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

By Thierry Sousbie. 2010

509 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/5016b8ab616d9ea09d9e43e7134ce06a9bf3a1c4

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Citations in the corpus

On the universality of interstellar filaments: theory meets simulations and observations (2015, methodology): “In order to identify filaments in the column density maps produced from our simulations, we apply the opensource tool DisPerSE (Sousbie 2011; Sousbie et al. 2011) as in Arzoumanian et al. (2011).”
Connecting the cosmic web to the spin of dark haloes: implications for galaxy formation (2012, background): “Indeed, the code DisPerSE (Sousbie 2011) which identifies filaments using persistence, can accurately deal with discrete and sparse datasets and should provide a good estimator for the direction of observed filaments.”
Filament Identification through Mathematical Morphology (2015, methodology): “The DisPerSE algorithm (Sousbie 2011) was originally developed for identifying structures in three-dimensional cosmological simulations.”
A census of dense cores in the Aquila cloud complex: SPIRE/PACS observations from the Herschel Gould Belt survey (2015, methodology): “For more mathematical and algorithmic definitions of a filament, the reader is referred to Sousbie (2011) and Men’shchikov (2013), respectively.”
The spine of the swan: a Herschel study of the DR21 ridge and filaments in Cygnus X (2012, methodology): “In the first step to characterise the DR21 filaments, we applied the DisPerSE software (Sousbie 2011) on the column density map to identify the filament crests (cf. Arzoumanian et al. 2011; Hill et al. 2011) using a persistence threshold of 3×1021 cm−2.”
FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope (FUGIN) I: Project Overview and Initial Results (2017, methodology): “…clumps and filaments in the Galactic plane by using cloud/clump finding tools, e.g., Clumpfind (Williams et al. 1994) and Dedrograms (Rosolowsky et al. 2008), filament finding tool (DisPerSE: Sousbie 2011), and also catalogs of shell and arc structures that correspond to Spitzer bubbles and SNRs.”
Filaments and ridges in Vela C revealed by Herschel: from low-mass to high-mass star-forming sites (2011, background): “DisPerSE works on the principles of computational topology, namely the Morse theory, and the concept of persistence, to identify topological structure such as filaments, and connect their saddle-points to maxima with integral lines (Sousbie 2011; Sousbie et al. 2011).”
Tracing the cosmic web (2017, background): “On the basis of these values, and the mutual connections between the various simplices, one may identify discrete simplicial analogues to the singularity points, gradient vector field, integral lines and Morse complex (see e.g. Gyulassy 2008; Sousbie 2011, for a detailed treatment).”
Topological Data Analysis (2016, methodology): “Sousbie et al. (2011); Sousbie (2011) uses Morse theory to model the filamentary structures of the cosmic web.”
Evolution of the cosmic web (2014, unknown): “Morse theory (see Colombi, Pogosyan & Souradeep 2000) forms the basis of the skeleton analysis (Novikov, Colombi & Doré 2006; Sousbie et al. 2008a) and of its more rigorous and mathematically motivated implementation, the DisPerSE algorithm (Sousbie 2011; Sousbie, Pichon & Kawahara 2011).”
Detecting filamentary pattern in the cosmic web: a catalogue of filaments for the SDSS (2013, background): “…tessellations (Doroshkevich, Gottlöber & Madsen 1997; Aragón-Calvo et al. 2007b; Aragón-Calvo, van de Weygaert & Jones 2010a; González & Padilla 2010; Sousbie 2011; Sousbie, Pichon & Kawahara 2011; Shandarin, Habib & Heitmann 2012; Aragón-Calvo 2013), Bayesian sampling of the density field…”
NEXUS: Tracing the cosmic web connection (2012, background): “Given the fact that in general, cosmic density fields behave like a proper Morse function, the assumption is that filaments and walls in the mass distribution can be identified with the manifolds in the density field connecting maxima via saddle points of the field Sousbie (2011).”