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Register a new userThe position-dependent matter density probability distribution function
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We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model and has distinct dependence on cosmological parameters. We demonstrate that the position-dependent PDF is characterized by variations in the local mean density, and we compute the linear response of the PDF to the local density using separate universe N-body simulations. The linear response of the PDF to the local density field can be thought of as the linear bias of regions of the matter field selected based on density. We provide a model for the linear response, which accurately predicts our simulation measurements. We also validate our results and test the separate universe consistency relation for the local PDF using global universe simulations. We find excellent agreement between the two, and we demonstrate that the separate universe method gives a lower variance determination of the linear response.
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We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which approximates the Lagrangian density field. For halos, the Voronoi densities contain information about the local environment of each halo. We measure the halo virial masses, the total amount of dark matter within each halo Voronoi cell, and the halo Voronoi cell volumes, and we show how halo abundances depend on these three quantities. We then study the position-dependent Voronoi density PDF, measured within finite subregions of the Universe, using separate universe simulations. We demonstrate that the spatial variation of the position-dependent PDF is due to large-scale density fluctuations, indicating that the position-dependent PDF is a biased tracer of large-scale structure. We measure this bias for the dark matter, and interpret it as the bias of regions of the Lagrangian density field that are selected based on density. For the halos, this bias can be interpreted as a form of assembly bias. We present the mapping from late-time to early-time Voronoi density for each simulation dark matter particle, which is highly stochastic. We compare the median of this stochastic map with spherical collapse calculations and discuss challenges involved in modeling the evolution of the density field on these scales.
The probability distribution functions (PDFs) for atomic, molecular, and total gas surface densities of M33 are determined at a resolution of about 50~pc over regions that share coherent morphological properties to unveil fingerprints of self-gravity across the star-forming disk. Most of the total gas PDFs from the central region to the edge of the star-forming disk are well-fitted by log-normal functions whose width decreases radially outwards. Because the HI velocity dispersion is approximately constant across the disk, the decrease of the PDF width is consistent with a lower Mach number for the turbulent ISM at large galactocentric radii where a higher fraction of HI is in the warm phase. The atomic gas is found mostly at face-on column densities below N$_{H}^{lim}$=2.5 10$^{21}$~cm$^{-2}$, with small radial variations of N$_{H}^{lim}$. The molecular gas PDFs do not show strong deviations from log-normal functions in the central region where molecular fractions are high. Here the high pressure and rate of star formation shapes the PDF as a log-normal function dispersing self-gravitating complexes with intense feedback at all column densities that are spatially resolved. Power law PDFs for the molecules are found near and above N$_H^{lim}$, in the well defined southern spiral arm and in a continuous dense filament extending at larger galactocentric radii; this is evident in cloud samples at different evolutionary stages along the star formation cycle. In the filament nearly half of the molecular gas departs from a log-normal PDF and power laws are also observed in pre-star forming molecular complexes. The slope of the power law is between -1 and -2. This slope, combined with maps showing where the different parts of the power law PDFs come from, suggest a power-law stratification of density within molecular cloud complexes, which is consistent with the dominance of self-gravity.
We provide a systematic study of the position-dependent correlation function in weak lensing convergence maps and its relation to the squeezed limit of the three-point correlation function (3PCF) using state-of-the-art numerical simulations. We relate the position-dependent correlation function to its harmonic counterpart, i.e., the position-dependent power spectrum or equivalently the integrated bispectrum. We use a recently proposed improved fitting function, BiHalofit, for the bispectrum to compute the theoretical predictions as a function of source redshifts. In addition to low redshift results ($z_s=1.0-2.0$) we also provide results for maps inferred from lensing of the cosmic microwave background, i.e., $z_s=1100$. We include a {em Euclid}-type realistic survey mask and noise. In agreement with the recent studies on the position-dependent power spectrum, we find that the results from simulations are consistent with the theoretical expectations when appropriate corrections are included.
Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: $n_s$, the spectral slope, and $sigma_L$, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, $s_L={sqrt{langle(dv^L_{rm pec}/dr)^2rangle}}/{H}$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.
We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium (MS) and Millennium-II (MS-II) simulations. The DTFE technique is based directly on the particle positions, without requiring any type of smoothing or analysis grid, thereby providing high sensitivity to all non-linear structures resolved by the simulations. In order to identify the detailed origin of the shape of the one-point density probability distribution function (PDF), we decompose the simulation particles according to the mass of their host FoF halos, and examine the contributions of different halo mass ranges to the global density PDF. We model the one-point distribution of the FoF halos in each halo mass bin with a set of Monte Carlo realizations of idealized NFW dark matter halos, finding that this reproduces the measurements from the N-body simulations reasonably well, except for a small excess present in simulation results. This excess increases with increasing halo mass. We show that its origin lies in substructure, which becomes progressively more abundant and better resolved in more massive dark matter halos. We demonstrate that the high density tail of the one-point distribution function in less massive halos is severely affected by the gravitational softening length and the mass resolution. In particular, we find these two parameters to be more important for an accurate measurement of the density PDF than the simulated volume. Combining our results from individual halo mass bins we find that the part of the one-point density PDF originating from collapsed halos can nevertheless be quite well described by a simple superposition of a set of NFW halos with the expected cosmological abundance over the resolved mass range. The transition region to the low-density unbound material is however not well captured by such an analytic halo model.
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