Topology of Large-Scale Structure. IV. Topology in Two Dimensions
Abstract
In a recent series of papers we have developed an algorithm for quantitatively measuring the topology of the large-scale structure of the universe and applied this algorithm to numerical models and to three- dimensional observational data sets. In this paper we show that topological information can be derived from a two-dimensional cross section of a density field, and we give analytic expressions for a Gaussian random field. We demonstrate the application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models similar to those examined in previous papers in this series, and we show that the results are understandable by analogy to three-dimensional results. We discuss prospects for applying this method to nearly two-dimensional observational data sets.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- October 1989
- DOI:
- 10.1086/167935
- Bibcode:
- 1989ApJ...345..618M
- Keywords:
-
- Cosmology;
- Galactic Clusters;
- Topology;
- Universe;
- Algorithms;
- Gauss Equation;
- Power Spectra;
- Three Dimensional Models;
- Two Dimensional Models;
- Astrophysics;
- COSMOLOGY;
- GALAXIES: CLUSTERING