaxies around voids using galaxy redshift surveys. We measure for the first time the strength of this alignment, showing how it falls off with increasing distance to the centre of the void. We also confirm the correlation between the intensity of this alignment and the halo mass. The analysis of the orientation of the halo main axes confirms the results of previous works. Moreover, we find a similar alignment for the baryonic matter inside dark matter haloes, which is much stronger in their inner parts. [ABSTRACT FROM AUTHOR]

We present a comparison of the properties of galaxies in the most underdense regions of the Universe, where the galaxy number density is less than 10 per cent of the mean density, with galaxies from more typical regions. We have compiled a sample of galaxies in 46 large nearby voids that were identified using the Sloan Digital Sky Survey DR4, which provides the largest coverage of the sky. We study the u− r colour distribution, morphology, specific star formation rate (SFR) and radial number density profiles for a total of 495 galaxies fainter than located inside the voids and compare these properties with a control sample of field galaxies. We show that there is an excess of blue galaxies inside the voids. However, inspecting the properties of blue and red galaxies separately, we find that galaxy properties such as colour distribution, bulge-to-total ratios and concentrations are remarkably similar between the void and overall sample. The void galaxies also show the same specific SFR at fixed colour as the control galaxies. We compare our results with the predictions of cosmological simulations of galaxy formation using the Millennium Run semi-analytic galaxy catalogue. We show that the properties of the simulated galaxies in large voids are in reasonably good agreement with those found in similar environments in the real Universe. To summarize, in spite of the fact that galaxies in voids live in the least dense large-scale environment, this environment makes very little impact on the properties of galaxies. [ABSTRACT FROM AUTHOR]

We present a statistical analysis of voids in the two-degree Field Galaxy Redshift Survey (2dFGRS). In order to detect the voids, we have developed two robust algorithms. We define voids as non-overlapping maximal spheres empty of haloes or galaxies with mass or luminosity above a given value. We search for voids in cosmological N-Body simulations to test the performance of our void finders. We obtain and analyse the void statistics for several volume-limited samples for the North Galactic Pole (NGP) and the South Galactic Pole (SGP) constructed from the 2dFGRS full data release. We find that the results obtained from the NGP and the SGP are statistically compatible. From the results of several statistical tests we conclude that voids are essentially uncorrelated, with at most a mild anticorrelation and that at the 99.5 per cent confidence level there is a dependence of the void number density on redshift. We develop a technique to correct the distortion caused by the fact that we use the redshift as the radial coordinate. We calibrate this technique with mock catalogues and find that the correction might be of some relevance to carry out accurate inferences from void statistics. We study the statistics of the galaxies inside nine nearby voids. We find that galaxies in voids are not randomly distributed: they form structures like filaments. We also obtain the galaxy number density profile in voids. This profile follow a similar but steeper trend to that followed by haloes in voids. [ABSTRACT FROM AUTHOR]