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The $beta$-skeleton is a mathematical method to construct graphs from a set of points that has been widely applied in the areas of image analysis, machine learning, visual perception, and pattern recognition. In this work, we apply the $beta$-skeleton to study the cosmic web. We use this tool on observed and simulated data to identify the filamentary structures and characterize the statistical properties of the skeleton. In particular, we compare the $beta$-skeletons built from SDSS-III galaxies to those obtained from MD-PATCHY mocks, and also to mocks directly built from the Big MultiDark $N$-body simulation. We find that the $beta$-skeleton is able to reveal the underlying structures in observed and simulated samples without any parameter fine-tuning. A different degree of sparseness can be obtained by adjusting the value of $beta$; in addition, the statistical properties of the length and direction of the skeleton connections show a clear dependence on redshift space distortions (RSDs), cosmological effects and galaxy bias. We also find that the $N$-body simulation accurately reproduces the RSD effect in the data, while the MD-PATCHY mocks appear to underestimate its magnitude. Our proof-of-concept study shows that the statistical properties of the $beta$-skeleton can be used to probe cosmological parameters and galaxy evolution.
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We present a general formalism for identifying the caustic structure of an evolving mass distribution in an arbitrary dimensional space. For the class of Hamiltonian fluids the identification corresponds to the classification of singularities in Lagrangian catastrophe theory. Based on this we develop a theoretical framework for the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. The present work represents an extension of the work by Arnold et al., who classified the caustics for the 1- and 2-dimensional Zeldovich approximation. His seminal work established the role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. We introduce an alternative and transparent proof for Lagrangian catastrophe theory, and derive the caustic conditions for general Lagrangian fluids, with arbitrary dynamics, including dissipative terms and vorticity. The new proof allows us to describe the full 3-dimensional complexity of the gravitationally evolving cosmic matter field. One of our key findings is the significance of the eigenvector field of the deformation field for outlining the spatial structure of the caustic skeleton. We consider the caustic conditions for the 3-dimensional Zeldovich approximation, extending earlier work on those for 1- and 2-dimensional fluids towards the full spatial richness of the cosmic web.
Increasing evidence suggests that cosmological sheets, filaments, and voids may be substantially magnetized today. The origin of magnetic fields in the intergalactic medium (IGM) is, however, currently uncertain. It seems well known that non-standard extensions to the physics of the standard model can provide mechanisms susceptible of magnetizing the universe at large. Perhaps less well known is the fact that standard, classical physics of matter--radiation interactions actually possesses the same potential. We discuss a magnetogenesis mechanism based on the exchange of momentum between hard photons and electrons in an inhomogeneous IGM. Operating in the neighborhood of ionizing sources during the epoch of reionization, this mechanism is capable of generating magnetic seeds of relevant strengths over scales comparable to the distance between ionizing sources. In addition, summing up the contributions of all ionizing sources and taking into account the distribution of gas inhomogeneities, we show that this mechanism leaves the IGM, at the end of reionization, with a level of magnetization that might account, when amplification mechanisms take over, for the magnetic fields strengths in the current cosmic web.
The growth of large-scale cosmic structure is a beautiful exemplification of how complexity can emerge in our Universe, starting from simple initial conditions and simple physical laws. Using {enzo} cosmological numerical simulations, I applied tools from Information Theory (namely, statistical complexity) to quantify the amount of complexity in the simulated cosmic volume, as a function of cosmic epoch and environment. This analysis can quantify how much difficult to predict, at least in a statistical sense, is the evolution of the thermal, kinetic and magnetic energy of the dominant component of ordinary matter in the Universe (the intragalactic medium plasma). The most complex environment in the simulated cosmic web is generally found to be the periphery of large-scale structures (e.g. galaxy clusters and filaments), where the complexity is on average $sim 10-10^2$ times larger than in more rarefied regions, even if the latter dominate the volume-integrated complexity of the simulated Universe. If the energy evolution of gas in the cosmic web is measured on a $approx 100 $ $rm kpc/h$ resolution and over a $approx 200$ $rm Myr$ timescale, its total complexity is the range of $sim 10^{16}-10^{17} rm ~bits$, with little dependence on the assumed gas physics, cosmology or cosmic variance.
Aims. We develop an extended percolation method to allow the comparison of geometrical properties of the real cosmic web with the simulated dark matter web for an ensemble of over- and under-density systems. Methods. We scan density fields of dark matter (DM) model and SDSS observational samples, and find connected over- and underdensity regions in a large range of threshold densities. Lengths, filling factors and numbers of largest clusters and voids as functions of the threshold density are used as percolation functions. Results. We find that percolation functions of DM models of different box sizes are very similar to each other. This stability suggests that properties of the cosmic web, as found in the present paper, can be applied to the cosmic web as a whole. Percolation functions depend strongly on the smoothing length. At smoothing length 1 $h^{-1}$ Mpc the percolation threshold density for clusters is $log P_C = 0.718 pm 0.014$, and for voids is $log P_V = -0.816 pm 0.015$, very different from percolation thresholds for random samples, $log P_0 = 0.00 pm 0.02$. Conclusions. The extended percolation analysis is a versatile method to study various geometrical properties of the cosmic web in a wide range of parameters. Percolation functions of the SDSS sample are very different from percolation functions of DM model samples. The SDSS sample has only one large percolating void which fills almost the whole volume. The SDSS sample contains numerous small isolated clusters at low threshold densities, instead of one single percolating DM cluster. These differences are due to the tenuous dark matter web, present in model samples, but absent in real observational samples.
We explore the characteristics of the cosmic web around Local Group(LG) like pairs using a cosmological simulation in the $Lambda$CDM cosmology. We use the Hessian of the gravitational potential to classify regions on scales of $sim 2$ Mpc as a peak, sheet, filament or void. The sample of LG counterparts is represented by two samples of halo pairs. The first is a general sample composed by pairs with similar masses and isolation criteria as observed for the LG. The second is a subset with additional observed kinematic constraints such as relative pair velocity and separation. We find that the pairs in the LG sample with all constraints are: (i) Preferentially located in filaments and sheets, (ii) Located in in a narrow range of local overdensity $0<delta<2$, web ellipticity $0.1<e<1.0$ and prolateness $-0.4<p<0.4$. (iii) Strongly aligned with the cosmic web. The alignments are such that the pair orbital angular momentum tends to be perpendicular to the smallest tidal eigenvector, $hat{e}_3$, which lies along the filament direction or the sheet plane. A stronger alignment is present for the vector linking the two halos with the vector $hat{e}_3$. Additionally, we fail to find a strong correlation of the spin of each halo in the pair with the cosmic web. All these trends are expected to a great extent from the selection on the LG total mass on the general sample. Applied to the observed LG, there is a potential conflict between the alignments of the different planes of satellites and the numerical evidence for satellite accretion along filaments; the direction defined by $hat{e}_3$. This highlights the relevance of achieving a precise characterization of the place of the LG in the cosmic web in the cosmological context provided by $Lambda$CDM.
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