ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic

The persistent cosmic web and its filamentary structure II: Illustrations

The recently introduced discrete persistent structure extractor (DisPerSE, Soubie 2010, paper I) is implemented on realistic 3D cosmological simulations and observed redshift catalogues (SDSS); it is found that DisPerSE traces equally well the observed filaments, walls, and voids in both cases. In either setting, filaments are shown to connect onto halos, outskirt walls, which circumvent voids. Indeed this algorithm operates directly on the particles without assuming anything about the distribution, and yields a natural (topologically motivated) self-consistent criterion for selecting the significance level of the identified structures. It is shown that this extraction is possible even for very sparsely sampled point processes, as a function of the persistence ratio. Hence astrophysicists should be in a position to trace and measure precisely the filaments, walls and voids from such samples and assess the confidence of the post-processed sets as a function of this threshold, which can be expressed relative to the expected amplitude of shot noise. In a cosmic framework, this criterion is comparable to friend of friend for the identifications of peaks, while it also identifies the connected filaments and walls, and quantitatively recovers the full set of topological invariants (Betti numbers) {\sl directly from the particles} as a function of the persistence threshold. This criterion is found to be sufficient even if one particle out of two is noise, when the persistence ratio is set to 3-sigma or more. The algorithm is also implemented on the SDSS catalogue and used to locat interesting configurations of the filamentary structure. In this context we carried the identification of an ``optically faint'' cluster at the intersection of filaments through the recent observation of its X-ray counterpart by SUZAKU. The corresponding filament catalogue will be made available online.Comment: A higher resolution version is available at http://www.iap.fr/users/sousbie together with complementary material (movie and data). Submitted to MNRA

The Skeleton: Connecting Large Scale Structures to Galaxy Formation

We report on two quantitative, morphological estimators of the filamentary structure of the Cosmic Web, the so-called global and local skeletons. The first, based on a global study of the matter density gradient flow, allows us to study the connectivity between a density peak and its surroundings, with direct relevance to the anisotropic accretion via cold flows on galactic halos. From the second, based on a local constraint equation involving the derivatives of the field, we can derive predictions for powerful statistics, such as the differential length and the relative saddle to extrema counts of the Cosmic web as a function of density threshold (with application to percolation of structures and connectivity), as well as a theoretical framework to study their cosmic evolution through the onset of gravity-induced non-linearities.Comment: 10 pages, 8 figures; proceedings of the "Invisible Universe" 200

Connecting the cosmic web to the spin of dark halos: implications for galaxy formation

We investigate the alignment of the spin of dark matter halos relative (i) to the surrounding large-scale filamentary structure, and (ii) to the tidal tensor eigenvectors using the Horizon 4pi dark matter simulation which resolves over 43 million dark matter halos at redshift zero. We detect a clear mass transition: the spin of dark matter halos above a critical mass tends to be perpendicular to the closest filament, and aligned with the intermediate axis of the tidal tensor, whereas the spin of low-mass halos is more likely to be aligned with the closest filament. Furthermore, this critical mass of 5 10^12 is redshift-dependent and scales as (1+z)^-2.5. We propose an interpretation of this signal in terms of large-scale cosmic flows. In this picture, most low-mass halos are formed through the winding of flows embedded in misaligned walls; hence they acquire a spin parallel to the axis of the resulting filaments forming at the intersection of these walls. On the other hand, more massive halos are typically the products of later mergers along such filaments, and thus they acquire a spin perpendicular to this direction when their orbital angular momentum is converted into spin. We show that this scenario is consistent with both the measured excess probabilities of alignment w.r.t. the eigen-directions of the tidal tensor, and halo merger histories. On a more qualitative level, it also seems compatible with 3D visualization of the structure of the cosmic web as traced by "smoothed" dark matter simulations or gas tracer particles. Finally, it provides extra support to the disc forming paradigm presented by Pichon et al (2011) as it extends it by characterizing the geometry of secondary infall at high redshift.Comment: 18 pages; 14 figures; accepted by MNRA

Swirling around filaments: are large-scale structure vortices spinning up dark halos?

The kinematic analysis of dark matter and hydrodynamical simulations suggests that the vorticity in large-scale structure is mostly confined to, and predominantly aligned with their filaments, with an excess of probability of 20 per cent to have the angle between vorticity and filaments direction lower than 60 degrees relative to random orientations. The cross sections of these filaments are typically partitioned into four quadrants with opposite vorticity sign, arising from multiple flows, originating from neighbouring walls. The spins of halos embedded within these filaments are consistently aligned with this vorticity for any halo mass, with a stronger alignment for the most massive structures up to an excess of probability of 165 per cent. On large scales, adiabatic/cooling hydrodynamical simulations display the same vorticity in the gas as in the dark matter. The global geometry of the flow within the cosmic web is therefore qualitatively consistent with a spin acquisition for smaller halos induced by this large-scale coherence, as argued in Codis et al. (2012). In effect, secondary anisotropic infall (originating from the vortex-rich filament within which these lower-mass halos form) dominates the angular momentum budget of these halos. The transition mass from alignment to orthogonality is related to the size of a given multi-flow region with a given polarity. This transition may be reconciled with the standard tidal torque theory if the latter is augmented so as to account for the larger scale anisotropic environment of walls and filaments.Comment: 17 pages, 19 figures, 3 tables. accepted for publication in MNRA

LE SQUELETTE DE L'UNIVERS: Un outil d'analyse topologique des grandes structures

La distribution de la matière dans l'Univers est supposée homogène et isotrope à très grande échelle mais l'observation de la distribution des galaxies lorsde grandes campagnes de recensements comme le SDSS nous montre un véritable réseau d'amas et de filaments sur des échelles de plusieurs centaines demégaparsecs.\\De nombreuses méthodes ont été développées dans le but de caractériser cette distribution et nous nous proposons dans cette thèse de présenter l'adaptation en trois dimensions d'un nouvel outil: le squelette.Cette méthode vise à donner une définition mathématique claire des filaments ainsi qu'un algorithme numérique robuste permettant leur identification ainsi que le calcul de leurs propriétés. \\Afin de pouvoir comparer les résultats obtenus à partir des simulations N-corps de matière noire aux observations, une nouvelle méthode, baptisée MoLUSC, spécialisée dans la création de catalogues virtuels degalaxies a aussi été élaborée. Elle se base sur les modèles semi-analytiques et est particulièrement efficace pour la fabrication de catalogues de grandetaille simulant de manière suffisamment réaliste les propriétés galactiques.\\Les utilisations de ces deux outils sont nombreuses et nous montrons par exemple qu'il est possible en mesurant la densité de longueur des filaments àune échelle donnée de contraindre la quantité de matière dans l'univers$\Omega_m$. Ces méthodes peuvent aussi être appliquées avec succès à la mesure statistique des propriétés du flux de matière noire le long des filaments, une mesure inédite. Nous présentons enfin de nombreuses applications possibles dont les résultats préliminaires sont très encourageants

The Skeleton: Connecting Large Scale Structures to Galaxy Formation

International audienceWe report on two quantitative, morphological estimators of the filamentary structure of the Cosmic Web, the so-called global and local skeletons. The first, based on a global study of the matter density gradient flow, allows us to study the connectivity between a density peak and its surroundings, with direct relevance to the anisotropic accretion via cold flows on galactic halos. From the second, based on a local constraint equation involving the derivatives of the field, we can derive predictions for powerful statistics, such as the differential length and the relative saddle to extrema counts of the Cosmic web as a function of density threshold (with application to percolation of structures and connectivity), as well as a theoretical framework to study their cosmic evolution through the onset of gravity-induced non-linearities