Vlasov versus N-body: the H\'enon sphere

We perform a detailed comparison of the phase-space density traced by the particle distribution in Gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized H\'enon spheres with two values of the virial ratio, R ~ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N-body simulations, visual and quantitative comparisons are performed. In particular we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the N-body and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where nontrivial physical instabilities develop. However, in the colder case, R=0.1, it was not possible to prove actual numerical convergence of the N-body results after a number of dynamical times, even with N=10$^8$ particles.Comment: 19 pages, 11 figures, MNRAS, in pres

The three dimensional skeleton: tracing the filamentary structure of the universe

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields. This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+ n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark halos and the orientation of the flow near the skeleton is computed for dark matter simulations. The flow is laminar along the filaments, while spins of dark halos within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA

On the Onset of Stochasticity in Λ\LambdaCDM Cosmological Simulations

The onset of stochasticity is measured in $\Lambda$CDM cosmological simulations using a set of classical observables. It is quantified as the local derivative of the logarithm of the dispersion of a given observable (within a set of different simulations differing weakly through their initial realization), with respect to the cosmic growth factor. In an Eulerian framework, it is shown here that chaos appears at small scales, where dynamic is non-linear, while it vanishes at larger scales, allowing the computation of a critical transition scale corresponding to ~ 3.5 Mpc/h. This picture is confirmed by Lagrangian measurements which show that the distribution of substructures within clusters is partially sensitive to initial conditions, with a critical mass upper bound scaling roughly like the perturbation's amplitude to the power 0.15. The corresponding characteristic mass, $M_{\rm crit}=2 10^{13} M_{\odot}$, is roughly of the order of the critical mass of non linearities at z=1 and accounts for the decoupling induced by the dark energy triggered acceleration. The sensitivity to detailed initial conditions spills to some of the overall physical properties of the host halo (spin and velocity dispersion tensor orientation) while other "global" properties are quite robust and show no chaos (mass, spin parameter, connexity and center of mass position). This apparent discrepancy may reflect the fact that quantities which are integrals over particles rapidly average out details of difference in orbits, while the other observables are more sensitive to the detailed environment of forming halos and reflect the non-linear scale coupling characterizing the environments of halos.Comment: 11 pages, 10 figures. Accepted for publication, MNRA

On the filamentary environment of galaxies

The correlation between the large-scale distribution of galaxies and their spectroscopic properties at z=1.5 is investigated using the Horizon MareNostrum cosmological run. We have extracted a large sample of 10^5 galaxies from this large hydrodynamical simulation featuring standard galaxy formation physics. Spectral synthesis is applied to these single stellar populations to generate spectra and colours for all galaxies. We use the skeleton as a tracer of the cosmic web and study how our galaxy catalogue depends on the distance to the skeleton. We show that galaxies closer to the skeleton tend to be redder, but that the effect is mostly due to the proximity of large haloes at the nodes of the skeleton, rather than the filaments themselves. This effects translate into a bimodality in the colour distribution of our sample. The origin of this bimodality is investigated and seems to follow from the ram pressure stripping of satellite galaxies within the more massive clusters of the simulation. The virtual catalogues (spectroscopical properties of the MareNostrum galaxies at various redshifts) are available online at http://www.iap.fr/users/pichon/MareNostrum/cataloguesComment: 18 pages, 27 figures, accepted for publication in MNRA

The persistent cosmic web and its filamentary structure I: Theory and implementation

We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and corresponding piece of software allows a genuinely scale free and parameter free identification of the voids, walls, filaments, clusters and their configuration within the cosmic web, directly from the discrete distribution of particles in N-body simulations or galaxies in sparse observational catalogues. To achieve that goal, the method works directly over the Delaunay tessellation of the discrete sample and uses the DTFE density computed at each tracer particle; no further sampling, smoothing or processing of the density field is required. The idea is based on recent advances in distinct sub-domains of computational topology, which allows a rigorous application of topological principles to astrophysical data sets, taking into account uncertainties and Poisson noise. Practically, the user can define a given persistence level in terms of robustness with respect to noise (defined as a "number of sigmas") and the algorithm returns the structures with the corresponding significance as sets of critical points, lines, surfaces and volumes corresponding to the clusters, filaments, walls and voids; filaments, connected at cluster nodes, crawling along the edges of walls bounding the voids. The method is also interesting as it allows for a robust quantification of the topological properties of a discrete distribution in terms of Betti numbers or Euler characteristics, without having to resort to smoothing or having to define a particular scale. In this paper, we introduce the necessary mathematical background and describe the method and implementation, while we address the application to 3D simulated and observed data sets to the companion paper.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material. Submitted to MNRA

The fully connected N-dimensional skeleton: probing the evolution of the cosmic web

