Discriminating topology in galaxy distributions using network analysis
Abstract
The largescale distribution of galaxies is generally analysed using the twopoint 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 twopoint 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 10^{8} M_{☉}. The twopoint 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 twopoint 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 friendsoffriends recipe with various linking lengths. Unlike the abundance and twopoint 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 July 2016
 DOI:
 10.1093/mnras/stw803
 arXiv:
 arXiv:1603.02285
 Bibcode:
 2016MNRAS.459.2690H
 Keywords:

 methods: data analysis;
 galaxies: evolution;
 galaxies: formation;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 11 pages, 5 figures, submitted to MNRAS on 12/15/2015, now fully reviewed for publication