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We investigate the spatial distribution of Ly α-emitting galaxies (LAEs) at z ≈ 2.67, selected from the NOAO Deep Wide-Field Survey, using two-point statistics and topological diagnostics adopted from network science. We measure the clustering length, r 0 ≈ 4  h −1 Mpc, and the bias,   |$b_{\mathrm{ LAE}} = 2.2^{+0.2}_{-0.1}$|⁠. Fitting the clustering with halo occupation distribution (HOD) models results in two disparate possibilities: (1) where the fraction of central galaxies is <1 per cent in haloes of mass >1012 M⊙ and (2) where the fraction is ≈20 per cent. We refer to these two scenarios as the 'Dusty Core Scenario' for Model#1, since most of the central galaxies in massive haloes are dead in Ly α emission, and the 'Pristine Core Scenario' for Model#2, since the central galaxies are bright in Ly α emission. Traditional two-point statistics cannot distinguish between these disparate models given the current data sets. To overcome this degeneracy, we generate mock catalogues for each HOD model using a high-resolution N -body simulation and adopt a network statistics approach, which provides excellent topological diagnostics for galaxy point distributions. We find three topological anomalies from the spatial distribution of observed LAEs, which are not reproduced by the HOD mocks. We find that Model#2 matches better all network statistics than Model#1, suggesting that the central galaxies in >1012  h −1 M⊙ haloes at z ≈ 2.67 need to be less dusty to be bright as LAEs, potentially implying some replenishing channels of pristine gas such as the cold mode accretion. [ABSTRACT FROM AUTHOR]

We apply simple analyses techniques developed for the study of complex networks to the study of the cosmic web, the large-scale galaxy distribution. In this paper, we measure three network centralities (ranks of topological importance): degree centrality (DC), closeness centrality (CL), and betweenness centrality (BC) from a network built from the Cosmological Evolution Survey (COSMOS) catalogue. We define eight galaxy populations according to the centrality measures: void, wall, and cluster by DC; main branch and dangling leaf by BC; and kernel, backbone, and fracture by CL. We also define three populations by Voronoi tessellation density to compare these with the DC selection. We apply the topological selections to galaxies in the (photometric) redshift range 0.91 < z < 0.94 from the COSMOS survey, and explore whether the red and blue galaxy populations show differences in colour, star formation rate, and stellar mass in the different topological regions. Despite the limitations and uncertainties associated with using photometric redshift and indirect measurements of galactic parameters, the preliminary results illustrate the potential of network analysis. Future surveys will provide better statistical samples to test and improve this 'network cosmology'. [ABSTRACT FROM AUTHOR]

The large-scale distribution of galaxies is generally analysed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order correlations to break degeneracies. We demonstrate that an alternate approach using network analysis can discriminate between topologically different distributions that have similar two-point correlations. We investigate two galaxy point distributions, one produced by a cosmological simulation and the other by a Lévy walk. For the cosmological simulation, we adopt the redshift z = 0.58 slice from Illustris and select galaxies with stellar masses greater than 108M☉. The two-point correlation function of these simulated galaxies follows a single power law, ξ (r) ∼ r-1.5. Then, we generate Lévy walks matching the correlation function and abundance with the simulated galaxies. We find that, while the two simulated galaxy point distributions have the same abundance and two-point correlation function, their spatial distributions are very different; most prominently, filamentary structures, absent in Lévy fractals. To quantify these missing topologies, we adopt network analysis tools and measure diameter, giant component, and transitivity from networks built by a conventional friends-of-friends recipe with various linking lengths. Unlike the abundance and two-point correlation function, these network quantities reveal a clear separation between the two simulated distributions; therefore, the galaxy distribution simulated by Illustris is not a Lévy fractal quantitatively. We find that the described network quantities offer an efficient tool for discriminating topologies and for comparing observed and theoretical distributions. [ABSTRACT FROM AUTHOR]