A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a $d$-dimensional space, a $d-1$ succession of $n$-dimensional subspaces that fully characterize the topology of the density field. The final 1D manifold of the hierarchy is the fully connected network of the primary critical lines of the field : the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc... When the skeleton extraction is applied to initial conditions of cosmological N-body simulations and their present day non linear counterparts, it is shown that the time evolution of the cosmic web, as traced by the skeleton, is well accounted for by the Zel'dovich approximation. Comparing this skeleton to the initial skeleton undergoing the Zel'dovich mapping shows that two effects are competing during the formation of the cosmic web: a general dilation of the larger filaments that is captured by a simple deformation of the skeleton of the initial conditions on the one hand, and the shrinking, fusion and disappearance of the more numerous smaller filaments on the other hand. Other applications of the N dimensional skeleton and its peak patch hierarchy are discussed.Comment: Accepted for publication in MNRA

aski: full-sky lensing map-making algorithms

Within the context of upcoming full-sky lensing surveys, the edge-preserving non-linear algorithm aski (All-Sky κ Inversion) is presented. Using the framework of Maximum A Posteriori inversion, it aims at recovering the optimal full-sky convergence map from noisy surveys with masks. aski contributes two steps: (i) CCD images of possibly crowded galactic fields are deblurred using automated edge-preserving deconvolution; (ii) once the reduced shear is estimated using standard techniques, the partially masked convergence map is also inverted via an edge-preserving method. The efficiency of the deblurring of the image is quantified by the relative gain in the quality factor of the reduced shear, as estimated by SExtractor. Cross-validation as a function of the number of stars removed yields an automatic estimate of the optimal level of regularization for the deconvolution of the galaxies. It is found that when the observed field is crowded, this gain can be quite significant for realistic ground-based 8-m class surveys. The most significant improvement occurs when both positivity and edge-preserving ℓ1−ℓ2 penalties are imposed during the iterative deconvolution. The quality of the convergence inversion is investigated on noisy maps derived from the horizon-4πN-body simulation with a signal-to-noise ratio (S/N) within the range ℓcut= 500-2500, with and without Galactic cuts, and quantified using one-point statistics (S3 and S4), power spectra, cluster counts, peak patches and the skeleton. It is found that (i) the reconstruction is able to interpolate and extrapolate within the Galactic cuts/non-uniform noise; (ii) its sharpness-preserving penalization avoids strong biasing near the clusters of the map; (iii) it reconstructs well the shape of the PDF as traced by its skewness and kurtosis; (iv) the geometry and topology of the reconstructed map are close to the initial map as traced by the peak patch distribution and the skeleton's differential length; (v) the two-point statistics of the recovered map are consistent with the corresponding smoothed version of the initial map; (vi) the distribution of point sources is also consistent with the corresponding smoothing, with a significant improvement when ℓ1−ℓ2 prior is applied. The contamination of B modes when realistic Galactic cuts are present is also investigated. Leakage mainly occurs on large scales. The non-linearities implemented in the model are significant on small scales near the peaks in the fiel

Small-Angle CMB Temperature Anisotropies Induced by Cosmic Strings

We use Nambu-Goto numerical simulations to compute the cosmic microwave background (CMB) temperature anisotropies induced at arcminute angular scales by a network of cosmic strings in a Friedmann-Lemaitre-Robertson-Walker (FLRW) expanding universe. We generate 84 statistically independent maps on a 7.2 degree field of view, which we use to derive basic statistical estimators such as the one-point distribution and two-point correlation functions. At high multipoles, the mean angular power spectrum of string-induced CMB temperature anisotropies can be described by a power law slowly decaying as \ell^{-p}, with p=0.889 (+0.001,-0.090) (including only systematic errors). Such a behavior suggests that a nonvanishing string contribution to the overall CMB anisotropies may become the dominant source of fluctuations at small angular scales. We therefore discuss how well the temperature gradient magnitude operator can trace strings in the context of a typical arcminute diffraction-limited experiment. Including both the thermal and nonlinear kinetic Sunyaev-Zel'dovich effects, the Ostriker-Vishniac effect, and the currently favored adiabatic primary anisotropies, we find that, on such a map, strings should be ``eye visible,'' with at least of order ten distinctive string features observable on a 7.2 degree gradient map, for tensions U down to GU \simeq 2 x 10^{-7} (in Planck units). This suggests that, with upcoming experiments such as the Atacama Cosmology Telescope (ACT), optimal non-Gaussian, string-devoted statistical estimators applied to small-angle CMB temperature or gradient maps may put stringent constraints on a possible cosmic string contribution to the CMB anisotropies.Comment: 17 pages, 9 figures. v2: matches published version, minor clarifications added, typo in Eq. (8) fixed, results unchange

The Pipe Nebula as seen with Herschel: Formation of filamentary structures by large-scale compression ?

A growing body of evidence indicates that the formation of filaments in interstellar clouds is a key component of the star formation process. In this paper, we present new Herschel PACS and SPIRE observations of the B59 and Stem regions in the Pipe Nebula complex, revealing a rich, organized network of filaments. The asymmetric column density profiles observed for several filaments, along with the bow-like edge of B59, indicates that the Pipe Nebula is being compressed from its western side, most likely by the winds from the nearby Sco OB2 association. We suggest that this compressive flow has contributed to the formation of some of the observed filamentary structures. In B59, the only region of the entire Pipe complex showing star formation activity, the same compressive flow has likely enhanced the initial column density of the clump, allowing it to become globally gravitationally unstable. Although more speculative, we propose that gravity has also been responsible for shaping the converging filamentary pattern observed in B59. While the question of the relative impact of large-scale compression and gravity remains open in B59, large-scale compression appears to be a plausible mechanism for the initial formation of filamentary structures in the rest of the complexComment: 9 pages, 9 figures, accepted for publication in A&